class getset_descriptor: pass class dictproxy: pass class member_descriptor: pass ALLOW_THREADS = int() BUFSIZE = int() CLIP = int() class ComplexWarning: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() args = getset_descriptor() message = getset_descriptor() class DataSource: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _cache(self, _): """Cache the file specified by path. Creates a copy of the file in the datasource cache. """ return None def _findfile(self, _): """Searches for ``path`` and returns full path if found. If path is an URL, _findfile will cache a local copy and return the path to the cached file. If path is a local file, _findfile will return a path to that local file. The search will include possible compressed versions of the file and return the first occurrence found. """ return None def _isurl(self, _): """Test if path is a net location. Tests the scheme and netloc.""" return None def _iswritemode(self, _): """Test if the given mode will open a file for writing.""" return None def _iszip(self, _): """Test if the filename is a zip file by looking at the file extension. """ return None def _possible_names(self, _): """Return a tuple containing compressed filename variations.""" return None def _sanitize_relative_path(self, _): """Return a sanitised relative path for which os.path.abspath(os.path.join(base, path)).startswith(base) """ return None def _splitzipext(self, _): """Split zip extension from filename and return filename. *Returns*: base, zip_ext : {tuple} """ return None def abspath(self, path): """ Return absolute path of file in the DataSource directory. If `path` is an URL, then `abspath` will return either the location the file exists locally or the location it would exist when opened using the `open` method. Parameters ---------- path : str Can be a local file or a remote URL. Returns ------- out : str Complete path, including the `DataSource` destination directory. Notes ----- The functionality is based on `os.path.abspath`. """ return str() def exists(self, path): """ Test if path exists. Test if `path` exists as (and in this order): - a local file. - a remote URL that has been downloaded and stored locally in the `DataSource` directory. - a remote URL that has not been downloaded, but is valid and accessible. Parameters ---------- path : str Can be a local file or a remote URL. Returns ------- out : bool True if `path` exists. Notes ----- When `path` is an URL, `exists` will return True if it's either stored locally in the `DataSource` directory, or is a valid remote URL. `DataSource` does not discriminate between the two, the file is accessible if it exists in either location. """ return bool() def open(self, path="r", mode="r"): """ Open and return file-like object. If `path` is an URL, it will be downloaded, stored in the `DataSource` directory and opened from there. Parameters ---------- path : str Local file path or URL to open. mode : {'r', 'w', 'a'}, optional Mode to open `path`. Mode 'r' for reading, 'w' for writing, 'a' to append. Available modes depend on the type of object specified by `path`. Default is 'r'. Returns ------- out : file object File object. """ return file() ERR_CALL = int() ERR_DEFAULT = int() ERR_DEFAULT2 = int() ERR_IGNORE = int() ERR_LOG = int() ERR_PRINT = int() ERR_RAISE = int() ERR_WARN = int() FLOATING_POINT_SUPPORT = int() FPE_DIVIDEBYZERO = int() FPE_INVALID = int() FPE_OVERFLOW = int() FPE_UNDERFLOW = int() False_ = bool_() Inf = float() Infinity = float() MAXDIMS = int() class MachAr: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _do_init(self, _): """None""" return None class ModuleDeprecationWarning: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() args = getset_descriptor() message = getset_descriptor() NAN = float() NINF = float() NZERO = float() NaN = float() PINF = float() PZERO = float() class PackageLoader: __dict__ = dictproxy() __doc__ = None __module__ = str() __weakref__ = getset_descriptor() def _execcmd(self, _): """ Execute command in parent_frame.""" return None def _format_titles(self, titles="---", colsep="---"): """None""" return None def _get_doc_title(self, _): """ Get the title from a package info.py file. """ return None def _get_info_files(self, package_dir, parent_path=None, parent_package=None): """ Return list of (package name,info.py file) from parent_path subdirectories. """ return None def _get_sorted_names(self, _): """ Return package names sorted in the order as they should be imported due to dependence relations between packages. """ return None def _init_info_modules(self=None, packages=None): """Initialize info_modules = {: }. """ return None def _obj2repr(self, obj): """ Return repr(obj) with""" return None def error(self, _): """None""" return None def get_pkgdocs(self, _): """ Return documentation summary of subpackages. """ return None def log(self, _): """None""" return None def warn(self, _): """None""" return None RAISE = int() class RankWarning: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() args = getset_descriptor() message = getset_descriptor() SHIFT_DIVIDEBYZERO = int() SHIFT_INVALID = int() SHIFT_OVERFLOW = int() SHIFT_UNDERFLOW = int() ScalarType = tuple() class NoseTester: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _get_custom_doctester(self, _): """ Return instantiated plugin for doctests Allows subclassing of this class to override doctester A return value of None means use the nose builtin doctest plugin """ return None def _show_system_info(self, _): """None""" return None def _test_argv(self, label, verbose, extra_argv): """ Generate argv for nosetest command Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional see ``test`` docstring verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- argv : list command line arguments that will be passed to nose """ return list() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() excludes = list() def prepare_test_args(self=False, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False): """ Run tests for module using nose. This method does the heavy lifting for the `test` method. It takes all the same arguments, for details see `test`. See Also -------- test """ return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() True_ = bool_() UFUNC_BUFSIZE_DEFAULT = int() UFUNC_PYVALS_NAME = str() WRAP = int() __NUMPY_SETUP__ = bool() __all__ = list() __builtins__ = dict() __doc__ = str() __file__ = str() __git_revision__ = str() __name__ = str() __package__ = str() __path__ = list() __version__ = str() def absolute(x, out=None): """absolute(x[, out]) Calculate the absolute value element-wise. Parameters ---------- x : array_like Input array. Returns ------- absolute : ndarray An ndarray containing the absolute value of each element in `x`. For complex input, ``a + ib``, the absolute value is :math:`\sqrt{ a^2 + b^2 }`. Examples -------- >>> x = np.array([-1.2, 1.2]) >>> np.absolute(x) array([ 1.2, 1.2]) >>> np.absolute(1.2 + 1j) 1.5620499351813308 Plot the function over ``[-10, 10]``: >>> import matplotlib.pyplot as plt >>> x = np.linspace(start=-10, stop=10, num=101) >>> plt.plot(x, np.absolute(x)) >>> plt.show() Plot the function over the complex plane: >>> xx = x + 1j * x[:, np.newaxis] >>> plt.imshow(np.abs(xx), extent=[-10, 10, -10, 10]) >>> plt.show()""" return ndarray() def absolute(x, out=None): """absolute(x[, out]) Calculate the absolute value element-wise. Parameters ---------- x : array_like Input array. Returns ------- absolute : ndarray An ndarray containing the absolute value of each element in `x`. For complex input, ``a + ib``, the absolute value is :math:`\sqrt{ a^2 + b^2 }`. Examples -------- >>> x = np.array([-1.2, 1.2]) >>> np.absolute(x) array([ 1.2, 1.2]) >>> np.absolute(1.2 + 1j) 1.5620499351813308 Plot the function over ``[-10, 10]``: >>> import matplotlib.pyplot as plt >>> x = np.linspace(start=-10, stop=10, num=101) >>> plt.plot(x, np.absolute(x)) >>> plt.show() Plot the function over the complex plane: >>> xx = x + 1j * x[:, np.newaxis] >>> plt.imshow(np.abs(xx), extent=[-10, 10, -10, 10]) >>> plt.show()""" return ndarray() absolute_import = instance() def add(x1, x2, out=None): """add(x1, x2[, out]) Add arguments element-wise. Parameters ---------- x1, x2 : array_like The arrays to be added. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). Returns ------- add : ndarray or scalar The sum of `x1` and `x2`, element-wise. Returns a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` + `x2` in terms of array broadcasting. Examples -------- >>> np.add(1.0, 4.0) 5.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.add(x1, x2) array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]])""" return ndarray() if False else float() def add_docstring(obj, docstring): """add_docstring(obj, docstring) Add a docstring to a built-in obj if possible. If the obj already has a docstring raise a RuntimeError If this routine does not know how to add a docstring to the object raise a TypeError""" return None def add_newdoc(): """Adds documentation to obj which is in module place. If doc is a string add it to obj as a docstring If doc is a tuple, then the first element is interpreted as an attribute of obj and the second as the docstring (method, docstring) If doc is a list, then each element of the list should be a sequence of length two --> [(method1, docstring1), (method2, docstring2), ...] This routine never raises an error. This routine cannot modify read-only docstrings, as appear in new-style classes or built-in functions. Because this routine never raises an error the caller must check manually that the docstrings were changed. """ return None def add_newdoc_ufunc(ufunc, new_docstring): """add_ufunc_docstring(ufunc, new_docstring) Replace the docstring for a ufunc with new_docstring. This method will only work if the current docstring for the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.) Parameters ---------- ufunc : numpy.ufunc A ufunc whose current doc is NULL. new_docstring : string The new docstring for the ufunc. Notes ----- This method allocates memory for new_docstring on the heap. Technically this creates a mempory leak, since this memory will not be reclaimed until the end of the program even if the ufunc itself is removed. However this will only be a problem if the user is repeatedly creating ufuncs with no documentation, adding documentation via add_newdoc_ufunc, and then throwing away the ufunc.""" return None def alen(a): """ Return the length of the first dimension of the input array. Parameters ---------- a : array_like Input array. Returns ------- alen : int Length of the first dimension of `a`. See Also -------- shape, size Examples -------- >>> a = np.zeros((7,4,5)) >>> a.shape[0] 7 >>> np.alen(a) 7 """ return int() def all(a=False, axis=None, out=None, keepdims=False): """ Test whether all array elements along a given axis evaluate to True. Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : None or int or tuple of ints, optional Axis or axes along which a logical AND reduction is performed. The default (`axis` = `None`) is perform a logical OR over all the dimensions of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if ``dtype(out)`` is float, the result will consist of 0.0's and 1.0's). See `doc.ufuncs` (Section "Output arguments") for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- all : ndarray, bool A new boolean or array is returned unless `out` is specified, in which case a reference to `out` is returned. See Also -------- ndarray.all : equivalent method any : Test whether any element along a given axis evaluates to True. Notes ----- Not a Number (NaN), positive infinity and negative infinity evaluate to `True` because these are not equal to zero. Examples -------- >>> np.all([[True,False],[True,True]]) False >>> np.all([[True,False],[True,True]], axis=0) array([ True, False], dtype=bool) >>> np.all([-1, 4, 5]) True >>> np.all([1.0, np.nan]) True >>> o=np.array([False]) >>> z=np.all([-1, 4, 5], out=o) >>> id(z), id(o), z # doctest: +SKIP (28293632, 28293632, array([ True], dtype=bool)) """ return ndarray() def allclose(a, b=1e-08, rtol=1e-05, atol=1e-08): """ Returns True if two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolute difference between `a` and `b`. If either array contains one or more NaNs, False is returned. Infs are treated as equal if they are in the same place and of the same sign in both arrays. Parameters ---------- a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). Returns ------- allclose : bool Returns True if the two arrays are equal within the given tolerance; False otherwise. See Also -------- isclose, all, any Notes ----- If the following equation is element-wise True, then allclose returns True. absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`)) The above equation is not symmetric in `a` and `b`, so that `allclose(a, b)` might be different from `allclose(b, a)` in some rare cases. Examples -------- >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8]) False >>> np.allclose([1e10,1e-8], [1.00001e10,1e-9]) True >>> np.allclose([1e10,1e-8], [1.0001e10,1e-9]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan]) False """ return bool() def alltrue(a=False, axis=None, out=None, keepdims=False): """ Check if all elements of input array are true. See Also -------- numpy.all : Equivalent function; see for details. """ return None def alterdot(): """Change `dot`, `vdot`, and `inner` to use accelerated BLAS functions. Typically, as a user of Numpy, you do not explicitly call this function. If Numpy is built with an accelerated BLAS, this function is automatically called when Numpy is imported. When Numpy is built with an accelerated BLAS like ATLAS, these functions are replaced to make use of the faster implementations. The faster implementations only affect float32, float64, complex64, and complex128 arrays. Furthermore, the BLAS API only includes matrix-matrix, matrix-vector, and vector-vector products. Products of arrays with larger dimensionalities use the built in functions and are not accelerated. See Also -------- restoredot : `restoredot` undoes the effects of `alterdot`.""" return None def amax(a=False, axis=None, out=None, keepdims=False): """ Return the maximum of an array or maximum along an axis. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default, flattened input is used. out : ndarray, optional Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See `doc.ufuncs` (Section "Output arguments") for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- amax : ndarray or scalar Maximum of `a`. If `axis` is None, the result is a scalar value. If `axis` is given, the result is an array of dimension ``a.ndim - 1``. See Also -------- amin : The minimum value of an array along a given axis, propagating any NaNs. nanmax : The maximum value of an array along a given axis, ignoring any NaNs. maximum : Element-wise maximum of two arrays, propagating any NaNs. fmax : Element-wise maximum of two arrays, ignoring any NaNs. argmax : Return the indices of the maximum values. nanmin, minimum, fmin Notes ----- NaN values are propagated, that is if at least one item is NaN, the corresponding max value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmax. Don't use `amax` for element-wise comparison of 2 arrays; when ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than ``amax(a, axis=0)``. Examples -------- >>> a = np.arange(4).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amax(a) # Maximum of the flattened array 3 >>> np.amax(a, axis=0) # Maxima along the first axis array([2, 3]) >>> np.amax(a, axis=1) # Maxima along the second axis array([1, 3]) >>> b = np.arange(5, dtype=np.float) >>> b[2] = np.NaN >>> np.amax(b) nan >>> np.nanmax(b) 4.0 """ return ndarray() if False else float() def amin(a=False, axis=None, out=None, keepdims=False): """ Return the minimum of an array or minimum along an axis. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default, flattened input is used. out : ndarray, optional Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See `doc.ufuncs` (Section "Output arguments") for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- amin : ndarray or scalar Minimum of `a`. If `axis` is None, the result is a scalar value. If `axis` is given, the result is an array of dimension ``a.ndim - 1``. See Also -------- amax : The maximum value of an array along a given axis, propagating any NaNs. nanmin : The minimum value of an array along a given axis, ignoring any NaNs. minimum : Element-wise minimum of two arrays, propagating any NaNs. fmin : Element-wise minimum of two arrays, ignoring any NaNs. argmin : Return the indices of the minimum values. nanmax, maximum, fmax Notes ----- NaN values are propagated, that is if at least one item is NaN, the corresponding min value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmin. Don't use `amin` for element-wise comparison of 2 arrays; when ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than ``amin(a, axis=0)``. Examples -------- >>> a = np.arange(4).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amin(a) # Minimum of the flattened array 0 >>> np.amin(a, axis=0) # Minima along the first axis array([0, 1]) >>> np.amin(a, axis=1) # Minima along the second axis array([0, 2]) >>> b = np.arange(5, dtype=np.float) >>> b[2] = np.NaN >>> np.amin(b) nan >>> np.nanmin(b) 0.0 """ return ndarray() if False else float() def angle(z=0, deg=0): """ Return the angle of the complex argument. Parameters ---------- z : array_like A complex number or sequence of complex numbers. deg : bool, optional Return angle in degrees if True, radians if False (default). Returns ------- angle : {ndarray, scalar} The counterclockwise angle from the positive real axis on the complex plane, with dtype as numpy.float64. See Also -------- arctan2 absolute Examples -------- >>> np.angle([1.0, 1.0j, 1+1j]) # in radians array([ 0. , 1.57079633, 0.78539816]) >>> np.angle(1+1j, deg=True) # in degrees 45.0 """ return ndarray() def any(a=False, axis=None, out=None, keepdims=False): """ Test whether any array element along a given axis evaluates to True. Returns single boolean unless `axis` is not ``None`` Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : None or int or tuple of ints, optional Axis or axes along which a logical OR reduction is performed. The default (`axis` = `None`) is perform a logical OR over all the dimensions of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if it is of type float, then it will remain so, returning 1.0 for True and 0.0 for False, regardless of the type of `a`). See `doc.ufuncs` (Section "Output arguments") for details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- any : bool or ndarray A new boolean or `ndarray` is returned unless `out` is specified, in which case a reference to `out` is returned. See Also -------- ndarray.any : equivalent method all : Test whether all elements along a given axis evaluate to True. Notes ----- Not a Number (NaN), positive infinity and negative infinity evaluate to `True` because these are not equal to zero. Examples -------- >>> np.any([[True, False], [True, True]]) True >>> np.any([[True, False], [False, False]], axis=0) array([ True, False], dtype=bool) >>> np.any([-1, 0, 5]) True >>> np.any(np.nan) True >>> o=np.array([False]) >>> z=np.any([-1, 4, 5], out=o) >>> z, o (array([ True], dtype=bool), array([ True], dtype=bool)) >>> # Check now that z is a reference to o >>> z is o True >>> id(z), id(o) # identity of z and o # doctest: +SKIP (191614240, 191614240) """ return bool() if False else ndarray() def append(arr, values=None, axis=None): """ Append values to the end of an array. Parameters ---------- arr : array_like Values are appended to a copy of this array. values : array_like These values are appended to a copy of `arr`. It must be of the correct shape (the same shape as `arr`, excluding `axis`). If `axis` is not specified, `values` can be any shape and will be flattened before use. axis : int, optional The axis along which `values` are appended. If `axis` is not given, both `arr` and `values` are flattened before use. Returns ------- append : ndarray A copy of `arr` with `values` appended to `axis`. Note that `append` does not occur in-place: a new array is allocated and filled. If `axis` is None, `out` is a flattened array. See Also -------- insert : Insert elements into an array. delete : Delete elements from an array. Examples -------- >>> np.append([1, 2, 3], [[4, 5, 6], [7, 8, 9]]) array([1, 2, 3, 4, 5, 6, 7, 8, 9]) When `axis` is specified, `values` must have the correct shape. >>> np.append([[1, 2, 3], [4, 5, 6]], [[7, 8, 9]], axis=0) array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> np.append([[1, 2, 3], [4, 5, 6]], [7, 8, 9], axis=0) Traceback (most recent call last): ... ValueError: arrays must have same number of dimensions """ return ndarray() def apply_along_axis(func1d, axis, arr, args): """ Apply a function to 1-D slices along the given axis. Execute `func1d(a, *args)` where `func1d` operates on 1-D arrays and `a` is a 1-D slice of `arr` along `axis`. Parameters ---------- func1d : function This function should accept 1-D arrays. It is applied to 1-D slices of `arr` along the specified axis. axis : integer Axis along which `arr` is sliced. arr : ndarray Input array. args : any Additional arguments to `func1d`. Returns ------- apply_along_axis : ndarray The output array. The shape of `outarr` is identical to the shape of `arr`, except along the `axis` dimension, where the length of `outarr` is equal to the size of the return value of `func1d`. If `func1d` returns a scalar `outarr` will have one fewer dimensions than `arr`. See Also -------- apply_over_axes : Apply a function repeatedly over multiple axes. Examples -------- >>> def my_func(a): ... ___Average first and last element of a 1-D array___ ... return (a[0] + a[-1]) * 0.5 >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) >>> np.apply_along_axis(my_func, 0, b) array([ 4., 5., 6.]) >>> np.apply_along_axis(my_func, 1, b) array([ 2., 5., 8.]) For a function that doesn't return a scalar, the number of dimensions in `outarr` is the same as `arr`. >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]]) >>> np.apply_along_axis(sorted, 1, b) array([[1, 7, 8], [3, 4, 9], [2, 5, 6]]) """ return ndarray() def apply_over_axes(func, a, axes): """ Apply a function repeatedly over multiple axes. `func` is called as `res = func(a, axis)`, where `axis` is the first element of `axes`. The result `res` of the function call must have either the same dimensions as `a` or one less dimension. If `res` has one less dimension than `a`, a dimension is inserted before `axis`. The call to `func` is then repeated for each axis in `axes`, with `res` as the first argument. Parameters ---------- func : function This function must take two arguments, `func(a, axis)`. a : array_like Input array. axes : array_like Axes over which `func` is applied; the elements must be integers. Returns ------- apply_over_axis : ndarray The output array. The number of dimensions is the same as `a`, but the shape can be different. This depends on whether `func` changes the shape of its output with respect to its input. See Also -------- apply_along_axis : Apply a function to 1-D slices of an array along the given axis. Examples -------- >>> a = np.arange(24).reshape(2,3,4) >>> a array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) Sum over axes 0 and 2. The result has same number of dimensions as the original array: >>> np.apply_over_axes(np.sum, a, [0,2]) array([[[ 60], [ 92], [124]]]) """ return ndarray() def arange(start=None, stop=None, step=None, _=None, dtype=None): """arange([start,] stop[, step,], dtype=None) Return evenly spaced values within a given interval. Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). For integer arguments the function is equivalent to the Python built-in `range `_ function, but returns an ndarray rather than a list. When using a non-integer step, such as 0.1, the results will often not be consistent. It is better to use ``linspace`` for these cases. Parameters ---------- start : number, optional Start of interval. The interval includes this value. The default start value is 0. stop : number End of interval. The interval does not include this value, except in some cases where `step` is not an integer and floating point round-off affects the length of `out`. step : number, optional Spacing between values. For any output `out`, this is the distance between two adjacent values, ``out[i+1] - out[i]``. The default step size is 1. If `step` is specified, `start` must also be given. dtype : dtype The type of the output array. If `dtype` is not given, infer the data type from the other input arguments. Returns ------- arange : ndarray Array of evenly spaced values. For floating point arguments, the length of the result is ``ceil((stop - start)/step)``. Because of floating point overflow, this rule may result in the last element of `out` being greater than `stop`. See Also -------- linspace : Evenly spaced numbers with careful handling of endpoints. ogrid: Arrays of evenly spaced numbers in N-dimensions. mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions. Examples -------- >>> np.arange(3) array([0, 1, 2]) >>> np.arange(3.0) array([ 0., 1., 2.]) >>> np.arange(3,7) array([3, 4, 5, 6]) >>> np.arange(3,7,2) array([3, 5])""" return ndarray() def arccos(x, out): """arccos(x[, out]) Trigonometric inverse cosine, element-wise. The inverse of `cos` so that, if ``y = cos(x)``, then ``x = arccos(y)``. Parameters ---------- x : array_like `x`-coordinate on the unit circle. For real arguments, the domain is [-1, 1]. out : ndarray, optional Array of the same shape as `a`, to store results in. See `doc.ufuncs` (Section "Output arguments") for more details. Returns ------- angle : ndarray The angle of the ray intersecting the unit circle at the given `x`-coordinate in radians [0, pi]. If `x` is a scalar then a scalar is returned, otherwise an array of the same shape as `x` is returned. See Also -------- cos, arctan, arcsin, emath.arccos Notes ----- `arccos` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `cos(z) = x`. The convention is to return the angle `z` whose real part lies in `[0, pi]`. For real-valued input data types, `arccos` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arccos` is a complex analytic function that has branch cuts `[-inf, -1]` and `[1, inf]` and is continuous from above on the former and from below on the latter. The inverse `cos` is also known as `acos` or cos^-1. References ---------- M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/ Examples -------- We expect the arccos of 1 to be 0, and of -1 to be pi: >>> np.arccos([1, -1]) array([ 0. , 3.14159265]) Plot arccos: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-1, 1, num=100) >>> plt.plot(x, np.arccos(x)) >>> plt.axis('tight') >>> plt.show()""" return ndarray() def arccosh(x, out): """arccosh(x[, out]) Inverse hyperbolic cosine, elementwise. Parameters ---------- x : array_like Input array. out : ndarray, optional Array of the same shape as `x`, to store results in. See `doc.ufuncs` (Section "Output arguments") for details. Returns ------- arccosh : ndarray Array of the same shape as `x`. See Also -------- cosh, arcsinh, sinh, arctanh, tanh Notes ----- `arccosh` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `cosh(z) = x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]` and the real part in ``[0, inf]``. For real-valued input data types, `arccosh` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arccosh` is a complex analytical function that has a branch cut `[-inf, 1]` and is continuous from above on it. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ .. [2] Wikipedia, "Inverse hyperbolic function", http://en.wikipedia.org/wiki/Arccosh Examples -------- >>> np.arccosh([np.e, 10.0]) array([ 1.65745445, 2.99322285]) >>> np.arccosh(1) 0.0""" return ndarray() def arcsin(x, out): """arcsin(x[, out]) Inverse sine, element-wise. Parameters ---------- x : array_like `y`-coordinate on the unit circle. out : ndarray, optional Array of the same shape as `x`, in which to store the results. See `doc.ufuncs` (Section "Output arguments") for more details. Returns ------- angle : ndarray The inverse sine of each element in `x`, in radians and in the closed interval ``[-pi/2, pi/2]``. If `x` is a scalar, a scalar is returned, otherwise an array. See Also -------- sin, cos, arccos, tan, arctan, arctan2, emath.arcsin Notes ----- `arcsin` is a multivalued function: for each `x` there are infinitely many numbers `z` such that :math:`sin(z) = x`. The convention is to return the angle `z` whose real part lies in [-pi/2, pi/2]. For real-valued input data types, *arcsin* always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arcsin` is a complex analytic function that has, by convention, the branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter. The inverse sine is also known as `asin` or sin^{-1}. References ---------- Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 79ff. http://www.math.sfu.ca/~cbm/aands/ Examples -------- >>> np.arcsin(1) # pi/2 1.5707963267948966 >>> np.arcsin(-1) # -pi/2 -1.5707963267948966 >>> np.arcsin(0) 0.0""" return ndarray() def arcsinh(x, out): """arcsinh(x[, out]) Inverse hyperbolic sine elementwise. Parameters ---------- x : array_like Input array. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See `doc.ufuncs`. Returns ------- out : ndarray Array of of the same shape as `x`. Notes ----- `arcsinh` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `sinh(z) = x`. The convention is to return the `z` whose imaginary part lies in `[-pi/2, pi/2]`. For real-valued input data types, `arcsinh` always returns real output. For each value that cannot be expressed as a real number or infinity, it returns ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arccos` is a complex analytical function that has branch cuts `[1j, infj]` and `[-1j, -infj]` and is continuous from the right on the former and from the left on the latter. The inverse hyperbolic sine is also known as `asinh` or ``sinh^-1``. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ .. [2] Wikipedia, "Inverse hyperbolic function", http://en.wikipedia.org/wiki/Arcsinh Examples -------- >>> np.arcsinh(np.array([np.e, 10.0])) array([ 1.72538256, 2.99822295])""" return ndarray() def arctan(x, out=None): """arctan(x[, out]) Trigonometric inverse tangent, element-wise. The inverse of tan, so that if ``y = tan(x)`` then ``x = arctan(y)``. Parameters ---------- x : array_like Input values. `arctan` is applied to each element of `x`. Returns ------- out : ndarray Out has the same shape as `x`. Its real part is in ``[-pi/2, pi/2]`` (``arctan(+/-inf)`` returns ``+/-pi/2``). It is a scalar if `x` is a scalar. See Also -------- arctan2 : The "four quadrant" arctan of the angle formed by (`x`, `y`) and the positive `x`-axis. angle : Argument of complex values. Notes ----- `arctan` is a multi-valued function: for each `x` there are infinitely many numbers `z` such that tan(`z`) = `x`. The convention is to return the angle `z` whose real part lies in [-pi/2, pi/2]. For real-valued input data types, `arctan` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arctan` is a complex analytic function that has [`1j, infj`] and [`-1j, -infj`] as branch cuts, and is continuous from the left on the former and from the right on the latter. The inverse tangent is also known as `atan` or tan^{-1}. References ---------- Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/ Examples -------- We expect the arctan of 0 to be 0, and of 1 to be pi/4: >>> np.arctan([0, 1]) array([ 0. , 0.78539816]) >>> np.pi/4 0.78539816339744828 Plot arctan: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-10, 10) >>> plt.plot(x, np.arctan(x)) >>> plt.axis('tight') >>> plt.show()""" return ndarray() def arctan2(x1, x2, out=None): """arctan2(x1, x2[, out]) Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly. The quadrant (i.e., branch) is chosen so that ``arctan2(x1, x2)`` is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (`x2`, `x1`). (Note the role reversal: the "`y`-coordinate" is the first function parameter, the "`x`-coordinate" is the second.) By IEEE convention, this function is defined for `x2` = +/-0 and for either or both of `x1` and `x2` = +/-inf (see Notes for specific values). This function is not defined for complex-valued arguments; for the so-called argument of complex values, use `angle`. Parameters ---------- x1 : array_like, real-valued `y`-coordinates. x2 : array_like, real-valued `x`-coordinates. `x2` must be broadcastable to match the shape of `x1` or vice versa. Returns ------- angle : ndarray Array of angles in radians, in the range ``[-pi, pi]``. See Also -------- arctan, tan, angle Notes ----- *arctan2* is identical to the `atan2` function of the underlying C library. The following special values are defined in the C standard: [1]_ ====== ====== ================ `x1` `x2` `arctan2(x1,x2)` ====== ====== ================ +/- 0 +0 +/- 0 +/- 0 -0 +/- pi > 0 +/-inf +0 / +pi < 0 +/-inf -0 / -pi +/-inf +inf +/- (pi/4) +/-inf -inf +/- (3*pi/4) ====== ====== ================ Note that +0 and -0 are distinct floating point numbers, as are +inf and -inf. References ---------- .. [1] ISO/IEC standard 9899:1999, "Programming language C." Examples -------- Consider four points in different quadrants: >>> x = np.array([-1, +1, +1, -1]) >>> y = np.array([-1, -1, +1, +1]) >>> np.arctan2(y, x) * 180 / np.pi array([-135., -45., 45., 135.]) Note the order of the parameters. `arctan2` is defined also when `x2` = 0 and at several other special points, obtaining values in the range ``[-pi, pi]``: >>> np.arctan2([1., -1.], [0., 0.]) array([ 1.57079633, -1.57079633]) >>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf]) array([ 0. , 3.14159265, 0.78539816])""" return ndarray() def arctanh(x, out=None): """arctanh(x[, out]) Inverse hyperbolic tangent elementwise. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray Array of the same shape as `x`. See Also -------- emath.arctanh Notes ----- `arctanh` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `tanh(z) = x`. The convention is to return the `z` whose imaginary part lies in `[-pi/2, pi/2]`. For real-valued input data types, `arctanh` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arctanh` is a complex analytical function that has branch cuts `[-1, -inf]` and `[1, inf]` and is continuous from above on the former and from below on the latter. The inverse hyperbolic tangent is also known as `atanh` or ``tanh^-1``. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ .. [2] Wikipedia, "Inverse hyperbolic function", http://en.wikipedia.org/wiki/Arctanh Examples -------- >>> np.arctanh([0, -0.5]) array([ 0. , -0.54930614])""" return ndarray() def argmax(a=None, axis=None): """ Indices of the maximum values along an axis. Parameters ---------- a : array_like Input array. axis : int, optional By default, the index is into the flattened array, otherwise along the specified axis. Returns ------- index_array : ndarray of ints Array of indices into the array. It has the same shape as `a.shape` with the dimension along `axis` removed. See Also -------- ndarray.argmax, argmin amax : The maximum value along a given axis. unravel_index : Convert a flat index into an index tuple. Notes ----- In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned. Examples -------- >>> a = np.arange(6).reshape(2,3) >>> a array([[0, 1, 2], [3, 4, 5]]) >>> np.argmax(a) 5 >>> np.argmax(a, axis=0) array([1, 1, 1]) >>> np.argmax(a, axis=1) array([2, 2]) >>> b = np.arange(6) >>> b[1] = 5 >>> b array([0, 5, 2, 3, 4, 5]) >>> np.argmax(b) # Only the first occurrence is returned. 1 """ return ndarray() def argmin(a=None, axis=None): """ Return the indices of the minimum values along an axis. See Also -------- argmax : Similar function. Please refer to `numpy.argmax` for detailed documentation. """ return None def argpartition(a, kth=None, axis=-1, kind="introselect", order=None): """ Perform an indirect partition along the given axis using the algorithm specified by the `kind` keyword. It returns an array of indices of the same shape as `a` that index data along the given axis in partitioned order. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array to sort. kth : int or sequence of ints Element index to partition by. The kth element will be in its final sorted position and all smaller elements will be moved before it and all larger elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all of them into their sorted position at once. axis : int or None, optional Axis along which to sort. The default is -1 (the last axis). If None, the flattened array is used. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect' order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. Returns ------- index_array : ndarray, int Array of indices that partition `a` along the specified axis. In other words, ``a[index_array]`` yields a sorted `a`. See Also -------- partition : Describes partition algorithms used. ndarray.partition : Inplace partition. argsort : Full indirect sort Notes ----- See `partition` for notes on the different selection algorithms. Examples -------- One dimensional array: >>> x = np.array([3, 4, 2, 1]) >>> x[np.argpartition(x, 3)] array([2, 1, 3, 4]) >>> x[np.argpartition(x, (1, 3))] array([1, 2, 3, 4]) """ return ndarray() def argsort(a=None, axis=-1, kind="quicksort", order=None): """ Returns the indices that would sort an array. Perform an indirect sort along the given axis using the algorithm specified by the `kind` keyword. It returns an array of indices of the same shape as `a` that index data along the given axis in sorted order. Parameters ---------- a : array_like Array to sort. axis : int or None, optional Axis along which to sort. The default is -1 (the last axis). If None, the flattened array is used. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. Returns ------- index_array : ndarray, int Array of indices that sort `a` along the specified axis. In other words, ``a[index_array]`` yields a sorted `a`. See Also -------- sort : Describes sorting algorithms used. lexsort : Indirect stable sort with multiple keys. ndarray.sort : Inplace sort. argpartition : Indirect partial sort. Notes ----- See `sort` for notes on the different sorting algorithms. As of NumPy 1.4.0 `argsort` works with real/complex arrays containing nan values. The enhanced sort order is documented in `sort`. Examples -------- One dimensional array: >>> x = np.array([3, 1, 2]) >>> np.argsort(x) array([1, 2, 0]) Two-dimensional array: >>> x = np.array([[0, 3], [2, 2]]) >>> x array([[0, 3], [2, 2]]) >>> np.argsort(x, axis=0) array([[0, 1], [1, 0]]) >>> np.argsort(x, axis=1) array([[0, 1], [0, 1]]) Sorting with keys: >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '>> x array([(1, 0), (0, 1)], dtype=[('x', '>> np.argsort(x, order=('x','y')) array([1, 0]) >>> np.argsort(x, order=('y','x')) array([0, 1]) """ return ndarray() def argwhere(a): """ Find the indices of array elements that are non-zero, grouped by element. Parameters ---------- a : array_like Input data. Returns ------- index_array : ndarray Indices of elements that are non-zero. Indices are grouped by element. See Also -------- where, nonzero Notes ----- ``np.argwhere(a)`` is the same as ``np.transpose(np.nonzero(a))``. The output of ``argwhere`` is not suitable for indexing arrays. For this purpose use ``where(a)`` instead. Examples -------- >>> x = np.arange(6).reshape(2,3) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.argwhere(x>1) array([[0, 2], [1, 0], [1, 1], [1, 2]]) """ return ndarray() def around(a=None, decimals=0, out=None): """ Evenly round to the given number of decimals. Parameters ---------- a : array_like Input data. decimals : int, optional Number of decimal places to round to (default: 0). If decimals is negative, it specifies the number of positions to the left of the decimal point. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. See `doc.ufuncs` (Section "Output arguments") for details. Returns ------- rounded_array : ndarray An array of the same type as `a`, containing the rounded values. Unless `out` was specified, a new array is created. A reference to the result is returned. The real and imaginary parts of complex numbers are rounded separately. The result of rounding a float is a float. See Also -------- ndarray.round : equivalent method ceil, fix, floor, rint, trunc Notes ----- For values exactly halfway between rounded decimal values, Numpy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, -0.5 and 0.5 round to 0.0, etc. Results may also be surprising due to the inexact representation of decimal fractions in the IEEE floating point standard [1]_ and errors introduced when scaling by powers of ten. References ---------- .. [1] "Lecture Notes on the Status of IEEE 754", William Kahan, http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF .. [2] "How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?", William Kahan, http://www.cs.berkeley.edu/~wkahan/Mindless.pdf Examples -------- >>> np.around([0.37, 1.64]) array([ 0., 2.]) >>> np.around([0.37, 1.64], decimals=1) array([ 0.4, 1.6]) >>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value array([ 0., 2., 2., 4., 4.]) >>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned array([ 1, 2, 3, 11]) >>> np.around([1,2,3,11], decimals=-1) array([ 0, 0, 0, 10]) """ return ndarray() def array(object, dtype, copy, order, subok, ndmin): """array(object, dtype=None, copy=True, order=None, subok=False, ndmin=0) Create an array. Parameters ---------- object : array_like An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence. dtype : data-type, optional The desired data-type for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. This argument can only be used to 'upcast' the array. For downcasting, use the .astype(t) method. copy : bool, optional If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (`dtype`, `order`, etc.). order : {'C', 'F', 'A'}, optional Specify the order of the array. If order is 'C' (default), then the array will be in C-contiguous order (last-index varies the fastest). If order is 'F', then the returned array will be in Fortran-contiguous order (first-index varies the fastest). If order is 'A', then the returned array may be in any order (either C-, Fortran-contiguous, or even discontiguous). subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (default). ndmin : int, optional Specifies the minimum number of dimensions that the resulting array should have. Ones will be pre-pended to the shape as needed to meet this requirement. Returns ------- out : ndarray An array object satisfying the specified requirements. See Also -------- empty, empty_like, zeros, zeros_like, ones, ones_like, fill Examples -------- >>> np.array([1, 2, 3]) array([1, 2, 3]) Upcasting: >>> np.array([1, 2, 3.0]) array([ 1., 2., 3.]) More than one dimension: >>> np.array([[1, 2], [3, 4]]) array([[1, 2], [3, 4]]) Minimum dimensions 2: >>> np.array([1, 2, 3], ndmin=2) array([[1, 2, 3]]) Type provided: >>> np.array([1, 2, 3], dtype=complex) array([ 1.+0.j, 2.+0.j, 3.+0.j]) Data-type consisting of more than one element: >>> x = np.array([(1,2),(3,4)],dtype=[('a','>> x['a'] array([1, 3]) Creating an array from sub-classes: >>> np.array(np.mat('1 2; 3 4')) array([[1, 2], [3, 4]]) >>> np.array(np.mat('1 2; 3 4'), subok=True) matrix([[1, 2], [3, 4]])""" return ndarray() def array2string(a=None, max_line_width=None, precision=None, suppress_small=None, separator=" ", prefix="", style="", formatter=None): """ Return a string representation of an array. Parameters ---------- a : ndarray Input array. max_line_width : int, optional The maximum number of columns the string should span. Newline characters splits the string appropriately after array elements. precision : int, optional Floating point precision. Default is the current printing precision (usually 8), which can be altered using `set_printoptions`. suppress_small : bool, optional Represent very small numbers as zero. A number is "very small" if it is smaller than the current printing precision. separator : str, optional Inserted between elements. prefix : str, optional An array is typically printed as:: 'prefix(' + array2string(a) + ')' The length of the prefix string is used to align the output correctly. style : function, optional A function that accepts an ndarray and returns a string. Used only when the shape of `a` is equal to ``()``, i.e. for 0-D arrays. formatter : dict of callables, optional If not None, the keys should indicate the type(s) that the respective formatting function applies to. Callables should return a string. Types that are not specified (by their corresponding keys) are handled by the default formatters. Individual types for which a formatter can be set are:: - 'bool' - 'int' - 'timedelta' : a `numpy.timedelta64` - 'datetime' : a `numpy.datetime64` - 'float' - 'longfloat' : 128-bit floats - 'complexfloat' - 'longcomplexfloat' : composed of two 128-bit floats - 'numpy_str' : types `numpy.string_` and `numpy.unicode_` - 'str' : all other strings Other keys that can be used to set a group of types at once are:: - 'all' : sets all types - 'int_kind' : sets 'int' - 'float_kind' : sets 'float' and 'longfloat' - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat' - 'str_kind' : sets 'str' and 'numpystr' Returns ------- array_str : str String representation of the array. Raises ------ TypeError if a callable in `formatter` does not return a string. See Also -------- array_str, array_repr, set_printoptions, get_printoptions Notes ----- If a formatter is specified for a certain type, the `precision` keyword is ignored for that type. Examples -------- >>> x = np.array([1e-16,1,2,3]) >>> print np.array2string(x, precision=2, separator=',', ... suppress_small=True) [ 0., 1., 2., 3.] >>> x = np.arange(3.) >>> np.array2string(x, formatter={'float_kind':lambda x: "%.2f" % x}) '[0.00 1.00 2.00]' >>> x = np.arange(3) >>> np.array2string(x, formatter={'int':lambda x: hex(x)}) '[0x0L 0x1L 0x2L]' """ return str() def array_equal(a1a2): """ True if two arrays have the same shape and elements, False otherwise. Parameters ---------- a1, a2 : array_like Input arrays. Returns ------- b : bool Returns True if the arrays are equal. See Also -------- allclose: Returns True if two arrays are element-wise equal within a tolerance. array_equiv: Returns True if input arrays are shape consistent and all elements equal. Examples -------- >>> np.array_equal([1, 2], [1, 2]) True >>> np.array_equal(np.array([1, 2]), np.array([1, 2])) True >>> np.array_equal([1, 2], [1, 2, 3]) False >>> np.array_equal([1, 2], [1, 4]) False """ return bool() def array_equiv(a1a2): """ Returns True if input arrays are shape consistent and all elements equal. Shape consistent means they are either the same shape, or one input array can be broadcasted to create the same shape as the other one. Parameters ---------- a1, a2 : array_like Input arrays. Returns ------- out : bool True if equivalent, False otherwise. Examples -------- >>> np.array_equiv([1, 2], [1, 2]) True >>> np.array_equiv([1, 2], [1, 3]) False Showing the shape equivalence: >>> np.array_equiv([1, 2], [[1, 2], [1, 2]]) True >>> np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]]) False >>> np.array_equiv([1, 2], [[1, 2], [1, 3]]) False """ return bool() def array_repr(arr=None, max_line_width=None, precision=None, suppress_small=None): """ Return the string representation of an array. Parameters ---------- arr : ndarray Input array. max_line_width : int, optional The maximum number of columns the string should span. Newline characters split the string appropriately after array elements. precision : int, optional Floating point precision. Default is the current printing precision (usually 8), which can be altered using `set_printoptions`. suppress_small : bool, optional Represent very small numbers as zero, default is False. Very small is defined by `precision`, if the precision is 8 then numbers smaller than 5e-9 are represented as zero. Returns ------- string : str The string representation of an array. See Also -------- array_str, array2string, set_printoptions Examples -------- >>> np.array_repr(np.array([1,2])) 'array([1, 2])' >>> np.array_repr(np.ma.array([0.])) 'MaskedArray([ 0.])' >>> np.array_repr(np.array([], np.int32)) 'array([], dtype=int32)' >>> x = np.array([1e-6, 4e-7, 2, 3]) >>> np.array_repr(x, precision=6, suppress_small=True) 'array([ 0.000001, 0. , 2. , 3. ])' """ return str() def array_split(ary, indices_or_sections=0, axis=0): """ Split an array into multiple sub-arrays. Please refer to the ``split`` documentation. The only difference between these functions is that ``array_split`` allows `indices_or_sections` to be an integer that does *not* equally divide the axis. See Also -------- split : Split array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(8.0) >>> np.array_split(x, 3) [array([ 0., 1., 2.]), array([ 3., 4., 5.]), array([ 6., 7.])] """ return None def array_str(a=None, max_line_width=None, precision=None, suppress_small=None): """ Return a string representation of the data in an array. The data in the array is returned as a single string. This function is similar to `array_repr`, the difference being that `array_repr` also returns information on the kind of array and its data type. Parameters ---------- a : ndarray Input array. max_line_width : int, optional Inserts newlines if text is longer than `max_line_width`. The default is, indirectly, 75. precision : int, optional Floating point precision. Default is the current printing precision (usually 8), which can be altered using `set_printoptions`. suppress_small : bool, optional Represent numbers "very close" to zero as zero; default is False. Very close is defined by precision: if the precision is 8, e.g., numbers smaller (in absolute value) than 5e-9 are represented as zero. See Also -------- array2string, array_repr, set_printoptions Examples -------- >>> np.array_str(np.arange(3)) '[0 1 2]' """ return None def asanyarray(a=None, dtype=None, order=None): """ Convert the input to an ndarray, but pass ndarray subclasses through. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes scalars, lists, lists of tuples, tuples, tuples of tuples, tuples of lists, and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F'}, optional Whether to use row-major ('C') or column-major ('F') memory representation. Defaults to 'C'. Returns ------- out : ndarray or an ndarray subclass Array interpretation of `a`. If `a` is an ndarray or a subclass of ndarray, it is returned as-is and no copy is performed. See Also -------- asarray : Similar function which always returns ndarrays. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. asarray_chkfinite : Similar function which checks input for NaNs and Infs. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array: >>> a = [1, 2] >>> np.asanyarray(a) array([1, 2]) Instances of `ndarray` subclasses are passed through as-is: >>> a = np.matrix([1, 2]) >>> np.asanyarray(a) is a True """ return ndarray() if False else an() def asarray(a=None, dtype=None, order=None): """ Convert the input to an array. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F'}, optional Whether to use row-major ('C') or column-major ('F' for FORTRAN) memory representation. Defaults to 'C'. Returns ------- out : ndarray Array interpretation of `a`. No copy is performed if the input is already an ndarray. If `a` is a subclass of ndarray, a base class ndarray is returned. See Also -------- asanyarray : Similar function which passes through subclasses. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. asarray_chkfinite : Similar function which checks input for NaNs and Infs. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array: >>> a = [1, 2] >>> np.asarray(a) array([1, 2]) Existing arrays are not copied: >>> a = np.array([1, 2]) >>> np.asarray(a) is a True If `dtype` is set, array is copied only if dtype does not match: >>> a = np.array([1, 2], dtype=np.float32) >>> np.asarray(a, dtype=np.float32) is a True >>> np.asarray(a, dtype=np.float64) is a False Contrary to `asanyarray`, ndarray subclasses are not passed through: >>> issubclass(np.matrix, np.ndarray) True >>> a = np.matrix([[1, 2]]) >>> np.asarray(a) is a False >>> np.asanyarray(a) is a True """ return ndarray() def asarray_chkfinite(a=None, dtype=None, order=None): """ Convert the input to an array, checking for NaNs or Infs. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. Success requires no NaNs or Infs. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F'}, optional Whether to use row-major ('C') or column-major ('FORTRAN') memory representation. Defaults to 'C'. Returns ------- out : ndarray Array interpretation of `a`. No copy is performed if the input is already an ndarray. If `a` is a subclass of ndarray, a base class ndarray is returned. Raises ------ ValueError Raises ValueError if `a` contains NaN (Not a Number) or Inf (Infinity). See Also -------- asarray : Create and array. asanyarray : Similar function which passes through subclasses. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array. If all elements are finite ``asarray_chkfinite`` is identical to ``asarray``. >>> a = [1, 2] >>> np.asarray_chkfinite(a, dtype=float) array([1., 2.]) Raises ValueError if array_like contains Nans or Infs. >>> a = [1, 2, np.inf] >>> try: ... np.asarray_chkfinite(a) ... except ValueError: ... print 'ValueError' ... ValueError """ return ndarray() def ascontiguousarray(a=None, dtype=None): """ Return a contiguous array in memory (C order). Parameters ---------- a : array_like Input array. dtype : str or dtype object, optional Data-type of returned array. Returns ------- out : ndarray Contiguous array of same shape and content as `a`, with type `dtype` if specified. See Also -------- asfortranarray : Convert input to an ndarray with column-major memory order. require : Return an ndarray that satisfies requirements. ndarray.flags : Information about the memory layout of the array. Examples -------- >>> x = np.arange(6).reshape(2,3) >>> np.ascontiguousarray(x, dtype=np.float32) array([[ 0., 1., 2.], [ 3., 4., 5.]], dtype=float32) >>> x.flags['C_CONTIGUOUS'] True """ return ndarray() def asfarray(a=typenumpy.float64(), dtype=typenumpy.float64()): """ Return an array converted to a float type. Parameters ---------- a : array_like The input array. dtype : str or dtype object, optional Float type code to coerce input array `a`. If `dtype` is one of the 'int' dtypes, it is replaced with float64. Returns ------- out : ndarray The input `a` as a float ndarray. Examples -------- >>> np.asfarray([2, 3]) array([ 2., 3.]) >>> np.asfarray([2, 3], dtype='float') array([ 2., 3.]) >>> np.asfarray([2, 3], dtype='int8') array([ 2., 3.]) """ return ndarray() def asfortranarray(a=None, dtype=None): """ Return an array laid out in Fortran order in memory. Parameters ---------- a : array_like Input array. dtype : str or dtype object, optional By default, the data-type is inferred from the input data. Returns ------- out : ndarray The input `a` in Fortran, or column-major, order. See Also -------- ascontiguousarray : Convert input to a contiguous (C order) array. asanyarray : Convert input to an ndarray with either row or column-major memory order. require : Return an ndarray that satisfies requirements. ndarray.flags : Information about the memory layout of the array. Examples -------- >>> x = np.arange(6).reshape(2,3) >>> y = np.asfortranarray(x) >>> x.flags['F_CONTIGUOUS'] False >>> y.flags['F_CONTIGUOUS'] True """ return ndarray() def asmatrix(data=None, dtype=None): """ Interpret the input as a matrix. Unlike `matrix`, `asmatrix` does not make a copy if the input is already a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``. Parameters ---------- data : array_like Input data. Returns ------- mat : matrix `data` interpreted as a matrix. Examples -------- >>> x = np.array([[1, 2], [3, 4]]) >>> m = np.asmatrix(x) >>> x[0,0] = 5 >>> m matrix([[5, 2], [3, 4]]) """ return matrix() def asscalar(a): """ Convert an array of size 1 to its scalar equivalent. Parameters ---------- a : ndarray Input array of size 1. Returns ------- out : scalar Scalar representation of `a`. The output data type is the same type returned by the input's `item` method. Examples -------- >>> np.asscalar(np.array([24])) 24 """ return None def atleast_1d(): """ Convert inputs to arrays with at least one dimension. Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved. Parameters ---------- arys1, arys2, ... : array_like One or more input arrays. Returns ------- ret : ndarray An array, or sequence of arrays, each with ``a.ndim >= 1``. Copies are made only if necessary. See Also -------- atleast_2d, atleast_3d Examples -------- >>> np.atleast_1d(1.0) array([ 1.]) >>> x = np.arange(9.0).reshape(3,3) >>> np.atleast_1d(x) array([[ 0., 1., 2.], [ 3., 4., 5.], [ 6., 7., 8.]]) >>> np.atleast_1d(x) is x True >>> np.atleast_1d(1, [3, 4]) [array([1]), array([3, 4])] """ return ndarray() def atleast_2d(): """ View inputs as arrays with at least two dimensions. Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have two or more dimensions are preserved. Returns ------- res, res2, ... : ndarray An array, or tuple of arrays, each with ``a.ndim >= 2``. Copies are avoided where possible, and views with two or more dimensions are returned. See Also -------- atleast_1d, atleast_3d Examples -------- >>> np.atleast_2d(3.0) array([[ 3.]]) >>> x = np.arange(3.0) >>> np.atleast_2d(x) array([[ 0., 1., 2.]]) >>> np.atleast_2d(x).base is x True >>> np.atleast_2d(1, [1, 2], [[1, 2]]) [array([[1]]), array([[1, 2]]), array([[1, 2]])] """ return ndarray() def atleast_3d(): """ View inputs as arrays with at least three dimensions. Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have three or more dimensions are preserved. Returns ------- res1, res2, ... : ndarray An array, or tuple of arrays, each with ``a.ndim >= 3``. Copies are avoided where possible, and views with three or more dimensions are returned. For example, a 1-D array of shape ``(N,)`` becomes a view of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a view of shape ``(M, N, 1)``. See Also -------- atleast_1d, atleast_2d Examples -------- >>> np.atleast_3d(3.0) array([[[ 3.]]]) >>> x = np.arange(3.0) >>> np.atleast_3d(x).shape (1, 3, 1) >>> x = np.arange(12.0).reshape(4,3) >>> np.atleast_3d(x).shape (4, 3, 1) >>> np.atleast_3d(x).base is x True >>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]): ... print arr, arr.shape ... [[[1] [2]]] (1, 2, 1) [[[1] [2]]] (1, 2, 1) [[[1 2]]] (1, 1, 2) """ return ndarray() def average(a=False, axis=None, weights=None, returned=False): """ Compute the weighted average along the specified axis. Parameters ---------- a : array_like Array containing data to be averaged. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which to average `a`. If `None`, averaging is done over the flattened array. weights : array_like, optional An array of weights associated with the values in `a`. Each value in `a` contributes to the average according to its associated weight. The weights array can either be 1-D (in which case its length must be the size of `a` along the given axis) or of the same shape as `a`. If `weights=None`, then all data in `a` are assumed to have a weight equal to one. returned : bool, optional Default is `False`. If `True`, the tuple (`average`, `sum_of_weights`) is returned, otherwise only the average is returned. If `weights=None`, `sum_of_weights` is equivalent to the number of elements over which the average is taken. Returns ------- average, [sum_of_weights] : {array_type, double} Return the average along the specified axis. When returned is `True`, return a tuple with the average as the first element and the sum of the weights as the second element. The return type is `Float` if `a` is of integer type, otherwise it is of the same type as `a`. `sum_of_weights` is of the same type as `average`. Raises ------ ZeroDivisionError When all weights along axis are zero. See `numpy.ma.average` for a version robust to this type of error. TypeError When the length of 1D `weights` is not the same as the shape of `a` along axis. See Also -------- mean ma.average : average for masked arrays -- useful if your data contains "missing" values Examples -------- >>> data = range(1,5) >>> data [1, 2, 3, 4] >>> np.average(data) 2.5 >>> np.average(range(1,11), weights=range(10,0,-1)) 4.0 >>> data = np.arange(6).reshape((3,2)) >>> data array([[0, 1], [2, 3], [4, 5]]) >>> np.average(data, axis=1, weights=[1./4, 3./4]) array([ 0.75, 2.75, 4.75]) >>> np.average(data, weights=[1./4, 3./4]) Traceback (most recent call last): ... TypeError: Axis must be specified when shapes of a and weights differ. """ return array_type() def bartlett(M): """ Return the Bartlett window. The Bartlett window is very similar to a triangular window, except that the end points are at zero. It is often used in signal processing for tapering a signal, without generating too much ripple in the frequency domain. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : array The triangular window, with the maximum value normalized to one (the value one appears only if the number of samples is odd), with the first and last samples equal to zero. See Also -------- blackman, hamming, hanning, kaiser Notes ----- The Bartlett window is defined as .. math:: w(n) = \frac{2}{M-1} \left( \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right| \right) Most references to the Bartlett window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. Note that convolution with this window produces linear interpolation. It is also known as an apodization (which means"removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. The fourier transform of the Bartlett is the product of two sinc functions. Note the excellent discussion in Kanasewich. References ---------- .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra", Biometrika 37, 1-16, 1950. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 109-110. .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal Processing", Prentice-Hall, 1999, pp. 468-471. .. [4] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function .. [5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 429. Examples -------- >>> np.bartlett(12) array([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, 0.90909091, 0.90909091, 0.72727273, 0.54545455, 0.36363636, 0.18181818, 0. ]) Plot the window and its frequency response (requires SciPy and matplotlib): >>> from numpy.fft import fft, fftshift >>> window = np.bartlett(51) >>> plt.plot(window) [] >>> plt.title("Bartlett window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Bartlett window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() """ return array() def base_repr(number=0, base=2, padding=0): """ Return a string representation of a number in the given base system. Parameters ---------- number : int The value to convert. Only positive values are handled. base : int, optional Convert `number` to the `base` number system. The valid range is 2-36, the default value is 2. padding : int, optional Number of zeros padded on the left. Default is 0 (no padding). Returns ------- out : str String representation of `number` in `base` system. See Also -------- binary_repr : Faster version of `base_repr` for base 2. Examples -------- >>> np.base_repr(5) '101' >>> np.base_repr(6, 5) '11' >>> np.base_repr(7, base=5, padding=3) '00012' >>> np.base_repr(10, base=16) 'A' >>> np.base_repr(32, base=16) '20' """ return str() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() def binary_repr(num=None, width=None): """ Return the binary representation of the input number as a string. For negative numbers, if width is not given, a minus sign is added to the front. If width is given, the two's complement of the number is returned, with respect to that width. In a two's-complement system negative numbers are represented by the two's complement of the absolute value. This is the most common method of representing signed integers on computers [1]_. A N-bit two's-complement system can represent every integer in the range :math:`-2^{N-1}` to :math:`+2^{N-1}-1`. Parameters ---------- num : int Only an integer decimal number can be used. width : int, optional The length of the returned string if `num` is positive, the length of the two's complement if `num` is negative. Returns ------- bin : str Binary representation of `num` or two's complement of `num`. See Also -------- base_repr: Return a string representation of a number in the given base system. Notes ----- `binary_repr` is equivalent to using `base_repr` with base 2, but about 25x faster. References ---------- .. [1] Wikipedia, "Two's complement", http://en.wikipedia.org/wiki/Two's_complement Examples -------- >>> np.binary_repr(3) '11' >>> np.binary_repr(-3) '-11' >>> np.binary_repr(3, width=4) '0011' The two's complement is returned when the input number is negative and width is specified: >>> np.binary_repr(-3, width=4) '1101' """ return str() def bincount(x, weights, minlength): """bincount(x, weights=None, minlength=None) Count number of occurrences of each value in array of non-negative ints. The number of bins (of size 1) is one larger than the largest value in `x`. If `minlength` is specified, there will be at least this number of bins in the output array (though it will be longer if necessary, depending on the contents of `x`). Each bin gives the number of occurrences of its index value in `x`. If `weights` is specified the input array is weighted by it, i.e. if a value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead of ``out[n] += 1``. Parameters ---------- x : array_like, 1 dimension, nonnegative ints Input array. weights : array_like, optional Weights, array of the same shape as `x`. minlength : int, optional .. versionadded:: 1.6.0 A minimum number of bins for the output array. Returns ------- out : ndarray of ints The result of binning the input array. The length of `out` is equal to ``np.amax(x)+1``. Raises ------ ValueError If the input is not 1-dimensional, or contains elements with negative values, or if `minlength` is non-positive. TypeError If the type of the input is float or complex. See Also -------- histogram, digitize, unique Examples -------- >>> np.bincount(np.arange(5)) array([1, 1, 1, 1, 1]) >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7])) array([1, 3, 1, 1, 0, 0, 0, 1]) >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23]) >>> np.bincount(x).size == np.amax(x)+1 True The input array needs to be of integer dtype, otherwise a TypeError is raised: >>> np.bincount(np.arange(5, dtype=np.float)) Traceback (most recent call last): File "", line 1, in TypeError: array cannot be safely cast to required type A possible use of ``bincount`` is to perform sums over variable-size chunks of an array, using the ``weights`` keyword. >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights >>> x = np.array([0, 1, 1, 2, 2, 2]) >>> np.bincount(x, weights=w) array([ 0.3, 0.7, 1.1])""" return ndarray() def bitwise_and(x1, x2, out=None): """bitwise_and(x1, x2[, out]) Compute the bit-wise AND of two arrays element-wise. Computes the bit-wise AND of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``&``. Parameters ---------- x1, x2 : array_like Only integer types are handled (including booleans). Returns ------- out : array_like Result. See Also -------- logical_and bitwise_or bitwise_xor binary_repr : Return the binary representation of the input number as a string. Examples -------- The number 13 is represented by ``00001101``. Likewise, 17 is represented by ``00010001``. The bit-wise AND of 13 and 17 is therefore ``000000001``, or 1: >>> np.bitwise_and(13, 17) 1 >>> np.bitwise_and(14, 13) 12 >>> np.binary_repr(12) '1100' >>> np.bitwise_and([14,3], 13) array([12, 1]) >>> np.bitwise_and([11,7], [4,25]) array([0, 1]) >>> np.bitwise_and(np.array([2,5,255]), np.array([3,14,16])) array([ 2, 4, 16]) >>> np.bitwise_and([True, True], [False, True]) array([False, True], dtype=bool)""" return ndarray() def invert(x, out=None): """invert(x[, out]) Compute bit-wise inversion, or bit-wise NOT, element-wise. Computes the bit-wise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``~``. For signed integer inputs, the two's complement is returned. In a two's-complement system negative numbers are represented by the two's complement of the absolute value. This is the most common method of representing signed integers on computers [1]_. A N-bit two's-complement system can represent every integer in the range :math:`-2^{N-1}` to :math:`+2^{N-1}-1`. Parameters ---------- x1 : array_like Only integer types are handled (including booleans). Returns ------- out : array_like Result. See Also -------- bitwise_and, bitwise_or, bitwise_xor logical_not binary_repr : Return the binary representation of the input number as a string. Notes ----- `bitwise_not` is an alias for `invert`: >>> np.bitwise_not is np.invert True References ---------- .. [1] Wikipedia, "Two's complement", http://en.wikipedia.org/wiki/Two's_complement Examples -------- We've seen that 13 is represented by ``00001101``. The invert or bit-wise NOT of 13 is then: >>> np.invert(np.array([13], dtype=uint8)) array([242], dtype=uint8) >>> np.binary_repr(x, width=8) '00001101' >>> np.binary_repr(242, width=8) '11110010' The result depends on the bit-width: >>> np.invert(np.array([13], dtype=uint16)) array([65522], dtype=uint16) >>> np.binary_repr(x, width=16) '0000000000001101' >>> np.binary_repr(65522, width=16) '1111111111110010' When using signed integer types the result is the two's complement of the result for the unsigned type: >>> np.invert(np.array([13], dtype=int8)) array([-14], dtype=int8) >>> np.binary_repr(-14, width=8) '11110010' Booleans are accepted as well: >>> np.invert(array([True, False])) array([False, True], dtype=bool)""" return ndarray() def bitwise_or(x1, x2, out=None): """bitwise_or(x1, x2[, out]) Compute the bit-wise OR of two arrays element-wise. Computes the bit-wise OR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``|``. Parameters ---------- x1, x2 : array_like Only integer types are handled (including booleans). out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- out : array_like Result. See Also -------- logical_or bitwise_and bitwise_xor binary_repr : Return the binary representation of the input number as a string. Examples -------- The number 13 has the binaray representation ``00001101``. Likewise, 16 is represented by ``00010000``. The bit-wise OR of 13 and 16 is then ``000111011``, or 29: >>> np.bitwise_or(13, 16) 29 >>> np.binary_repr(29) '11101' >>> np.bitwise_or(32, 2) 34 >>> np.bitwise_or([33, 4], 1) array([33, 5]) >>> np.bitwise_or([33, 4], [1, 2]) array([33, 6]) >>> np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4])) array([ 6, 5, 255]) >>> np.array([2, 5, 255]) | np.array([4, 4, 4]) array([ 6, 5, 255]) >>> np.bitwise_or(np.array([2, 5, 255, 2147483647L], dtype=np.int32), ... np.array([4, 4, 4, 2147483647L], dtype=np.int32)) array([ 6, 5, 255, 2147483647]) >>> np.bitwise_or([True, True], [False, True]) array([ True, True], dtype=bool)""" return ndarray() def bitwise_xor(x1, x2, out=None): """bitwise_xor(x1, x2[, out]) Compute the bit-wise XOR of two arrays element-wise. Computes the bit-wise XOR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``^``. Parameters ---------- x1, x2 : array_like Only integer types are handled (including booleans). Returns ------- out : array_like Result. See Also -------- logical_xor bitwise_and bitwise_or binary_repr : Return the binary representation of the input number as a string. Examples -------- The number 13 is represented by ``00001101``. Likewise, 17 is represented by ``00010001``. The bit-wise XOR of 13 and 17 is therefore ``00011100``, or 28: >>> np.bitwise_xor(13, 17) 28 >>> np.binary_repr(28) '11100' >>> np.bitwise_xor(31, 5) 26 >>> np.bitwise_xor([31,3], 5) array([26, 6]) >>> np.bitwise_xor([31,3], [5,6]) array([26, 5]) >>> np.bitwise_xor([True, True], [False, True]) array([ True, False], dtype=bool)""" return ndarray() def blackman(M): """ Return the Blackman window. The Blackman window is a taper formed by using the the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, hamming, hanning, kaiser Notes ----- The Blackman window is defined as .. math:: w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M) Most references to the Blackman window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. It is known as a "near optimal" tapering function, almost as good (by some measures) as the kaiser window. References ---------- Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471. Examples -------- >>> np.blackman(12) array([ -1.38777878e-17, 3.26064346e-02, 1.59903635e-01, 4.14397981e-01, 7.36045180e-01, 9.67046769e-01, 9.67046769e-01, 7.36045180e-01, 4.14397981e-01, 1.59903635e-01, 3.26064346e-02, -1.38777878e-17]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.blackman(51) >>> plt.plot(window) [] >>> plt.title("Blackman window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Blackman window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() """ return ndarray() def bmat(obj=None, ldict=None, gdict=None): """ Build a matrix object from a string, nested sequence, or array. Parameters ---------- obj : str or array_like Input data. Names of variables in the current scope may be referenced, even if `obj` is a string. Returns ------- out : matrix Returns a matrix object, which is a specialized 2-D array. See Also -------- matrix Examples -------- >>> A = np.mat('1 1; 1 1') >>> B = np.mat('2 2; 2 2') >>> C = np.mat('3 4; 5 6') >>> D = np.mat('7 8; 9 0') All the following expressions construct the same block matrix: >>> np.bmat([[A, B], [C, D]]) matrix([[1, 1, 2, 2], [1, 1, 2, 2], [3, 4, 7, 8], [5, 6, 9, 0]]) >>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]]) matrix([[1, 1, 2, 2], [1, 1, 2, 2], [3, 4, 7, 8], [5, 6, 9, 0]]) >>> np.bmat('A,B; C,D') matrix([[1, 1, 2, 2], [1, 1, 2, 2], [3, 4, 7, 8], [5, 6, 9, 0]]) """ return matrix() class bool: __doc__ = str() def bit_length(self, _): """int.bit_length() -> int Number of bits necessary to represent self in binary. >>> bin(37) '0b100101' >>> (37).bit_length() 6""" return None def conjugate(self, _): """Returns self, the complex conjugate of any int.""" return None denominator = getset_descriptor() imag = getset_descriptor() numerator = getset_descriptor() real = getset_descriptor() class bool_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class bool_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class broadcast: __doc__ = str() index = getset_descriptor() iters = getset_descriptor() nd = member_descriptor() def next(self, _): """x.next() -> the next value, or raise StopIteration""" return None numiter = member_descriptor() def reset(self, _): """reset() Reset the broadcasted result's iterator(s). Parameters ---------- None Returns ------- None Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]] >>> b = np.broadcast(x, y) >>> b.index 0 >>> b.next(), b.next(), b.next() ((1, 4), (2, 4), (3, 4)) >>> b.index 3 >>> b.reset() >>> b.index 0""" return None shape = getset_descriptor() size = getset_descriptor() def broadcast_arrays(): """ Broadcast any number of arrays against each other. Parameters ---------- `*args` : array_likes The arrays to broadcast. Returns ------- broadcasted : list of arrays These arrays are views on the original arrays. They are typically not contiguous. Furthermore, more than one element of a broadcasted array may refer to a single memory location. If you need to write to the arrays, make copies first. Examples -------- >>> x = np.array([[1,2,3]]) >>> y = np.array([[1],[2],[3]]) >>> np.broadcast_arrays(x, y) [array([[1, 2, 3], [1, 2, 3], [1, 2, 3]]), array([[1, 1, 1], [2, 2, 2], [3, 3, 3]])] Here is a useful idiom for getting contiguous copies instead of non-contiguous views. >>> [np.array(a) for a in np.broadcast_arrays(x, y)] [array([[1, 2, 3], [1, 2, 3], [1, 2, 3]]), array([[1, 1, 1], [2, 2, 2], [3, 3, 3]])] """ return list() def busday_count(begindates, enddates, weekmask, holidays, busdaycal, out): """busday_count(begindates, enddates, weekmask='1111100', holidays=[], busdaycal=None, out=None) Counts the number of valid days between `begindates` and `enddates`, not including the day of `enddates`. If ``enddates`` specifies a date value that is earlier than the corresponding ``begindates`` date value, the count will be negative. .. versionadded:: 1.7.0 Parameters ---------- begindates : array_like of datetime64[D] The array of the first dates for counting. enddates : array_like of datetime64[D] The array of the end dates for counting, which are excluded from the count themselves. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of int, optional If provided, this array is filled with the result. Returns ------- out : array of int An array with a shape from broadcasting ``begindates`` and ``enddates`` together, containing the number of valid days between the begin and end dates. See Also -------- busdaycalendar: An object that specifies a custom set of valid days. is_busday : Returns a boolean array indicating valid days. busday_offset : Applies an offset counted in valid days. Examples -------- >>> # Number of weekdays in January 2011 ... np.busday_count('2011-01', '2011-02') 21 >>> # Number of weekdays in 2011 ... np.busday_count('2011', '2012') 260 >>> # Number of Saturdays in 2011 ... np.busday_count('2011', '2012', weekmask='Sat') 53""" return array() def busday_offset(dates, offsets, roll, weekmask, holidays, busdaycal, out): """busday_offset(dates, offsets, roll='raise', weekmask='1111100', holidays=None, busdaycal=None, out=None) First adjusts the date to fall on a valid day according to the ``roll`` rule, then applies offsets to the given dates counted in valid days. .. versionadded:: 1.7.0 Parameters ---------- dates : array_like of datetime64[D] The array of dates to process. offsets : array_like of int The array of offsets, which is broadcast with ``dates``. roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', 'modifiedfollowing', 'modifiedpreceding'}, optional How to treat dates that do not fall on a valid day. The default is 'raise'. * 'raise' means to raise an exception for an invalid day. * 'nat' means to return a NaT (not-a-time) for an invalid day. * 'forward' and 'following' mean to take the first valid day later in time. * 'backward' and 'preceding' mean to take the first valid day earlier in time. * 'modifiedfollowing' means to take the first valid day later in time unless it is across a Month boundary, in which case to take the first valid day earlier in time. * 'modifiedpreceding' means to take the first valid day earlier in time unless it is across a Month boundary, in which case to take the first valid day later in time. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of datetime64[D], optional If provided, this array is filled with the result. Returns ------- out : array of datetime64[D] An array with a shape from broadcasting ``dates`` and ``offsets`` together, containing the dates with offsets applied. See Also -------- busdaycalendar: An object that specifies a custom set of valid days. is_busday : Returns a boolean array indicating valid days. busday_count : Counts how many valid days are in a half-open date range. Examples -------- >>> # First business day in October 2011 (not accounting for holidays) ... np.busday_offset('2011-10', 0, roll='forward') numpy.datetime64('2011-10-03','D') >>> # Last business day in February 2012 (not accounting for holidays) ... np.busday_offset('2012-03', -1, roll='forward') numpy.datetime64('2012-02-29','D') >>> # Third Wednesday in January 2011 ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed') numpy.datetime64('2011-01-19','D') >>> # 2012 Mother's Day in Canada and the U.S. ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun') numpy.datetime64('2012-05-13','D') >>> # First business day on or after a date ... np.busday_offset('2011-03-20', 0, roll='forward') numpy.datetime64('2011-03-21','D') >>> np.busday_offset('2011-03-22', 0, roll='forward') numpy.datetime64('2011-03-22','D') >>> # First business day after a date ... np.busday_offset('2011-03-20', 1, roll='backward') numpy.datetime64('2011-03-21','D') >>> np.busday_offset('2011-03-22', 1, roll='backward') numpy.datetime64('2011-03-23','D')""" return array() class busdaycalendar: __doc__ = str() holidays = getset_descriptor() weekmask = getset_descriptor() class int8: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def byte_bounds(a): """ Returns pointers to the end-points of an array. Parameters ---------- a : ndarray Input array. It must conform to the Python-side of the array interface. Returns ------- (low, high) : tuple of 2 integers The first integer is the first byte of the array, the second integer is just past the last byte of the array. If `a` is not contiguous it will not use every byte between the (`low`, `high`) values. Examples -------- >>> I = np.eye(2, dtype='f'); I.dtype dtype('float32') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True >>> I = np.eye(2, dtype='G'); I.dtype dtype('complex192') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True """ return tuple() class string_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None base = getset_descriptor() def capitalize(self, _): """S.capitalize() -> string Return a copy of the string S with only its first character capitalized.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> string Return S centered in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def conj(self, _): """None""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None data = getset_descriptor() def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> object Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None dtype = getset_descriptor() def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> object Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that is able to handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> string Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None flags = getset_descriptor() flat = getset_descriptor() def format(self, args, kwargs): """S.format(*args, **kwargs) -> string Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None imag = getset_descriptor() def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. uppercase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None itemsize = getset_descriptor() def join(self, iterable): """S.join(iterable) -> string Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> string Return S left-justified in a string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> string Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> string or unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None real = getset_descriptor() def replace(self, old, new, count): """S.replace(old, new[, count]) -> string Return a copy of string S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> string Return S right-justified in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> string or unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None shape = getset_descriptor() size = getset_descriptor() def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None strides = getset_descriptor() def strip(self, chars): """S.strip([chars]) -> string or unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> string Return a copy of the string S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> string Return a titlecased version of S, i.e. words start with uppercase characters, all remaining cased characters have lowercase.""" return None def translate(self, table, deletechars): """S.translate(table [,deletechars]) -> string Return a copy of the string S, where all characters occurring in the optional argument deletechars are removed, and the remaining characters have been mapped through the given translation table, which must be a string of length 256 or None. If the table argument is None, no translation is applied and the operation simply removes the characters in deletechars.""" return None def upper(self, _): """S.upper() -> string Return a copy of the string S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> string Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None c_ = CClass() def can_cast(_from, totype, casting): """can_cast(from, totype, casting = 'safe') Returns True if cast between data types can occur according to the casting rule. If from is a scalar or array scalar, also returns True if the scalar value can be cast without overflow or truncation to an integer. Parameters ---------- from : dtype, dtype specifier, scalar, or array Data type, scalar, or array to cast from. totype : dtype or dtype specifier Data type to cast to. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. Returns ------- out : bool True if cast can occur according to the casting rule. See also -------- dtype, result_type Examples -------- Basic examples >>> np.can_cast(np.int32, np.int64) True >>> np.can_cast(np.float64, np.complex) True >>> np.can_cast(np.complex, np.float) False >>> np.can_cast('i8', 'f8') True >>> np.can_cast('i8', 'f4') False >>> np.can_cast('i4', 'S4') True Casting scalars >>> np.can_cast(100, 'i1') True >>> np.can_cast(150, 'i1') False >>> np.can_cast(150, 'u1') True >>> np.can_cast(3.5e100, np.float32) False >>> np.can_cast(1000.0, np.float32) True Array scalar checks the value, array does not >>> np.can_cast(np.array(1000.0), np.float32) True >>> np.can_cast(np.array([1000.0]), np.float32) False Using the casting rules >>> np.can_cast('i8', 'i8', 'no') True >>> np.can_cast('i8', 'no') False >>> np.can_cast('i8', 'equiv') True >>> np.can_cast('i8', 'equiv') False >>> np.can_cast('i8', 'safe') True >>> np.can_cast('i4', 'safe') False >>> np.can_cast('i4', 'same_kind') True >>> np.can_cast('u4', 'same_kind') False >>> np.can_cast('u4', 'unsafe') True""" return bool() cast = _typedict() class complex128: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def ceil(x, out=None): """ceil(x[, out]) Return the ceiling of the input, element-wise. The ceil of the scalar `x` is the smallest integer `i`, such that `i >= x`. It is often denoted as :math:`\lceil x \rceil`. Parameters ---------- x : array_like Input data. Returns ------- y : {ndarray, scalar} The ceiling of each element in `x`, with `float` dtype. See Also -------- floor, trunc, rint Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.ceil(a) array([-1., -1., -0., 1., 2., 2., 2.])""" return None class complex128: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class character: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class chararray: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __dict__ = dictproxy() __doc__ = str() __module__ = str() def all(self, axis=None, out=None): """a.all(axis=None, out=None) Returns True if all elements evaluate to True. Refer to `numpy.all` for full documentation. See Also -------- numpy.all : equivalent function""" return None def any(self, axis=None, out=None): """a.any(axis=None, out=None) Returns True if any of the elements of `a` evaluate to True. Refer to `numpy.any` for full documentation. See Also -------- numpy.any : equivalent function""" return None def argmax(self, axis=None, out=None): """a.argmax(axis=None, out=None) Return indices of the maximum values along the given axis. Refer to `numpy.argmax` for full documentation. See Also -------- numpy.argmax : equivalent function""" return None def argmin(self, axis=None, out=None): """a.argmin(axis=None, out=None) Return indices of the minimum values along the given axis of `a`. Refer to `numpy.argmin` for detailed documentation. See Also -------- numpy.argmin : equivalent function""" return None def argpartition(self, kth, axis=_1, kind=quickselect, order=None): """a.argpartition(kth, axis=-1, kind='quickselect', order=None) Returns the indices that would partition this array. Refer to `numpy.argpartition` for full documentation. .. versionadded:: 1.8.0 See Also -------- numpy.argpartition : equivalent function""" return None def argsort(self=None, axis=-1, kind="quicksort", order=None): """None""" return None def astype(self, dtype, order, casting, subok, copy): """a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) Copy of the array, cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to false, and the `dtype`, `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy. Returns ------- arr_t : ndarray Unless `copy` is False and the other conditions for returning the input array are satisfied (see description for `copy` input paramter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by `dtype`, `order`. Raises ------ ComplexWarning When casting from complex to float or int. To avoid this, one should use ``a.real.astype(t)``. Examples -------- >>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5]) >>> x.astype(int) array([1, 2, 2])""" return ndarray() base = getset_descriptor() def byteswap(self, inplace): """a.byteswap(inplace) Swap the bytes of the array elements Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Parameters ---------- inplace : bool, optional If ``True``, swap bytes in-place, default is ``False``. Returns ------- out : ndarray The byteswapped array. If `inplace` is ``True``, this is a view to self. Examples -------- >>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322'] Arrays of strings are not swapped >>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')""" return ndarray() def capitalize(self, _): """ Return a copy of `self` with only the first character of each element capitalized. See also -------- char.capitalize """ return None def center(self, width=" ", fillchar=" "): """ Return a copy of `self` with its elements centered in a string of length `width`. See also -------- center """ return None def choose(self, choices, out=None, mode=_raise): """a.choose(choices, out=None, mode='raise') Use an index array to construct a new array from a set of choices. Refer to `numpy.choose` for full documentation. See Also -------- numpy.choose : equivalent function""" return None def clip(self, a_min, a_max, out=None): """a.clip(a_min, a_max, out=None) Return an array whose values are limited to ``[a_min, a_max]``. Refer to `numpy.clip` for full documentation. See Also -------- numpy.clip : equivalent function""" return None def compress(self, condition, axis=None, out=None): """a.compress(condition, axis=None, out=None) Return selected slices of this array along given axis. Refer to `numpy.compress` for full documentation. See Also -------- numpy.compress : equivalent function""" return None def conj(self, _): """a.conj() Complex-conjugate all elements. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def conjugate(self, _): """a.conjugate() Return the complex conjugate, element-wise. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def copy(self, order): """a.copy(order='C') Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :func:numpy.copy are very similar, but have different default values for their order= arguments.) See also -------- numpy.copy numpy.copyto Examples -------- >>> x = np.array([[1,2,3],[4,5,6]], order='F') >>> y = x.copy() >>> x.fill(0) >>> x array([[0, 0, 0], [0, 0, 0]]) >>> y array([[1, 2, 3], [4, 5, 6]]) >>> y.flags['C_CONTIGUOUS'] True""" return None def count(self, sub=None, start=0, end=None): """ Returns an array with the number of non-overlapping occurrences of substring `sub` in the range [`start`, `end`]. See also -------- char.count """ return None ctypes = getset_descriptor() def cumprod(self, axis=None, dtype=None, out=None): """a.cumprod(axis=None, dtype=None, out=None) Return the cumulative product of the elements along the given axis. Refer to `numpy.cumprod` for full documentation. See Also -------- numpy.cumprod : equivalent function""" return None def cumsum(self, axis=None, dtype=None, out=None): """a.cumsum(axis=None, dtype=None, out=None) Return the cumulative sum of the elements along the given axis. Refer to `numpy.cumsum` for full documentation. See Also -------- numpy.cumsum : equivalent function""" return None data = getset_descriptor() def decode(self=None, encoding=None, errors=None): """ Calls `str.decode` element-wise. See also -------- char.decode """ return None def diagonal(self, offset=0, axis1=0, axis2=1): """a.diagonal(offset=0, axis1=0, axis2=1) Return specified diagonals. Refer to :func:`numpy.diagonal` for full documentation. See Also -------- numpy.diagonal : equivalent function""" return None def dot(self, b, out=None): """a.dot(b, out=None) Dot product of two arrays. Refer to `numpy.dot` for full documentation. See Also -------- numpy.dot : equivalent function Examples -------- >>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]]) This array method can be conveniently chained: >>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])""" return None dtype = getset_descriptor() def dump(self, file): """a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load. Parameters ---------- file : str A string naming the dump file.""" return None def dumps(self, _): """a.dumps() Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array. Parameters ---------- None""" return None def encode(self=None, encoding=None, errors=None): """ Calls `str.encode` element-wise. See also -------- char.encode """ return None def endswith(self, suffix=None, start=0, end=None): """ Returns a boolean array which is `True` where the string element in `self` ends with `suffix`, otherwise `False`. See also -------- char.endswith """ return None def expandtabs(self=8, tabsize=8): """ Return a copy of each string element where all tab characters are replaced by one or more spaces. See also -------- char.expandtabs """ return None def fill(self, value): """a.fill(value) Fill the array with a scalar value. Parameters ---------- value : scalar All elements of `a` will be assigned this value. Examples -------- >>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])""" return None def find(self, sub=None, start=0, end=None): """ For each element, return the lowest index in the string where substring `sub` is found. See also -------- char.find """ return None flags = getset_descriptor() flat = getset_descriptor() def flatten(self, order): """a.flatten(order='C') Return a copy of the array collapsed into one dimension. Parameters ---------- order : {'C', 'F', 'A'}, optional Whether to flatten in C (row-major), Fortran (column-major) order, or preserve the C/Fortran ordering from `a`. The default is 'C'. Returns ------- y : ndarray A copy of the input array, flattened to one dimension. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the array. Examples -------- >>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])""" return ndarray() def getfield(self, dtype, offset): """a.getfield(dtype, offset=0) Returns a field of the given array as a certain type. A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes. Parameters ---------- dtype : str or dtype The data type of the view. The dtype size of the view can not be larger than that of the array itself. offset : int Number of bytes to skip before beginning the element view. Examples -------- >>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]]) By choosing an offset of 8 bytes we can select the complex part of the array for our view: >>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])""" return array() imag = getset_descriptor() def index(self, sub=None, start=0, end=None): """ Like `find`, but raises `ValueError` when the substring is not found. See also -------- char.index """ return None def isalnum(self, _): """ Returns true for each element if all characters in the string are alphanumeric and there is at least one character, false otherwise. See also -------- char.isalnum """ return None def isalpha(self, _): """ Returns true for each element if all characters in the string are alphabetic and there is at least one character, false otherwise. See also -------- char.isalpha """ return None def isdecimal(self, _): """ For each element in `self`, return True if there are only decimal characters in the element. See also -------- char.isdecimal """ return None def isdigit(self, _): """ Returns true for each element if all characters in the string are digits and there is at least one character, false otherwise. See also -------- char.isdigit """ return None def islower(self, _): """ Returns true for each element if all cased characters in the string are lowercase and there is at least one cased character, false otherwise. See also -------- char.islower """ return None def isnumeric(self, _): """ For each element in `self`, return True if there are only numeric characters in the element. See also -------- char.isnumeric """ return None def isspace(self, _): """ Returns true for each element if there are only whitespace characters in the string and there is at least one character, false otherwise. See also -------- char.isspace """ return None def istitle(self, _): """ Returns true for each element if the element is a titlecased string and there is at least one character, false otherwise. See also -------- char.istitle """ return None def isupper(self, _): """ Returns true for each element if all cased characters in the string are uppercase and there is at least one character, false otherwise. See also -------- char.isupper """ return None def item(self, ESCargs): """a.item(*args) Copy an element of an array to a standard Python scalar and return it. Parameters ---------- \*args : Arguments (variable number and type) * none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned. * int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return. * tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array. Returns ------- z : Standard Python scalar object A copy of the specified element of the array as a suitable Python scalar Notes ----- When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned. `item` is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python's optimized math. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3""" return Standard() def itemset(self, ESCargs): """a.itemset(*args) Insert scalar into an array (scalar is cast to array's dtype, if possible) There must be at least 1 argument, and define the last argument as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster than ``a[args] = item``. The item should be a scalar value and `args` must select a single item in the array `a`. Parameters ---------- \*args : Arguments If one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple. Notes ----- Compared to indexing syntax, `itemset` provides some speed increase for placing a scalar into a particular location in an `ndarray`, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using `itemset` (and `item`) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])""" return None itemsize = getset_descriptor() def join(self, _): """ Return a string which is the concatenation of the strings in the sequence `seq`. See also -------- char.join """ return None def ljust(self, width=" ", fillchar=" "): """ Return an array with the elements of `self` left-justified in a string of length `width`. See also -------- char.ljust """ return None def lower(self, _): """ Return an array with the elements of `self` converted to lowercase. See also -------- char.lower """ return None def lstrip(self=None, chars=None): """ For each element in `self`, return a copy with the leading characters removed. See also -------- char.lstrip """ return None def max(self, axis=None, out=None): """a.max(axis=None, out=None) Return the maximum along a given axis. Refer to `numpy.amax` for full documentation. See Also -------- numpy.amax : equivalent function""" return None def mean(self, axis=None, dtype=None, out=None): """a.mean(axis=None, dtype=None, out=None) Returns the average of the array elements along given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean : equivalent function""" return None def min(self, axis=None, out=None): """a.min(axis=None, out=None) Return the minimum along a given axis. Refer to `numpy.amin` for full documentation. See Also -------- numpy.amin : equivalent function""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """arr.newbyteorder(new_order='S') Return the array with the same data viewed with a different byte order. Equivalent to:: arr.view(arr.dtype.newbytorder(new_order)) Changes are also made in all fields and sub-arrays of the array data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications above. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_arr : array New array object with the dtype reflecting given change to the byte order.""" return array() def nonzero(self, _): """a.nonzero() Return the indices of the elements that are non-zero. Refer to `numpy.nonzero` for full documentation. See Also -------- numpy.nonzero : equivalent function""" return None def partition(self, _): """ Partition each element in `self` around `sep`. See also -------- partition """ return None def prod(self, axis=None, dtype=None, out=None): """a.prod(axis=None, dtype=None, out=None) Return the product of the array elements over the given axis Refer to `numpy.prod` for full documentation. See Also -------- numpy.prod : equivalent function""" return None def ptp(self, axis=None, out=None): """a.ptp(axis=None, out=None) Peak to peak (maximum - minimum) value along a given axis. Refer to `numpy.ptp` for full documentation. See Also -------- numpy.ptp : equivalent function""" return None def put(self, indices, values, mode=_raise): """a.put(indices, values, mode='raise') Set ``a.flat[n] = values[n]`` for all `n` in indices. Refer to `numpy.put` for full documentation. See Also -------- numpy.put : equivalent function""" return None def ravel(self, order): """a.ravel([order]) Return a flattened array. Refer to `numpy.ravel` for full documentation. See Also -------- numpy.ravel : equivalent function ndarray.flat : a flat iterator on the array.""" return None real = getset_descriptor() def repeat(self, repeats, axis=None): """a.repeat(repeats, axis=None) Repeat elements of an array. Refer to `numpy.repeat` for full documentation. See Also -------- numpy.repeat : equivalent function""" return None def replace(self, old, new=None, count=None): """ For each element in `self`, return a copy of the string with all occurrences of substring `old` replaced by `new`. See also -------- char.replace """ return None def reshape(self, shape, order=C): """a.reshape(shape, order='C') Returns an array containing the same data with a new shape. Refer to `numpy.reshape` for full documentation. See Also -------- numpy.reshape : equivalent function""" return None def resize(self, new_shape, refcheck): """a.resize(new_shape, refcheck=True) Change shape and size of array in-place. Parameters ---------- new_shape : tuple of ints, or `n` ints Shape of resized array. refcheck : bool, optional If False, reference count will not be checked. Default is True. Returns ------- None Raises ------ ValueError If `a` does not own its own data or references or views to it exist, and the data memory must be changed. SystemError If the `order` keyword argument is specified. This behaviour is a bug in NumPy. See Also -------- resize : Return a new array with the specified shape. Notes ----- This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False. Examples -------- Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]]) >>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]]) Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]]) Referencing an array prevents resizing... >>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ... Unless `refcheck` is False: >>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])""" return None def rfind(self, sub=None, start=0, end=None): """ For each element in `self`, return the highest index in the string where substring `sub` is found, such that `sub` is contained within [`start`, `end`]. See also -------- char.rfind """ return None def rindex(self, sub=None, start=0, end=None): """ Like `rfind`, but raises `ValueError` when the substring `sub` is not found. See also -------- char.rindex """ return None def rjust(self, width=" ", fillchar=" "): """ Return an array with the elements of `self` right-justified in a string of length `width`. See also -------- char.rjust """ return None def round(self, decimals=0, out=None): """a.round(decimals=0, out=None) Return `a` with each element rounded to the given number of decimals. Refer to `numpy.around` for full documentation. See Also -------- numpy.around : equivalent function""" return None def rpartition(self, _): """ Partition each element in `self` around `sep`. See also -------- rpartition """ return None def rsplit(self=None, sep=None, maxsplit=None): """ For each element in `self`, return a list of the words in the string, using `sep` as the delimiter string. See also -------- char.rsplit """ return None def rstrip(self=None, chars=None): """ For each element in `self`, return a copy with the trailing characters removed. See also -------- char.rstrip """ return None def searchsorted(self, v, side=left, sorter=None): """a.searchsorted(v, side='left', sorter=None) Find indices where elements of v should be inserted in a to maintain order. For full documentation, see `numpy.searchsorted` See Also -------- numpy.searchsorted : equivalent function""" return None def setfield(self, val, dtype, offset): """a.setfield(val, dtype, offset=0) Put a value into a specified place in a field defined by a data-type. Place `val` into `a`'s field defined by `dtype` and beginning `offset` bytes into the field. Parameters ---------- val : object Value to be placed in field. dtype : dtype object Data-type of the field in which to place `val`. offset : int, optional The number of bytes into the field at which to place `val`. Returns ------- None See Also -------- getfield Examples -------- >>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])""" return None def setflags(self, write, align, uic): """a.setflags(write=None, align=None, uic=None) Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively. These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The UPDATEIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters ---------- write : bool, optional Describes whether or not `a` can be written to. align : bool, optional Describes whether or not `a` is aligned properly for its type. uic : bool, optional Describes whether or not `a` is a copy of another "base" array. Notes ----- Array flags provide information about how the memory area used for the array is to be interpreted. There are 6 Boolean flags in use, only three of which can be changed by the user: UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array. All flags can be accessed using their first (upper case) letter as well as the full name. Examples -------- >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "", line 1, in ValueError: cannot set UPDATEIFCOPY flag to True""" return None shape = getset_descriptor() size = getset_descriptor() def sort(self, axis, kind, order): """a.sort(axis=-1, kind='quicksort', order=None) Sort an array, in-place. Parameters ---------- axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort. Notes ----- See ``sort`` for notes on the different sorting algorithms. Examples -------- >>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]""" return list() def tostring(self, order): """a.tostring(order='C') Construct a Python string containing the raw data bytes in the array. Constructs a Python string showing a copy of the raw contents of data memory. The string can be produced in either 'C' or 'Fortran', or 'Any' order (the default is 'C'-order). 'Any' order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means 'Fortran' order. Parameters ---------- order : {'C', 'F', None}, optional Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array. Returns ------- s : str A Python string exhibiting a copy of `a`'s raw data. Examples -------- >>> x = np.array([[0, 1], [2, 3]]) >>> x.tostring() '\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tostring('C') == x.tostring() True >>> x.tostring('F') '\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'""" return str() def trace(self, offset=0, axis1=0, axis2=1, dtype=None, out=None): """a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) Return the sum along diagonals of the array. Refer to `numpy.trace` for full documentation. See Also -------- numpy.trace : equivalent function""" return None def translate(self, table=None, deletechars=None): """ For each element in `self`, return a copy of the string where all characters occurring in the optional argument `deletechars` are removed, and the remaining characters have been mapped through the given translation table. See also -------- char.translate """ return None def transpose(self, axes): """a.transpose(*axes) Returns a view of the array with axes transposed. For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. Parameters ---------- axes : None, tuple of ints, or `n` ints * None or no argument: reverses the order of the axes. * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s `i`-th axis becomes `a.transpose()`'s `j`-th axis. * `n` ints: same as an n-tuple of the same ints (this form is intended simply as a "convenience" alternative to the tuple form) Returns ------- out : ndarray View of `a`, with axes suitably permuted. See Also -------- ndarray.T : Array property returning the array transposed. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])""" return ndarray() def upper(self, _): """ Return an array with the elements of `self` converted to uppercase. See also -------- char.upper """ return None def var(self, axis=None, dtype=None, out=None, ddof=0): """a.var(axis=None, dtype=None, out=None, ddof=0) Returns the variance of the array elements, along given axis. Refer to `numpy.var` for full documentation. See Also -------- numpy.var : equivalent function""" return None def view(self, dtype, type): """a.view(dtype=None, type=None) New view of array with the same data. Parameters ---------- dtype : data-type or ndarray sub-class, optional Data-type descriptor of the returned view, e.g., float32 or int16. The default, None, results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the ``type`` parameter). type : Python type, optional Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation. Notes ----- ``a.view()`` is used two different ways: ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view of the array's memory with a different data-type. This can cause a reinterpretation of the bytes of memory. ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory. For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of ``a`` (shown by ``print(a)``). It also depends on exactly how ``a`` is stored in memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results. Examples -------- >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) Viewing array data using a different type and dtype: >>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print type(y) Creating a view on a structured array so it can be used in calculations >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.]) Making changes to the view changes the underlying array >>> xv[0,1] = 20 >>> print x [(1, 20) (3, 4)] Using a view to convert an array to a record array: >>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8) Views share data: >>> x[0] = (9, 10) >>> z[0] (9, 10) Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.: >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "", line 1, in ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', ' n-1 are mapped to n-1 Returns ------- merged_array : array The merged result. Raises ------ ValueError: shape mismatch If `a` and each choice array are not all broadcastable to the same shape. See Also -------- ndarray.choose : equivalent method Notes ----- To reduce the chance of misinterpretation, even though the following "abuse" is nominally supported, `choices` should neither be, nor be thought of as, a single array, i.e., the outermost sequence-like container should be either a list or a tuple. Examples -------- >>> choices = [[0, 1, 2, 3], [10, 11, 12, 13], ... [20, 21, 22, 23], [30, 31, 32, 33]] >>> np.choose([2, 3, 1, 0], choices ... # the first element of the result will be the first element of the ... # third (2+1) "array" in choices, namely, 20; the second element ... # will be the second element of the fourth (3+1) choice array, i.e., ... # 31, etc. ... ) array([20, 31, 12, 3]) >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1) array([20, 31, 12, 3]) >>> # because there are 4 choice arrays >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4) array([20, 1, 12, 3]) >>> # i.e., 0 A couple examples illustrating how choose broadcasts: >>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]] >>> choices = [-10, 10] >>> np.choose(a, choices) array([[ 10, -10, 10], [-10, 10, -10], [ 10, -10, 10]]) >>> # With thanks to Anne Archibald >>> a = np.array([0, 1]).reshape((2,1,1)) >>> c1 = np.array([1, 2, 3]).reshape((1,3,1)) >>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5)) >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2 array([[[ 1, 1, 1, 1, 1], [ 2, 2, 2, 2, 2], [ 3, 3, 3, 3, 3]], [[-1, -2, -3, -4, -5], [-1, -2, -3, -4, -5], [-1, -2, -3, -4, -5]]]) """ return array() def clip(a, a_min, a_max=None, out=None): """ Clip (limit) the values in an array. Given an interval, values outside the interval are clipped to the interval edges. For example, if an interval of ``[0, 1]`` is specified, values smaller than 0 become 0, and values larger than 1 become 1. Parameters ---------- a : array_like Array containing elements to clip. a_min : scalar or array_like Minimum value. a_max : scalar or array_like Maximum value. If `a_min` or `a_max` are array_like, then they will be broadcasted to the shape of `a`. out : ndarray, optional The results will be placed in this array. It may be the input array for in-place clipping. `out` must be of the right shape to hold the output. Its type is preserved. Returns ------- clipped_array : ndarray An array with the elements of `a`, but where values < `a_min` are replaced with `a_min`, and those > `a_max` with `a_max`. See Also -------- numpy.doc.ufuncs : Section "Output arguments" Examples -------- >>> a = np.arange(10) >>> np.clip(a, 1, 8) array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8]) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, 3, 6, out=a) array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6]) >>> a = np.arange(10) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, [3,4,1,1,1,4,4,4,4,4], 8) array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8]) """ return ndarray() class complex256: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class complex256: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def column_stack(tup): """ Stack 1-D arrays as columns into a 2-D array. Take a sequence of 1-D arrays and stack them as columns to make a single 2-D array. 2-D arrays are stacked as-is, just like with `hstack`. 1-D arrays are turned into 2-D columns first. Parameters ---------- tup : sequence of 1-D or 2-D arrays. Arrays to stack. All of them must have the same first dimension. Returns ------- stacked : 2-D array The array formed by stacking the given arrays. See Also -------- hstack, vstack, concatenate Notes ----- This function is equivalent to ``np.vstack(tup).T``. Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.column_stack((a,b)) array([[1, 2], [2, 3], [3, 4]]) """ return _2_D() def common_type(): """ Return a scalar type which is common to the input arrays. The return type will always be an inexact (i.e. floating point) scalar type, even if all the arrays are integer arrays. If one of the inputs is an integer array, the minimum precision type that is returned is a 64-bit floating point dtype. All input arrays can be safely cast to the returned dtype without loss of information. Parameters ---------- array1, array2, ... : ndarrays Input arrays. Returns ------- out : data type code Data type code. See Also -------- dtype, mintypecode Examples -------- >>> np.common_type(np.arange(2, dtype=np.float32)) >>> np.common_type(np.arange(2, dtype=np.float32), np.arange(2)) >>> np.common_type(np.arange(4), np.array([45, 6.j]), np.array([45.0])) """ return data() def compare_chararrays(): """None""" return None class complex: __doc__ = str() def conjugate(self, _): """complex.conjugate() -> complex Return the complex conjugate of its argument. (3-4j).conjugate() == 3+4j.""" return None imag = member_descriptor() real = member_descriptor() class complex128: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class complex256: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class complex64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class complex128: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class complexfloating: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def compress(condition, a=None, axis=None, out=None): """ Return selected slices of an array along given axis. When working along a given axis, a slice along that axis is returned in `output` for each index where `condition` evaluates to True. When working on a 1-D array, `compress` is equivalent to `extract`. Parameters ---------- condition : 1-D array of bools Array that selects which entries to return. If len(condition) is less than the size of `a` along the given axis, then output is truncated to the length of the condition array. a : array_like Array from which to extract a part. axis : int, optional Axis along which to take slices. If None (default), work on the flattened array. out : ndarray, optional Output array. Its type is preserved and it must be of the right shape to hold the output. Returns ------- compressed_array : ndarray A copy of `a` without the slices along axis for which `condition` is false. See Also -------- take, choose, diag, diagonal, select ndarray.compress : Equivalent method in ndarray np.extract: Equivalent method when working on 1-D arrays numpy.doc.ufuncs : Section "Output arguments" Examples -------- >>> a = np.array([[1, 2], [3, 4], [5, 6]]) >>> a array([[1, 2], [3, 4], [5, 6]]) >>> np.compress([0, 1], a, axis=0) array([[3, 4]]) >>> np.compress([False, True, True], a, axis=0) array([[3, 4], [5, 6]]) >>> np.compress([False, True], a, axis=1) array([[2], [4], [6]]) Working on the flattened array does not return slices along an axis but selects elements. >>> np.compress([False, True], a) array([2]) """ return ndarray() def concatenate(a1, a2, more_args, axis=0): """concatenate((a1, a2, ...), axis=0) Join a sequence of arrays together. Parameters ---------- a1, a2, ... : sequence of array_like The arrays must have the same shape, except in the dimension corresponding to `axis` (the first, by default). axis : int, optional The axis along which the arrays will be joined. Default is 0. Returns ------- res : ndarray The concatenated array. See Also -------- ma.concatenate : Concatenate function that preserves input masks. array_split : Split an array into multiple sub-arrays of equal or near-equal size. split : Split array into a list of multiple sub-arrays of equal size. hsplit : Split array into multiple sub-arrays horizontally (column wise) vsplit : Split array into multiple sub-arrays vertically (row wise) dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). hstack : Stack arrays in sequence horizontally (column wise) vstack : Stack arrays in sequence vertically (row wise) dstack : Stack arrays in sequence depth wise (along third dimension) Notes ----- When one or more of the arrays to be concatenated is a MaskedArray, this function will return a MaskedArray object instead of an ndarray, but the input masks are *not* preserved. In cases where a MaskedArray is expected as input, use the ma.concatenate function from the masked array module instead. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> b = np.array([[5, 6]]) >>> np.concatenate((a, b), axis=0) array([[1, 2], [3, 4], [5, 6]]) >>> np.concatenate((a, b.T), axis=1) array([[1, 2, 5], [3, 4, 6]]) This function will not preserve masking of MaskedArray inputs. >>> a = np.ma.arange(3) >>> a[1] = np.ma.masked >>> b = np.arange(2, 5) >>> a masked_array(data = [0 -- 2], mask = [False True False], fill_value = 999999) >>> b array([2, 3, 4]) >>> np.concatenate([a, b]) masked_array(data = [0 1 2 2 3 4], mask = False, fill_value = 999999) >>> np.ma.concatenate([a, b]) masked_array(data = [0 -- 2 2 3 4], mask = [False True False False False False], fill_value = 999999)""" return ndarray() def conjugate(x, out=None): """conjugate(x[, out]) Return the complex conjugate, element-wise. The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. Parameters ---------- x : array_like Input value. Returns ------- y : ndarray The complex conjugate of `x`, with same dtype as `y`. Examples -------- >>> np.conjugate(1+2j) (1-2j) >>> x = np.eye(2) + 1j * np.eye(2) >>> np.conjugate(x) array([[ 1.-1.j, 0.-0.j], [ 0.-0.j, 1.-1.j]])""" return ndarray() def conjugate(x, out=None): """conjugate(x[, out]) Return the complex conjugate, element-wise. The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. Parameters ---------- x : array_like Input value. Returns ------- y : ndarray The complex conjugate of `x`, with same dtype as `y`. Examples -------- >>> np.conjugate(1+2j) (1-2j) >>> x = np.eye(2) + 1j * np.eye(2) >>> np.conjugate(x) array([[ 1.-1.j, 0.-0.j], [ 0.-0.j, 1.-1.j]])""" return ndarray() def convolve(a, v="full", mode="full"): """ Returns the discrete, linear convolution of two one-dimensional sequences. The convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal [1]_. In probability theory, the sum of two independent random variables is distributed according to the convolution of their individual distributions. Parameters ---------- a : (N,) array_like First one-dimensional input array. v : (M,) array_like Second one-dimensional input array. mode : {'full', 'valid', 'same'}, optional 'full': By default, mode is 'full'. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At the end-points of the convolution, the signals do not overlap completely, and boundary effects may be seen. 'same': Mode `same` returns output of length ``max(M, N)``. Boundary effects are still visible. 'valid': Mode `valid` returns output of length ``max(M, N) - min(M, N) + 1``. The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect. Returns ------- out : ndarray Discrete, linear convolution of `a` and `v`. See Also -------- scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier Transform. scipy.linalg.toeplitz : Used to construct the convolution operator. Notes ----- The discrete convolution operation is defined as .. math:: (f * g)[n] = \sum_{m = -\infty}^{\infty} f[m] g[n - m] It can be shown that a convolution :math:`x(t) * y(t)` in time/space is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier domain, after appropriate padding (padding is necessary to prevent circular convolution). Since multiplication is more efficient (faster) than convolution, the function `scipy.signal.fftconvolve` exploits the FFT to calculate the convolution of large data-sets. References ---------- .. [1] Wikipedia, "Convolution", http://en.wikipedia.org/wiki/Convolution. Examples -------- Note how the convolution operator flips the second array before "sliding" the two across one another: >>> np.convolve([1, 2, 3], [0, 1, 0.5]) array([ 0. , 1. , 2.5, 4. , 1.5]) Only return the middle values of the convolution. Contains boundary effects, where zeros are taken into account: >>> np.convolve([1,2,3],[0,1,0.5], 'same') array([ 1. , 2.5, 4. ]) The two arrays are of the same length, so there is only one position where they completely overlap: >>> np.convolve([1,2,3],[0,1,0.5], 'valid') array([ 2.5]) """ return ndarray() def copy(a="K", order="K"): """ Return an array copy of the given object. Parameters ---------- a : array_like Input data. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :meth:ndarray.copy are very similar, but have different default values for their order= arguments.) Returns ------- arr : ndarray Array interpretation of `a`. Notes ----- This is equivalent to >>> np.array(a, copy=True) #doctest: +SKIP Examples -------- Create an array x, with a reference y and a copy z: >>> x = np.array([1, 2, 3]) >>> y = x >>> z = np.copy(x) Note that, when we modify x, y changes, but not z: >>> x[0] = 10 >>> x[0] == y[0] True >>> x[0] == z[0] False """ return ndarray() def copysign(x1, x2, out): """copysign(x1, x2[, out]) Change the sign of x1 to that of x2, element-wise. If both arguments are arrays or sequences, they have to be of the same length. If `x2` is a scalar, its sign will be copied to all elements of `x1`. Parameters ---------- x1 : array_like Values to change the sign of. x2 : array_like The sign of `x2` is copied to `x1`. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- out : array_like The values of `x1` with the sign of `x2`. Examples -------- >>> np.copysign(1.3, -1) -1.3 >>> 1/np.copysign(0, 1) inf >>> 1/np.copysign(0, -1) -inf >>> np.copysign([-1, 0, 1], -1.1) array([-1., -0., -1.]) >>> np.copysign([-1, 0, 1], np.arange(3)-1) array([-1., 0., 1.])""" return ndarray() def copyto(dst, src, casting=same_kind, where=None, preservena=False): """copyto(dst, src, casting='same_kind', where=None, preservena=False) Copies values from one array to another, broadcasting as necessary. Raises a TypeError if the `casting` rule is violated, and if `where` is provided, it selects which elements to copy. .. versionadded:: 1.7.0 Parameters ---------- dst : ndarray The array into which values are copied. src : array_like The array from which values are copied. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur when copying. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. where : array_like of bool, optional A boolean array which is broadcasted to match the dimensions of `dst`, and selects elements to copy from `src` to `dst` wherever it contains the value True. preservena : bool, optional If set to True, leaves any NA values in `dst` untouched. This is similar to the "hard mask" feature in numpy.ma.""" return None def corrcoef(x=None, y=None, rowvar=1, bias=0, ddof=None): """ Return correlation coefficients. Please refer to the documentation for `cov` for more detail. The relationship between the correlation coefficient matrix, `P`, and the covariance matrix, `C`, is .. math:: P_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } } The values of `P` are between -1 and 1, inclusive. Parameters ---------- x : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of `m` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below. y : array_like, optional An additional set of variables and observations. `y` has the same shape as `m`. rowvar : int, optional If `rowvar` is non-zero (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : int, optional Default normalization is by ``(N - 1)``, where ``N`` is the number of observations (unbiased estimate). If `bias` is 1, then normalization is by ``N``. These values can be overridden by using the keyword ``ddof`` in numpy versions >= 1.5. ddof : {None, int}, optional .. versionadded:: 1.5 If not ``None`` normalization is by ``(N - ddof)``, where ``N`` is the number of observations; this overrides the value implied by ``bias``. The default value is ``None``. Returns ------- out : ndarray The correlation coefficient matrix of the variables. See Also -------- cov : Covariance matrix """ return ndarray() def correlate(a, v=False, mode="valid", old_behavior=False): """ Cross-correlation of two 1-dimensional sequences. This function computes the correlation as generally defined in signal processing texts:: z[k] = sum_n a[n] * conj(v[n+k]) with a and v sequences being zero-padded where necessary and conj being the conjugate. Parameters ---------- a, v : array_like Input sequences. mode : {'valid', 'same', 'full'}, optional Refer to the `convolve` docstring. Note that the default is `valid`, unlike `convolve`, which uses `full`. old_behavior : bool If True, uses the old behavior from Numeric, (correlate(a,v) == correlate(v,a), and the conjugate is not taken for complex arrays). If False, uses the conventional signal processing definition. See Also -------- convolve : Discrete, linear convolution of two one-dimensional sequences. Examples -------- >>> np.correlate([1, 2, 3], [0, 1, 0.5]) array([ 3.5]) >>> np.correlate([1, 2, 3], [0, 1, 0.5], "same") array([ 2. , 3.5, 3. ]) >>> np.correlate([1, 2, 3], [0, 1, 0.5], "full") array([ 0.5, 2. , 3.5, 3. , 0. ]) """ return None def cos(x, out): """cos(x[, out]) Cosine elementwise. Parameters ---------- x : array_like Input array in radians. out : ndarray, optional Output array of same shape as `x`. Returns ------- y : ndarray The corresponding cosine values. Raises ------ ValueError: invalid return array shape if `out` is provided and `out.shape` != `x.shape` (See Examples) Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972. Examples -------- >>> np.cos(np.array([0, np.pi/2, np.pi])) array([ 1.00000000e+00, 6.12303177e-17, -1.00000000e+00]) >>> >>> # Example of providing the optional output parameter >>> out2 = np.cos([0.1], out1) >>> out2 is out1 True >>> >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.cos(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: invalid return array shape""" return ndarray() def cosh(x, out=None): """cosh(x[, out]) Hyperbolic cosine, element-wise. Equivalent to ``1/2 * (np.exp(x) + np.exp(-x))`` and ``np.cos(1j*x)``. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray Output array of same shape as `x`. Examples -------- >>> np.cosh(0) 1.0 The hyperbolic cosine describes the shape of a hanging cable: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-4, 4, 1000) >>> plt.plot(x, np.cosh(x)) >>> plt.show()""" return ndarray() def count_nonzero(a): """count_nonzero(a) Counts the number of non-zero values in the array ``a``. Parameters ---------- a : array_like The array for which to count non-zeros. Returns ------- count : int or array of int Number of non-zero values in the array. See Also -------- nonzero : Return the coordinates of all the non-zero values. Examples -------- >>> np.count_nonzero(np.eye(4)) 4 >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]]) 5""" return int() if False else array() def cov(m=None, y=None, rowvar=1, bias=0, ddof=None): """ Estimate a covariance matrix, given data. Covariance indicates the level to which two variables vary together. If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`, then the covariance matrix element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance of :math:`x_i`. Parameters ---------- m : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of `m` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below. y : array_like, optional An additional set of variables and observations. `y` has the same form as that of `m`. rowvar : int, optional If `rowvar` is non-zero (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : int, optional Default normalization is by ``(N - 1)``, where ``N`` is the number of observations given (unbiased estimate). If `bias` is 1, then normalization is by ``N``. These values can be overridden by using the keyword ``ddof`` in numpy versions >= 1.5. ddof : int, optional .. versionadded:: 1.5 If not ``None`` normalization is by ``(N - ddof)``, where ``N`` is the number of observations; this overrides the value implied by ``bias``. The default value is ``None``. Returns ------- out : ndarray The covariance matrix of the variables. See Also -------- corrcoef : Normalized covariance matrix Examples -------- Consider two variables, :math:`x_0` and :math:`x_1`, which correlate perfectly, but in opposite directions: >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T >>> x array([[0, 1, 2], [2, 1, 0]]) Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance matrix shows this clearly: >>> np.cov(x) array([[ 1., -1.], [-1., 1.]]) Note that element :math:`C_{0,1}`, which shows the correlation between :math:`x_0` and :math:`x_1`, is negative. Further, note how `x` and `y` are combined: >>> x = [-2.1, -1, 4.3] >>> y = [3, 1.1, 0.12] >>> X = np.vstack((x,y)) >>> print np.cov(X) [[ 11.71 -4.286 ] [ -4.286 2.14413333]] >>> print np.cov(x, y) [[ 11.71 -4.286 ] [ -4.286 2.14413333]] >>> print np.cov(x) 11.71 """ return ndarray() def cross(a, b=None, axisa=-1, axisb=-1, axisc=-1, axis=None): """ Return the cross product of two (arrays of) vectors. The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular to both `a` and `b`. If `a` and `b` are arrays of vectors, the vectors are defined by the last axis of `a` and `b` by default, and these axes can have dimensions 2 or 3. Where the dimension of either `a` or `b` is 2, the third component of the input vector is assumed to be zero and the cross product calculated accordingly. In cases where both input vectors have dimension 2, the z-component of the cross product is returned. Parameters ---------- a : array_like Components of the first vector(s). b : array_like Components of the second vector(s). axisa : int, optional Axis of `a` that defines the vector(s). By default, the last axis. axisb : int, optional Axis of `b` that defines the vector(s). By default, the last axis. axisc : int, optional Axis of `c` containing the cross product vector(s). By default, the last axis. axis : int, optional If defined, the axis of `a`, `b` and `c` that defines the vector(s) and cross product(s). Overrides `axisa`, `axisb` and `axisc`. Returns ------- c : ndarray Vector cross product(s). Raises ------ ValueError When the dimension of the vector(s) in `a` and/or `b` does not equal 2 or 3. See Also -------- inner : Inner product outer : Outer product. ix_ : Construct index arrays. Examples -------- Vector cross-product. >>> x = [1, 2, 3] >>> y = [4, 5, 6] >>> np.cross(x, y) array([-3, 6, -3]) One vector with dimension 2. >>> x = [1, 2] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, -6, -3]) Equivalently: >>> x = [1, 2, 0] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, -6, -3]) Both vectors with dimension 2. >>> x = [1,2] >>> y = [4,5] >>> np.cross(x, y) -3 Multiple vector cross-products. Note that the direction of the cross product vector is defined by the `right-hand rule`. >>> x = np.array([[1,2,3], [4,5,6]]) >>> y = np.array([[4,5,6], [1,2,3]]) >>> np.cross(x, y) array([[-3, 6, -3], [ 3, -6, 3]]) The orientation of `c` can be changed using the `axisc` keyword. >>> np.cross(x, y, axisc=0) array([[-3, 3], [ 6, -6], [-3, 3]]) Change the vector definition of `x` and `y` using `axisa` and `axisb`. >>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]]) >>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]]) >>> np.cross(x, y) array([[ -6, 12, -6], [ 0, 0, 0], [ 6, -12, 6]]) >>> np.cross(x, y, axisa=0, axisb=0) array([[-24, 48, -24], [-30, 60, -30], [-36, 72, -36]]) """ return ndarray() class complex64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def cumprod(a=None, axis=None, dtype=None, out=None): """ Return the cumulative product of elements along a given axis. Parameters ---------- a : array_like Input array. axis : int, optional Axis along which the cumulative product is computed. By default the input is flattened. dtype : dtype, optional Type of the returned array, as well as of the accumulator in which the elements are multiplied. If *dtype* is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary. Returns ------- cumprod : ndarray A new array holding the result is returned unless `out` is specified, in which case a reference to out is returned. See Also -------- numpy.doc.ufuncs : Section "Output arguments" Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. Examples -------- >>> a = np.array([1,2,3]) >>> np.cumprod(a) # intermediate results 1, 1*2 ... # total product 1*2*3 = 6 array([1, 2, 6]) >>> a = np.array([[1, 2, 3], [4, 5, 6]]) >>> np.cumprod(a, dtype=float) # specify type of output array([ 1., 2., 6., 24., 120., 720.]) The cumulative product for each column (i.e., over the rows) of `a`: >>> np.cumprod(a, axis=0) array([[ 1, 2, 3], [ 4, 10, 18]]) The cumulative product for each row (i.e. over the columns) of `a`: >>> np.cumprod(a,axis=1) array([[ 1, 2, 6], [ 4, 20, 120]]) """ return ndarray() def cumproduct(a=None, axis=None, dtype=None, out=None): """ Return the cumulative product over the given axis. See Also -------- cumprod : equivalent function; see for details. """ return None def cumsum(a=None, axis=None, dtype=None, out=None): """ Return the cumulative sum of the elements along a given axis. Parameters ---------- a : array_like Input array. axis : int, optional Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array. dtype : dtype, optional Type of the returned array and of the accumulator in which the elements are summed. If `dtype` is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See `doc.ufuncs` (Section "Output arguments") for more details. Returns ------- cumsum_along_axis : ndarray. A new array holding the result is returned unless `out` is specified, in which case a reference to `out` is returned. The result has the same size as `a`, and the same shape as `a` if `axis` is not None or `a` is a 1-d array. See Also -------- sum : Sum array elements. trapz : Integration of array values using the composite trapezoidal rule. diff : Calculate the n-th order discrete difference along given axis. Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. Examples -------- >>> a = np.array([[1,2,3], [4,5,6]]) >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.cumsum(a) array([ 1, 3, 6, 10, 15, 21]) >>> np.cumsum(a, dtype=float) # specifies type of output value(s) array([ 1., 3., 6., 10., 15., 21.]) >>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns array([[1, 2, 3], [5, 7, 9]]) >>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows array([[ 1, 3, 6], [ 4, 9, 15]]) """ return ndarray() class datetime64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def datetime_as_string(): """None""" return None def datetime_data(): """None""" return None def deg2rad(x, out=None): """deg2rad(x[, out]) Convert angles from degrees to radians. Parameters ---------- x : array_like Angles in degrees. Returns ------- y : ndarray The corresponding angle in radians. See Also -------- rad2deg : Convert angles from radians to degrees. unwrap : Remove large jumps in angle by wrapping. Notes ----- .. versionadded:: 1.3.0 ``deg2rad(x)`` is ``x * pi / 180``. Examples -------- >>> np.deg2rad(180) 3.1415926535897931""" return ndarray() def degrees(x, out): """degrees(x[, out]) Convert angles from radians to degrees. Parameters ---------- x : array_like Input array in radians. out : ndarray, optional Output array of same shape as x. Returns ------- y : ndarray of floats The corresponding degree values; if `out` was supplied this is a reference to it. See Also -------- rad2deg : equivalent function Examples -------- Convert a radian array to degrees >>> rad = np.arange(12.)*np.pi/6 >>> np.degrees(rad) array([ 0., 30., 60., 90., 120., 150., 180., 210., 240., 270., 300., 330.]) >>> out = np.zeros((rad.shape)) >>> r = degrees(rad, out) >>> np.all(r == out) True""" return ndarray() def delete(arr, obj=None, axis=None): """ Return a new array with sub-arrays along an axis deleted. For a one dimensional array, this returns those entries not returned by `arr[obj]`. Parameters ---------- arr : array_like Input array. obj : slice, int or array of ints Indicate which sub-arrays to remove. axis : int, optional The axis along which to delete the subarray defined by `obj`. If `axis` is None, `obj` is applied to the flattened array. Returns ------- out : ndarray A copy of `arr` with the elements specified by `obj` removed. Note that `delete` does not occur in-place. If `axis` is None, `out` is a flattened array. See Also -------- insert : Insert elements into an array. append : Append elements at the end of an array. Notes ----- Often it is preferable to use a boolean mask. For example: >>> mask = np.ones(len(arr), dtype=bool) >>> mask[[0,2,4]] = False >>> result = arr[mask,...] Is equivalent to `np.delete(arr, [0,2,4], axis=0)`, but allows further use of `mask`. Examples -------- >>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) >>> arr array([[ 1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]]) >>> np.delete(arr, 1, 0) array([[ 1, 2, 3, 4], [ 9, 10, 11, 12]]) >>> np.delete(arr, np.s_[::2], 1) array([[ 2, 4], [ 6, 8], [10, 12]]) >>> np.delete(arr, [1,3,5], None) array([ 1, 3, 5, 7, 8, 9, 10, 11, 12]) """ return ndarray() def deprecate(): """ Issues a DeprecationWarning, adds warning to `old_name`'s docstring, rebinds ``old_name.__name__`` and returns the new function object. This function may also be used as a decorator. Parameters ---------- func : function The function to be deprecated. old_name : str, optional The name of the function to be deprecated. Default is None, in which case the name of `func` is used. new_name : str, optional The new name for the function. Default is None, in which case the deprecation message is that `old_name` is deprecated. If given, the deprecation message is that `old_name` is deprecated and `new_name` should be used instead. message : str, optional Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- old_func : function The deprecated function. Examples -------- Note that ``olduint`` returns a value after printing Deprecation Warning: >>> olduint = np.deprecate(np.uint) >>> olduint(6) /usr/lib/python2.5/site-packages/numpy/lib/utils.py:114: DeprecationWarning: uint32 is deprecated warnings.warn(str1, DeprecationWarning) 6 """ return None def _lambda(): """None""" return None def diag(v=0, k=0): """ Extract a diagonal or construct a diagonal array. See the more detailed documentation for ``numpy.diagonal`` if you use this function to extract a diagonal and wish to write to the resulting array; whether it returns a copy or a view depends on what version of numpy you are using. Parameters ---------- v : array_like If `v` is a 2-D array, return a copy of its `k`-th diagonal. If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th diagonal. k : int, optional Diagonal in question. The default is 0. Use `k>0` for diagonals above the main diagonal, and `k<0` for diagonals below the main diagonal. Returns ------- out : ndarray The extracted diagonal or constructed diagonal array. See Also -------- diagonal : Return specified diagonals. diagflat : Create a 2-D array with the flattened input as a diagonal. trace : Sum along diagonals. triu : Upper triangle of an array. tril : Lower triange of an array. Examples -------- >>> x = np.arange(9).reshape((3,3)) >>> x array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> np.diag(x) array([0, 4, 8]) >>> np.diag(x, k=1) array([1, 5]) >>> np.diag(x, k=-1) array([3, 7]) >>> np.diag(np.diag(x)) array([[0, 0, 0], [0, 4, 0], [0, 0, 8]]) """ return ndarray() def diag_indices(n=2, ndim=2): """ Return the indices to access the main diagonal of an array. This returns a tuple of indices that can be used to access the main diagonal of an array `a` with ``a.ndim >= 2`` dimensions and shape (n, n, ..., n). For ``a.ndim = 2`` this is the usual diagonal, for ``a.ndim > 2`` this is the set of indices to access ``a[i, i, ..., i]`` for ``i = [0..n-1]``. Parameters ---------- n : int The size, along each dimension, of the arrays for which the returned indices can be used. ndim : int, optional The number of dimensions. See also -------- diag_indices_from Notes ----- .. versionadded:: 1.4.0 Examples -------- Create a set of indices to access the diagonal of a (4, 4) array: >>> di = np.diag_indices(4) >>> di (array([0, 1, 2, 3]), array([0, 1, 2, 3])) >>> a = np.arange(16).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) >>> a[di] = 100 >>> a array([[100, 1, 2, 3], [ 4, 100, 6, 7], [ 8, 9, 100, 11], [ 12, 13, 14, 100]]) Now, we create indices to manipulate a 3-D array: >>> d3 = np.diag_indices(2, 3) >>> d3 (array([0, 1]), array([0, 1]), array([0, 1])) And use it to set the diagonal of an array of zeros to 1: >>> a = np.zeros((2, 2, 2), dtype=np.int) >>> a[d3] = 1 >>> a array([[[1, 0], [0, 0]], [[0, 0], [0, 1]]]) """ return None def diag_indices__from(arr): """ Return the indices to access the main diagonal of an n-dimensional array. See `diag_indices` for full details. Parameters ---------- arr : array, at least 2-D See Also -------- diag_indices Notes ----- .. versionadded:: 1.4.0 """ return None def diagflat(v=0, k=0): """ Create a two-dimensional array with the flattened input as a diagonal. Parameters ---------- v : array_like Input data, which is flattened and set as the `k`-th diagonal of the output. k : int, optional Diagonal to set; 0, the default, corresponds to the "main" diagonal, a positive (negative) `k` giving the number of the diagonal above (below) the main. Returns ------- out : ndarray The 2-D output array. See Also -------- diag : MATLAB work-alike for 1-D and 2-D arrays. diagonal : Return specified diagonals. trace : Sum along diagonals. Examples -------- >>> np.diagflat([[1,2], [3,4]]) array([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]) >>> np.diagflat([1,2], 1) array([[0, 1, 0], [0, 0, 2], [0, 0, 0]]) """ return ndarray() def diagonal(a=1, offset=0, axis1=0, axis2=1): """ Return specified diagonals. If `a` is 2-D, returns the diagonal of `a` with the given offset, i.e., the collection of elements of the form ``a[i, i+offset]``. If `a` has more than two dimensions, then the axes specified by `axis1` and `axis2` are used to determine the 2-D sub-array whose diagonal is returned. The shape of the resulting array can be determined by removing `axis1` and `axis2` and appending an index to the right equal to the size of the resulting diagonals. In versions of NumPy prior to 1.7, this function always returned a new, independent array containing a copy of the values in the diagonal. In NumPy 1.7, it continues to return a copy of the diagonal, but depending on this fact is deprecated. Writing to the resulting array continues to work as it used to, but a FutureWarning will be issued. In NumPy 1.9, it will switch to returning a read-only view on the original array. Attempting to write to the resulting array will produce an error. In NumPy 1.10, it will still return a view, but this view will no longer be marked read-only. Writing to the returned array will alter your original array as well. If you don't write to the array returned by this function, then you can just ignore all of the above. If you depend on the current behavior, then we suggest copying the returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead of just ``np.diagonal(a)``. This will work with both past and future versions of NumPy. Parameters ---------- a : array_like Array from which the diagonals are taken. offset : int, optional Offset of the diagonal from the main diagonal. Can be positive or negative. Defaults to main diagonal (0). axis1 : int, optional Axis to be used as the first axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults to first axis (0). axis2 : int, optional Axis to be used as the second axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults to second axis (1). Returns ------- array_of_diagonals : ndarray If `a` is 2-D, a 1-D array containing the diagonal is returned. If the dimension of `a` is larger, then an array of diagonals is returned, "packed" from left-most dimension to right-most (e.g., if `a` is 3-D, then the diagonals are "packed" along rows). Raises ------ ValueError If the dimension of `a` is less than 2. See Also -------- diag : MATLAB work-a-like for 1-D and 2-D arrays. diagflat : Create diagonal arrays. trace : Sum along diagonals. Examples -------- >>> a = np.arange(4).reshape(2,2) >>> a array([[0, 1], [2, 3]]) >>> a.diagonal() array([0, 3]) >>> a.diagonal(1) array([1]) A 3-D example: >>> a = np.arange(8).reshape(2,2,2); a array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> a.diagonal(0, # Main diagonals of two arrays created by skipping ... 0, # across the outer(left)-most axis last and ... 1) # the "middle" (row) axis first. array([[0, 6], [1, 7]]) The sub-arrays whose main diagonals we just obtained; note that each corresponds to fixing the right-most (column) axis, and that the diagonals are "packed" in rows. >>> a[:,:,0] # main diagonal is [0 6] array([[0, 2], [4, 6]]) >>> a[:,:,1] # main diagonal is [1 7] array([[1, 3], [5, 7]]) """ return ndarray() def diff(a=-1, n=1, axis=-1): """ Calculate the n-th order discrete difference along given axis. The first order difference is given by ``out[n] = a[n+1] - a[n]`` along the given axis, higher order differences are calculated by using `diff` recursively. Parameters ---------- a : array_like Input array n : int, optional The number of times values are differenced. axis : int, optional The axis along which the difference is taken, default is the last axis. Returns ------- diff : ndarray The `n` order differences. The shape of the output is the same as `a` except along `axis` where the dimension is smaller by `n`. See Also -------- gradient, ediff1d, cumsum Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.diff(x) array([ 1, 2, 3, -7]) >>> np.diff(x, n=2) array([ 1, 1, -10]) >>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]]) >>> np.diff(x) array([[2, 3, 4], [5, 1, 2]]) >>> np.diff(x, axis=0) array([[-1, 2, 0, -2]]) """ return ndarray() def digitize(x, bins, right): """digitize(x, bins, right=False) Return the indices of the bins to which each value in input array belongs. Each index ``i`` returned is such that ``bins[i-1] <= x < bins[i]`` if `bins` is monotonically increasing, or ``bins[i-1] > x >= bins[i]`` if `bins` is monotonically decreasing. If values in `x` are beyond the bounds of `bins`, 0 or ``len(bins)`` is returned as appropriate. If right is True, then the right bin is closed so that the index ``i`` is such that ``bins[i-1] < x <= bins[i]`` or bins[i-1] >= x > bins[i]`` if `bins` is monotonically increasing or decreasing, respectively. Parameters ---------- x : array_like Input array to be binned. It has to be 1-dimensional. bins : array_like Array of bins. It has to be 1-dimensional and monotonic. right : bool, optional Indicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin and is open in this case. Ie., bins[i-1] <= x < bins[i] is the default behavior for monotonically increasing bins. Returns ------- out : ndarray of ints Output array of indices, of same shape as `x`. Raises ------ ValueError If the input is not 1-dimensional, or if `bins` is not monotonic. TypeError If the type of the input is complex. See Also -------- bincount, histogram, unique Notes ----- If values in `x` are such that they fall outside the bin range, attempting to index `bins` with the indices that `digitize` returns will result in an IndexError. Examples -------- >>> x = np.array([0.2, 6.4, 3.0, 1.6]) >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) >>> inds = np.digitize(x, bins) >>> inds array([1, 4, 3, 2]) >>> for n in range(x.size): ... print bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]] ... 0.0 <= 0.2 < 1.0 4.0 <= 6.4 < 10.0 2.5 <= 3.0 < 4.0 1.0 <= 1.6 < 2.5 >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) >>> bins = np.array([0,5,10,15,20]) >>> np.digitize(x,bins,right=True) array([1, 2, 3, 4, 4]) >>> np.digitize(x,bins,right=False) array([1, 3, 3, 4, 5])""" return ndarray() def disp(mesg=True, device=None, linefeed=True): """ Display a message on a device. Parameters ---------- mesg : str Message to display. device : object Device to write message. If None, defaults to ``sys.stdout`` which is very similar to ``print``. `device` needs to have ``write()`` and ``flush()`` methods. linefeed : bool, optional Option whether to print a line feed or not. Defaults to True. Raises ------ AttributeError If `device` does not have a ``write()`` or ``flush()`` method. Examples -------- Besides ``sys.stdout``, a file-like object can also be used as it has both required methods: >>> from StringIO import StringIO >>> buf = StringIO() >>> np.disp('"Display" in a file', device=buf) >>> buf.getvalue() '"Display" in a file\n' """ return None def divide(x1, x2, out): """divide(x1, x2[, out]) Divide arguments element-wise. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- y : {ndarray, scalar} The quotient `x1/x2`, element-wise. Returns a scalar if both `x1` and `x2` are scalars. See Also -------- seterr : Set whether to raise or warn on overflow, underflow and division by zero. Notes ----- Equivalent to `x1` / `x2` in terms of array-broadcasting. Behavior on division by zero can be changed using `seterr`. When both `x1` and `x2` are of an integer type, `divide` will return integers and throw away the fractional part. Moreover, division by zero always yields zero in integer arithmetic. Examples -------- >>> np.divide(2.0, 4.0) 0.5 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.divide(x1, x2) array([[ NaN, 1. , 1. ], [ Inf, 4. , 2.5], [ Inf, 7. , 4. ]]) Note the behavior with integer types: >>> np.divide(2, 4) 0 >>> np.divide(2, 4.) 0.5 Division by zero always yields zero in integer arithmetic, and does not raise an exception or a warning: >>> np.divide(np.array([0, 1], dtype=int), np.array([0, 0], dtype=int)) array([0, 0]) Division by zero can, however, be caught using `seterr`: >>> old_err_state = np.seterr(divide='raise') >>> np.divide(1, 0) Traceback (most recent call last): File "", line 1, in FloatingPointError: divide by zero encountered in divide >>> ignored_states = np.seterr(**old_err_state) >>> np.divide(1, 0) 0""" return ndarray() division = instance() def dot(a, b, out): """dot(a, b, out=None) Dot product of two arrays. For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of `a` and the second-to-last of `b`:: dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m]) Parameters ---------- a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for `dot(a,b)`. This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. Returns ------- output : ndarray Returns the dot product of `a` and `b`. If `a` and `b` are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If `out` is given, then it is returned. Raises ------ ValueError If the last dimension of `a` is not the same size as the second-to-last dimension of `b`. See Also -------- vdot : Complex-conjugating dot product. tensordot : Sum products over arbitrary axes. einsum : Einstein summation convention. Examples -------- >>> np.dot(3, 4) 12 Neither argument is complex-conjugated: >>> np.dot([2j, 3j], [2j, 3j]) (-13+0j) For 2-D arrays it's the matrix product: >>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.dot(a, b) array([[4, 1], [2, 2]]) >>> a = np.arange(3*4*5*6).reshape((3,4,5,6)) >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3)) >>> np.dot(a, b)[2,3,2,1,2,2] 499128 >>> sum(a[2,3,2,:] * b[1,2,:,2]) 499128""" return ndarray() class float64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() def as_integer_ratio(self, _): """float.as_integer_ratio() -> (int, int) Return a pair of integers, whose ratio is exactly equal to the original float and with a positive denominator. Raise OverflowError on infinities and a ValueError on NaNs. >>> (10.0).as_integer_ratio() (10, 1) >>> (0.0).as_integer_ratio() (0, 1) >>> (-.25).as_integer_ratio() (-1, 4)""" return None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() def _fromhex(self, string): """float.fromhex(string) -> float Create a floating-point number from a hexadecimal string. >>> float.fromhex('0x1.ffffp10') 2047.984375 >>> float.fromhex('-0x1p-1074') -4.9406564584124654e-324""" return None def hex(self, _): """float.hex() -> string Return a hexadecimal representation of a floating-point number. >>> (-0.1).hex() '-0x1.999999999999ap-4' >>> 3.14159.hex() '0x1.921f9f01b866ep+1'""" return None imag = getset_descriptor() def is_integer(self, _): """Return True if the float is an integer.""" return None itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def dsplit(): """ Split array into multiple sub-arrays along the 3rd axis (depth). Please refer to the `split` documentation. `dsplit` is equivalent to `split` with ``axis=2``, the array is always split along the third axis provided the array dimension is greater than or equal to 3. See Also -------- split : Split an array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(16.0).reshape(2, 2, 4) >>> x array([[[ 0., 1., 2., 3.], [ 4., 5., 6., 7.]], [[ 8., 9., 10., 11.], [ 12., 13., 14., 15.]]]) >>> np.dsplit(x, 2) [array([[[ 0., 1.], [ 4., 5.]], [[ 8., 9.], [ 12., 13.]]]), array([[[ 2., 3.], [ 6., 7.]], [[ 10., 11.], [ 14., 15.]]])] >>> np.dsplit(x, np.array([3, 6])) [array([[[ 0., 1., 2.], [ 4., 5., 6.]], [[ 8., 9., 10.], [ 12., 13., 14.]]]), array([[[ 3.], [ 7.]], [[ 11.], [ 15.]]]), array([], dtype=float64)] """ return None def dstack(tup): """ Stack arrays in sequence depth wise (along third axis). Takes a sequence of arrays and stack them along the third axis to make a single array. Rebuilds arrays divided by `dsplit`. This is a simple way to stack 2D arrays (images) into a single 3D array for processing. Parameters ---------- tup : sequence of arrays Arrays to stack. All of them must have the same shape along all but the third axis. Returns ------- stacked : ndarray The array formed by stacking the given arrays. See Also -------- vstack : Stack along first axis. hstack : Stack along second axis. concatenate : Join arrays. dsplit : Split array along third axis. Notes ----- Equivalent to ``np.concatenate(tup, axis=2)``. Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.dstack((a,b)) array([[[1, 2], [2, 3], [3, 4]]]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.dstack((a,b)) array([[[1, 2]], [[2, 3]], [[3, 4]]]) """ return ndarray() class dtype: __doc__ = str() alignment = member_descriptor() base = getset_descriptor() byteorder = member_descriptor() char = member_descriptor() descr = getset_descriptor() fields = getset_descriptor() flags = member_descriptor() hasobject = getset_descriptor() isalignedstruct = getset_descriptor() isbuiltin = getset_descriptor() isnative = getset_descriptor() itemsize = member_descriptor() kind = member_descriptor() metadata = getset_descriptor() name = getset_descriptor() names = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new dtype with a different byte order. Changes are also made in all fields and sub-arrays of the data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications below. The default value ('S') results in swapping the current byte order. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The code does a case-insensitive check on the first letter of `new_order` for these alternatives. For example, any of '>' or 'B' or 'b' or 'brian' are valid to specify big-endian. Returns ------- new_dtype : dtype New dtype object with the given change to the byte order. Notes ----- Changes are also made in all fields and sub-arrays of the data type. Examples -------- >>> import sys >>> sys_is_le = sys.byteorder == 'little' >>> native_code = sys_is_le and '<' or '>' >>> swapped_code = sys_is_le and '>' or '<' >>> native_dt = np.dtype(native_code+'i2') >>> swapped_dt = np.dtype(swapped_code+'i2') >>> native_dt.newbyteorder('S') == swapped_dt True >>> native_dt.newbyteorder() == swapped_dt True >>> native_dt == swapped_dt.newbyteorder('S') True >>> native_dt == swapped_dt.newbyteorder('=') True >>> native_dt == swapped_dt.newbyteorder('N') True >>> native_dt == native_dt.newbyteorder('|') True >>> np.dtype('>> np.dtype('>> np.dtype('>i2') == native_dt.newbyteorder('>') True >>> np.dtype('>i2') == native_dt.newbyteorder('B') True""" return dtype() num = member_descriptor() shape = getset_descriptor() str = getset_descriptor() subdtype = getset_descriptor() type = member_descriptor() e = float() def ediff1d(ary=None, to_end=None, to_begin=None): """ The differences between consecutive elements of an array. Parameters ---------- ary : array_like If necessary, will be flattened before the differences are taken. to_end : array_like, optional Number(s) to append at the end of the returned differences. to_begin : array_like, optional Number(s) to prepend at the beginning of the returned differences. Returns ------- ediff1d : ndarray The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``. See Also -------- diff, gradient Notes ----- When applied to masked arrays, this function drops the mask information if the `to_begin` and/or `to_end` parameters are used. Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.ediff1d(x) array([ 1, 2, 3, -7]) >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99])) array([-99, 1, 2, 3, -7, 88, 99]) The returned array is always 1D. >>> y = [[1, 2, 4], [1, 6, 24]] >>> np.ediff1d(y) array([ 1, 2, -3, 5, 18]) """ return ndarray() def einsum(subscripts, operands, out, dtype, order, casting): """einsum(subscripts, *operands, out=None, dtype=None, order='K', casting='safe') Evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional array operations can be represented in a simple fashion. This function provides a way compute such summations. The best way to understand this function is to try the examples below, which show how many common NumPy functions can be implemented as calls to `einsum`. Parameters ---------- subscripts : str Specifies the subscripts for summation. operands : list of array_like These are the arrays for the operation. out : ndarray, optional If provided, the calculation is done into this array. dtype : data-type, optional If provided, forces the calculation to use the data type specified. Note that you may have to also give a more liberal `casting` parameter to allow the conversions. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the output. 'C' means it should be C contiguous. 'F' means it should be Fortran contiguous, 'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise. 'K' means it should be as close to the layout as the inputs as is possible, including arbitrarily permuted axes. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Setting this to 'unsafe' is not recommended, as it can adversely affect accumulations. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. Returns ------- output : ndarray The calculation based on the Einstein summation convention. See Also -------- dot, inner, outer, tensordot Notes ----- .. versionadded:: 1.6.0 The subscripts string is a comma-separated list of subscript labels, where each label refers to a dimension of the corresponding operand. Repeated subscripts labels in one operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent to ``np.trace(a)``. Whenever a label is repeated, it is summed, so ``np.einsum('i,i', a, b)`` is equivalent to ``np.inner(a,b)``. If a label appears only once, it is not summed, so ``np.einsum('i', a)`` produces a view of ``a`` with no changes. The order of labels in the output is by default alphabetical. This means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while ``np.einsum('ji', a)`` takes its transpose. The output can be controlled by specifying output subscript labels as well. This specifies the label order, and allows summing to be disallowed or forced when desired. The call ``np.einsum('i->', a)`` is like ``np.sum(a, axis=-1)``, and ``np.einsum('ii->i', a)`` is like ``np.diag(a)``. The difference is that `einsum` does not allow broadcasting by default. To enable and control broadcasting, use an ellipsis. Default NumPy-style broadcasting is done by adding an ellipsis to the left of each term, like ``np.einsum('...ii->...i', a)``. To take the trace along the first and last axes, you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix product with the left-most indices instead of rightmost, you can do ``np.einsum('ij...,jk...->ik...', a, b)``. When there is only one operand, no axes are summed, and no output parameter is provided, a view into the operand is returned instead of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)`` produces a view. An alternative way to provide the subscripts and operands is as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``. The examples below have corresponding `einsum` calls with the two parameter methods. Examples -------- >>> a = np.arange(25).reshape(5,5) >>> b = np.arange(5) >>> c = np.arange(6).reshape(2,3) >>> np.einsum('ii', a) 60 >>> np.einsum(a, [0,0]) 60 >>> np.trace(a) 60 >>> np.einsum('ii->i', a) array([ 0, 6, 12, 18, 24]) >>> np.einsum(a, [0,0], [0]) array([ 0, 6, 12, 18, 24]) >>> np.diag(a) array([ 0, 6, 12, 18, 24]) >>> np.einsum('ij,j', a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum(a, [0,1], b, [1]) array([ 30, 80, 130, 180, 230]) >>> np.dot(a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum('ji', c) array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum(c, [1,0]) array([[0, 3], [1, 4], [2, 5]]) >>> c.T array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum('..., ...', 3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum(3, [Ellipsis], c, [Ellipsis]) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.multiply(3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum('i,i', b, b) 30 >>> np.einsum(b, [0], b, [0]) 30 >>> np.inner(b,b) 30 >>> np.einsum('i,j', np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.einsum(np.arange(2)+1, [0], b, [1]) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.outer(np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.einsum('i...->...', a) array([50, 55, 60, 65, 70]) >>> np.einsum(a, [0,Ellipsis], [Ellipsis]) array([50, 55, 60, 65, 70]) >>> np.sum(a, axis=0) array([50, 55, 60, 65, 70]) >>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> np.einsum('ijk,jil->kl', a, b) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3]) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.tensordot(a,b, axes=([1,0],[0,1])) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]])""" return ndarray() def empty(shape, dtype, order): """empty(shape, dtype=float, order='C') Return a new array of given shape and type, without initializing entries. Parameters ---------- shape : int or tuple of int Shape of the empty array dtype : data-type, optional Desired output data-type. order : {'C', 'F'}, optional Whether to store multi-dimensional data in C (row-major) or Fortran (column-major) order in memory. See Also -------- empty_like, zeros, ones Notes ----- `empty`, unlike `zeros`, does not set the array values to zero, and may therefore be marginally faster. On the other hand, it requires the user to manually set all the values in the array, and should be used with caution. Examples -------- >>> np.empty([2, 2]) array([[ -9.74499359e+001, 6.69583040e-309], [ 2.13182611e-314, 3.06959433e-309]]) #random >>> np.empty([2, 2], dtype=int) array([[-1073741821, -1067949133], [ 496041986, 19249760]]) #random""" return None def empty_like(a, dtype, order, subok): """empty_like(a, dtype=None, order='K', subok=True) Return a new array with the same shape and type as a given array. Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. dtype : data-type, optional .. versionadded:: 1.6.0 Overrides the data type of the result. order : {'C', 'F', 'A', or 'K'}, optional .. versionadded:: 1.6.0 Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if ``a`` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of ``a`` as closely as possible. subok : bool, optional. If True, then the newly created array will use the sub-class type of 'a', otherwise it will be a base-class array. Defaults to True. Returns ------- out : ndarray Array of uninitialized (arbitrary) data with the same shape and type as `a`. See Also -------- ones_like : Return an array of ones with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. empty : Return a new uninitialized array. ones : Return a new array setting values to one. zeros : Return a new array setting values to zero. Notes ----- This function does *not* initialize the returned array; to do that use `zeros_like` or `ones_like` instead. It may be marginally faster than the functions that do set the array values. Examples -------- >>> a = ([1,2,3], [4,5,6]) # a is array-like >>> np.empty_like(a) array([[-1073741821, -1073741821, 3], #random [ 0, 0, -1073741821]]) >>> a = np.array([[1., 2., 3.],[4.,5.,6.]]) >>> np.empty_like(a) array([[ -2.00000715e+000, 1.48219694e-323, -2.00000572e+000],#random [ 4.38791518e-305, -2.00000715e+000, 4.17269252e-309]])""" return ndarray() def equal(x1, x2, out=None): """equal(x1, x2[, out]) Return (x1 == x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays of the same shape. Returns ------- out : {ndarray, bool} Output array of bools, or a single bool if x1 and x2 are scalars. See Also -------- not_equal, greater_equal, less_equal, greater, less Examples -------- >>> np.equal([0, 1, 3], np.arange(3)) array([ True, True, False], dtype=bool) What is compared are values, not types. So an int (1) and an array of length one can evaluate as True: >>> np.equal(1, np.ones(1)) array([ True], dtype=bool)""" return ndarray() class errstate: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() euler_gamma = float() def exp(x, out=None): """exp(x[, out]) Calculate the exponential of all elements in the input array. Parameters ---------- x : array_like Input values. Returns ------- out : ndarray Output array, element-wise exponential of `x`. See Also -------- expm1 : Calculate ``exp(x) - 1`` for all elements in the array. exp2 : Calculate ``2**x`` for all elements in the array. Notes ----- The irrational number ``e`` is also known as Euler's number. It is approximately 2.718281, and is the base of the natural logarithm, ``ln`` (this means that, if :math:`x = \ln y = \log_e y`, then :math:`e^x = y`. For real input, ``exp(x)`` is always positive. For complex arguments, ``x = a + ib``, we can write :math:`e^x = e^a e^{ib}`. The first term, :math:`e^a`, is already known (it is the real argument, described above). The second term, :math:`e^{ib}`, is :math:`\cos b + i \sin b`, a function with magnitude 1 and a periodic phase. References ---------- .. [1] Wikipedia, "Exponential function", http://en.wikipedia.org/wiki/Exponential_function .. [2] M. Abramovitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables," Dover, 1964, p. 69, http://www.math.sfu.ca/~cbm/aands/page_69.htm Examples -------- Plot the magnitude and phase of ``exp(x)`` in the complex plane: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-2*np.pi, 2*np.pi, 100) >>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane >>> out = np.exp(xx) >>> plt.subplot(121) >>> plt.imshow(np.abs(out), ... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi]) >>> plt.title('Magnitude of exp(x)') >>> plt.subplot(122) >>> plt.imshow(np.angle(out), ... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi]) >>> plt.title('Phase (angle) of exp(x)') >>> plt.show()""" return ndarray() def exp2(x, out): """exp2(x[, out]) Calculate `2**p` for all `p` in the input array. Parameters ---------- x : array_like Input values. out : ndarray, optional Array to insert results into. Returns ------- out : ndarray Element-wise 2 to the power `x`. See Also -------- power Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> np.exp2([2, 3]) array([ 4., 8.])""" return ndarray() def expand_dims(a, axis): """ Expand the shape of an array. Insert a new axis, corresponding to a given position in the array shape. Parameters ---------- a : array_like Input array. axis : int Position (amongst axes) where new axis is to be inserted. Returns ------- res : ndarray Output array. The number of dimensions is one greater than that of the input array. See Also -------- doc.indexing, atleast_1d, atleast_2d, atleast_3d Examples -------- >>> x = np.array([1,2]) >>> x.shape (2,) The following is equivalent to ``x[np.newaxis,:]`` or ``x[np.newaxis]``: >>> y = np.expand_dims(x, axis=0) >>> y array([[1, 2]]) >>> y.shape (1, 2) >>> y = np.expand_dims(x, axis=1) # Equivalent to x[:,newaxis] >>> y array([[1], [2]]) >>> y.shape (2, 1) Note that some examples may use ``None`` instead of ``np.newaxis``. These are the same objects: >>> np.newaxis is None True """ return ndarray() def expm1(x, out=None): """expm1(x[, out]) Calculate ``exp(x) - 1`` for all elements in the array. Parameters ---------- x : array_like Input values. Returns ------- out : ndarray Element-wise exponential minus one: ``out = exp(x) - 1``. See Also -------- log1p : ``log(1 + x)``, the inverse of expm1. Notes ----- This function provides greater precision than the formula ``exp(x) - 1`` for small values of ``x``. Examples -------- The true value of ``exp(1e-10) - 1`` is ``1.00000000005e-10`` to about 32 significant digits. This example shows the superiority of expm1 in this case. >>> np.expm1(1e-10) 1.00000000005e-10 >>> np.exp(1e-10) - 1 1.000000082740371e-10""" return ndarray() def extract(condition, arr): """ Return the elements of an array that satisfy some condition. This is equivalent to ``np.compress(ravel(condition), ravel(arr))``. If `condition` is boolean ``np.extract`` is equivalent to ``arr[condition]``. Parameters ---------- condition : array_like An array whose nonzero or True entries indicate the elements of `arr` to extract. arr : array_like Input array of the same size as `condition`. Returns ------- extract : ndarray Rank 1 array of values from `arr` where `condition` is True. See Also -------- take, put, copyto, compress Examples -------- >>> arr = np.arange(12).reshape((3, 4)) >>> arr array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> condition = np.mod(arr, 3)==0 >>> condition array([[ True, False, False, True], [False, False, True, False], [False, True, False, False]], dtype=bool) >>> np.extract(condition, arr) array([0, 3, 6, 9]) If `condition` is boolean: >>> arr[condition] array([0, 3, 6, 9]) """ return ndarray() def eye(N=typefloat(), M=None, k=0, dtype=typefloat()): """ Return a 2-D array with ones on the diagonal and zeros elsewhere. Parameters ---------- N : int Number of rows in the output. M : int, optional Number of columns in the output. If None, defaults to `N`. k : int, optional Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal. dtype : data-type, optional Data-type of the returned array. Returns ------- I : ndarray of shape (N,M) An array where all elements are equal to zero, except for the `k`-th diagonal, whose values are equal to one. See Also -------- identity : (almost) equivalent function diag : diagonal 2-D array from a 1-D array specified by the user. Examples -------- >>> np.eye(2, dtype=int) array([[1, 0], [0, 1]]) >>> np.eye(3, k=1) array([[ 0., 1., 0.], [ 0., 0., 1.], [ 0., 0., 0.]]) """ return ndarray() def fabs(x, out): """fabs(x[, out]) Compute the absolute values elementwise. This function returns the absolute values (positive magnitude) of the data in `x`. Complex values are not handled, use `absolute` to find the absolute values of complex data. Parameters ---------- x : array_like The array of numbers for which the absolute values are required. If `x` is a scalar, the result `y` will also be a scalar. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- y : {ndarray, scalar} The absolute values of `x`, the returned values are always floats. See Also -------- absolute : Absolute values including `complex` types. Examples -------- >>> np.fabs(-1) 1.0 >>> np.fabs([-1.2, 1.2]) array([ 1.2, 1.2])""" return ndarray() def _fastCopyAndTranspose(a): """_fastCopyAndTranspose(a)""" return None def fill_diagonal(a, val=False, wrap=False): """Fill the main diagonal of the given array of any dimensionality. For an array `a` with ``a.ndim > 2``, the diagonal is the list of locations with indices ``a[i, i, ..., i]`` all identical. This function modifies the input array in-place, it does not return a value. Parameters ---------- a : array, at least 2-D. Array whose diagonal is to be filled, it gets modified in-place. val : scalar Value to be written on the diagonal, its type must be compatible with that of the array a. wrap : bool For tall matrices in NumPy version up to 1.6.2, the diagonal "wrapped" after N columns. You can have this behavior with this option. This affect only tall matrices. See also -------- diag_indices, diag_indices_from Notes ----- .. versionadded:: 1.4.0 This functionality can be obtained via `diag_indices`, but internally this version uses a much faster implementation that never constructs the indices and uses simple slicing. Examples -------- >>> a = np.zeros((3, 3), int) >>> np.fill_diagonal(a, 5) >>> a array([[5, 0, 0], [0, 5, 0], [0, 0, 5]]) The same function can operate on a 4-D array: >>> a = np.zeros((3, 3, 3, 3), int) >>> np.fill_diagonal(a, 4) We only show a few blocks for clarity: >>> a[0, 0] array([[4, 0, 0], [0, 0, 0], [0, 0, 0]]) >>> a[1, 1] array([[0, 0, 0], [0, 4, 0], [0, 0, 0]]) >>> a[2, 2] array([[0, 0, 0], [0, 0, 0], [0, 0, 4]]) # tall matrices no wrap >>> a = np.zeros((5, 3),int) >>> fill_diagonal(a, 4) array([[4, 0, 0], [0, 4, 0], [0, 0, 4], [0, 0, 0], [0, 0, 0]]) # tall matrices wrap >>> a = np.zeros((5, 3),int) >>> fill_diagonal(a, 4) array([[4, 0, 0], [0, 4, 0], [0, 0, 4], [0, 0, 0], [4, 0, 0]]) # wide matrices >>> a = np.zeros((3, 5),int) >>> fill_diagonal(a, 4) array([[4, 0, 0, 0, 0], [0, 4, 0, 0, 0], [0, 0, 4, 0, 0]]) """ return None def find_common_type(array_types, scalar_types): """ Determine common type following standard coercion rules. Parameters ---------- array_types : sequence A list of dtypes or dtype convertible objects representing arrays. scalar_types : sequence A list of dtypes or dtype convertible objects representing scalars. Returns ------- datatype : dtype The common data type, which is the maximum of `array_types` ignoring `scalar_types`, unless the maximum of `scalar_types` is of a different kind (`dtype.kind`). If the kind is not understood, then None is returned. See Also -------- dtype, common_type, can_cast, mintypecode Examples -------- >>> np.find_common_type([], [np.int64, np.float32, np.complex]) dtype('complex128') >>> np.find_common_type([np.int64, np.float32], []) dtype('float64') The standard casting rules ensure that a scalar cannot up-cast an array unless the scalar is of a fundamentally different kind of data (i.e. under a different hierarchy in the data type hierarchy) then the array: >>> np.find_common_type([np.float32], [np.int64, np.float64]) dtype('float32') Complex is of a different type, so it up-casts the float in the `array_types` argument: >>> np.find_common_type([np.float32], [np.complex]) dtype('complex128') Type specifier strings are convertible to dtypes and can therefore be used instead of dtypes: >>> np.find_common_type(['f4', 'f4', 'i4'], ['c8']) dtype('complex128') """ return dtype() class finfo: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() _finfo_cache = dict() def _init(self, _): """None""" return None def fix(x=None, y=None): """ Round to nearest integer towards zero. Round an array of floats element-wise to nearest integer towards zero. The rounded values are returned as floats. Parameters ---------- x : array_like An array of floats to be rounded y : ndarray, optional Output array Returns ------- out : ndarray of floats The array of rounded numbers See Also -------- trunc, floor, ceil around : Round to given number of decimals Examples -------- >>> np.fix(3.14) 3.0 >>> np.fix(3) 3.0 >>> np.fix([2.1, 2.9, -2.1, -2.9]) array([ 2., 2., -2., -2.]) """ return ndarray() class flatiter: __doc__ = str() base = member_descriptor() coords = getset_descriptor() def copy(self, _): """copy() Get a copy of the iterator as a 1-D array. Examples -------- >>> x = np.arange(6).reshape(2, 3) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> fl = x.flat >>> fl.copy() array([0, 1, 2, 3, 4, 5])""" return None index = member_descriptor() def next(self, _): """x.next() -> the next value, or raise StopIteration""" return None def flatnonzero(a): """ Return indices that are non-zero in the flattened version of a. This is equivalent to a.ravel().nonzero()[0]. Parameters ---------- a : ndarray Input array. Returns ------- res : ndarray Output array, containing the indices of the elements of `a.ravel()` that are non-zero. See Also -------- nonzero : Return the indices of the non-zero elements of the input array. ravel : Return a 1-D array containing the elements of the input array. Examples -------- >>> x = np.arange(-2, 3) >>> x array([-2, -1, 0, 1, 2]) >>> np.flatnonzero(x) array([0, 1, 3, 4]) Use the indices of the non-zero elements as an index array to extract these elements: >>> x.ravel()[np.flatnonzero(x)] array([-2, -1, 1, 2]) """ return ndarray() class flexible: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def fliplr(m): """ Flip array in the left/right direction. Flip the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array. Returns ------- f : ndarray A view of `m` with the columns reversed. Since a view is returned, this operation is :math:`\mathcal O(1)`. See Also -------- flipud : Flip array in the up/down direction. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to A[:,::-1]. Does not require the array to be two-dimensional. Examples -------- >>> A = np.diag([1.,2.,3.]) >>> A array([[ 1., 0., 0.], [ 0., 2., 0.], [ 0., 0., 3.]]) >>> np.fliplr(A) array([[ 0., 0., 1.], [ 0., 2., 0.], [ 3., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.fliplr(A)==A[:,::-1,...]) True """ return ndarray() def flipud(m): """ Flip array in the up/down direction. Flip the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array. Returns ------- out : array_like A view of `m` with the rows reversed. Since a view is returned, this operation is :math:`\mathcal O(1)`. See Also -------- fliplr : Flip array in the left/right direction. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``A[::-1,...]``. Does not require the array to be two-dimensional. Examples -------- >>> A = np.diag([1.0, 2, 3]) >>> A array([[ 1., 0., 0.], [ 0., 2., 0.], [ 0., 0., 3.]]) >>> np.flipud(A) array([[ 0., 0., 3.], [ 0., 2., 0.], [ 1., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.flipud(A)==A[::-1,...]) True >>> np.flipud([1,2]) array([2, 1]) """ return ndarray() class float: __doc__ = str() def as_integer_ratio(self, _): """float.as_integer_ratio() -> (int, int) Return a pair of integers, whose ratio is exactly equal to the original float and with a positive denominator. Raise OverflowError on infinities and a ValueError on NaNs. >>> (10.0).as_integer_ratio() (10, 1) >>> (0.0).as_integer_ratio() (0, 1) >>> (-.25).as_integer_ratio() (-1, 4)""" return None def conjugate(self, _): """Return self, the complex conjugate of any float.""" return None def _fromhex(self, string): """float.fromhex(string) -> float Create a floating-point number from a hexadecimal string. >>> float.fromhex('0x1.ffffp10') 2047.984375 >>> float.fromhex('-0x1p-1074') -4.9406564584124654e-324""" return None def hex(self, _): """float.hex() -> string Return a hexadecimal representation of a floating-point number. >>> (-0.1).hex() '-0x1.999999999999ap-4' >>> 3.14159.hex() '0x1.921f9f01b866ep+1'""" return None imag = getset_descriptor() def is_integer(self, _): """Return True if the float is an integer.""" return None real = getset_descriptor() class float128: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class float16: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class float32: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class float64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() def as_integer_ratio(self, _): """float.as_integer_ratio() -> (int, int) Return a pair of integers, whose ratio is exactly equal to the original float and with a positive denominator. Raise OverflowError on infinities and a ValueError on NaNs. >>> (10.0).as_integer_ratio() (10, 1) >>> (0.0).as_integer_ratio() (0, 1) >>> (-.25).as_integer_ratio() (-1, 4)""" return None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() def _fromhex(self, string): """float.fromhex(string) -> float Create a floating-point number from a hexadecimal string. >>> float.fromhex('0x1.ffffp10') 2047.984375 >>> float.fromhex('-0x1p-1074') -4.9406564584124654e-324""" return None def hex(self, _): """float.hex() -> string Return a hexadecimal representation of a floating-point number. >>> (-0.1).hex() '-0x1.999999999999ap-4' >>> 3.14159.hex() '0x1.921f9f01b866ep+1'""" return None imag = getset_descriptor() def is_integer(self, _): """Return True if the float is an integer.""" return None itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class float64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() def as_integer_ratio(self, _): """float.as_integer_ratio() -> (int, int) Return a pair of integers, whose ratio is exactly equal to the original float and with a positive denominator. Raise OverflowError on infinities and a ValueError on NaNs. >>> (10.0).as_integer_ratio() (10, 1) >>> (0.0).as_integer_ratio() (0, 1) >>> (-.25).as_integer_ratio() (-1, 4)""" return None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() def _fromhex(self, string): """float.fromhex(string) -> float Create a floating-point number from a hexadecimal string. >>> float.fromhex('0x1.ffffp10') 2047.984375 >>> float.fromhex('-0x1p-1074') -4.9406564584124654e-324""" return None def hex(self, _): """float.hex() -> string Return a hexadecimal representation of a floating-point number. >>> (-0.1).hex() '-0x1.999999999999ap-4' >>> 3.14159.hex() '0x1.921f9f01b866ep+1'""" return None imag = getset_descriptor() def is_integer(self, _): """Return True if the float is an integer.""" return None itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class floating: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def floor(x, out=None): """floor(x[, out]) Return the floor of the input, element-wise. The floor of the scalar `x` is the largest integer `i`, such that `i <= x`. It is often denoted as :math:`\lfloor x \rfloor`. Parameters ---------- x : array_like Input data. Returns ------- y : {ndarray, scalar} The floor of each element in `x`. See Also -------- ceil, trunc, rint Notes ----- Some spreadsheet programs calculate the "floor-towards-zero", in other words ``floor(-2.5) == -2``. NumPy, however, uses the a definition of `floor` such that `floor(-2.5) == -3`. Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.floor(a) array([-2., -2., -1., 0., 1., 1., 2.])""" return ndarray() def floor_divide(x1, x2, out=None): """floor_divide(x1, x2[, out]) Return the largest integer smaller or equal to the division of the inputs. Parameters ---------- x1 : array_like Numerator. x2 : array_like Denominator. Returns ------- y : ndarray y = floor(`x1`/`x2`) See Also -------- divide : Standard division. floor : Round a number to the nearest integer toward minus infinity. ceil : Round a number to the nearest integer toward infinity. Examples -------- >>> np.floor_divide(7,3) 2 >>> np.floor_divide([1., 2., 3., 4.], 2.5) array([ 0., 0., 1., 1.])""" return ndarray() def fmax(x1, x2, out=None): """fmax(x1, x2[, out]) Element-wise maximum of array elements. Compare two arrays and returns a new array containing the element-wise maxima. If one of the elements being compared is a nan, then the non-nan element is returned. If both elements are nans then the first is returned. The latter distinction is important for complex nans, which are defined as at least one of the real or imaginary parts being a nan. The net effect is that nans are ignored when possible. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. They must have the same shape. Returns ------- y : {ndarray, scalar} The minimum of `x1` and `x2`, element-wise. Returns scalar if both `x1` and `x2` are scalars. See Also -------- fmin : Element-wise minimum of two arrays, ignoring any NaNs. maximum : Element-wise maximum of two arrays, propagating any NaNs. amax : The maximum value of an array along a given axis, propagating any NaNs. nanmax : The maximum value of an array along a given axis, ignoring any NaNs. minimum, amin, nanmin Notes ----- .. versionadded:: 1.3.0 The fmax is equivalent to ``np.where(x1 >= x2, x1, x2)`` when neither x1 nor x2 are nans, but it is faster and does proper broadcasting. Examples -------- >>> np.fmax([2, 3, 4], [1, 5, 2]) array([ 2., 5., 4.]) >>> np.fmax(np.eye(2), [0.5, 2]) array([[ 1. , 2. ], [ 0.5, 2. ]]) >>> np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ 0., 0., NaN])""" return ndarray() def fmin(x1, x2, out=None): """fmin(x1, x2[, out]) Element-wise minimum of array elements. Compare two arrays and returns a new array containing the element-wise minima. If one of the elements being compared is a nan, then the non-nan element is returned. If both elements are nans then the first is returned. The latter distinction is important for complex nans, which are defined as at least one of the real or imaginary parts being a nan. The net effect is that nans are ignored when possible. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. They must have the same shape. Returns ------- y : {ndarray, scalar} The minimum of `x1` and `x2`, element-wise. Returns scalar if both `x1` and `x2` are scalars. See Also -------- fmax : Element-wise maximum of two arrays, ignoring any NaNs. minimum : Element-wise minimum of two arrays, propagating any NaNs. amin : The minimum value of an array along a given axis, propagating any NaNs. nanmin : The minimum value of an array along a given axis, ignoring any NaNs. maximum, amax, nanmax Notes ----- .. versionadded:: 1.3.0 The fmin is equivalent to ``np.where(x1 <= x2, x1, x2)`` when neither x1 nor x2 are nans, but it is faster and does proper broadcasting. Examples -------- >>> np.fmin([2, 3, 4], [1, 5, 2]) array([2, 5, 4]) >>> np.fmin(np.eye(2), [0.5, 2]) array([[ 1. , 2. ], [ 0.5, 2. ]]) >>> np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ 0., 0., NaN])""" return ndarray() def fmod(x1, x2, out=None): """fmod(x1, x2[, out]) Return the element-wise remainder of division. This is the NumPy implementation of the Python modulo operator `%`. Parameters ---------- x1 : array_like Dividend. x2 : array_like Divisor. Returns ------- y : array_like The remainder of the division of `x1` by `x2`. See Also -------- remainder : Modulo operation where the quotient is `floor(x1/x2)`. divide Notes ----- The result of the modulo operation for negative dividend and divisors is bound by conventions. In `fmod`, the sign of the remainder is the sign of the dividend. In `remainder`, the sign of the divisor does not affect the sign of the result. Examples -------- >>> np.fmod([-3, -2, -1, 1, 2, 3], 2) array([-1, 0, -1, 1, 0, 1]) >>> np.remainder([-3, -2, -1, 1, 2, 3], 2) array([1, 0, 1, 1, 0, 1]) >>> np.fmod([5, 3], [2, 2.]) array([ 1., 1.]) >>> a = np.arange(-3, 3).reshape(3, 2) >>> a array([[-3, -2], [-1, 0], [ 1, 2]]) >>> np.fmod(a, [2,2]) array([[-1, 0], [-1, 0], [ 1, 0]])""" return ndarray() class format_parser: __doc__ = str() __module__ = str() def _createdescr(self, _): """None""" return None def _parseFormats(self, formats=0, aligned=0): """ Parse the field formats """ return None def _setfieldnames(self, _): """convert input field names into a list and assign to the _names attribute """ return None def frexp(x, out1, out2): """frexp(x[, out1, out2]) Split the number, x, into a normalized fraction (y1) and exponent (y2)""" return None def _frombuffer(buffer, dtype, count, offset): """frombuffer(buffer, dtype=float, count=-1, offset=0) Interpret a buffer as a 1-dimensional array. Parameters ---------- buffer : buffer_like An object that exposes the buffer interface. dtype : data-type, optional Data-type of the returned array; default: float. count : int, optional Number of items to read. ``-1`` means all data in the buffer. offset : int, optional Start reading the buffer from this offset; default: 0. Notes ----- If the buffer has data that is not in machine byte-order, this should be specified as part of the data-type, e.g.:: >>> dt = np.dtype(int) >>> dt = dt.newbyteorder('>') >>> np.frombuffer(buf, dtype=dt) The data of the resulting array will not be byteswapped, but will be interpreted correctly. Examples -------- >>> s = 'hello world' >>> np.frombuffer(s, dtype='S1', count=5, offset=6) array(['w', 'o', 'r', 'l', 'd'], dtype='|S1')""" return None def _fromfile(file, dtype, count, sep): """fromfile(file, dtype=float, count=-1, sep='') Construct an array from data in a text or binary file. A highly efficient way of reading binary data with a known data-type, as well as parsing simply formatted text files. Data written using the `tofile` method can be read using this function. Parameters ---------- file : file or str Open file object or filename. dtype : data-type Data type of the returned array. For binary files, it is used to determine the size and byte-order of the items in the file. count : int Number of items to read. ``-1`` means all items (i.e., the complete file). sep : str Separator between items if file is a text file. Empty ("") separator means the file should be treated as binary. Spaces (" ") in the separator match zero or more whitespace characters. A separator consisting only of spaces must match at least one whitespace. See also -------- load, save ndarray.tofile loadtxt : More flexible way of loading data from a text file. Notes ----- Do not rely on the combination of `tofile` and `fromfile` for data storage, as the binary files generated are are not platform independent. In particular, no byte-order or data-type information is saved. Data can be stored in the platform independent ``.npy`` format using `save` and `load` instead. Examples -------- Construct an ndarray: >>> dt = np.dtype([('time', [('min', int), ('sec', int)]), ... ('temp', float)]) >>> x = np.zeros((1,), dtype=dt) >>> x['time']['min'] = 10; x['temp'] = 98.25 >>> x array([((10, 0), 98.25)], dtype=[('time', [('min', '>> import os >>> fname = os.tmpnam() >>> x.tofile(fname) Read the raw data from disk: >>> np.fromfile(fname, dtype=dt) array([((10, 0), 98.25)], dtype=[('time', [('min', '>> np.save(fname, x) >>> np.load(fname + '.npy') array([((10, 0), 98.25)], dtype=[('time', [('min', '>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int) array([[ True, False, False], [False, True, False], [False, False, True]], dtype=bool) >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int) array([[0, 1, 2], [1, 2, 3], [2, 3, 4]]) """ return any() def _fromiter(iterable, dtype, count): """fromiter(iterable, dtype, count=-1) Create a new 1-dimensional array from an iterable object. Parameters ---------- iterable : iterable object An iterable object providing data for the array. dtype : data-type The data-type of the returned array. count : int, optional The number of items to read from *iterable*. The default is -1, which means all data is read. Returns ------- out : ndarray The output array. Notes ----- Specify `count` to improve performance. It allows ``fromiter`` to pre-allocate the output array, instead of resizing it on demand. Examples -------- >>> iterable = (x*x for x in range(5)) >>> np.fromiter(iterable, np.float) array([ 0., 1., 4., 9., 16.])""" return ndarray() def _frompyfunc(func, nin, nout): """frompyfunc(func, nin, nout) Takes an arbitrary Python function and returns a Numpy ufunc. Can be used, for example, to add broadcasting to a built-in Python function (see Examples section). Parameters ---------- func : Python function object An arbitrary Python function. nin : int The number of input arguments. nout : int The number of objects returned by `func`. Returns ------- out : ufunc Returns a Numpy universal function (``ufunc``) object. Notes ----- The returned ufunc always returns PyObject arrays. Examples -------- Use frompyfunc to add broadcasting to the Python function ``oct``: >>> oct_array = np.frompyfunc(oct, 1, 1) >>> oct_array(np.array((10, 30, 100))) array([012, 036, 0144], dtype=object) >>> np.array((oct(10), oct(30), oct(100))) # for comparison array(['012', '036', '0144'], dtype='|S4')""" return ufunc() def _fromregex(file, regexp, dtype): """ Construct an array from a text file, using regular expression parsing. The returned array is always a structured array, and is constructed from all matches of the regular expression in the file. Groups in the regular expression are converted to fields of the structured array. Parameters ---------- file : str or file File name or file object to read. regexp : str or regexp Regular expression used to parse the file. Groups in the regular expression correspond to fields in the dtype. dtype : dtype or list of dtypes Dtype for the structured array. Returns ------- output : ndarray The output array, containing the part of the content of `file` that was matched by `regexp`. `output` is always a structured array. Raises ------ TypeError When `dtype` is not a valid dtype for a structured array. See Also -------- fromstring, loadtxt Notes ----- Dtypes for structured arrays can be specified in several forms, but all forms specify at least the data type and field name. For details see `doc.structured_arrays`. Examples -------- >>> f = open('test.dat', 'w') >>> f.write("1312 foo\n1534 bar\n444 qux") >>> f.close() >>> regexp = r"(\d+)\s+(...)" # match [digits, whitespace, anything] >>> output = np.fromregex('test.dat', regexp, ... [('num', np.int64), ('key', 'S3')]) >>> output array([(1312L, 'foo'), (1534L, 'bar'), (444L, 'qux')], dtype=[('num', '>> output['num'] array([1312, 1534, 444], dtype=int64) """ return ndarray() def _fromstring(string, dtype, count, sep): """fromstring(string, dtype=float, count=-1, sep='') A new 1-D array initialized from raw binary or text data in a string. Parameters ---------- string : str A string containing the data. dtype : data-type, optional The data type of the array; default: float. For binary input data, the data must be in exactly this format. count : int, optional Read this number of `dtype` elements from the data. If this is negative (the default), the count will be determined from the length of the data. sep : str, optional If not provided or, equivalently, the empty string, the data will be interpreted as binary data; otherwise, as ASCII text with decimal numbers. Also in this latter case, this argument is interpreted as the string separating numbers in the data; extra whitespace between elements is also ignored. Returns ------- arr : ndarray The constructed array. Raises ------ ValueError If the string is not the correct size to satisfy the requested `dtype` and `count`. See Also -------- frombuffer, fromfile, fromiter Examples -------- >>> np.fromstring('\x01\x02', dtype=np.uint8) array([1, 2], dtype=uint8) >>> np.fromstring('1 2', dtype=int, sep=' ') array([1, 2]) >>> np.fromstring('1, 2', dtype=int, sep=',') array([1, 2]) >>> np.fromstring('\x01\x02\x03\x04\x05', dtype=np.uint8, count=3) array([1, 2, 3], dtype=uint8)""" return ndarray() def full(shape, fill_value="C", dtype=None, order="C"): """ Return a new array of given shape and type, filled with `fill_value`. Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. fill_value : scalar Fill value. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is is chosen as `np.array(fill_value).dtype`. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. Returns ------- out : ndarray Array of `fill_value` with the given shape, dtype, and order. See Also -------- zeros_like : Return an array of zeros with shape and type of input. ones_like : Return an array of ones with shape and type of input. empty_like : Return an empty array with shape and type of input. full_like : Fill an array with shape and type of input. zeros : Return a new array setting values to zero. ones : Return a new array setting values to one. empty : Return a new uninitialized array. Examples -------- >>> np.full((2, 2), np.inf) array([[ inf, inf], [ inf, inf]]) >>> np.full((2, 2), 10, dtype=np.int) array([[10, 10], [10, 10]]) """ return ndarray() def full_like(a, fill_value=True, dtype=None, order="K", subok=True): """ Return a full array with the same shape and type as a given array. Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. fill_value : scalar Fill value. dtype : data-type, optional Overrides the data type of the result. order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. subok : bool, optional. If True, then the newly created array will use the sub-class type of 'a', otherwise it will be a base-class array. Defaults to True. Returns ------- out : ndarray Array of `fill_value` with the same shape and type as `a`. See Also -------- zeros_like : Return an array of zeros with shape and type of input. ones_like : Return an array of ones with shape and type of input. empty_like : Return an empty array with shape and type of input. zeros : Return a new array setting values to zero. ones : Return a new array setting values to one. empty : Return a new uninitialized array. full : Fill a new array. Examples -------- >>> x = np.arange(6, dtype=np.int) >>> np.full_like(x, 1) array([1, 1, 1, 1, 1, 1]) >>> np.full_like(x, 0.1) array([0, 0, 0, 0, 0, 0]) >>> np.full_like(x, 0.1, dtype=np.double) array([ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) >>> np.full_like(x, np.nan, dtype=np.double) array([ nan, nan, nan, nan, nan, nan]) >>> y = np.arange(6, dtype=np.double) >>> np.full_like(y, 0.1) array([ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) """ return ndarray() def fv(rate, nper, pmt, pv="end", when="end"): """ Compute the future value. Given: * a present value, `pv` * an interest `rate` compounded once per period, of which there are * `nper` total * a (fixed) payment, `pmt`, paid either * at the beginning (`when` = {'begin', 1}) or the end (`when` = {'end', 0}) of each period Return: the value at the end of the `nper` periods Parameters ---------- rate : scalar or array_like of shape(M, ) Rate of interest as decimal (not per cent) per period nper : scalar or array_like of shape(M, ) Number of compounding periods pmt : scalar or array_like of shape(M, ) Payment pv : scalar or array_like of shape(M, ) Present value when : {{'begin', 1}, {'end', 0}}, {string, int}, optional When payments are due ('begin' (1) or 'end' (0)). Defaults to {'end', 0}. Returns ------- out : ndarray Future values. If all input is scalar, returns a scalar float. If any input is array_like, returns future values for each input element. If multiple inputs are array_like, they all must have the same shape. Notes ----- The future value is computed by solving the equation:: fv + pv*(1+rate)**nper + pmt*(1 + rate*when)/rate*((1 + rate)**nper - 1) == 0 or, when ``rate == 0``:: fv + pv + pmt * nper == 0 References ---------- .. [WRW] Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May). Open Document Format for Office Applications (OpenDocument)v1.2, Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version, Pre-Draft 12. Organization for the Advancement of Structured Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula OpenDocument-formula-20090508.odt Examples -------- What is the future value after 10 years of saving $100 now, with an additional monthly savings of $100. Assume the interest rate is 5% (annually) compounded monthly? >>> np.fv(0.05/12, 10*12, -100, -100) 15692.928894335748 By convention, the negative sign represents cash flow out (i.e. money not available today). Thus, saving $100 a month at 5% annual interest leads to $15,692.93 available to spend in 10 years. If any input is array_like, returns an array of equal shape. Let's compare different interest rates from the example above. >>> a = np.array((0.05, 0.06, 0.07))/12 >>> np.fv(a, 10*12, -100, -100) array([ 15692.92889434, 16569.87435405, 17509.44688102]) """ return ndarray() class generic: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def gen_fromtxt(fname=True, dtype=typefloat(), comments="#", delimiter=None, skiprows=0, skip_header=0, skip_footer=0, converters=None, missing="", missing_values=None, filling_values=None, usecols=None, names=None, excludelist=None, deletechars=None, replace_space="_", autostrip=False, case_sensitive=True, defaultfmt="f%i", unpack=None, usemask=False, loose=True, invalid_raise=True): """ Load data from a text file, with missing values handled as specified. Each line past the first `skip_header` lines is split at the `delimiter` character, and characters following the `comments` character are discarded. Parameters ---------- fname : file or str File, filename, or generator to read. If the filename extension is `.gz` or `.bz2`, the file is first decompressed. Note that generators must return byte strings in Python 3k. dtype : dtype, optional Data type of the resulting array. If None, the dtypes will be determined by the contents of each column, individually. comments : str, optional The character used to indicate the start of a comment. All the characters occurring on a line after a comment are discarded delimiter : str, int, or sequence, optional The string used to separate values. By default, any consecutive whitespaces act as delimiter. An integer or sequence of integers can also be provided as width(s) of each field. skip_header : int, optional The numbers of lines to skip at the beginning of the file. skip_footer : int, optional The numbers of lines to skip at the end of the file converters : variable, optional The set of functions that convert the data of a column to a value. The converters can also be used to provide a default value for missing data: ``converters = {3: lambda s: float(s or 0)}``. missing_values : variable, optional The set of strings corresponding to missing data. filling_values : variable, optional The set of values to be used as default when the data are missing. usecols : sequence, optional Which columns to read, with 0 being the first. For example, ``usecols = (1, 4, 5)`` will extract the 2nd, 5th and 6th columns. names : {None, True, str, sequence}, optional If `names` is True, the field names are read from the first valid line after the first `skip_header` lines. If `names` is a sequence or a single-string of comma-separated names, the names will be used to define the field names in a structured dtype. If `names` is None, the names of the dtype fields will be used, if any. excludelist : sequence, optional A list of names to exclude. This list is appended to the default list ['return','file','print']. Excluded names are appended an underscore: for example, `file` would become `file_`. deletechars : str, optional A string combining invalid characters that must be deleted from the names. defaultfmt : str, optional A format used to define default field names, such as "f%i" or "f_%02i". autostrip : bool, optional Whether to automatically strip white spaces from the variables. replace_space : char, optional Character(s) used in replacement of white spaces in the variables names. By default, use a '_'. case_sensitive : {True, False, 'upper', 'lower'}, optional If True, field names are case sensitive. If False or 'upper', field names are converted to upper case. If 'lower', field names are converted to lower case. unpack : bool, optional If True, the returned array is transposed, so that arguments may be unpacked using ``x, y, z = loadtxt(...)`` usemask : bool, optional If True, return a masked array. If False, return a regular array. invalid_raise : bool, optional If True, an exception is raised if an inconsistency is detected in the number of columns. If False, a warning is emitted and the offending lines are skipped. Returns ------- out : ndarray Data read from the text file. If `usemask` is True, this is a masked array. See Also -------- numpy.loadtxt : equivalent function when no data is missing. Notes ----- * When spaces are used as delimiters, or when no delimiter has been given as input, there should not be any missing data between two fields. * When the variables are named (either by a flexible dtype or with `names`, there must not be any header in the file (else a ValueError exception is raised). * Individual values are not stripped of spaces by default. When using a custom converter, make sure the function does remove spaces. References ---------- .. [1] Numpy User Guide, section `I/O with Numpy `_. Examples --------- >>> from StringIO import StringIO >>> import numpy as np Comma delimited file with mixed dtype >>> s = StringIO("1,1.3,abcde") >>> data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'), ... ('mystring','S5')], delimiter=",") >>> data array((1, 1.3, 'abcde'), dtype=[('myint', '>> s.seek(0) # needed for StringIO example only >>> data = np.genfromtxt(s, dtype=None, ... names = ['myint','myfloat','mystring'], delimiter=",") >>> data array((1, 1.3, 'abcde'), dtype=[('myint', '>> s.seek(0) >>> data = np.genfromtxt(s, dtype="i8,f8,S5", ... names=['myint','myfloat','mystring'], delimiter=",") >>> data array((1, 1.3, 'abcde'), dtype=[('myint', '>> s = StringIO("11.3abcde") >>> data = np.genfromtxt(s, dtype=None, names=['intvar','fltvar','strvar'], ... delimiter=[1,3,5]) >>> data array((1, 1.3, 'abcde'), dtype=[('intvar', '>> buf = np.getbuffer(np.ones(5), 1, 3) >>> len(buf) 3 >>> buf[0] '\x00' >>> buf """ return buffer() def getbufsize(): """ Return the size of the buffer used in ufuncs. Returns ------- getbufsize : int Size of ufunc buffer in bytes. """ return None def geterr(): """ Get the current way of handling floating-point errors. Returns ------- res : dict A dictionary with keys "divide", "over", "under", and "invalid", whose values are from the strings "ignore", "print", "log", "warn", "raise", and "call". The keys represent possible floating-point exceptions, and the values define how these exceptions are handled. See Also -------- geterrcall, seterr, seterrcall Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> np.geterr() {'over': 'warn', 'divide': 'warn', 'invalid': 'warn', 'under': 'ignore'} >>> np.arange(3.) / np.arange(3.) array([ NaN, 1., 1.]) >>> oldsettings = np.seterr(all='warn', over='raise') >>> np.geterr() {'over': 'raise', 'divide': 'warn', 'invalid': 'warn', 'under': 'warn'} >>> np.arange(3.) / np.arange(3.) __main__:1: RuntimeWarning: invalid value encountered in divide array([ NaN, 1., 1.]) """ return None def geterrcall(): """ Return the current callback function used on floating-point errors. When the error handling for a floating-point error (one of "divide", "over", "under", or "invalid") is set to 'call' or 'log', the function that is called or the log instance that is written to is returned by `geterrcall`. This function or log instance has been set with `seterrcall`. Returns ------- errobj : callable, log instance or None The current error handler. If no handler was set through `seterrcall`, ``None`` is returned. See Also -------- seterrcall, seterr, geterr Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> np.geterrcall() # we did not yet set a handler, returns None >>> oldsettings = np.seterr(all='call') >>> def err_handler(type, flag): ... print "Floating point error (%s), with flag %s" % (type, flag) >>> oldhandler = np.seterrcall(err_handler) >>> np.array([1, 2, 3]) / 0.0 Floating point error (divide by zero), with flag 1 array([ Inf, Inf, Inf]) >>> cur_handler = np.geterrcall() >>> cur_handler is err_handler True """ return None def geterrobj(_): """geterrobj() Return the current object that defines floating-point error handling. The error object contains all information that defines the error handling behavior in Numpy. `geterrobj` is used internally by the other functions that get and set error handling behavior (`geterr`, `seterr`, `geterrcall`, `seterrcall`). Returns ------- errobj : list The error object, a list containing three elements: [internal numpy buffer size, error mask, error callback function]. The error mask is a single integer that holds the treatment information on all four floating point errors. The information for each error type is contained in three bits of the integer. If we print it in base 8, we can see what treatment is set for "invalid", "under", "over", and "divide" (in that order). The printed string can be interpreted with * 0 : 'ignore' * 1 : 'warn' * 2 : 'raise' * 3 : 'call' * 4 : 'print' * 5 : 'log' See Also -------- seterrobj, seterr, geterr, seterrcall, geterrcall getbufsize, setbufsize Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> np.geterrobj() # first get the defaults [10000, 0, None] >>> def err_handler(type, flag): ... print "Floating point error (%s), with flag %s" % (type, flag) ... >>> old_bufsize = np.setbufsize(20000) >>> old_err = np.seterr(divide='raise') >>> old_handler = np.seterrcall(err_handler) >>> np.geterrobj() [20000, 2, ] >>> old_err = np.seterr(all='ignore') >>> np.base_repr(np.geterrobj()[1], 8) '0' >>> old_err = np.seterr(divide='warn', over='log', under='call', invalid='print') >>> np.base_repr(np.geterrobj()[1], 8) '4351'""" return None def gradient(f, varargs): """ Return the gradient of an N-dimensional array. The gradient is computed using central differences in the interior and first differences at the boundaries. The returned gradient hence has the same shape as the input array. Parameters ---------- f : array_like An N-dimensional array containing samples of a scalar function. `*varargs` : scalars 0, 1, or N scalars specifying the sample distances in each direction, that is: `dx`, `dy`, `dz`, ... The default distance is 1. Returns ------- gradient : ndarray N arrays of the same shape as `f` giving the derivative of `f` with respect to each dimension. Examples -------- >>> x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float) >>> np.gradient(x) array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ]) >>> np.gradient(x, 2) array([ 0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ]) >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float)) [array([[ 2., 2., -1.], [ 2., 2., -1.]]), array([[ 1. , 2.5, 4. ], [ 1. , 1. , 1. ]])] """ return ndarray() def greater(x1, x2, out=None): """greater(x1, x2[, out]) Return the truth value of (x1 > x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). Returns ------- out : bool or ndarray of bool Array of bools, or a single bool if `x1` and `x2` are scalars. See Also -------- greater_equal, less, less_equal, equal, not_equal Examples -------- >>> np.greater([4,2],[2,2]) array([ True, False], dtype=bool) If the inputs are ndarrays, then np.greater is equivalent to '>'. >>> a = np.array([4,2]) >>> b = np.array([2,2]) >>> a > b array([ True, False], dtype=bool)""" return bool() if False else ndarray() def greater_equal(x1, x2, out=None): """greater_equal(x1, x2[, out]) Return the truth value of (x1 >= x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). Returns ------- out : bool or ndarray of bool Array of bools, or a single bool if `x1` and `x2` are scalars. See Also -------- greater, less, less_equal, equal, not_equal Examples -------- >>> np.greater_equal([4, 2, 1], [2, 2, 2]) array([ True, True, False], dtype=bool)""" return bool() if False else ndarray() class float16: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def hamming(M): """ Return the Hamming window. The Hamming window is a taper formed by using a weighted cosine. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, blackman, hanning, kaiser Notes ----- The Hamming window is defined as .. math:: w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1 The Hamming was named for R. W. Hamming, an associate of J. W. Tukey and is described in Blackman and Tukey. It was recommended for smoothing the truncated autocovariance function in the time domain. Most references to the Hamming window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 109-110. .. [3] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. Examples -------- >>> np.hamming(12) array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909, 0.15302337, 0.08 ]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.hamming(51) >>> plt.plot(window) [] >>> plt.title("Hamming window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Hamming window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() """ return ndarray() def hanning(M): """ Return the Hanning window. The Hanning window is a taper formed by using a weighted cosine. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray, shape(M,) The window, with the maximum value normalized to one (the value one appears only if `M` is odd). See Also -------- bartlett, blackman, hamming, kaiser Notes ----- The Hanning window is defined as .. math:: w(n) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1 The Hanning was named for Julius van Hann, an Austrian meterologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window. Most references to the Hanning window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 106-108. .. [3] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. Examples -------- >>> np.hanning(12) array([ 0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037, 0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249, 0.07937323, 0. ]) Plot the window and its frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.hanning(51) >>> plt.plot(window) [] >>> plt.title("Hann window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of the Hann window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() """ return ndarray() def histogram(a=None, bins=10, range=None, normed=False, weights=None, density=None): """ Compute the histogram of a set of data. Parameters ---------- a : array_like Input data. The histogram is computed over the flattened array. bins : int or sequence of scalars, optional If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default). If `bins` is a sequence, it defines the bin edges, including the rightmost edge, allowing for non-uniform bin widths. range : (float, float), optional The lower and upper range of the bins. If not provided, range is simply ``(a.min(), a.max())``. Values outside the range are ignored. normed : bool, optional This keyword is deprecated in Numpy 1.6 due to confusing/buggy behavior. It will be removed in Numpy 2.0. Use the density keyword instead. If False, the result will contain the number of samples in each bin. If True, the result is the value of the probability *density* function at the bin, normalized such that the *integral* over the range is 1. Note that this latter behavior is known to be buggy with unequal bin widths; use `density` instead. weights : array_like, optional An array of weights, of the same shape as `a`. Each value in `a` only contributes its associated weight towards the bin count (instead of 1). If `normed` is True, the weights are normalized, so that the integral of the density over the range remains 1 density : bool, optional If False, the result will contain the number of samples in each bin. If True, the result is the value of the probability *density* function at the bin, normalized such that the *integral* over the range is 1. Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability *mass* function. Overrides the `normed` keyword if given. Returns ------- hist : array The values of the histogram. See `normed` and `weights` for a description of the possible semantics. bin_edges : array of dtype float Return the bin edges ``(length(hist)+1)``. See Also -------- histogramdd, bincount, searchsorted, digitize Notes ----- All but the last (righthand-most) bin is half-open. In other words, if `bins` is:: [1, 2, 3, 4] then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which *includes* 4. Examples -------- >>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3]) (array([0, 2, 1]), array([0, 1, 2, 3])) >>> np.histogram(np.arange(4), bins=np.arange(5), density=True) (array([ 0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4])) >>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3]) (array([1, 4, 1]), array([0, 1, 2, 3])) >>> a = np.arange(5) >>> hist, bin_edges = np.histogram(a, density=True) >>> hist array([ 0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5]) >>> hist.sum() 2.4999999999999996 >>> np.sum(hist*np.diff(bin_edges)) 1.0 """ return array() def histogram2d(x, y=None, bins=10, range=None, normed=False, weights=None): """ Compute the bi-dimensional histogram of two data samples. Parameters ---------- x : array_like, shape (N,) An array containing the x coordinates of the points to be histogrammed. y : array_like, shape (N,) An array containing the y coordinates of the points to be histogrammed. bins : int or [int, int] or array_like or [array, array], optional The bin specification: * If int, the number of bins for the two dimensions (nx=ny=bins). * If [int, int], the number of bins in each dimension (nx, ny = bins). * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins). * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins). range : array_like, shape(2,2), optional The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins` parameters): ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range will be considered outliers and not tallied in the histogram. normed : bool, optional If False, returns the number of samples in each bin. If True, returns the bin density, i.e. the bin count divided by the bin area. weights : array_like, shape(N,), optional An array of values ``w_i`` weighing each sample ``(x_i, y_i)``. Weights are normalized to 1 if `normed` is True. If `normed` is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray, shape(nx, ny) The bi-dimensional histogram of samples `x` and `y`. Values in `x` are histogrammed along the first dimension and values in `y` are histogrammed along the second dimension. xedges : ndarray, shape(nx,) The bin edges along the first dimension. yedges : ndarray, shape(ny,) The bin edges along the second dimension. See Also -------- histogram : 1D histogram histogramdd : Multidimensional histogram Notes ----- When `normed` is True, then the returned histogram is the sample density, defined such that: .. math:: \sum_{i=0}^{nx-1} \sum_{j=0}^{ny-1} H_{i,j} \Delta x_i \Delta y_j = 1 where `H` is the histogram array and :math:`\Delta x_i \Delta y_i` the area of bin ``{i,j}``. Please note that the histogram does not follow the Cartesian convention where `x` values are on the abcissa and `y` values on the ordinate axis. Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y` along the second dimension of the array (horizontal). This ensures compatibility with `histogramdd`. Examples -------- >>> import matplotlib as mpl >>> import matplotlib.pyplot as plt Construct a 2D-histogram with variable bin width. First define the bin edges: >>> xedges = [0, 1, 1.5, 3, 5] >>> yedges = [0, 2, 3, 4, 6] Next we create a histogram H with random bin content: >>> x = np.random.normal(3, 1, 100) >>> y = np.random.normal(1, 1, 100) >>> H, xedges, yedges = np.histogram2d(y, x, bins=(xedges, yedges)) Or we fill the histogram H with a determined bin content: >>> H = np.ones((4, 4)).cumsum().reshape(4, 4) >>> print H[::-1] # This shows the bin content in the order as plotted [[ 13. 14. 15. 16.] [ 9. 10. 11. 12.] [ 5. 6. 7. 8.] [ 1. 2. 3. 4.]] Imshow can only do an equidistant representation of bins: >>> fig = plt.figure(figsize=(7, 3)) >>> ax = fig.add_subplot(131) >>> ax.set_title('imshow: equidistant') >>> im = plt.imshow(H, interpolation='nearest', origin='low', extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) pcolormesh can displaying exact bin edges: >>> ax = fig.add_subplot(132) >>> ax.set_title('pcolormesh: exact bin edges') >>> X, Y = np.meshgrid(xedges, yedges) >>> ax.pcolormesh(X, Y, H) >>> ax.set_aspect('equal') NonUniformImage displays exact bin edges with interpolation: >>> ax = fig.add_subplot(133) >>> ax.set_title('NonUniformImage: interpolated') >>> im = mpl.image.NonUniformImage(ax, interpolation='bilinear') >>> xcenters = xedges[:-1] + 0.5 * (xedges[1:] - xedges[:-1]) >>> ycenters = yedges[:-1] + 0.5 * (yedges[1:] - yedges[:-1]) >>> im.set_data(xcenters, ycenters, H) >>> ax.images.append(im) >>> ax.set_xlim(xedges[0], xedges[-1]) >>> ax.set_ylim(yedges[0], yedges[-1]) >>> ax.set_aspect('equal') >>> plt.show() """ return ndarray() def histogramdd(sample=None, bins=10, range=None, normed=False, weights=None): """ Compute the multidimensional histogram of some data. Parameters ---------- sample : array_like The data to be histogrammed. It must be an (N,D) array or data that can be converted to such. The rows of the resulting array are the coordinates of points in a D dimensional polytope. bins : sequence or int, optional The bin specification: * A sequence of arrays describing the bin edges along each dimension. * The number of bins for each dimension (nx, ny, ... =bins) * The number of bins for all dimensions (nx=ny=...=bins). range : sequence, optional A sequence of lower and upper bin edges to be used if the edges are not given explicitely in `bins`. Defaults to the minimum and maximum values along each dimension. normed : bool, optional If False, returns the number of samples in each bin. If True, returns the bin density, ie, the bin count divided by the bin hypervolume. weights : array_like (N,), optional An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`. Weights are normalized to 1 if normed is True. If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray The multidimensional histogram of sample x. See normed and weights for the different possible semantics. edges : list A list of D arrays describing the bin edges for each dimension. See Also -------- histogram: 1-D histogram histogram2d: 2-D histogram Examples -------- >>> r = np.random.randn(100,3) >>> H, edges = np.histogramdd(r, bins = (5, 8, 4)) >>> H.shape, edges[0].size, edges[1].size, edges[2].size ((5, 8, 4), 6, 9, 5) """ return ndarray() def hsplit(): """ Split an array into multiple sub-arrays horizontally (column-wise). Please refer to the `split` documentation. `hsplit` is equivalent to `split` with ``axis=1``, the array is always split along the second axis regardless of the array dimension. See Also -------- split : Split an array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(16.0).reshape(4, 4) >>> x array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 12., 13., 14., 15.]]) >>> np.hsplit(x, 2) [array([[ 0., 1.], [ 4., 5.], [ 8., 9.], [ 12., 13.]]), array([[ 2., 3.], [ 6., 7.], [ 10., 11.], [ 14., 15.]])] >>> np.hsplit(x, np.array([3, 6])) [array([[ 0., 1., 2.], [ 4., 5., 6.], [ 8., 9., 10.], [ 12., 13., 14.]]), array([[ 3.], [ 7.], [ 11.], [ 15.]]), array([], dtype=float64)] With a higher dimensional array the split is still along the second axis. >>> x = np.arange(8.0).reshape(2, 2, 2) >>> x array([[[ 0., 1.], [ 2., 3.]], [[ 4., 5.], [ 6., 7.]]]) >>> np.hsplit(x, 2) [array([[[ 0., 1.]], [[ 4., 5.]]]), array([[[ 2., 3.]], [[ 6., 7.]]])] """ return None def hstack(tup): """ Stack arrays in sequence horizontally (column wise). Take a sequence of arrays and stack them horizontally to make a single array. Rebuild arrays divided by `hsplit`. Parameters ---------- tup : sequence of ndarrays All arrays must have the same shape along all but the second axis. Returns ------- stacked : ndarray The array formed by stacking the given arrays. See Also -------- vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third axis). concatenate : Join a sequence of arrays together. hsplit : Split array along second axis. Notes ----- Equivalent to ``np.concatenate(tup, axis=1)`` Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.hstack((a,b)) array([1, 2, 3, 2, 3, 4]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.hstack((a,b)) array([[1, 2], [2, 3], [3, 4]]) """ return ndarray() def hypot(x1, x2, out=None): """hypot(x1, x2[, out]) Given the "legs" of a right triangle, return its hypotenuse. Equivalent to ``sqrt(x1**2 + x2**2)``, element-wise. If `x1` or `x2` is scalar_like (i.e., unambiguously cast-able to a scalar type), it is broadcast for use with each element of the other argument. (See Examples) Parameters ---------- x1, x2 : array_like Leg of the triangle(s). out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- z : ndarray The hypotenuse of the triangle(s). Examples -------- >>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3))) array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]]) Example showing broadcast of scalar_like argument: >>> np.hypot(3*np.ones((3, 3)), [4]) array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]])""" return ndarray() def i0(x): """ Modified Bessel function of the first kind, order 0. Usually denoted :math:`I_0`. This function does broadcast, but will *not* "up-cast" int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below). Parameters ---------- x : array_like, dtype float or complex Argument of the Bessel function. Returns ------- out : ndarray, shape = x.shape, dtype = x.dtype The modified Bessel function evaluated at each of the elements of `x`. Raises ------ TypeError: array cannot be safely cast to required type If argument consists exclusively of int dtypes. See Also -------- scipy.special.iv, scipy.special.ive Notes ----- We use the algorithm published by Clenshaw [1]_ and referenced by Abramowitz and Stegun [2]_, for which the function domain is partitioned into the two intervals [0,8] and (8,inf), and Chebyshev polynomial expansions are employed in each interval. Relative error on the domain [0,30] using IEEE arithmetic is documented [3]_ as having a peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000). References ---------- .. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in *National Physical Laboratory Mathematical Tables*, vol. 5, London: Her Majesty's Stationery Office, 1962. .. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 379. http://www.math.sfu.ca/~cbm/aands/page_379.htm .. [3] http://kobesearch.cpan.org/htdocs/Math-Cephes/Math/Cephes.html Examples -------- >>> np.i0([0.]) array(1.0) >>> np.i0([0., 1. + 2j]) array([ 1.00000000+0.j , 0.18785373+0.64616944j]) """ return ndarray() def identity(n=None, dtype=None): """ Return the identity array. The identity array is a square array with ones on the main diagonal. Parameters ---------- n : int Number of rows (and columns) in `n` x `n` output. dtype : data-type, optional Data-type of the output. Defaults to ``float``. Returns ------- out : ndarray `n` x `n` array with its main diagonal set to one, and all other elements 0. Examples -------- >>> np.identity(3) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) """ return ndarray() class iinfo: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() _max_vals = dict() _min_vals = dict() max = property() min = property() def imag(val): """ Return the imaginary part of the elements of the array. Parameters ---------- val : array_like Input array. Returns ------- out : ndarray Output array. If `val` is real, the type of `val` is used for the output. If `val` has complex elements, the returned type is float. See Also -------- real, angle, real_if_close Examples -------- >>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.imag array([ 2., 4., 6.]) >>> a.imag = np.array([8, 10, 12]) >>> a array([ 1. +8.j, 3.+10.j, 5.+12.j]) """ return ndarray() def in1d(ar1, ar2=False, assume_unique=False, invert=False): """ Test whether each element of a 1-D array is also present in a second array. Returns a boolean array the same length as `ar1` that is True where an element of `ar1` is in `ar2` and False otherwise. Parameters ---------- ar1 : (M,) array_like Input array. ar2 : array_like The values against which to test each value of `ar1`. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted (that is, False where an element of `ar1` is in `ar2` and True otherwise). Default is False. ``np.in1d(a, b, invert=True)`` is equivalent to (but is faster than) ``np.invert(in1d(a, b))``. .. versionadded:: 1.8.0 Returns ------- in1d : (M,) ndarray, bool The values `ar1[in1d]` are in `ar2`. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Notes ----- `in1d` can be considered as an element-wise function version of the python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly equivalent to ``np.array([item in b for item in a])``. .. versionadded:: 1.4.0 Examples -------- >>> test = np.array([0, 1, 2, 5, 0]) >>> states = [0, 2] >>> mask = np.in1d(test, states) >>> mask array([ True, False, True, False, True], dtype=bool) >>> test[mask] array([0, 2, 0]) >>> mask = np.in1d(test, states, invert=True) >>> mask array([False, True, False, True, False], dtype=bool) >>> test[mask] array([1, 5]) """ return M() index_exp = IndexExpression() def indices(dimensions=typeint(), dtype=typeint()): """ Return an array representing the indices of a grid. Compute an array where the subarrays contain index values 0,1,... varying only along the corresponding axis. Parameters ---------- dimensions : sequence of ints The shape of the grid. dtype : dtype, optional Data type of the result. Returns ------- grid : ndarray The array of grid indices, ``grid.shape = (len(dimensions),) + tuple(dimensions)``. See Also -------- mgrid, meshgrid Notes ----- The output shape is obtained by prepending the number of dimensions in front of the tuple of dimensions, i.e. if `dimensions` is a tuple ``(r0, ..., rN-1)`` of length ``N``, the output shape is ``(N,r0,...,rN-1)``. The subarrays ``grid[k]`` contains the N-D array of indices along the ``k-th`` axis. Explicitly:: grid[k,i0,i1,...,iN-1] = ik Examples -------- >>> grid = np.indices((2, 3)) >>> grid.shape (2, 2, 3) >>> grid[0] # row indices array([[0, 0, 0], [1, 1, 1]]) >>> grid[1] # column indices array([[0, 1, 2], [0, 1, 2]]) The indices can be used as an index into an array. >>> x = np.arange(20).reshape(5, 4) >>> row, col = np.indices((2, 3)) >>> x[row, col] array([[0, 1, 2], [4, 5, 6]]) Note that it would be more straightforward in the above example to extract the required elements directly with ``x[:2, :3]``. """ return ndarray() class inexact: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() inf = float() def info(object=None, maxwidth=76, output="", toplevel="numpy"): """ Get help information for a function, class, or module. Parameters ---------- object : object or str, optional Input object or name to get information about. If `object` is a numpy object, its docstring is given. If it is a string, available modules are searched for matching objects. If None, information about `info` itself is returned. maxwidth : int, optional Printing width. output : file like object, optional File like object that the output is written to, default is ``stdout``. The object has to be opened in 'w' or 'a' mode. toplevel : str, optional Start search at this level. See Also -------- source, lookfor Notes ----- When used interactively with an object, ``np.info(obj)`` is equivalent to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython prompt. Examples -------- >>> np.info(np.polyval) # doctest: +SKIP polyval(p, x) Evaluate the polynomial p at x. ... When using a string for `object` it is possible to get multiple results. >>> np.info('fft') # doctest: +SKIP *** Found in numpy *** Core FFT routines ... *** Found in numpy.fft *** fft(a, n=None, axis=-1) ... *** Repeat reference found in numpy.fft.fftpack *** *** Total of 3 references found. *** """ return None infty = float() def inner(a, b): """inner(a, b) Inner product of two arrays. Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes. Parameters ---------- a, b : array_like If `a` and `b` are nonscalar, their last dimensions of must match. Returns ------- out : ndarray `out.shape = a.shape[:-1] + b.shape[:-1]` Raises ------ ValueError If the last dimension of `a` and `b` has different size. See Also -------- tensordot : Sum products over arbitrary axes. dot : Generalised matrix product, using second last dimension of `b`. einsum : Einstein summation convention. Notes ----- For vectors (1-D arrays) it computes the ordinary inner-product:: np.inner(a, b) = sum(a[:]*b[:]) More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`:: np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1)) or explicitly:: np.inner(a, b)[i0,...,ir-1,j0,...,js-1] = sum(a[i0,...,ir-1,:]*b[j0,...,js-1,:]) In addition `a` or `b` may be scalars, in which case:: np.inner(a,b) = a*b Examples -------- Ordinary inner product for vectors: >>> a = np.array([1,2,3]) >>> b = np.array([0,1,0]) >>> np.inner(a, b) 2 A multidimensional example: >>> a = np.arange(24).reshape((2,3,4)) >>> b = np.arange(4) >>> np.inner(a, b) array([[ 14, 38, 62], [ 86, 110, 134]]) An example where `b` is a scalar: >>> np.inner(np.eye(2), 7) array([[ 7., 0.], [ 0., 7.]])""" return ndarray() def insert(arr, obj, values=None, axis=None): """ Insert values along the given axis before the given indices. Parameters ---------- arr : array_like Input array. obj : int, slice or sequence of ints Object that defines the index or indices before which `values` is inserted. .. versionadded:: 1.8.0 Support for multiple insertions when `obj` is a single scalar or a sequence with one element (similar to calling insert multiple times). values : array_like Values to insert into `arr`. If the type of `values` is different from that of `arr`, `values` is converted to the type of `arr`. `values` should be shaped so that ``arr[...,obj,...] = values`` is legal. axis : int, optional Axis along which to insert `values`. If `axis` is None then `arr` is flattened first. Returns ------- out : ndarray A copy of `arr` with `values` inserted. Note that `insert` does not occur in-place: a new array is returned. If `axis` is None, `out` is a flattened array. See Also -------- append : Append elements at the end of an array. concatenate : Join a sequence of arrays together. delete : Delete elements from an array. Notes ----- Note that for higher dimensional inserts `obj=0` behaves very different from `obj=[0]` just like `arr[:,0,:] = values` is different from `arr[:,[0],:] = values`. Examples -------- >>> a = np.array([[1, 1], [2, 2], [3, 3]]) >>> a array([[1, 1], [2, 2], [3, 3]]) >>> np.insert(a, 1, 5) array([1, 5, 1, 2, 2, 3, 3]) >>> np.insert(a, 1, 5, axis=1) array([[1, 5, 1], [2, 5, 2], [3, 5, 3]]) Difference between sequence and scalars: >>> np.insert(a, [1], [[1],[2],[3]], axis=1) array([[1, 1, 1], [2, 2, 2], [3, 3, 3]]) >>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1), ... np.insert(a, [1], [[1],[2],[3]], axis=1)) True >>> b = a.flatten() >>> b array([1, 1, 2, 2, 3, 3]) >>> np.insert(b, [2, 2], [5, 6]) array([1, 1, 5, 6, 2, 2, 3, 3]) >>> np.insert(b, slice(2, 4), [5, 6]) array([1, 1, 5, 2, 6, 2, 3, 3]) >>> np.insert(b, [2, 2], [7.13, False]) # type casting array([1, 1, 7, 0, 2, 2, 3, 3]) >>> x = np.arange(8).reshape(2, 4) >>> idx = (1, 3) >>> np.insert(x, idx, 999, axis=1) array([[ 0, 999, 1, 2, 999, 3], [ 4, 999, 5, 6, 999, 7]]) """ return ndarray() class int: __doc__ = str() def bit_length(self, _): """int.bit_length() -> int Number of bits necessary to represent self in binary. >>> bin(37) '0b100101' >>> (37).bit_length() 6""" return None def conjugate(self, _): """Returns self, the complex conjugate of any int.""" return None denominator = getset_descriptor() imag = getset_descriptor() numerator = getset_descriptor() real = getset_descriptor() class int64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def bit_length(self, _): """int.bit_length() -> int Number of bits necessary to represent self in binary. >>> bin(37) '0b100101' >>> (37).bit_length() 6""" return None def conj(self, _): """None""" return None data = getset_descriptor() denominator = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() numerator = getset_descriptor() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class int16: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class int32: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class int64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def bit_length(self, _): """int.bit_length() -> int Number of bits necessary to represent self in binary. >>> bin(37) '0b100101' >>> (37).bit_length() 6""" return None def conj(self, _): """None""" return None data = getset_descriptor() denominator = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() numerator = getset_descriptor() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class int8: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class int64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def bit_length(self, _): """int.bit_length() -> int Number of bits necessary to represent self in binary. >>> bin(37) '0b100101' >>> (37).bit_length() 6""" return None def conj(self, _): """None""" return None data = getset_descriptor() denominator = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() numerator = getset_descriptor() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def int_asbuffer(): """None""" return None class int32: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class integer: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def interp(x, xp, fp=None, left=None, right=None): """ One-dimensional linear interpolation. Returns the one-dimensional piecewise linear interpolant to a function with given values at discrete data-points. Parameters ---------- x : array_like The x-coordinates of the interpolated values. xp : 1-D sequence of floats The x-coordinates of the data points, must be increasing. fp : 1-D sequence of floats The y-coordinates of the data points, same length as `xp`. left : float, optional Value to return for `x < xp[0]`, default is `fp[0]`. right : float, optional Value to return for `x > xp[-1]`, defaults is `fp[-1]`. Returns ------- y : {float, ndarray} The interpolated values, same shape as `x`. Raises ------ ValueError If `xp` and `fp` have different length Notes ----- Does not check that the x-coordinate sequence `xp` is increasing. If `xp` is not increasing, the results are nonsense. A simple check for increasingness is:: np.all(np.diff(xp) > 0) Examples -------- >>> xp = [1, 2, 3] >>> fp = [3, 2, 0] >>> np.interp(2.5, xp, fp) 1.0 >>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp) array([ 3. , 3. , 2.5 , 0.56, 0. ]) >>> UNDEF = -99.0 >>> np.interp(3.14, xp, fp, right=UNDEF) -99.0 Plot an interpolant to the sine function: >>> x = np.linspace(0, 2*np.pi, 10) >>> y = np.sin(x) >>> xvals = np.linspace(0, 2*np.pi, 50) >>> yinterp = np.interp(xvals, x, y) >>> import matplotlib.pyplot as plt >>> plt.plot(x, y, 'o') [] >>> plt.plot(xvals, yinterp, '-x') [] >>> plt.show() """ return float() def intersect1d(ar1, ar2=False, assume_unique=False): """ Find the intersection of two arrays. Return the sorted, unique values that are in both of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- intersect1d : ndarray Sorted 1D array of common and unique elements. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1]) array([1, 3]) """ return ndarray() class int64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def bit_length(self, _): """int.bit_length() -> int Number of bits necessary to represent self in binary. >>> bin(37) '0b100101' >>> (37).bit_length() 6""" return None def conj(self, _): """None""" return None data = getset_descriptor() denominator = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() numerator = getset_descriptor() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def invert(x, out=None): """invert(x[, out]) Compute bit-wise inversion, or bit-wise NOT, element-wise. Computes the bit-wise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``~``. For signed integer inputs, the two's complement is returned. In a two's-complement system negative numbers are represented by the two's complement of the absolute value. This is the most common method of representing signed integers on computers [1]_. A N-bit two's-complement system can represent every integer in the range :math:`-2^{N-1}` to :math:`+2^{N-1}-1`. Parameters ---------- x1 : array_like Only integer types are handled (including booleans). Returns ------- out : array_like Result. See Also -------- bitwise_and, bitwise_or, bitwise_xor logical_not binary_repr : Return the binary representation of the input number as a string. Notes ----- `bitwise_not` is an alias for `invert`: >>> np.bitwise_not is np.invert True References ---------- .. [1] Wikipedia, "Two's complement", http://en.wikipedia.org/wiki/Two's_complement Examples -------- We've seen that 13 is represented by ``00001101``. The invert or bit-wise NOT of 13 is then: >>> np.invert(np.array([13], dtype=uint8)) array([242], dtype=uint8) >>> np.binary_repr(x, width=8) '00001101' >>> np.binary_repr(242, width=8) '11110010' The result depends on the bit-width: >>> np.invert(np.array([13], dtype=uint16)) array([65522], dtype=uint16) >>> np.binary_repr(x, width=16) '0000000000001101' >>> np.binary_repr(65522, width=16) '1111111111110010' When using signed integer types the result is the two's complement of the result for the unsigned type: >>> np.invert(np.array([13], dtype=int8)) array([-14], dtype=int8) >>> np.binary_repr(-14, width=8) '11110010' Booleans are accepted as well: >>> np.invert(array([True, False])) array([False, True], dtype=bool)""" return ndarray() def ipmt(rate, per, nper, pv="end", fv=0.0, when="end"): """ Compute the interest portion of a payment. Parameters ---------- rate : scalar or array_like of shape(M, ) Rate of interest as decimal (not per cent) per period per : scalar or array_like of shape(M, ) Interest paid against the loan changes during the life or the loan. The `per` is the payment period to calculate the interest amount. nper : scalar or array_like of shape(M, ) Number of compounding periods pv : scalar or array_like of shape(M, ) Present value fv : scalar or array_like of shape(M, ), optional Future value when : {{'begin', 1}, {'end', 0}}, {string, int}, optional When payments are due ('begin' (1) or 'end' (0)). Defaults to {'end', 0}. Returns ------- out : ndarray Interest portion of payment. If all input is scalar, returns a scalar float. If any input is array_like, returns interest payment for each input element. If multiple inputs are array_like, they all must have the same shape. See Also -------- ppmt, pmt, pv Notes ----- The total payment is made up of payment against principal plus interest. ``pmt = ppmt + ipmt`` Examples -------- What is the amortization schedule for a 1 year loan of $2500 at 8.24% interest per year compounded monthly? >>> principal = 2500.00 The 'per' variable represents the periods of the loan. Remember that financial equations start the period count at 1! >>> per = np.arange(1*12) + 1 >>> ipmt = np.ipmt(0.0824/12, per, 1*12, principal) >>> ppmt = np.ppmt(0.0824/12, per, 1*12, principal) Each element of the sum of the 'ipmt' and 'ppmt' arrays should equal 'pmt'. >>> pmt = np.pmt(0.0824/12, 1*12, principal) >>> np.allclose(ipmt + ppmt, pmt) True >>> fmt = '{0:2d} {1:8.2f} {2:8.2f} {3:8.2f}' >>> for payment in per: ... index = payment - 1 ... principal = principal + ppmt[index] ... print fmt.format(payment, ppmt[index], ipmt[index], principal) 1 -200.58 -17.17 2299.42 2 -201.96 -15.79 2097.46 3 -203.35 -14.40 1894.11 4 -204.74 -13.01 1689.37 5 -206.15 -11.60 1483.22 6 -207.56 -10.18 1275.66 7 -208.99 -8.76 1066.67 8 -210.42 -7.32 856.25 9 -211.87 -5.88 644.38 10 -213.32 -4.42 431.05 11 -214.79 -2.96 216.26 12 -216.26 -1.49 -0.00 >>> interestpd = np.sum(ipmt) >>> np.round(interestpd, 2) -112.98 """ return ndarray() def irr(values): """ Return the Internal Rate of Return (IRR). This is the "average" periodically compounded rate of return that gives a net present value of 0.0; for a more complete explanation, see Notes below. Parameters ---------- values : array_like, shape(N,) Input cash flows per time period. By convention, net "deposits" are negative and net "withdrawals" are positive. Thus, for example, at least the first element of `values`, which represents the initial investment, will typically be negative. Returns ------- out : float Internal Rate of Return for periodic input values. Notes ----- The IRR is perhaps best understood through an example (illustrated using np.irr in the Examples section below). Suppose one invests 100 units and then makes the following withdrawals at regular (fixed) intervals: 39, 59, 55, 20. Assuming the ending value is 0, one's 100 unit investment yields 173 units; however, due to the combination of compounding and the periodic withdrawals, the "average" rate of return is neither simply 0.73/4 nor (1.73)^0.25-1. Rather, it is the solution (for :math:`r`) of the equation: .. math:: -100 + \frac{39}{1+r} + \frac{59}{(1+r)^2} + \frac{55}{(1+r)^3} + \frac{20}{(1+r)^4} = 0 In general, for `values` :math:`= [v_0, v_1, ... v_M]`, irr is the solution of the equation: [G]_ .. math:: \sum_{t=0}^M{\frac{v_t}{(1+irr)^{t}}} = 0 References ---------- .. [G] L. J. Gitman, "Principles of Managerial Finance, Brief," 3rd ed., Addison-Wesley, 2003, pg. 348. Examples -------- >>> print round(np.irr([-100, 39, 59, 55, 20]), 5) 0.28095 (Compare with the Example given for numpy.lib.financial.npv) """ return float() def is_busday(dates, weekmask, holidays, busdaycal, out): """is_busday(dates, weekmask='1111100', holidays=None, busdaycal=None, out=None) Calculates which of the given dates are valid days, and which are not. .. versionadded:: 1.7.0 Parameters ---------- dates : array_like of datetime64[D] The array of dates to process. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of bool, optional If provided, this array is filled with the result. Returns ------- out : array of bool An array with the same shape as ``dates``, containing True for each valid day, and False for each invalid day. See Also -------- busdaycalendar: An object that specifies a custom set of valid days. busday_offset : Applies an offset counted in valid days. busday_count : Counts how many valid days are in a half-open date range. Examples -------- >>> # The weekdays are Friday, Saturday, and Monday ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'], ... holidays=['2011-07-01', '2011-07-04', '2011-07-17']) array([False, False, True], dtype='bool')""" return array() def isclose(a, b=False, rtol=1e-05, atol=1e-08, equal_nan=False): """ Returns a boolean array where two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolute difference between `a` and `b`. Parameters ---------- a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). equal_nan : bool Whether to compare NaN's as equal. If True, NaN's in `a` will be considered equal to NaN's in `b` in the output array. Returns ------- y : array_like Returns a boolean array of where `a` and `b` are equal within the given tolerance. If both `a` and `b` are scalars, returns a single boolean value. See Also -------- allclose Notes ----- .. versionadded:: 1.7.0 For finite values, isclose uses the following equation to test whether two floating point values are equivalent. absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`)) The above equation is not symmetric in `a` and `b`, so that `isclose(a, b)` might be different from `isclose(b, a)` in some rare cases. Examples -------- >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8]) array([True, False]) >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9]) array([True, True]) >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9]) array([False, True]) >>> np.isclose([1.0, np.nan], [1.0, np.nan]) array([True, False]) >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) array([True, True]) """ return ndarray() def iscomplex(x): """ Returns a bool array, where True if input element is complex. What is tested is whether the input has a non-zero imaginary part, not if the input type is complex. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray of bools Output array. See Also -------- isreal iscomplexobj : Return True if x is a complex type or an array of complex numbers. Examples -------- >>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j]) array([ True, False, False, False, False, True], dtype=bool) """ return ndarray() def iscomplexobj(x): """ Check for a complex type or an array of complex numbers. The type of the input is checked, not the value. Even if the input has an imaginary part equal to zero, `iscomplexobj` evaluates to True. Parameters ---------- x : any The input can be of any type and shape. Returns ------- iscomplexobj : bool The return value, True if `x` is of a complex type or has at least one complex element. See Also -------- isrealobj, iscomplex Examples -------- >>> np.iscomplexobj(1) False >>> np.iscomplexobj(1+0j) True >>> np.iscomplexobj([3, 1+0j, True]) True """ return bool() def isfinite(x, out): """isfinite(x[, out]) Test element-wise for finite-ness (not infinity or not Not a Number). The result is returned as a boolean array. Parameters ---------- x : array_like Input values. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See `doc.ufuncs`. Returns ------- y : ndarray, bool For scalar input, the result is a new boolean with value True if the input is finite; otherwise the value is False (input is either positive infinity, negative infinity or Not a Number). For array input, the result is a boolean array with the same dimensions as the input and the values are True if the corresponding element of the input is finite; otherwise the values are False (element is either positive infinity, negative infinity or Not a Number). See Also -------- isinf, isneginf, isposinf, isnan Notes ----- Not a Number, positive infinity and negative infinity are considered to be non-finite. Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. Errors result if the second argument is also supplied when `x` is a scalar input, or if first and second arguments have different shapes. Examples -------- >>> np.isfinite(1) True >>> np.isfinite(0) True >>> np.isfinite(np.nan) False >>> np.isfinite(np.inf) False >>> np.isfinite(np.NINF) False >>> np.isfinite([np.log(-1.),1.,np.log(0)]) array([False, True, False], dtype=bool) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isfinite(x, y) array([0, 1, 0]) >>> y array([0, 1, 0])""" return ndarray() def isfortran(a): """ Returns True if array is arranged in Fortran-order in memory and not C-order. Parameters ---------- a : ndarray Input array. Examples -------- np.array allows to specify whether the array is written in C-contiguous order (last index varies the fastest), or FORTRAN-contiguous order in memory (first index varies the fastest). >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(a) False >>> b = np.array([[1, 2, 3], [4, 5, 6]], order='FORTRAN') >>> b array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(b) True The transpose of a C-ordered array is a FORTRAN-ordered array. >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(a) False >>> b = a.T >>> b array([[1, 4], [2, 5], [3, 6]]) >>> np.isfortran(b) True C-ordered arrays evaluate as False even if they are also FORTRAN-ordered. >>> np.isfortran(np.array([1, 2], order='FORTRAN')) False """ return bool() def isinf(x, out): """isinf(x[, out]) Test element-wise for positive or negative infinity. Return a bool-type array, the same shape as `x`, True where ``x == +/-inf``, False everywhere else. Parameters ---------- x : array_like Input values out : array_like, optional An array with the same shape as `x` to store the result. Returns ------- y : bool (scalar) or bool-type ndarray For scalar input, the result is a new boolean with value True if the input is positive or negative infinity; otherwise the value is False. For array input, the result is a boolean array with the same shape as the input and the values are True where the corresponding element of the input is positive or negative infinity; elsewhere the values are False. If a second argument was supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True, respectively. The return value `y` is then a reference to that array. See Also -------- isneginf, isposinf, isnan, isfinite Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Errors result if the second argument is supplied when the first argument is a scalar, or if the first and second arguments have different shapes. Examples -------- >>> np.isinf(np.inf) True >>> np.isinf(np.nan) False >>> np.isinf(np.NINF) True >>> np.isinf([np.inf, -np.inf, 1.0, np.nan]) array([ True, True, False, False], dtype=bool) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isinf(x, y) array([1, 0, 1]) >>> y array([1, 0, 1])""" return bool() if False else bool_type() def isnan(x, out=None): """isnan(x[, out]) Test element-wise for Not a Number (NaN), return result as a bool array. Parameters ---------- x : array_like Input array. Returns ------- y : {ndarray, bool} For scalar input, the result is a new boolean with value True if the input is NaN; otherwise the value is False. For array input, the result is a boolean array with the same dimensions as the input and the values are True if the corresponding element of the input is NaN; otherwise the values are False. See Also -------- isinf, isneginf, isposinf, isfinite Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Examples -------- >>> np.isnan(np.nan) True >>> np.isnan(np.inf) False >>> np.isnan([np.log(-1.),1.,np.log(0)]) array([ True, False, False], dtype=bool)""" return ndarray() def isneginf(x=None, y=None): """ Test element-wise for negative infinity, return result as bool array. Parameters ---------- x : array_like The input array. y : array_like, optional A boolean array with the same shape and type as `x` to store the result. Returns ------- y : ndarray A boolean array with the same dimensions as the input. If second argument is not supplied then a numpy boolean array is returned with values True where the corresponding element of the input is negative infinity and values False where the element of the input is not negative infinity. If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value `y` is then a reference to that array. See Also -------- isinf, isposinf, isnan, isfinite Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Errors result if the second argument is also supplied when x is a scalar input, or if first and second arguments have different shapes. Examples -------- >>> np.isneginf(np.NINF) array(True, dtype=bool) >>> np.isneginf(np.inf) array(False, dtype=bool) >>> np.isneginf(np.PINF) array(False, dtype=bool) >>> np.isneginf([-np.inf, 0., np.inf]) array([ True, False, False], dtype=bool) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isneginf(x, y) array([1, 0, 0]) >>> y array([1, 0, 0]) """ return ndarray() def isposinf(x=None, y=None): """ Test element-wise for positive infinity, return result as bool array. Parameters ---------- x : array_like The input array. y : array_like, optional A boolean array with the same shape as `x` to store the result. Returns ------- y : ndarray A boolean array with the same dimensions as the input. If second argument is not supplied then a boolean array is returned with values True where the corresponding element of the input is positive infinity and values False where the element of the input is not positive infinity. If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value `y` is then a reference to that array. See Also -------- isinf, isneginf, isfinite, isnan Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Errors result if the second argument is also supplied when `x` is a scalar input, or if first and second arguments have different shapes. Examples -------- >>> np.isposinf(np.PINF) array(True, dtype=bool) >>> np.isposinf(np.inf) array(True, dtype=bool) >>> np.isposinf(np.NINF) array(False, dtype=bool) >>> np.isposinf([-np.inf, 0., np.inf]) array([False, False, True], dtype=bool) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isposinf(x, y) array([0, 0, 1]) >>> y array([0, 0, 1]) """ return ndarray() def isreal(x): """ Returns a bool array, where True if input element is real. If element has complex type with zero complex part, the return value for that element is True. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray, bool Boolean array of same shape as `x`. See Also -------- iscomplex isrealobj : Return True if x is not a complex type. Examples -------- >>> np.isreal([1+1j, 1+0j, 4.5, 3, 2, 2j]) array([False, True, True, True, True, False], dtype=bool) """ return ndarray() def isrealobj(x): """ Return True if x is a not complex type or an array of complex numbers. The type of the input is checked, not the value. So even if the input has an imaginary part equal to zero, `isrealobj` evaluates to False if the data type is complex. Parameters ---------- x : any The input can be of any type and shape. Returns ------- y : bool The return value, False if `x` is of a complex type. See Also -------- iscomplexobj, isreal Examples -------- >>> np.isrealobj(1) True >>> np.isrealobj(1+0j) False >>> np.isrealobj([3, 1+0j, True]) False """ return bool() def isscalar(num): """ Returns True if the type of `num` is a scalar type. Parameters ---------- num : any Input argument, can be of any type and shape. Returns ------- val : bool True if `num` is a scalar type, False if it is not. Examples -------- >>> np.isscalar(3.1) True >>> np.isscalar([3.1]) False >>> np.isscalar(False) True """ return bool() def issctype(rep): """ Determines whether the given object represents a scalar data-type. Parameters ---------- rep : any If `rep` is an instance of a scalar dtype, True is returned. If not, False is returned. Returns ------- out : bool Boolean result of check whether `rep` is a scalar dtype. See Also -------- issubsctype, issubdtype, obj2sctype, sctype2char Examples -------- >>> np.issctype(np.int32) True >>> np.issctype(list) False >>> np.issctype(1.1) False Strings are also a scalar type: >>> np.issctype(np.dtype('str')) True """ return bool() def issub_class_(arg1, arg2): """ Determine if a class is a subclass of a second class. `issubclass_` is equivalent to the Python built-in ``issubclass``, except that it returns False instead of raising a TypeError is one of the arguments is not a class. Parameters ---------- arg1 : class Input class. True is returned if `arg1` is a subclass of `arg2`. arg2 : class or tuple of classes. Input class. If a tuple of classes, True is returned if `arg1` is a subclass of any of the tuple elements. Returns ------- out : bool Whether `arg1` is a subclass of `arg2` or not. See Also -------- issubsctype, issubdtype, issctype Examples -------- >>> np.issubclass_(np.int32, np.int) True >>> np.issubclass_(np.int32, np.float) False """ return bool() def issubdtype(arg1arg2): """ Returns True if first argument is a typecode lower/equal in type hierarchy. Parameters ---------- arg1, arg2 : dtype_like dtype or string representing a typecode. Returns ------- out : bool See Also -------- issubsctype, issubclass_ numpy.core.numerictypes : Overview of numpy type hierarchy. Examples -------- >>> np.issubdtype('S1', str) True >>> np.issubdtype(np.float64, np.float32) False """ return bool() def issubsctype(arg1arg2): """ Determine if the first argument is a subclass of the second argument. Parameters ---------- arg1, arg2 : dtype or dtype specifier Data-types. Returns ------- out : bool The result. See Also -------- issctype, issubdtype,obj2sctype Examples -------- >>> np.issubsctype('S8', str) True >>> np.issubsctype(np.array([1]), np.int) True >>> np.issubsctype(np.array([1]), np.float) False """ return bool() def iterable(y): """ Check whether or not an object can be iterated over. Parameters ---------- y : object Input object. Returns ------- b : {0, 1} Return 1 if the object has an iterator method or is a sequence, and 0 otherwise. Examples -------- >>> np.iterable([1, 2, 3]) 1 >>> np.iterable(2) 0 """ return _0() def ix_(): """ Construct an open mesh from multiple sequences. This function takes N 1-D sequences and returns N outputs with N dimensions each, such that the shape is 1 in all but one dimension and the dimension with the non-unit shape value cycles through all N dimensions. Using `ix_` one can quickly construct index arrays that will index the cross product. ``a[np.ix_([1,3],[2,5])]`` returns the array ``[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]``. Parameters ---------- args : 1-D sequences Returns ------- out : tuple of ndarrays N arrays with N dimensions each, with N the number of input sequences. Together these arrays form an open mesh. See Also -------- ogrid, mgrid, meshgrid Examples -------- >>> a = np.arange(10).reshape(2, 5) >>> a array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) >>> ixgrid = np.ix_([0,1], [2,4]) >>> ixgrid (array([[0], [1]]), array([[2, 4]])) >>> ixgrid[0].shape, ixgrid[1].shape ((2, 1), (1, 2)) >>> a[ixgrid] array([[2, 4], [7, 9]]) """ return tuple() def kaiser(M, beta): """ Return the Kaiser window. The Kaiser window is a taper formed by using a Bessel function. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. beta : float Shape parameter for window. Returns ------- out : array The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, blackman, hamming, hanning Notes ----- The Kaiser window is defined as .. math:: w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}} \right)/I_0(\beta) with .. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2}, where :math:`I_0` is the modified zeroth-order Bessel function. The Kaiser was named for Jim Kaiser, who discovered a simple approximation to the DPSS window based on Bessel functions. The Kaiser window is a very good approximation to the Digital Prolate Spheroidal Sequence, or Slepian window, which is the transform which maximizes the energy in the main lobe of the window relative to total energy. The Kaiser can approximate many other windows by varying the beta parameter. ==== ======================= beta Window shape ==== ======================= 0 Rectangular 5 Similar to a Hamming 6 Similar to a Hanning 8.6 Similar to a Blackman ==== ======================= A beta value of 14 is probably a good starting point. Note that as beta gets large, the window narrows, and so the number of samples needs to be large enough to sample the increasingly narrow spike, otherwise NaNs will get returned. Most references to the Kaiser window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285. John Wiley and Sons, New York, (1966). .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 177-178. .. [3] Wikipedia, "Window function", http://en.wikipedia.org/wiki/Window_function Examples -------- >>> np.kaiser(12, 14) array([ 7.72686684e-06, 3.46009194e-03, 4.65200189e-02, 2.29737120e-01, 5.99885316e-01, 9.45674898e-01, 9.45674898e-01, 5.99885316e-01, 2.29737120e-01, 4.65200189e-02, 3.46009194e-03, 7.72686684e-06]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.kaiser(51, 14) >>> plt.plot(window) [] >>> plt.title("Kaiser window") >>> plt.ylabel("Amplitude") >>> plt.xlabel("Sample") >>> plt.show() >>> plt.figure() >>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Kaiser window") >>> plt.ylabel("Magnitude [dB]") >>> plt.xlabel("Normalized frequency [cycles per sample]") >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) >>> plt.show() """ return array() def kron(ab): """ Kronecker product of two arrays. Computes the Kronecker product, a composite array made of blocks of the second array scaled by the first. Parameters ---------- a, b : array_like Returns ------- out : ndarray See Also -------- outer : The outer product Notes ----- The function assumes that the number of dimenensions of `a` and `b` are the same, if necessary prepending the smallest with ones. If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`, the Kronecker product has shape `(r0*s0, r1*s1, ..., rN*SN)`. The elements are products of elements from `a` and `b`, organized explicitly by:: kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN] where:: kt = it * st + jt, t = 0,...,N In the common 2-D case (N=1), the block structure can be visualized:: [[ a[0,0]*b, a[0,1]*b, ... , a[0,-1]*b ], [ ... ... ], [ a[-1,0]*b, a[-1,1]*b, ... , a[-1,-1]*b ]] Examples -------- >>> np.kron([1,10,100], [5,6,7]) array([ 5, 6, 7, 50, 60, 70, 500, 600, 700]) >>> np.kron([5,6,7], [1,10,100]) array([ 5, 50, 500, 6, 60, 600, 7, 70, 700]) >>> np.kron(np.eye(2), np.ones((2,2))) array([[ 1., 1., 0., 0.], [ 1., 1., 0., 0.], [ 0., 0., 1., 1.], [ 0., 0., 1., 1.]]) >>> a = np.arange(100).reshape((2,5,2,5)) >>> b = np.arange(24).reshape((2,3,4)) >>> c = np.kron(a,b) >>> c.shape (2, 10, 6, 20) >>> I = (1,3,0,2) >>> J = (0,2,1) >>> J1 = (0,) + J # extend to ndim=4 >>> S1 = (1,) + b.shape >>> K = tuple(np.array(I) * np.array(S1) + np.array(J1)) >>> c[K] == a[I]*b[J] True """ return ndarray() def ldexp(x1, x2, out): """ldexp(x1, x2[, out]) Compute y = x1 * 2**x2.""" return None def left_shift(x1, x2, out=None): """left_shift(x1, x2[, out]) Shift the bits of an integer to the left. Bits are shifted to the left by appending `x2` 0s at the right of `x1`. Since the internal representation of numbers is in binary format, this operation is equivalent to multiplying `x1` by ``2**x2``. Parameters ---------- x1 : array_like of integer type Input values. x2 : array_like of integer type Number of zeros to append to `x1`. Has to be non-negative. Returns ------- out : array of integer type Return `x1` with bits shifted `x2` times to the left. See Also -------- right_shift : Shift the bits of an integer to the right. binary_repr : Return the binary representation of the input number as a string. Examples -------- >>> np.binary_repr(5) '101' >>> np.left_shift(5, 2) 20 >>> np.binary_repr(20) '10100' >>> np.left_shift(5, [1,2,3]) array([10, 20, 40])""" return array() def less(x1, x2, out=None): """less(x1, x2[, out]) Return the truth value of (x1 < x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). Returns ------- out : bool or ndarray of bool Array of bools, or a single bool if `x1` and `x2` are scalars. See Also -------- greater, less_equal, greater_equal, equal, not_equal Examples -------- >>> np.less([1, 2], [2, 2]) array([ True, False], dtype=bool)""" return bool() if False else ndarray() def less_equal(x1, x2, out=None): """less_equal(x1, x2[, out]) Return the truth value of (x1 =< x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). Returns ------- out : bool or ndarray of bool Array of bools, or a single bool if `x1` and `x2` are scalars. See Also -------- greater, less, greater_equal, equal, not_equal Examples -------- >>> np.less_equal([4, 2, 1], [2, 2, 2]) array([False, True, True], dtype=bool)""" return bool() if False else ndarray() def lexsort(keys, axis): """lexsort(keys, axis=-1) Perform an indirect sort using a sequence of keys. Given multiple sorting keys, which can be interpreted as columns in a spreadsheet, lexsort returns an array of integer indices that describes the sort order by multiple columns. The last key in the sequence is used for the primary sort order, the second-to-last key for the secondary sort order, and so on. The keys argument must be a sequence of objects that can be converted to arrays of the same shape. If a 2D array is provided for the keys argument, it's rows are interpreted as the sorting keys and sorting is according to the last row, second last row etc. Parameters ---------- keys : (k, N) array or tuple containing k (N,)-shaped sequences The `k` different "columns" to be sorted. The last column (or row if `keys` is a 2D array) is the primary sort key. axis : int, optional Axis to be indirectly sorted. By default, sort over the last axis. Returns ------- indices : (N,) ndarray of ints Array of indices that sort the keys along the specified axis. See Also -------- argsort : Indirect sort. ndarray.sort : In-place sort. sort : Return a sorted copy of an array. Examples -------- Sort names: first by surname, then by name. >>> surnames = ('Hertz', 'Galilei', 'Hertz') >>> first_names = ('Heinrich', 'Galileo', 'Gustav') >>> ind = np.lexsort((first_names, surnames)) >>> ind array([1, 2, 0]) >>> [surnames[i] + ", " + first_names[i] for i in ind] ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich'] Sort two columns of numbers: >>> a = [1,5,1,4,3,4,4] # First column >>> b = [9,4,0,4,0,2,1] # Second column >>> ind = np.lexsort((b,a)) # Sort by a, then by b >>> print ind [2 0 4 6 5 3 1] >>> [(a[i],b[i]) for i in ind] [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)] Note that sorting is first according to the elements of ``a``. Secondary sorting is according to the elements of ``b``. A normal ``argsort`` would have yielded: >>> [(a[i],b[i]) for i in np.argsort(a)] [(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)] Structured arrays are sorted lexically by ``argsort``: >>> x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)], ... dtype=np.dtype([('x', int), ('y', int)])) >>> np.argsort(x) # or np.argsort(x, order=('x', 'y')) array([2, 0, 4, 6, 5, 3, 1])""" return N() def linspace(start, stop=False, num=50, endpoint=True, retstep=False): """ Return evenly spaced numbers over a specified interval. Returns `num` evenly spaced samples, calculated over the interval [`start`, `stop` ]. The endpoint of the interval can optionally be excluded. Parameters ---------- start : scalar The starting value of the sequence. stop : scalar The end value of the sequence, unless `endpoint` is set to False. In that case, the sequence consists of all but the last of ``num + 1`` evenly spaced samples, so that `stop` is excluded. Note that the step size changes when `endpoint` is False. num : int, optional Number of samples to generate. Default is 50. endpoint : bool, optional If True, `stop` is the last sample. Otherwise, it is not included. Default is True. retstep : bool, optional If True, return (`samples`, `step`), where `step` is the spacing between samples. Returns ------- samples : ndarray There are `num` equally spaced samples in the closed interval ``[start, stop]`` or the half-open interval ``[start, stop)`` (depending on whether `endpoint` is True or False). step : float (only if `retstep` is True) Size of spacing between samples. See Also -------- arange : Similar to `linspace`, but uses a step size (instead of the number of samples). logspace : Samples uniformly distributed in log space. Examples -------- >>> np.linspace(2.0, 3.0, num=5) array([ 2. , 2.25, 2.5 , 2.75, 3. ]) >>> np.linspace(2.0, 3.0, num=5, endpoint=False) array([ 2. , 2.2, 2.4, 2.6, 2.8]) >>> np.linspace(2.0, 3.0, num=5, retstep=True) (array([ 2. , 2.25, 2.5 , 2.75, 3. ]), 0.25) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 8 >>> y = np.zeros(N) >>> x1 = np.linspace(0, 10, N, endpoint=True) >>> x2 = np.linspace(0, 10, N, endpoint=False) >>> plt.plot(x1, y, 'o') [] >>> plt.plot(x2, y + 0.5, 'o') [] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() """ return ndarray() little_endian = bool() def load(file=None, mmap_mode=None): """ Load an array(s) or pickled objects from .npy, .npz, or pickled files. Parameters ---------- file : file-like object or string The file to read. It must support ``seek()`` and ``read()`` methods. If the filename extension is ``.gz``, the file is first decompressed. mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional If not None, then memory-map the file, using the given mode (see `numpy.memmap` for a detailed description of the modes). A memory-mapped array is kept on disk. However, it can be accessed and sliced like any ndarray. Memory mapping is especially useful for accessing small fragments of large files without reading the entire file into memory. Returns ------- result : array, tuple, dict, etc. Data stored in the file. For '.npz' files, the returned instance of NpzFile class must be closed to avoid leaking file descriptors. Raises ------ IOError If the input file does not exist or cannot be read. See Also -------- save, savez, loadtxt memmap : Create a memory-map to an array stored in a file on disk. Notes ----- - If the file contains pickle data, then whatever object is stored in the pickle is returned. - If the file is a ``.npy`` file, then a single array is returned. - If the file is a ``.npz`` file, then a dictionary-like object is returned, containing ``{filename: array}`` key-value pairs, one for each file in the archive. - If the file is a ``.npz`` file, the returned value supports the context manager protocol in a similar fashion to the open function:: with load('foo.npz') as data: a = data['a'] The underlyling file descriptor is closed when exiting the 'with' block. Examples -------- Store data to disk, and load it again: >>> np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]])) >>> np.load('/tmp/123.npy') array([[1, 2, 3], [4, 5, 6]]) Store compressed data to disk, and load it again: >>> a=np.array([[1, 2, 3], [4, 5, 6]]) >>> b=np.array([1, 2]) >>> np.savez('/tmp/123.npz', a=a, b=b) >>> data = np.load('/tmp/123.npz') >>> data['a'] array([[1, 2, 3], [4, 5, 6]]) >>> data['b'] array([1, 2]) >>> data.close() Mem-map the stored array, and then access the second row directly from disk: >>> X = np.load('/tmp/123.npy', mmap_mode='r') >>> X[1, :] memmap([4, 5, 6]) """ return array() def loads(string): """loads(string) -- Load a pickle from the given string""" return None def loadtxt(fname=0, dtype=typefloat(), comments="#", delimiter=None, converters=None, skiprows=0, usecols=None, unpack=False, ndmin=0): """ Load data from a text file. Each row in the text file must have the same number of values. Parameters ---------- fname : file or str File, filename, or generator to read. If the filename extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note that generators should return byte strings for Python 3k. dtype : data-type, optional Data-type of the resulting array; default: float. If this is a record data-type, the resulting array will be 1-dimensional, and each row will be interpreted as an element of the array. In this case, the number of columns used must match the number of fields in the data-type. comments : str, optional The character used to indicate the start of a comment; default: '#'. delimiter : str, optional The string used to separate values. By default, this is any whitespace. converters : dict, optional A dictionary mapping column number to a function that will convert that column to a float. E.g., if column 0 is a date string: ``converters = {0: datestr2num}``. Converters can also be used to provide a default value for missing data (but see also `genfromtxt`): ``converters = {3: lambda s: float(s.strip() or 0)}``. Default: None. skiprows : int, optional Skip the first `skiprows` lines; default: 0. usecols : sequence, optional Which columns to read, with 0 being the first. For example, ``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns. The default, None, results in all columns being read. unpack : bool, optional If True, the returned array is transposed, so that arguments may be unpacked using ``x, y, z = loadtxt(...)``. When used with a record data-type, arrays are returned for each field. Default is False. ndmin : int, optional The returned array will have at least `ndmin` dimensions. Otherwise mono-dimensional axes will be squeezed. Legal values: 0 (default), 1 or 2. .. versionadded:: 1.6.0 Returns ------- out : ndarray Data read from the text file. See Also -------- load, fromstring, fromregex genfromtxt : Load data with missing values handled as specified. scipy.io.loadmat : reads MATLAB data files Notes ----- This function aims to be a fast reader for simply formatted files. The `genfromtxt` function provides more sophisticated handling of, e.g., lines with missing values. Examples -------- >>> from StringIO import StringIO # StringIO behaves like a file object >>> c = StringIO("0 1\n2 3") >>> np.loadtxt(c) array([[ 0., 1.], [ 2., 3.]]) >>> d = StringIO("M 21 72\nF 35 58") >>> np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'), ... 'formats': ('S1', 'i4', 'f4')}) array([('M', 21, 72.0), ('F', 35, 58.0)], dtype=[('gender', '|S1'), ('age', '>> c = StringIO("1,0,2\n3,0,4") >>> x, y = np.loadtxt(c, delimiter=',', usecols=(0, 2), unpack=True) >>> x array([ 1., 3.]) >>> y array([ 2., 4.]) """ return ndarray() def log(x, out=None): """log(x[, out]) Natural logarithm, element-wise. The natural logarithm `log` is the inverse of the exponential function, so that `log(exp(x)) = x`. The natural logarithm is logarithm in base `e`. Parameters ---------- x : array_like Input value. Returns ------- y : ndarray The natural logarithm of `x`, element-wise. See Also -------- log10, log2, log1p, emath.log Notes ----- Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `exp(z) = x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log` is a complex analytical function that has a branch cut `[-inf, 0]` and is continuous from above on it. `log` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ .. [2] Wikipedia, "Logarithm". http://en.wikipedia.org/wiki/Logarithm Examples -------- >>> np.log([1, np.e, np.e**2, 0]) array([ 0., 1., 2., -Inf])""" return ndarray() def log10(x, out=None): """log10(x[, out]) Return the base 10 logarithm of the input array, element-wise. Parameters ---------- x : array_like Input values. Returns ------- y : ndarray The logarithm to the base 10 of `x`, element-wise. NaNs are returned where x is negative. See Also -------- emath.log10 Notes ----- Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `10**z = x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log10` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log10` is a complex analytical function that has a branch cut `[-inf, 0]` and is continuous from above on it. `log10` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ .. [2] Wikipedia, "Logarithm". http://en.wikipedia.org/wiki/Logarithm Examples -------- >>> np.log10([1e-15, -3.]) array([-15., NaN])""" return ndarray() def log1p(x, out=None): """log1p(x[, out]) Return the natural logarithm of one plus the input array, element-wise. Calculates ``log(1 + x)``. Parameters ---------- x : array_like Input values. Returns ------- y : ndarray Natural logarithm of `1 + x`, element-wise. See Also -------- expm1 : ``exp(x) - 1``, the inverse of `log1p`. Notes ----- For real-valued input, `log1p` is accurate also for `x` so small that `1 + x == 1` in floating-point accuracy. Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `exp(z) = 1 + x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log1p` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log1p` is a complex analytical function that has a branch cut `[-inf, -1]` and is continuous from above on it. `log1p` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ .. [2] Wikipedia, "Logarithm". http://en.wikipedia.org/wiki/Logarithm Examples -------- >>> np.log1p(1e-99) 1e-99 >>> np.log(1 + 1e-99) 0.0""" return ndarray() def log2(x, out=None): """log2(x[, out]) Base-2 logarithm of `x`. Parameters ---------- x : array_like Input values. Returns ------- y : ndarray Base-2 logarithm of `x`. See Also -------- log, log10, log1p, emath.log2 Notes ----- .. versionadded:: 1.3.0 Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `2**z = x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log2` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log2` is a complex analytical function that has a branch cut `[-inf, 0]` and is continuous from above on it. `log2` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. Examples -------- >>> x = np.array([0, 1, 2, 2**4]) >>> np.log2(x) array([-Inf, 0., 1., 4.]) >>> xi = np.array([0+1.j, 1, 2+0.j, 4.j]) >>> np.log2(xi) array([ 0.+2.26618007j, 0.+0.j , 1.+0.j , 2.+2.26618007j])""" return ndarray() def logaddexp(x1, x2, out=None): """logaddexp(x1, x2[, out]) Logarithm of the sum of exponentiations of the inputs. Calculates ``log(exp(x1) + exp(x2))``. This function is useful in statistics where the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the logarithm of the calculated probability is stored. This function allows adding probabilities stored in such a fashion. Parameters ---------- x1, x2 : array_like Input values. Returns ------- result : ndarray Logarithm of ``exp(x1) + exp(x2)``. See Also -------- logaddexp2: Logarithm of the sum of exponentiations of inputs in base-2. Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> prob1 = np.log(1e-50) >>> prob2 = np.log(2.5e-50) >>> prob12 = np.logaddexp(prob1, prob2) >>> prob12 -113.87649168120691 >>> np.exp(prob12) 3.5000000000000057e-50""" return ndarray() def logaddexp2(x1, x2, out=None): """logaddexp2(x1, x2[, out]) Logarithm of the sum of exponentiations of the inputs in base-2. Calculates ``log2(2**x1 + 2**x2)``. This function is useful in machine learning when the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the base-2 logarithm of the calculated probability can be used instead. This function allows adding probabilities stored in such a fashion. Parameters ---------- x1, x2 : array_like Input values. out : ndarray, optional Array to store results in. Returns ------- result : ndarray Base-2 logarithm of ``2**x1 + 2**x2``. See Also -------- logaddexp: Logarithm of the sum of exponentiations of the inputs. Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> prob1 = np.log2(1e-50) >>> prob2 = np.log2(2.5e-50) >>> prob12 = np.logaddexp2(prob1, prob2) >>> prob1, prob2, prob12 (-166.09640474436813, -164.77447664948076, -164.28904982231052) >>> 2**prob12 3.4999999999999914e-50""" return ndarray() def logical_and(x1, x2, out=None): """logical_and(x1, x2[, out]) Compute the truth value of x1 AND x2 elementwise. Parameters ---------- x1, x2 : array_like Input arrays. `x1` and `x2` must be of the same shape. Returns ------- y : {ndarray, bool} Boolean result with the same shape as `x1` and `x2` of the logical AND operation on corresponding elements of `x1` and `x2`. See Also -------- logical_or, logical_not, logical_xor bitwise_and Examples -------- >>> np.logical_and(True, False) False >>> np.logical_and([True, False], [False, False]) array([False, False], dtype=bool) >>> x = np.arange(5) >>> np.logical_and(x>1, x<4) array([False, False, True, True, False], dtype=bool)""" return None def logical_not(x, out=None): """logical_not(x[, out]) Compute the truth value of NOT x elementwise. Parameters ---------- x : array_like Logical NOT is applied to the elements of `x`. Returns ------- y : bool or ndarray of bool Boolean result with the same shape as `x` of the NOT operation on elements of `x`. See Also -------- logical_and, logical_or, logical_xor Examples -------- >>> np.logical_not(3) False >>> np.logical_not([True, False, 0, 1]) array([False, True, True, False], dtype=bool) >>> x = np.arange(5) >>> np.logical_not(x<3) array([False, False, False, True, True], dtype=bool)""" return bool() if False else ndarray() def logical_or(x1, x2, out=None): """logical_or(x1, x2[, out]) Compute the truth value of x1 OR x2 elementwise. Parameters ---------- x1, x2 : array_like Logical OR is applied to the elements of `x1` and `x2`. They have to be of the same shape. Returns ------- y : {ndarray, bool} Boolean result with the same shape as `x1` and `x2` of the logical OR operation on elements of `x1` and `x2`. See Also -------- logical_and, logical_not, logical_xor bitwise_or Examples -------- >>> np.logical_or(True, False) True >>> np.logical_or([True, False], [False, False]) array([ True, False], dtype=bool) >>> x = np.arange(5) >>> np.logical_or(x < 1, x > 3) array([ True, False, False, False, True], dtype=bool)""" return None def logical_xor(x1, x2, out=None): """logical_xor(x1, x2[, out]) Compute the truth value of x1 XOR x2, element-wise. Parameters ---------- x1, x2 : array_like Logical XOR is applied to the elements of `x1` and `x2`. They must be broadcastable to the same shape. Returns ------- y : bool or ndarray of bool Boolean result of the logical XOR operation applied to the elements of `x1` and `x2`; the shape is determined by whether or not broadcasting of one or both arrays was required. See Also -------- logical_and, logical_or, logical_not, bitwise_xor Examples -------- >>> np.logical_xor(True, False) True >>> np.logical_xor([True, True, False, False], [True, False, True, False]) array([False, True, True, False], dtype=bool) >>> x = np.arange(5) >>> np.logical_xor(x < 1, x > 3) array([ True, False, False, False, True], dtype=bool) Simple example showing support of broadcasting >>> np.logical_xor(0, np.eye(2)) array([[ True, False], [False, True]], dtype=bool)""" return bool() if False else ndarray() def logspace(start, stop=10.0, num=50, endpoint=True, base=10.0): """ Return numbers spaced evenly on a log scale. In linear space, the sequence starts at ``base ** start`` (`base` to the power of `start`) and ends with ``base ** stop`` (see `endpoint` below). Parameters ---------- start : float ``base ** start`` is the starting value of the sequence. stop : float ``base ** stop`` is the final value of the sequence, unless `endpoint` is False. In that case, ``num + 1`` values are spaced over the interval in log-space, of which all but the last (a sequence of length ``num``) are returned. num : integer, optional Number of samples to generate. Default is 50. endpoint : boolean, optional If true, `stop` is the last sample. Otherwise, it is not included. Default is True. base : float, optional The base of the log space. The step size between the elements in ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform. Default is 10.0. Returns ------- samples : ndarray `num` samples, equally spaced on a log scale. See Also -------- arange : Similar to linspace, with the step size specified instead of the number of samples. Note that, when used with a float endpoint, the endpoint may or may not be included. linspace : Similar to logspace, but with the samples uniformly distributed in linear space, instead of log space. Notes ----- Logspace is equivalent to the code >>> y = np.linspace(start, stop, num=num, endpoint=endpoint) ... # doctest: +SKIP >>> power(base, y) ... # doctest: +SKIP Examples -------- >>> np.logspace(2.0, 3.0, num=4) array([ 100. , 215.443469 , 464.15888336, 1000. ]) >>> np.logspace(2.0, 3.0, num=4, endpoint=False) array([ 100. , 177.827941 , 316.22776602, 562.34132519]) >>> np.logspace(2.0, 3.0, num=4, base=2.0) array([ 4. , 5.0396842 , 6.34960421, 8. ]) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 10 >>> x1 = np.logspace(0.1, 1, N, endpoint=True) >>> x2 = np.logspace(0.1, 1, N, endpoint=False) >>> y = np.zeros(N) >>> plt.plot(x1, y, 'o') [] >>> plt.plot(x2, y + 0.5, 'o') [] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() """ return ndarray() class long: __doc__ = str() def bit_length(self, _): """long.bit_length() -> int or long Number of bits necessary to represent self in binary. >>> bin(37L) '0b100101' >>> (37L).bit_length() 6""" return None def conjugate(self, _): """Returns self, the complex conjugate of any long.""" return None denominator = getset_descriptor() imag = getset_descriptor() numerator = getset_descriptor() real = getset_descriptor() class complex256: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class float128: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class float128: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class int64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def bit_length(self, _): """int.bit_length() -> int Number of bits necessary to represent self in binary. >>> bin(37) '0b100101' >>> (37).bit_length() 6""" return None def conj(self, _): """None""" return None data = getset_descriptor() denominator = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() numerator = getset_descriptor() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def lookfor(what=None, module=None, import_modules=True, regenerate=False, output=None): """ Do a keyword search on docstrings. A list of of objects that matched the search is displayed, sorted by relevance. All given keywords need to be found in the docstring for it to be returned as a result, but the order does not matter. Parameters ---------- what : str String containing words to look for. module : str or list, optional Name of module(s) whose docstrings to go through. import_modules : bool, optional Whether to import sub-modules in packages. Default is True. regenerate : bool, optional Whether to re-generate the docstring cache. Default is False. output : file-like, optional File-like object to write the output to. If omitted, use a pager. See Also -------- source, info Notes ----- Relevance is determined only roughly, by checking if the keywords occur in the function name, at the start of a docstring, etc. Examples -------- >>> np.lookfor('binary representation') Search results for 'binary representation' ------------------------------------------ numpy.binary_repr Return the binary representation of the input number as a string. numpy.core.setup_common.long_double_representation Given a binary dump as given by GNU od -b, look for long double numpy.base_repr Return a string representation of a number in the given base system. ... """ return None def ma_fromtxt(fnamekwargs): """ Load ASCII data stored in a text file and return a masked array. Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function to load ASCII data. """ return None def mask_indices(n, mask_func=0, k=0): """ Return the indices to access (n, n) arrays, given a masking function. Assume `mask_func` is a function that, for a square array a of size ``(n, n)`` with a possible offset argument `k`, when called as ``mask_func(a, k)`` returns a new array with zeros in certain locations (functions like `triu` or `tril` do precisely this). Then this function returns the indices where the non-zero values would be located. Parameters ---------- n : int The returned indices will be valid to access arrays of shape (n, n). mask_func : callable A function whose call signature is similar to that of `triu`, `tril`. That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`. `k` is an optional argument to the function. k : scalar An optional argument which is passed through to `mask_func`. Functions like `triu`, `tril` take a second argument that is interpreted as an offset. Returns ------- indices : tuple of arrays. The `n` arrays of indices corresponding to the locations where ``mask_func(np.ones((n, n)), k)`` is True. See Also -------- triu, tril, triu_indices, tril_indices Notes ----- .. versionadded:: 1.4.0 Examples -------- These are the indices that would allow you to access the upper triangular part of any 3x3 array: >>> iu = np.mask_indices(3, np.triu) For example, if `a` is a 3x3 array: >>> a = np.arange(9).reshape(3, 3) >>> a array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> a[iu] array([0, 1, 2, 4, 5, 8]) An offset can be passed also to the masking function. This gets us the indices starting on the first diagonal right of the main one: >>> iu1 = np.mask_indices(3, np.triu, 1) with which we now extract only three elements: >>> a[iu1] array([1, 2, 5]) """ return tuple() def asmatrix(data=None, dtype=None): """ Interpret the input as a matrix. Unlike `matrix`, `asmatrix` does not make a copy if the input is already a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``. Parameters ---------- data : array_like Input data. Returns ------- mat : matrix `data` interpreted as a matrix. Examples -------- >>> x = np.array([[1, 2], [3, 4]]) >>> m = np.asmatrix(x) >>> x[0,0] = 5 >>> m matrix([[5, 2], [3, 4]]) """ return matrix() class matrix: A = property() A1 = property() H = property() I = property() T = property() __array_interface__ = getset_descriptor() __array_priority__ = float() __array_struct__ = getset_descriptor() __dict__ = dictproxy() __doc__ = str() __module__ = str() def _align(self, _): """A convenience function for operations that need to preserve axis orientation. """ return None def _collapse(self, _): """A convenience function for operations that want to collapse to a scalar like _align, but are using keepdims=True """ return None def all(self=None, axis=None, out=None): """ Test whether all matrix elements along a given axis evaluate to True. Parameters ---------- See `numpy.all` for complete descriptions See Also -------- numpy.all Notes ----- This is the same as `ndarray.all`, but it returns a `matrix` object. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> y = x[0]; y matrix([[0, 1, 2, 3]]) >>> (x == y) matrix([[ True, True, True, True], [False, False, False, False], [False, False, False, False]], dtype=bool) >>> (x == y).all() False >>> (x == y).all(0) matrix([[False, False, False, False]], dtype=bool) >>> (x == y).all(1) matrix([[ True], [False], [False]], dtype=bool) """ return None def any(self=None, axis=None, out=None): """ Test whether any array element along a given axis evaluates to True. Refer to `numpy.any` for full documentation. Parameters ---------- axis : int, optional Axis along which logical OR is performed out : ndarray, optional Output to existing array instead of creating new one, must have same shape as expected output Returns ------- any : bool, ndarray Returns a single bool if `axis` is ``None``; otherwise, returns `ndarray` """ return bool() def argmax(self=None, axis=None, out=None): """ Indices of the maximum values along an axis. Parameters ---------- See `numpy.argmax` for complete descriptions See Also -------- numpy.argmax Notes ----- This is the same as `ndarray.argmax`, but returns a `matrix` object where `ndarray.argmax` would return an `ndarray`. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.argmax() 11 >>> x.argmax(0) matrix([[2, 2, 2, 2]]) >>> x.argmax(1) matrix([[3], [3], [3]]) """ return None def argmin(self=None, axis=None, out=None): """ Return the indices of the minimum values along an axis. Parameters ---------- See `numpy.argmin` for complete descriptions. See Also -------- numpy.argmin Notes ----- This is the same as `ndarray.argmin`, but returns a `matrix` object where `ndarray.argmin` would return an `ndarray`. Examples -------- >>> x = -np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, -1, -2, -3], [ -4, -5, -6, -7], [ -8, -9, -10, -11]]) >>> x.argmin() 11 >>> x.argmin(0) matrix([[2, 2, 2, 2]]) >>> x.argmin(1) matrix([[3], [3], [3]]) """ return None def argpartition(self, kth, axis=_1, kind=quickselect, order=None): """a.argpartition(kth, axis=-1, kind='quickselect', order=None) Returns the indices that would partition this array. Refer to `numpy.argpartition` for full documentation. .. versionadded:: 1.8.0 See Also -------- numpy.argpartition : equivalent function""" return None def argsort(self, axis=_1, kind=quicksort, order=None): """a.argsort(axis=-1, kind='quicksort', order=None) Returns the indices that would sort this array. Refer to `numpy.argsort` for full documentation. See Also -------- numpy.argsort : equivalent function""" return None def astype(self, dtype, order, casting, subok, copy): """a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) Copy of the array, cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to false, and the `dtype`, `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy. Returns ------- arr_t : ndarray Unless `copy` is False and the other conditions for returning the input array are satisfied (see description for `copy` input paramter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by `dtype`, `order`. Raises ------ ComplexWarning When casting from complex to float or int. To avoid this, one should use ``a.real.astype(t)``. Examples -------- >>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5]) >>> x.astype(int) array([1, 2, 2])""" return ndarray() base = getset_descriptor() def byteswap(self, inplace): """a.byteswap(inplace) Swap the bytes of the array elements Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Parameters ---------- inplace : bool, optional If ``True``, swap bytes in-place, default is ``False``. Returns ------- out : ndarray The byteswapped array. If `inplace` is ``True``, this is a view to self. Examples -------- >>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322'] Arrays of strings are not swapped >>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')""" return ndarray() def choose(self, choices, out=None, mode=_raise): """a.choose(choices, out=None, mode='raise') Use an index array to construct a new array from a set of choices. Refer to `numpy.choose` for full documentation. See Also -------- numpy.choose : equivalent function""" return None def clip(self, a_min, a_max, out=None): """a.clip(a_min, a_max, out=None) Return an array whose values are limited to ``[a_min, a_max]``. Refer to `numpy.clip` for full documentation. See Also -------- numpy.clip : equivalent function""" return None def compress(self, condition, axis=None, out=None): """a.compress(condition, axis=None, out=None) Return selected slices of this array along given axis. Refer to `numpy.compress` for full documentation. See Also -------- numpy.compress : equivalent function""" return None def conj(self, _): """a.conj() Complex-conjugate all elements. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def conjugate(self, _): """a.conjugate() Return the complex conjugate, element-wise. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def copy(self, order): """a.copy(order='C') Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :func:numpy.copy are very similar, but have different default values for their order= arguments.) See also -------- numpy.copy numpy.copyto Examples -------- >>> x = np.array([[1,2,3],[4,5,6]], order='F') >>> y = x.copy() >>> x.fill(0) >>> x array([[0, 0, 0], [0, 0, 0]]) >>> y array([[1, 2, 3], [4, 5, 6]]) >>> y.flags['C_CONTIGUOUS'] True""" return None ctypes = getset_descriptor() def cumprod(self, axis=None, dtype=None, out=None): """a.cumprod(axis=None, dtype=None, out=None) Return the cumulative product of the elements along the given axis. Refer to `numpy.cumprod` for full documentation. See Also -------- numpy.cumprod : equivalent function""" return None def cumsum(self, axis=None, dtype=None, out=None): """a.cumsum(axis=None, dtype=None, out=None) Return the cumulative sum of the elements along the given axis. Refer to `numpy.cumsum` for full documentation. See Also -------- numpy.cumsum : equivalent function""" return None data = getset_descriptor() def diagonal(self, offset=0, axis1=0, axis2=1): """a.diagonal(offset=0, axis1=0, axis2=1) Return specified diagonals. Refer to :func:`numpy.diagonal` for full documentation. See Also -------- numpy.diagonal : equivalent function""" return None def dot(self, b, out=None): """a.dot(b, out=None) Dot product of two arrays. Refer to `numpy.dot` for full documentation. See Also -------- numpy.dot : equivalent function Examples -------- >>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]]) This array method can be conveniently chained: >>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])""" return None dtype = getset_descriptor() def dump(self, file): """a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load. Parameters ---------- file : str A string naming the dump file.""" return None def dumps(self, _): """a.dumps() Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array. Parameters ---------- None""" return None def fill(self, value): """a.fill(value) Fill the array with a scalar value. Parameters ---------- value : scalar All elements of `a` will be assigned this value. Examples -------- >>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])""" return None flags = getset_descriptor() flat = getset_descriptor() def flatten(self, order): """a.flatten(order='C') Return a copy of the array collapsed into one dimension. Parameters ---------- order : {'C', 'F', 'A'}, optional Whether to flatten in C (row-major), Fortran (column-major) order, or preserve the C/Fortran ordering from `a`. The default is 'C'. Returns ------- y : ndarray A copy of the input array, flattened to one dimension. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the array. Examples -------- >>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])""" return ndarray() def getA(self, _): """ Return `self` as an `ndarray` object. Equivalent to ``np.asarray(self)``. Parameters ---------- None Returns ------- ret : ndarray `self` as an `ndarray` Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.getA() array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) """ return ndarray() def getA1(self, _): """ Return `self` as a flattened `ndarray`. Equivalent to ``np.asarray(x).ravel()`` Parameters ---------- None Returns ------- ret : ndarray `self`, 1-D, as an `ndarray` Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.getA1() array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) """ return ndarray() def getH(self, _): """ Returns the (complex) conjugate transpose of `self`. Equivalent to ``np.transpose(self)`` if `self` is real-valued. Parameters ---------- None Returns ------- ret : matrix object complex conjugate transpose of `self` Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))) >>> z = x - 1j*x; z matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j], [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j], [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]]) >>> z.getH() matrix([[ 0. +0.j, 4. +4.j, 8. +8.j], [ 1. +1.j, 5. +5.j, 9. +9.j], [ 2. +2.j, 6. +6.j, 10.+10.j], [ 3. +3.j, 7. +7.j, 11.+11.j]]) """ return matrix() def getI(self, _): """ Returns the (multiplicative) inverse of invertible `self`. Parameters ---------- None Returns ------- ret : matrix object If `self` is non-singular, `ret` is such that ``ret * self`` == ``self * ret`` == ``np.matrix(np.eye(self[0,:].size)`` all return ``True``. Raises ------ numpy.linalg.LinAlgError: Singular matrix If `self` is singular. See Also -------- linalg.inv Examples -------- >>> m = np.matrix('[1, 2; 3, 4]'); m matrix([[1, 2], [3, 4]]) >>> m.getI() matrix([[-2. , 1. ], [ 1.5, -0.5]]) >>> m.getI() * m matrix([[ 1., 0.], [ 0., 1.]]) """ return matrix() def getT(self, _): """ Returns the transpose of the matrix. Does *not* conjugate! For the complex conjugate transpose, use `getH`. Parameters ---------- None Returns ------- ret : matrix object The (non-conjugated) transpose of the matrix. See Also -------- transpose, getH Examples -------- >>> m = np.matrix('[1, 2; 3, 4]') >>> m matrix([[1, 2], [3, 4]]) >>> m.getT() matrix([[1, 3], [2, 4]]) """ return matrix() def getfield(self, dtype, offset): """a.getfield(dtype, offset=0) Returns a field of the given array as a certain type. A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes. Parameters ---------- dtype : str or dtype The data type of the view. The dtype size of the view can not be larger than that of the array itself. offset : int Number of bytes to skip before beginning the element view. Examples -------- >>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]]) By choosing an offset of 8 bytes we can select the complex part of the array for our view: >>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])""" return array() imag = getset_descriptor() def item(self, ESCargs): """a.item(*args) Copy an element of an array to a standard Python scalar and return it. Parameters ---------- \*args : Arguments (variable number and type) * none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned. * int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return. * tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array. Returns ------- z : Standard Python scalar object A copy of the specified element of the array as a suitable Python scalar Notes ----- When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned. `item` is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python's optimized math. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3""" return Standard() def itemset(self, ESCargs): """a.itemset(*args) Insert scalar into an array (scalar is cast to array's dtype, if possible) There must be at least 1 argument, and define the last argument as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster than ``a[args] = item``. The item should be a scalar value and `args` must select a single item in the array `a`. Parameters ---------- \*args : Arguments If one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple. Notes ----- Compared to indexing syntax, `itemset` provides some speed increase for placing a scalar into a particular location in an `ndarray`, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using `itemset` (and `item`) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])""" return None itemsize = getset_descriptor() def max(self=None, axis=None, out=None): """ Return the maximum value along an axis. Parameters ---------- See `amax` for complete descriptions See Also -------- amax, ndarray.max Notes ----- This is the same as `ndarray.max`, but returns a `matrix` object where `ndarray.max` would return an ndarray. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.max() 11 >>> x.max(0) matrix([[ 8, 9, 10, 11]]) >>> x.max(1) matrix([[ 3], [ 7], [11]]) """ return None def mean(self=None, axis=None, dtype=None, out=None): """ Returns the average of the matrix elements along the given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean Notes ----- Same as `ndarray.mean` except that, where that returns an `ndarray`, this returns a `matrix` object. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3, 4))) >>> x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.mean() 5.5 >>> x.mean(0) matrix([[ 4., 5., 6., 7.]]) >>> x.mean(1) matrix([[ 1.5], [ 5.5], [ 9.5]]) """ return None def min(self=None, axis=None, out=None): """ Return the minimum value along an axis. Parameters ---------- See `amin` for complete descriptions. See Also -------- amin, ndarray.min Notes ----- This is the same as `ndarray.min`, but returns a `matrix` object where `ndarray.min` would return an ndarray. Examples -------- >>> x = -np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, -1, -2, -3], [ -4, -5, -6, -7], [ -8, -9, -10, -11]]) >>> x.min() -11 >>> x.min(0) matrix([[ -8, -9, -10, -11]]) >>> x.min(1) matrix([[ -3], [ -7], [-11]]) """ return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """arr.newbyteorder(new_order='S') Return the array with the same data viewed with a different byte order. Equivalent to:: arr.view(arr.dtype.newbytorder(new_order)) Changes are also made in all fields and sub-arrays of the array data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications above. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_arr : array New array object with the dtype reflecting given change to the byte order.""" return array() def nonzero(self, _): """a.nonzero() Return the indices of the elements that are non-zero. Refer to `numpy.nonzero` for full documentation. See Also -------- numpy.nonzero : equivalent function""" return None def partition(self, kth, axis, kind, order): """a.partition(kth, axis=-1, kind='introselect', order=None) Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- kth : int or sequence of ints Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once. axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort. Notes ----- See ``np.partition`` for notes on the different algorithms. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> a.partition(a, 3) >>> a array([2, 1, 3, 4]) >>> a.partition((1, 3)) array([1, 2, 3, 4])""" return None def prod(self=None, axis=None, dtype=None, out=None): """ Return the product of the array elements over the given axis. Refer to `prod` for full documentation. See Also -------- prod, ndarray.prod Notes ----- Same as `ndarray.prod`, except, where that returns an `ndarray`, this returns a `matrix` object instead. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.prod() 0 >>> x.prod(0) matrix([[ 0, 45, 120, 231]]) >>> x.prod(1) matrix([[ 0], [ 840], [7920]]) """ return None def ptp(self=None, axis=None, out=None): """ Peak-to-peak (maximum - minimum) value along the given axis. Refer to `numpy.ptp` for full documentation. See Also -------- numpy.ptp Notes ----- Same as `ndarray.ptp`, except, where that would return an `ndarray` object, this returns a `matrix` object. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.ptp() 11 >>> x.ptp(0) matrix([[8, 8, 8, 8]]) >>> x.ptp(1) matrix([[3], [3], [3]]) """ return None def put(self, indices, values, mode=_raise): """a.put(indices, values, mode='raise') Set ``a.flat[n] = values[n]`` for all `n` in indices. Refer to `numpy.put` for full documentation. See Also -------- numpy.put : equivalent function""" return None def ravel(self, order): """a.ravel([order]) Return a flattened array. Refer to `numpy.ravel` for full documentation. See Also -------- numpy.ravel : equivalent function ndarray.flat : a flat iterator on the array.""" return None real = getset_descriptor() def repeat(self, repeats, axis=None): """a.repeat(repeats, axis=None) Repeat elements of an array. Refer to `numpy.repeat` for full documentation. See Also -------- numpy.repeat : equivalent function""" return None def reshape(self, shape, order=C): """a.reshape(shape, order='C') Returns an array containing the same data with a new shape. Refer to `numpy.reshape` for full documentation. See Also -------- numpy.reshape : equivalent function""" return None def resize(self, new_shape, refcheck): """a.resize(new_shape, refcheck=True) Change shape and size of array in-place. Parameters ---------- new_shape : tuple of ints, or `n` ints Shape of resized array. refcheck : bool, optional If False, reference count will not be checked. Default is True. Returns ------- None Raises ------ ValueError If `a` does not own its own data or references or views to it exist, and the data memory must be changed. SystemError If the `order` keyword argument is specified. This behaviour is a bug in NumPy. See Also -------- resize : Return a new array with the specified shape. Notes ----- This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False. Examples -------- Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]]) >>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]]) Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]]) Referencing an array prevents resizing... >>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ... Unless `refcheck` is False: >>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])""" return None def round(self, decimals=0, out=None): """a.round(decimals=0, out=None) Return `a` with each element rounded to the given number of decimals. Refer to `numpy.around` for full documentation. See Also -------- numpy.around : equivalent function""" return None def searchsorted(self, v, side=left, sorter=None): """a.searchsorted(v, side='left', sorter=None) Find indices where elements of v should be inserted in a to maintain order. For full documentation, see `numpy.searchsorted` See Also -------- numpy.searchsorted : equivalent function""" return None def setfield(self, val, dtype, offset): """a.setfield(val, dtype, offset=0) Put a value into a specified place in a field defined by a data-type. Place `val` into `a`'s field defined by `dtype` and beginning `offset` bytes into the field. Parameters ---------- val : object Value to be placed in field. dtype : dtype object Data-type of the field in which to place `val`. offset : int, optional The number of bytes into the field at which to place `val`. Returns ------- None See Also -------- getfield Examples -------- >>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])""" return None def setflags(self, write, align, uic): """a.setflags(write=None, align=None, uic=None) Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively. These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The UPDATEIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters ---------- write : bool, optional Describes whether or not `a` can be written to. align : bool, optional Describes whether or not `a` is aligned properly for its type. uic : bool, optional Describes whether or not `a` is a copy of another "base" array. Notes ----- Array flags provide information about how the memory area used for the array is to be interpreted. There are 6 Boolean flags in use, only three of which can be changed by the user: UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array. All flags can be accessed using their first (upper case) letter as well as the full name. Examples -------- >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "", line 1, in ValueError: cannot set UPDATEIFCOPY flag to True""" return None shape = getset_descriptor() size = getset_descriptor() def sort(self, axis, kind, order): """a.sort(axis=-1, kind='quicksort', order=None) Sort an array, in-place. Parameters ---------- axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort. Notes ----- See ``sort`` for notes on the different sorting algorithms. Examples -------- >>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '>> x = np.matrix(np.arange(12).reshape((3, 4))) >>> x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.std() 3.4520525295346629 >>> x.std(0) matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) >>> x.std(1) matrix([[ 1.11803399], [ 1.11803399], [ 1.11803399]]) """ return None strides = getset_descriptor() def sum(self=None, axis=None, dtype=None, out=None): """ Returns the sum of the matrix elements, along the given axis. Refer to `numpy.sum` for full documentation. See Also -------- numpy.sum Notes ----- This is the same as `ndarray.sum`, except that where an `ndarray` would be returned, a `matrix` object is returned instead. Examples -------- >>> x = np.matrix([[1, 2], [4, 3]]) >>> x.sum() 10 >>> x.sum(axis=1) matrix([[3], [7]]) >>> x.sum(axis=1, dtype='float') matrix([[ 3.], [ 7.]]) >>> out = np.zeros((1, 2), dtype='float') >>> x.sum(axis=1, dtype='float', out=out) matrix([[ 3.], [ 7.]]) """ return None def swapaxes(self, axis1, axis2): """a.swapaxes(axis1, axis2) Return a view of the array with `axis1` and `axis2` interchanged. Refer to `numpy.swapaxes` for full documentation. See Also -------- numpy.swapaxes : equivalent function""" return None def take(self, indices, axis=None, out=None, mode=_raise): """a.take(indices, axis=None, out=None, mode='raise') Return an array formed from the elements of `a` at the given indices. Refer to `numpy.take` for full documentation. See Also -------- numpy.take : equivalent function""" return None def tofile(self, fid, sep, format): """a.tofile(fid, sep="", format="%s") Write array to a file as text or binary (default). Data is always written in 'C' order, independent of the order of `a`. The data produced by this method can be recovered using the function fromfile(). Parameters ---------- fid : file or str An open file object, or a string containing a filename. sep : str Separator between array items for text output. If "" (empty), a binary file is written, equivalent to ``file.write(a.tostring())``. format : str Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using "format" % item. Notes ----- This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.""" return None def tolist(self, _): """ Return the matrix as a (possibly nested) list. See `ndarray.tolist` for full documentation. See Also -------- ndarray.tolist Examples -------- >>> x = np.matrix(np.arange(12).reshape((3,4))); x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.tolist() [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]] """ return None def tostring(self, order): """a.tostring(order='C') Construct a Python string containing the raw data bytes in the array. Constructs a Python string showing a copy of the raw contents of data memory. The string can be produced in either 'C' or 'Fortran', or 'Any' order (the default is 'C'-order). 'Any' order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means 'Fortran' order. Parameters ---------- order : {'C', 'F', None}, optional Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array. Returns ------- s : str A Python string exhibiting a copy of `a`'s raw data. Examples -------- >>> x = np.array([[0, 1], [2, 3]]) >>> x.tostring() '\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tostring('C') == x.tostring() True >>> x.tostring('F') '\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'""" return str() def trace(self, offset=0, axis1=0, axis2=1, dtype=None, out=None): """a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) Return the sum along diagonals of the array. Refer to `numpy.trace` for full documentation. See Also -------- numpy.trace : equivalent function""" return None def transpose(self, axes): """a.transpose(*axes) Returns a view of the array with axes transposed. For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. Parameters ---------- axes : None, tuple of ints, or `n` ints * None or no argument: reverses the order of the axes. * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s `i`-th axis becomes `a.transpose()`'s `j`-th axis. * `n` ints: same as an n-tuple of the same ints (this form is intended simply as a "convenience" alternative to the tuple form) Returns ------- out : ndarray View of `a`, with axes suitably permuted. See Also -------- ndarray.T : Array property returning the array transposed. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])""" return ndarray() def var(self=0, axis=None, dtype=None, out=None, ddof=0): """ Returns the variance of the matrix elements, along the given axis. Refer to `numpy.var` for full documentation. See Also -------- numpy.var Notes ----- This is the same as `ndarray.var`, except that where an `ndarray` would be returned, a `matrix` object is returned instead. Examples -------- >>> x = np.matrix(np.arange(12).reshape((3, 4))) >>> x matrix([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x.var() 11.916666666666666 >>> x.var(0) matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) >>> x.var(1) matrix([[ 1.25], [ 1.25], [ 1.25]]) """ return None def view(self, dtype, type): """a.view(dtype=None, type=None) New view of array with the same data. Parameters ---------- dtype : data-type or ndarray sub-class, optional Data-type descriptor of the returned view, e.g., float32 or int16. The default, None, results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the ``type`` parameter). type : Python type, optional Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation. Notes ----- ``a.view()`` is used two different ways: ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view of the array's memory with a different data-type. This can cause a reinterpretation of the bytes of memory. ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory. For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of ``a`` (shown by ``print(a)``). It also depends on exactly how ``a`` is stored in memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results. Examples -------- >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) Viewing array data using a different type and dtype: >>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print type(y) Creating a view on a structured array so it can be used in calculations >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.]) Making changes to the view changes the underlying array >>> xv[0,1] = 20 >>> print x [(1, 20) (3, 4)] Using a view to convert an array to a record array: >>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8) Views share data: >>> x[0] = (9, 10) >>> z[0] (9, 10) Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.: >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "", line 1, in ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', '>> a = np.arange(4).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amax(a) # Maximum of the flattened array 3 >>> np.amax(a, axis=0) # Maxima along the first axis array([2, 3]) >>> np.amax(a, axis=1) # Maxima along the second axis array([1, 3]) >>> b = np.arange(5, dtype=np.float) >>> b[2] = np.NaN >>> np.amax(b) nan >>> np.nanmax(b) 4.0 """ return ndarray() if False else float() def maximum(x1, x2, out=None): """maximum(x1, x2[, out]) Element-wise maximum of array elements. Compare two arrays and returns a new array containing the element-wise maxima. If one of the elements being compared is a nan, then that element is returned. If both elements are nans then the first is returned. The latter distinction is important for complex nans, which are defined as at least one of the real or imaginary parts being a nan. The net effect is that nans are propagated. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. They must have the same shape, or shapes that can be broadcast to a single shape. Returns ------- y : {ndarray, scalar} The maximum of `x1` and `x2`, element-wise. Returns scalar if both `x1` and `x2` are scalars. See Also -------- minimum : Element-wise minimum of two arrays, propagating any NaNs. fmax : Element-wise maximum of two arrays, ignoring any NaNs. amax : The maximum value of an array along a given axis, propagating any NaNs. nanmax : The maximum value of an array along a given axis, ignoring any NaNs. fmin, amin, nanmin Notes ----- The maximum is equivalent to ``np.where(x1 >= x2, x1, x2)`` when neither x1 nor x2 are nans, but it is faster and does proper broadcasting. Examples -------- >>> np.maximum([2, 3, 4], [1, 5, 2]) array([2, 5, 4]) >>> np.maximum(np.eye(2), [0.5, 2]) # broadcasting array([[ 1. , 2. ], [ 0.5, 2. ]]) >>> np.maximum([np.nan, 0, np.nan], [0, np.nan, np.nan]) array([ NaN, NaN, NaN]) >>> np.maximum(np.Inf, 1) inf""" return ndarray() def maximum_sctype(t): """ Return the scalar type of highest precision of the same kind as the input. Parameters ---------- t : dtype or dtype specifier The input data type. This can be a `dtype` object or an object that is convertible to a `dtype`. Returns ------- out : dtype The highest precision data type of the same kind (`dtype.kind`) as `t`. See Also -------- obj2sctype, mintypecode, sctype2char dtype Examples -------- >>> np.maximum_sctype(np.int) >>> np.maximum_sctype(np.uint8) >>> np.maximum_sctype(np.complex) >>> np.maximum_sctype(str) >>> np.maximum_sctype('i2') >>> np.maximum_sctype('f4') """ return dtype() def may_share_memory(ab): """Determine if two arrays can share memory The memory-bounds of a and b are computed. If they overlap then this function returns True. Otherwise, it returns False. A return of True does not necessarily mean that the two arrays share any element. It just means that they *might*. Parameters ---------- a, b : ndarray Returns ------- out : bool Examples -------- >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9])) False""" return bool() def mean(a=False, axis=None, dtype=None, out=None, keepdims=False): """ Compute the arithmetic mean along the specified axis. Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. `float64` intermediate and return values are used for integer inputs. Parameters ---------- a : array_like Array containing numbers whose mean is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the means are computed. The default is to compute the mean of the flattened array. dtype : data-type, optional Type to use in computing the mean. For integer inputs, the default is `float64`; for floating point inputs, it is the same as the input dtype. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See `doc.ufuncs` for details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- m : ndarray, see dtype parameter above If `out=None`, returns a new array containing the mean values, otherwise a reference to the output array is returned. See Also -------- average : Weighted average std, var, nanmean, nanstd, nanvar Notes ----- The arithmetic mean is the sum of the elements along the axis divided by the number of elements. Note that for floating-point input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32` (see example below). Specifying a higher-precision accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> np.mean(a) 2.5 >>> np.mean(a, axis=0) array([ 2., 3.]) >>> np.mean(a, axis=1) array([ 1.5, 3.5]) In single precision, `mean` can be inaccurate: >>> a = np.zeros((2, 512*512), dtype=np.float32) >>> a[0, :] = 1.0 >>> a[1, :] = 0.1 >>> np.mean(a) 0.546875 Computing the mean in float64 is more accurate: >>> np.mean(a, dtype=np.float64) 0.55000000074505806 """ return ndarray() def median(a=False, axis=None, out=None, overwrite_input=False): """ Compute the median along the specified axis. Returns the median of the array elements. Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : int, optional Axis along which the medians are computed. The default (axis=None) is to compute the median along a flattened version of the array. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow use of memory of input array (a) for calculations. The input array will be modified by the call to median. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. Note that, if `overwrite_input` is True and the input is not already an ndarray, an error will be raised. Returns ------- median : ndarray A new array holding the result (unless `out` is specified, in which case that array is returned instead). If the input contains integers, or floats of smaller precision than 64, then the output data-type is float64. Otherwise, the output data-type is the same as that of the input. See Also -------- mean, percentile Notes ----- Given a vector V of length N, the median of V is the middle value of a sorted copy of V, ``V_sorted`` - i.e., ``V_sorted[(N-1)/2]``, when N is odd. When N is even, it is the average of the two middle values of ``V_sorted``. Examples -------- >>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.median(a) 3.5 >>> np.median(a, axis=0) array([ 6.5, 4.5, 2.5]) >>> np.median(a, axis=1) array([ 7., 2.]) >>> m = np.median(a, axis=0) >>> out = np.zeros_like(m) >>> np.median(a, axis=0, out=m) array([ 6.5, 4.5, 2.5]) >>> m array([ 6.5, 4.5, 2.5]) >>> b = a.copy() >>> np.median(b, axis=1, overwrite_input=True) array([ 7., 2.]) >>> assert not np.all(a==b) >>> b = a.copy() >>> np.median(b, axis=None, overwrite_input=True) 3.5 >>> assert not np.all(a==b) """ return ndarray() class memmap: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = float() __array_struct__ = getset_descriptor() __dict__ = dictproxy() __doc__ = str() __module__ = str() def all(self, axis=None, out=None): """a.all(axis=None, out=None) Returns True if all elements evaluate to True. Refer to `numpy.all` for full documentation. See Also -------- numpy.all : equivalent function""" return None def any(self, axis=None, out=None): """a.any(axis=None, out=None) Returns True if any of the elements of `a` evaluate to True. Refer to `numpy.any` for full documentation. See Also -------- numpy.any : equivalent function""" return None def argmax(self, axis=None, out=None): """a.argmax(axis=None, out=None) Return indices of the maximum values along the given axis. Refer to `numpy.argmax` for full documentation. See Also -------- numpy.argmax : equivalent function""" return None def argmin(self, axis=None, out=None): """a.argmin(axis=None, out=None) Return indices of the minimum values along the given axis of `a`. Refer to `numpy.argmin` for detailed documentation. See Also -------- numpy.argmin : equivalent function""" return None def argpartition(self, kth, axis=_1, kind=quickselect, order=None): """a.argpartition(kth, axis=-1, kind='quickselect', order=None) Returns the indices that would partition this array. Refer to `numpy.argpartition` for full documentation. .. versionadded:: 1.8.0 See Also -------- numpy.argpartition : equivalent function""" return None def argsort(self, axis=_1, kind=quicksort, order=None): """a.argsort(axis=-1, kind='quicksort', order=None) Returns the indices that would sort this array. Refer to `numpy.argsort` for full documentation. See Also -------- numpy.argsort : equivalent function""" return None def astype(self, dtype, order, casting, subok, copy): """a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) Copy of the array, cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to false, and the `dtype`, `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy. Returns ------- arr_t : ndarray Unless `copy` is False and the other conditions for returning the input array are satisfied (see description for `copy` input paramter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by `dtype`, `order`. Raises ------ ComplexWarning When casting from complex to float or int. To avoid this, one should use ``a.real.astype(t)``. Examples -------- >>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5]) >>> x.astype(int) array([1, 2, 2])""" return ndarray() base = getset_descriptor() def byteswap(self, inplace): """a.byteswap(inplace) Swap the bytes of the array elements Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Parameters ---------- inplace : bool, optional If ``True``, swap bytes in-place, default is ``False``. Returns ------- out : ndarray The byteswapped array. If `inplace` is ``True``, this is a view to self. Examples -------- >>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322'] Arrays of strings are not swapped >>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')""" return ndarray() def choose(self, choices, out=None, mode=_raise): """a.choose(choices, out=None, mode='raise') Use an index array to construct a new array from a set of choices. Refer to `numpy.choose` for full documentation. See Also -------- numpy.choose : equivalent function""" return None def clip(self, a_min, a_max, out=None): """a.clip(a_min, a_max, out=None) Return an array whose values are limited to ``[a_min, a_max]``. Refer to `numpy.clip` for full documentation. See Also -------- numpy.clip : equivalent function""" return None def compress(self, condition, axis=None, out=None): """a.compress(condition, axis=None, out=None) Return selected slices of this array along given axis. Refer to `numpy.compress` for full documentation. See Also -------- numpy.compress : equivalent function""" return None def conj(self, _): """a.conj() Complex-conjugate all elements. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def conjugate(self, _): """a.conjugate() Return the complex conjugate, element-wise. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def copy(self, order): """a.copy(order='C') Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :func:numpy.copy are very similar, but have different default values for their order= arguments.) See also -------- numpy.copy numpy.copyto Examples -------- >>> x = np.array([[1,2,3],[4,5,6]], order='F') >>> y = x.copy() >>> x.fill(0) >>> x array([[0, 0, 0], [0, 0, 0]]) >>> y array([[1, 2, 3], [4, 5, 6]]) >>> y.flags['C_CONTIGUOUS'] True""" return None ctypes = getset_descriptor() def cumprod(self, axis=None, dtype=None, out=None): """a.cumprod(axis=None, dtype=None, out=None) Return the cumulative product of the elements along the given axis. Refer to `numpy.cumprod` for full documentation. See Also -------- numpy.cumprod : equivalent function""" return None def cumsum(self, axis=None, dtype=None, out=None): """a.cumsum(axis=None, dtype=None, out=None) Return the cumulative sum of the elements along the given axis. Refer to `numpy.cumsum` for full documentation. See Also -------- numpy.cumsum : equivalent function""" return None data = getset_descriptor() def diagonal(self, offset=0, axis1=0, axis2=1): """a.diagonal(offset=0, axis1=0, axis2=1) Return specified diagonals. Refer to :func:`numpy.diagonal` for full documentation. See Also -------- numpy.diagonal : equivalent function""" return None def dot(self, b, out=None): """a.dot(b, out=None) Dot product of two arrays. Refer to `numpy.dot` for full documentation. See Also -------- numpy.dot : equivalent function Examples -------- >>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]]) This array method can be conveniently chained: >>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])""" return None dtype = getset_descriptor() def dump(self, file): """a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load. Parameters ---------- file : str A string naming the dump file.""" return None def dumps(self, _): """a.dumps() Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array. Parameters ---------- None""" return None def fill(self, value): """a.fill(value) Fill the array with a scalar value. Parameters ---------- value : scalar All elements of `a` will be assigned this value. Examples -------- >>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])""" return None flags = getset_descriptor() flat = getset_descriptor() def flatten(self, order): """a.flatten(order='C') Return a copy of the array collapsed into one dimension. Parameters ---------- order : {'C', 'F', 'A'}, optional Whether to flatten in C (row-major), Fortran (column-major) order, or preserve the C/Fortran ordering from `a`. The default is 'C'. Returns ------- y : ndarray A copy of the input array, flattened to one dimension. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the array. Examples -------- >>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])""" return ndarray() def flush(self, _): """ Write any changes in the array to the file on disk. For further information, see `memmap`. Parameters ---------- None See Also -------- memmap """ return None def getfield(self, dtype, offset): """a.getfield(dtype, offset=0) Returns a field of the given array as a certain type. A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes. Parameters ---------- dtype : str or dtype The data type of the view. The dtype size of the view can not be larger than that of the array itself. offset : int Number of bytes to skip before beginning the element view. Examples -------- >>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]]) By choosing an offset of 8 bytes we can select the complex part of the array for our view: >>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])""" return array() imag = getset_descriptor() def item(self, ESCargs): """a.item(*args) Copy an element of an array to a standard Python scalar and return it. Parameters ---------- \*args : Arguments (variable number and type) * none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned. * int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return. * tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array. Returns ------- z : Standard Python scalar object A copy of the specified element of the array as a suitable Python scalar Notes ----- When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned. `item` is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python's optimized math. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3""" return Standard() def itemset(self, ESCargs): """a.itemset(*args) Insert scalar into an array (scalar is cast to array's dtype, if possible) There must be at least 1 argument, and define the last argument as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster than ``a[args] = item``. The item should be a scalar value and `args` must select a single item in the array `a`. Parameters ---------- \*args : Arguments If one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple. Notes ----- Compared to indexing syntax, `itemset` provides some speed increase for placing a scalar into a particular location in an `ndarray`, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using `itemset` (and `item`) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])""" return None itemsize = getset_descriptor() def max(self, axis=None, out=None): """a.max(axis=None, out=None) Return the maximum along a given axis. Refer to `numpy.amax` for full documentation. See Also -------- numpy.amax : equivalent function""" return None def mean(self, axis=None, dtype=None, out=None): """a.mean(axis=None, dtype=None, out=None) Returns the average of the array elements along given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean : equivalent function""" return None def min(self, axis=None, out=None): """a.min(axis=None, out=None) Return the minimum along a given axis. Refer to `numpy.amin` for full documentation. See Also -------- numpy.amin : equivalent function""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """arr.newbyteorder(new_order='S') Return the array with the same data viewed with a different byte order. Equivalent to:: arr.view(arr.dtype.newbytorder(new_order)) Changes are also made in all fields and sub-arrays of the array data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications above. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_arr : array New array object with the dtype reflecting given change to the byte order.""" return array() def nonzero(self, _): """a.nonzero() Return the indices of the elements that are non-zero. Refer to `numpy.nonzero` for full documentation. See Also -------- numpy.nonzero : equivalent function""" return None def partition(self, kth, axis, kind, order): """a.partition(kth, axis=-1, kind='introselect', order=None) Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- kth : int or sequence of ints Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once. axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort. Notes ----- See ``np.partition`` for notes on the different algorithms. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> a.partition(a, 3) >>> a array([2, 1, 3, 4]) >>> a.partition((1, 3)) array([1, 2, 3, 4])""" return None def prod(self, axis=None, dtype=None, out=None): """a.prod(axis=None, dtype=None, out=None) Return the product of the array elements over the given axis Refer to `numpy.prod` for full documentation. See Also -------- numpy.prod : equivalent function""" return None def ptp(self, axis=None, out=None): """a.ptp(axis=None, out=None) Peak to peak (maximum - minimum) value along a given axis. Refer to `numpy.ptp` for full documentation. See Also -------- numpy.ptp : equivalent function""" return None def put(self, indices, values, mode=_raise): """a.put(indices, values, mode='raise') Set ``a.flat[n] = values[n]`` for all `n` in indices. Refer to `numpy.put` for full documentation. See Also -------- numpy.put : equivalent function""" return None def ravel(self, order): """a.ravel([order]) Return a flattened array. Refer to `numpy.ravel` for full documentation. See Also -------- numpy.ravel : equivalent function ndarray.flat : a flat iterator on the array.""" return None real = getset_descriptor() def repeat(self, repeats, axis=None): """a.repeat(repeats, axis=None) Repeat elements of an array. Refer to `numpy.repeat` for full documentation. See Also -------- numpy.repeat : equivalent function""" return None def reshape(self, shape, order=C): """a.reshape(shape, order='C') Returns an array containing the same data with a new shape. Refer to `numpy.reshape` for full documentation. See Also -------- numpy.reshape : equivalent function""" return None def resize(self, new_shape, refcheck): """a.resize(new_shape, refcheck=True) Change shape and size of array in-place. Parameters ---------- new_shape : tuple of ints, or `n` ints Shape of resized array. refcheck : bool, optional If False, reference count will not be checked. Default is True. Returns ------- None Raises ------ ValueError If `a` does not own its own data or references or views to it exist, and the data memory must be changed. SystemError If the `order` keyword argument is specified. This behaviour is a bug in NumPy. See Also -------- resize : Return a new array with the specified shape. Notes ----- This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False. Examples -------- Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]]) >>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]]) Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]]) Referencing an array prevents resizing... >>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ... Unless `refcheck` is False: >>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])""" return None def round(self, decimals=0, out=None): """a.round(decimals=0, out=None) Return `a` with each element rounded to the given number of decimals. Refer to `numpy.around` for full documentation. See Also -------- numpy.around : equivalent function""" return None def searchsorted(self, v, side=left, sorter=None): """a.searchsorted(v, side='left', sorter=None) Find indices where elements of v should be inserted in a to maintain order. For full documentation, see `numpy.searchsorted` See Also -------- numpy.searchsorted : equivalent function""" return None def setfield(self, val, dtype, offset): """a.setfield(val, dtype, offset=0) Put a value into a specified place in a field defined by a data-type. Place `val` into `a`'s field defined by `dtype` and beginning `offset` bytes into the field. Parameters ---------- val : object Value to be placed in field. dtype : dtype object Data-type of the field in which to place `val`. offset : int, optional The number of bytes into the field at which to place `val`. Returns ------- None See Also -------- getfield Examples -------- >>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])""" return None def setflags(self, write, align, uic): """a.setflags(write=None, align=None, uic=None) Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively. These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The UPDATEIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters ---------- write : bool, optional Describes whether or not `a` can be written to. align : bool, optional Describes whether or not `a` is aligned properly for its type. uic : bool, optional Describes whether or not `a` is a copy of another "base" array. Notes ----- Array flags provide information about how the memory area used for the array is to be interpreted. There are 6 Boolean flags in use, only three of which can be changed by the user: UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array. All flags can be accessed using their first (upper case) letter as well as the full name. Examples -------- >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "", line 1, in ValueError: cannot set UPDATEIFCOPY flag to True""" return None shape = getset_descriptor() size = getset_descriptor() def sort(self, axis, kind, order): """a.sort(axis=-1, kind='quicksort', order=None) Sort an array, in-place. Parameters ---------- axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort. Notes ----- See ``sort`` for notes on the different sorting algorithms. Examples -------- >>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]""" return list() def tostring(self, order): """a.tostring(order='C') Construct a Python string containing the raw data bytes in the array. Constructs a Python string showing a copy of the raw contents of data memory. The string can be produced in either 'C' or 'Fortran', or 'Any' order (the default is 'C'-order). 'Any' order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means 'Fortran' order. Parameters ---------- order : {'C', 'F', None}, optional Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array. Returns ------- s : str A Python string exhibiting a copy of `a`'s raw data. Examples -------- >>> x = np.array([[0, 1], [2, 3]]) >>> x.tostring() '\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tostring('C') == x.tostring() True >>> x.tostring('F') '\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'""" return str() def trace(self, offset=0, axis1=0, axis2=1, dtype=None, out=None): """a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) Return the sum along diagonals of the array. Refer to `numpy.trace` for full documentation. See Also -------- numpy.trace : equivalent function""" return None def transpose(self, axes): """a.transpose(*axes) Returns a view of the array with axes transposed. For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. Parameters ---------- axes : None, tuple of ints, or `n` ints * None or no argument: reverses the order of the axes. * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s `i`-th axis becomes `a.transpose()`'s `j`-th axis. * `n` ints: same as an n-tuple of the same ints (this form is intended simply as a "convenience" alternative to the tuple form) Returns ------- out : ndarray View of `a`, with axes suitably permuted. See Also -------- ndarray.T : Array property returning the array transposed. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])""" return ndarray() def var(self, axis=None, dtype=None, out=None, ddof=0): """a.var(axis=None, dtype=None, out=None, ddof=0) Returns the variance of the array elements, along given axis. Refer to `numpy.var` for full documentation. See Also -------- numpy.var : equivalent function""" return None def view(self, dtype, type): """a.view(dtype=None, type=None) New view of array with the same data. Parameters ---------- dtype : data-type or ndarray sub-class, optional Data-type descriptor of the returned view, e.g., float32 or int16. The default, None, results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the ``type`` parameter). type : Python type, optional Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation. Notes ----- ``a.view()`` is used two different ways: ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view of the array's memory with a different data-type. This can cause a reinterpretation of the bytes of memory. ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory. For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of ``a`` (shown by ``print(a)``). It also depends on exactly how ``a`` is stored in memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results. Examples -------- >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) Viewing array data using a different type and dtype: >>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print type(y) Creating a view on a structured array so it can be used in calculations >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.]) Making changes to the view changes the underlying array >>> xv[0,1] = 20 >>> print x [(1, 20) (3, 4)] Using a view to convert an array to a record array: >>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8) Views share data: >>> x[0] = (9, 10) >>> z[0] (9, 10) Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.: >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "", line 1, in ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', '>> nx, ny = (3, 2) >>> x = np.linspace(0, 1, nx) >>> y = np.linspace(0, 1, ny) >>> xv, yv = meshgrid(x, y) >>> xv array([[ 0. , 0.5, 1. ], [ 0. , 0.5, 1. ]]) >>> yv array([[ 0., 0., 0.], [ 1., 1., 1.]]) >>> xv, yv = meshgrid(x, y, sparse=True) # make sparse output arrays >>> xv array([[ 0. , 0.5, 1. ]]) >>> yv array([[ 0.], [ 1.]]) `meshgrid` is very useful to evaluate functions on a grid. >>> x = np.arange(-5, 5, 0.1) >>> y = np.arange(-5, 5, 0.1) >>> xx, yy = meshgrid(x, y, sparse=True) >>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2) >>> h = plt.contourf(x,y,z) """ return ndarray() mgrid = nd_grid() def amin(a=False, axis=None, out=None, keepdims=False): """ Return the minimum of an array or minimum along an axis. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default, flattened input is used. out : ndarray, optional Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See `doc.ufuncs` (Section "Output arguments") for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- amin : ndarray or scalar Minimum of `a`. If `axis` is None, the result is a scalar value. If `axis` is given, the result is an array of dimension ``a.ndim - 1``. See Also -------- amax : The maximum value of an array along a given axis, propagating any NaNs. nanmin : The minimum value of an array along a given axis, ignoring any NaNs. minimum : Element-wise minimum of two arrays, propagating any NaNs. fmin : Element-wise minimum of two arrays, ignoring any NaNs. argmin : Return the indices of the minimum values. nanmax, maximum, fmax Notes ----- NaN values are propagated, that is if at least one item is NaN, the corresponding min value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmin. Don't use `amin` for element-wise comparison of 2 arrays; when ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than ``amin(a, axis=0)``. Examples -------- >>> a = np.arange(4).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amin(a) # Minimum of the flattened array 0 >>> np.amin(a, axis=0) # Minima along the first axis array([0, 1]) >>> np.amin(a, axis=1) # Minima along the second axis array([0, 2]) >>> b = np.arange(5, dtype=np.float) >>> b[2] = np.NaN >>> np.amin(b) nan >>> np.nanmin(b) 0.0 """ return ndarray() if False else float() def min_scalar_type(a): """min_scalar_type(a) For scalar ``a``, returns the data type with the smallest size and smallest scalar kind which can hold its value. For non-scalar array ``a``, returns the vector's dtype unmodified. Floating point values are not demoted to integers, and complex values are not demoted to floats. Parameters ---------- a : scalar or array_like The value whose minimal data type is to be found. Returns ------- out : dtype The minimal data type. Notes ----- .. versionadded:: 1.6.0 See Also -------- result_type, promote_types, dtype, can_cast Examples -------- >>> np.min_scalar_type(10) dtype('uint8') >>> np.min_scalar_type(-260) dtype('int16') >>> np.min_scalar_type(3.1) dtype('float16') >>> np.min_scalar_type(1e50) dtype('float64') >>> np.min_scalar_type(np.arange(4,dtype='f8')) dtype('float64')""" return dtype() def minimum(x1, x2, out=None): """minimum(x1, x2[, out]) Element-wise minimum of array elements. Compare two arrays and returns a new array containing the element-wise minima. If one of the elements being compared is a nan, then that element is returned. If both elements are nans then the first is returned. The latter distinction is important for complex nans, which are defined as at least one of the real or imaginary parts being a nan. The net effect is that nans are propagated. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. They must have the same shape, or shapes that can be broadcast to a single shape. Returns ------- y : {ndarray, scalar} The minimum of `x1` and `x2`, element-wise. Returns scalar if both `x1` and `x2` are scalars. See Also -------- maximum : Element-wise maximum of two arrays, propagating any NaNs. fmin : Element-wise minimum of two arrays, ignoring any NaNs. amin : The minimum value of an array along a given axis, propagating any NaNs. nanmin : The minimum value of an array along a given axis, ignoring any NaNs. fmax, amax, nanmax Notes ----- The minimum is equivalent to ``np.where(x1 <= x2, x1, x2)`` when neither x1 nor x2 are nans, but it is faster and does proper broadcasting. Examples -------- >>> np.minimum([2, 3, 4], [1, 5, 2]) array([1, 3, 2]) >>> np.minimum(np.eye(2), [0.5, 2]) # broadcasting array([[ 0.5, 0. ], [ 0. , 1. ]]) >>> np.minimum([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ NaN, NaN, NaN]) >>> np.minimum(-np.Inf, 1) -inf""" return ndarray() def mintypecode(typechars="d", typeset="GDFgdf", default="d"): """ Return the character for the minimum-size type to which given types can be safely cast. The returned type character must represent the smallest size dtype such that an array of the returned type can handle the data from an array of all types in `typechars` (or if `typechars` is an array, then its dtype.char). Parameters ---------- typechars : list of str or array_like If a list of strings, each string should represent a dtype. If array_like, the character representation of the array dtype is used. typeset : str or list of str, optional The set of characters that the returned character is chosen from. The default set is 'GDFgdf'. default : str, optional The default character, this is returned if none of the characters in `typechars` matches a character in `typeset`. Returns ------- typechar : str The character representing the minimum-size type that was found. See Also -------- dtype, sctype2char, maximum_sctype Examples -------- >>> np.mintypecode(['d', 'f', 'S']) 'd' >>> x = np.array([1.1, 2-3.j]) >>> np.mintypecode(x) 'D' >>> np.mintypecode('abceh', default='G') 'G' """ return str() def mirr(values, finance_rate, reinvest_rate): """ Modified internal rate of return. Parameters ---------- values : array_like Cash flows (must contain at least one positive and one negative value) or nan is returned. The first value is considered a sunk cost at time zero. finance_rate : scalar Interest rate paid on the cash flows reinvest_rate : scalar Interest rate received on the cash flows upon reinvestment Returns ------- out : float Modified internal rate of return """ return float() def remainder(x1, x2, out): """remainder(x1, x2[, out]) Return element-wise remainder of division. Computes ``x1 - floor(x1 / x2) * x2``. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- y : ndarray The remainder of the quotient ``x1/x2``, element-wise. Returns a scalar if both `x1` and `x2` are scalars. See Also -------- divide, floor Notes ----- Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of) integers. Examples -------- >>> np.remainder([4, 7], [2, 3]) array([0, 1]) >>> np.remainder(np.arange(7), 5) array([0, 1, 2, 3, 4, 0, 1])""" return ndarray() def modf(x, out1=None, out2=None): """modf(x[, out1, out2]) Return the fractional and integral parts of an array, element-wise. The fractional and integral parts are negative if the given number is negative. Parameters ---------- x : array_like Input array. Returns ------- y1 : ndarray Fractional part of `x`. y2 : ndarray Integral part of `x`. Notes ----- For integer input the return values are floats. Examples -------- >>> np.modf([0, 3.5]) (array([ 0. , 0.5]), array([ 0., 3.])) >>> np.modf(-0.5) (-0.5, -0)""" return ndarray() def msort(a): """ Return a copy of an array sorted along the first axis. Parameters ---------- a : array_like Array to be sorted. Returns ------- sorted_array : ndarray Array of the same type and shape as `a`. See Also -------- sort Notes ----- ``np.msort(a)`` is equivalent to ``np.sort(a, axis=0)``. """ return ndarray() def multiply(x1, x2, out=None): """multiply(x1, x2[, out]) Multiply arguments element-wise. Parameters ---------- x1, x2 : array_like Input arrays to be multiplied. Returns ------- y : ndarray The product of `x1` and `x2`, element-wise. Returns a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` * `x2` in terms of array broadcasting. Examples -------- >>> np.multiply(2.0, 4.0) 8.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.multiply(x1, x2) array([[ 0., 1., 4.], [ 0., 4., 10.], [ 0., 7., 16.]])""" return ndarray() nan = float() def nan_to_num(x): """ Replace nan with zero and inf with finite numbers. Returns an array or scalar replacing Not a Number (NaN) with zero, (positive) infinity with a very large number and negative infinity with a very small (or negative) number. Parameters ---------- x : array_like Input data. Returns ------- out : ndarray, float Array with the same shape as `x` and dtype of the element in `x` with the greatest precision. NaN is replaced by zero, and infinity (-infinity) is replaced by the largest (smallest or most negative) floating point value that fits in the output dtype. All finite numbers are upcast to the output dtype (default float64). See Also -------- isinf : Shows which elements are negative or negative infinity. isneginf : Shows which elements are negative infinity. isposinf : Shows which elements are positive infinity. isnan : Shows which elements are Not a Number (NaN). isfinite : Shows which elements are finite (not NaN, not infinity) Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Examples -------- >>> np.set_printoptions(precision=8) >>> x = np.array([np.inf, -np.inf, np.nan, -128, 128]) >>> np.nan_to_num(x) array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, -1.28000000e+002, 1.28000000e+002]) """ return ndarray() def nanargmax(a=None, axis=None): """ Return the indices of the maximum values in the specified axis ignoring NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results cannot be trusted if a slice contains only NaNs and -Infs. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default flattened input is used. Returns ------- index_array : ndarray An array of indices or a single index value. See Also -------- argmax, nanargmin Examples -------- >>> a = np.array([[np.nan, 4], [2, 3]]) >>> np.argmax(a) 0 >>> np.nanargmax(a) 1 >>> np.nanargmax(a, axis=0) array([1, 0]) >>> np.nanargmax(a, axis=1) array([1, 1]) """ return ndarray() def nanargmin(a=None, axis=None): """ Return the indices of the minimum values in the specified axis ignoring NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results cannot be trusted if a slice contains only NaNs and Infs. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default flattened input is used. Returns ------- index_array : ndarray An array of indices or a single index value. See Also -------- argmin, nanargmax Examples -------- >>> a = np.array([[np.nan, 4], [2, 3]]) >>> np.argmin(a) 0 >>> np.nanargmin(a) 2 >>> np.nanargmin(a, axis=0) array([1, 1]) >>> np.nanargmin(a, axis=1) array([1, 0]) """ return ndarray() def nanmax(a=False, axis=None, out=None, keepdims=False): """ Return the maximum of an array or maximum along an axis, ignoring any NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is raised and NaN is returned for that slice. Parameters ---------- a : array_like Array containing numbers whose maximum is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the maximum is computed. The default is to compute the maximum of the flattened array. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See `doc.ufuncs` for details. .. versionadded:: 1.8.0 keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. .. versionadded:: 1.8.0 Returns ------- nanmax : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned. See Also -------- nanmin : The minimum value of an array along a given axis, ignoring any NaNs. amax : The maximum value of an array along a given axis, propagating any NaNs. fmax : Element-wise maximum of two arrays, ignoring any NaNs. maximum : Element-wise maximum of two arrays, propagating any NaNs. isnan : Shows which elements are Not a Number (NaN). isfinite: Shows which elements are neither NaN nor infinity. amin, fmin, minimum Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number. If the input has a integer type the function is equivalent to np.max. Examples -------- >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmax(a) 3.0 >>> np.nanmax(a, axis=0) array([ 3., 2.]) >>> np.nanmax(a, axis=1) array([ 2., 3.]) When positive infinity and negative infinity are present: >>> np.nanmax([1, 2, np.nan, np.NINF]) 2.0 >>> np.nanmax([1, 2, np.nan, np.inf]) inf """ return ndarray() def nanmean(a=False, axis=None, dtype=None, out=None, keepdims=False): """ Compute the arithmetic mean along the specified axis, ignoring NaNs. Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. `float64` intermediate and return values are used for integer inputs. For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array containing numbers whose mean is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the means are computed. The default is to compute the mean of the flattened array. dtype : data-type, optional Type to use in computing the mean. For integer inputs, the default is `float64`; for inexact inputs, it is the same as the input dtype. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See `doc.ufuncs` for details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- m : ndarray, see dtype parameter above If `out=None`, returns a new array containing the mean values, otherwise a reference to the output array is returned. Nan is returned for slices that contain only NaNs. See Also -------- average : Weighted average mean : Arithmetic mean taken while not ignoring NaNs var, nanvar Notes ----- The arithmetic mean is the sum of the non-NaN elements along the axis divided by the number of non-NaN elements. Note that for floating-point input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32`. Specifying a higher-precision accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanmean(a) 2.6666666666666665 >>> np.nanmean(a, axis=0) array([ 2., 4.]) >>> np.nanmean(a, axis=1) array([ 1., 3.5]) """ return ndarray() def nanmin(a=False, axis=None, out=None, keepdims=False): """ Return minimum of an array or minimum along an axis, ignoring any NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is raised and Nan is returned for that slice. Parameters ---------- a : array_like Array containing numbers whose minimum is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the minimum is computed. The default is to compute the minimum of the flattened array. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See `doc.ufuncs` for details. .. versionadded:: 1.8.0 keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. .. versionadded:: 1.8.0 Returns ------- nanmin : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned. See Also -------- nanmax : The maximum value of an array along a given axis, ignoring any NaNs. amin : The minimum value of an array along a given axis, propagating any NaNs. fmin : Element-wise minimum of two arrays, ignoring any NaNs. minimum : Element-wise minimum of two arrays, propagating any NaNs. isnan : Shows which elements are Not a Number (NaN). isfinite: Shows which elements are neither NaN nor infinity. amax, fmax, maximum Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number. If the input has a integer type the function is equivalent to np.min. Examples -------- >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmin(a) 1.0 >>> np.nanmin(a, axis=0) array([ 1., 2.]) >>> np.nanmin(a, axis=1) array([ 1., 3.]) When positive infinity and negative infinity are present: >>> np.nanmin([1, 2, np.nan, np.inf]) 1.0 >>> np.nanmin([1, 2, np.nan, np.NINF]) -inf """ return ndarray() def nanstd(a=False, axis=None, dtype=None, out=None, ddof=0, keepdims=False): """ Compute the standard deviation along the specified axis, while ignoring NaNs. Returns the standard deviation, a measure of the spread of a distribution, of the non-NaN array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis. For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a `RuntimeWarning` is raised. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Calculate the standard deviation of the non-NaN values. axis : int, optional Axis along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array. dtype : dtype, optional Type to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary. ddof : int, optional Means Delta Degrees of Freedom. The divisor used in calculations is ``N - ddof``, where ``N`` represents the number of non-NaN elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- standard_deviation : ndarray, see dtype parameter above. If `out` is None, return a new array containing the standard deviation, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN. See Also -------- var, mean, std nanvar, nanmean numpy.doc.ufuncs : Section "Output arguments" Notes ----- The standard deviation is the square root of the average of the squared deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``. The average squared deviation is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of the infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with ``ddof=1``, it will not be an unbiased estimate of the standard deviation per se. Note that, for complex numbers, `std` takes the absolute value before squaring, so that the result is always real and nonnegative. For floating-point input, the *std* is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanstd(a) 1.247219128924647 >>> np.nanstd(a, axis=0) array([ 1., 0.]) >>> np.nanstd(a, axis=1) array([ 0., 0.5]) """ return ndarray() def nansum(a=0, axis=None, dtype=None, out=None, keepdims=0): """ Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. FutureWarning: In Numpy versions <= 1.8 Nan is returned for slices that are all-NaN or empty. In later versions zero will be returned. Parameters ---------- a : array_like Array containing numbers whose sum is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the sum is computed. The default is to compute the sum of the flattened array. dtype : data-type, optional The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of `a` is used. An exception is when `a` has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact. .. versionadded:: 1.8.0 out : ndarray, optional Alternate output array in which to place the result. The default is ``None``. If provided, it must have the same shape as the expected output, but the type will be cast if necessary. See `doc.ufuncs` for details. The casting of NaN to integer can yield unexpected results. .. versionadded:: 1.8.0 keepdims : bool, optional If True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. .. versionadded:: 1.8.0 Returns ------- y : ndarray or numpy scalar See Also -------- numpy.sum : Sum across array propagating NaNs. isnan : Show which elements are NaN. isfinite: Show which elements are not NaN or +/-inf. Notes ----- If both positive and negative infinity are present, the sum will be Not A Number (NaN). Numpy integer arithmetic is modular. If the size of a sum exceeds the size of an integer accumulator, its value will wrap around and the result will be incorrect. Specifying ``dtype=double`` can alleviate that problem. Examples -------- >>> np.nansum(1) 1 >>> np.nansum([1]) 1 >>> np.nansum([1, np.nan]) 1.0 >>> a = np.array([[1, 1], [1, np.nan]]) >>> np.nansum(a) 3.0 >>> np.nansum(a, axis=0) array([ 2., 1.]) >>> np.nansum([1, np.nan, np.inf]) inf >>> np.nansum([1, np.nan, np.NINF]) -inf >>> np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present nan """ return ndarray() if False else numpy() def nanvar(a=False, axis=None, dtype=None, out=None, ddof=0, keepdims=False): """ Compute the variance along the specified axis, while ignoring NaNs. Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis. For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a `RuntimeWarning` is raised. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the variance is computed. The default is to compute the variance of the flattened array. dtype : data-type, optional Type to use in computing the variance. For arrays of integer type the default is `float32`; for arrays of float types it is the same as the array type. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary. ddof : int, optional "Delta Degrees of Freedom": the divisor used in the calculation is ``N - ddof``, where ``N`` represents the number of non-NaN elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- variance : ndarray, see dtype parameter above If `out` is None, return a new array containing the variance, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN. See Also -------- std : Standard deviation mean : Average var : Variance while not ignoring NaNs nanstd, nanmean numpy.doc.ufuncs : Section "Output arguments" Notes ----- The variance is the average of the squared deviations from the mean, i.e., ``var = mean(abs(x - x.mean())**2)``. The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of a hypothetical infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative. For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32` (see example below). Specifying a higher-accuracy accumulator using the ``dtype`` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.var(a) 1.5555555555555554 >>> np.nanvar(a, axis=0) array([ 1., 0.]) >>> np.nanvar(a, axis=1) array([ 0., 0.25]) """ return ndarray() nbytes = _typedict() class ndarray: T = getset_descriptor() __array_finalize__ = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() def all(self, axis=None, out=None): """a.all(axis=None, out=None) Returns True if all elements evaluate to True. Refer to `numpy.all` for full documentation. See Also -------- numpy.all : equivalent function""" return None def any(self, axis=None, out=None): """a.any(axis=None, out=None) Returns True if any of the elements of `a` evaluate to True. Refer to `numpy.any` for full documentation. See Also -------- numpy.any : equivalent function""" return None def argmax(self, axis=None, out=None): """a.argmax(axis=None, out=None) Return indices of the maximum values along the given axis. Refer to `numpy.argmax` for full documentation. See Also -------- numpy.argmax : equivalent function""" return None def argmin(self, axis=None, out=None): """a.argmin(axis=None, out=None) Return indices of the minimum values along the given axis of `a`. Refer to `numpy.argmin` for detailed documentation. See Also -------- numpy.argmin : equivalent function""" return None def argpartition(self, kth, axis=_1, kind=quickselect, order=None): """a.argpartition(kth, axis=-1, kind='quickselect', order=None) Returns the indices that would partition this array. Refer to `numpy.argpartition` for full documentation. .. versionadded:: 1.8.0 See Also -------- numpy.argpartition : equivalent function""" return None def argsort(self, axis=_1, kind=quicksort, order=None): """a.argsort(axis=-1, kind='quicksort', order=None) Returns the indices that would sort this array. Refer to `numpy.argsort` for full documentation. See Also -------- numpy.argsort : equivalent function""" return None def astype(self, dtype, order, casting, subok, copy): """a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) Copy of the array, cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to false, and the `dtype`, `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy. Returns ------- arr_t : ndarray Unless `copy` is False and the other conditions for returning the input array are satisfied (see description for `copy` input paramter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by `dtype`, `order`. Raises ------ ComplexWarning When casting from complex to float or int. To avoid this, one should use ``a.real.astype(t)``. Examples -------- >>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5]) >>> x.astype(int) array([1, 2, 2])""" return ndarray() base = getset_descriptor() def byteswap(self, inplace): """a.byteswap(inplace) Swap the bytes of the array elements Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Parameters ---------- inplace : bool, optional If ``True``, swap bytes in-place, default is ``False``. Returns ------- out : ndarray The byteswapped array. If `inplace` is ``True``, this is a view to self. Examples -------- >>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322'] Arrays of strings are not swapped >>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')""" return ndarray() def choose(self, choices, out=None, mode=_raise): """a.choose(choices, out=None, mode='raise') Use an index array to construct a new array from a set of choices. Refer to `numpy.choose` for full documentation. See Also -------- numpy.choose : equivalent function""" return None def clip(self, a_min, a_max, out=None): """a.clip(a_min, a_max, out=None) Return an array whose values are limited to ``[a_min, a_max]``. Refer to `numpy.clip` for full documentation. See Also -------- numpy.clip : equivalent function""" return None def compress(self, condition, axis=None, out=None): """a.compress(condition, axis=None, out=None) Return selected slices of this array along given axis. Refer to `numpy.compress` for full documentation. See Also -------- numpy.compress : equivalent function""" return None def conj(self, _): """a.conj() Complex-conjugate all elements. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def conjugate(self, _): """a.conjugate() Return the complex conjugate, element-wise. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def copy(self, order): """a.copy(order='C') Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :func:numpy.copy are very similar, but have different default values for their order= arguments.) See also -------- numpy.copy numpy.copyto Examples -------- >>> x = np.array([[1,2,3],[4,5,6]], order='F') >>> y = x.copy() >>> x.fill(0) >>> x array([[0, 0, 0], [0, 0, 0]]) >>> y array([[1, 2, 3], [4, 5, 6]]) >>> y.flags['C_CONTIGUOUS'] True""" return None ctypes = getset_descriptor() def cumprod(self, axis=None, dtype=None, out=None): """a.cumprod(axis=None, dtype=None, out=None) Return the cumulative product of the elements along the given axis. Refer to `numpy.cumprod` for full documentation. See Also -------- numpy.cumprod : equivalent function""" return None def cumsum(self, axis=None, dtype=None, out=None): """a.cumsum(axis=None, dtype=None, out=None) Return the cumulative sum of the elements along the given axis. Refer to `numpy.cumsum` for full documentation. See Also -------- numpy.cumsum : equivalent function""" return None data = getset_descriptor() def diagonal(self, offset=0, axis1=0, axis2=1): """a.diagonal(offset=0, axis1=0, axis2=1) Return specified diagonals. Refer to :func:`numpy.diagonal` for full documentation. See Also -------- numpy.diagonal : equivalent function""" return None def dot(self, b, out=None): """a.dot(b, out=None) Dot product of two arrays. Refer to `numpy.dot` for full documentation. See Also -------- numpy.dot : equivalent function Examples -------- >>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]]) This array method can be conveniently chained: >>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])""" return None dtype = getset_descriptor() def dump(self, file): """a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load. Parameters ---------- file : str A string naming the dump file.""" return None def dumps(self, _): """a.dumps() Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array. Parameters ---------- None""" return None def fill(self, value): """a.fill(value) Fill the array with a scalar value. Parameters ---------- value : scalar All elements of `a` will be assigned this value. Examples -------- >>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])""" return None flags = getset_descriptor() flat = getset_descriptor() def flatten(self, order): """a.flatten(order='C') Return a copy of the array collapsed into one dimension. Parameters ---------- order : {'C', 'F', 'A'}, optional Whether to flatten in C (row-major), Fortran (column-major) order, or preserve the C/Fortran ordering from `a`. The default is 'C'. Returns ------- y : ndarray A copy of the input array, flattened to one dimension. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the array. Examples -------- >>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])""" return ndarray() def getfield(self, dtype, offset): """a.getfield(dtype, offset=0) Returns a field of the given array as a certain type. A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes. Parameters ---------- dtype : str or dtype The data type of the view. The dtype size of the view can not be larger than that of the array itself. offset : int Number of bytes to skip before beginning the element view. Examples -------- >>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]]) By choosing an offset of 8 bytes we can select the complex part of the array for our view: >>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])""" return array() imag = getset_descriptor() def item(self, ESCargs): """a.item(*args) Copy an element of an array to a standard Python scalar and return it. Parameters ---------- \*args : Arguments (variable number and type) * none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned. * int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return. * tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array. Returns ------- z : Standard Python scalar object A copy of the specified element of the array as a suitable Python scalar Notes ----- When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned. `item` is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python's optimized math. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3""" return Standard() def itemset(self, ESCargs): """a.itemset(*args) Insert scalar into an array (scalar is cast to array's dtype, if possible) There must be at least 1 argument, and define the last argument as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster than ``a[args] = item``. The item should be a scalar value and `args` must select a single item in the array `a`. Parameters ---------- \*args : Arguments If one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple. Notes ----- Compared to indexing syntax, `itemset` provides some speed increase for placing a scalar into a particular location in an `ndarray`, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using `itemset` (and `item`) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])""" return None itemsize = getset_descriptor() def max(self, axis=None, out=None): """a.max(axis=None, out=None) Return the maximum along a given axis. Refer to `numpy.amax` for full documentation. See Also -------- numpy.amax : equivalent function""" return None def mean(self, axis=None, dtype=None, out=None): """a.mean(axis=None, dtype=None, out=None) Returns the average of the array elements along given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean : equivalent function""" return None def min(self, axis=None, out=None): """a.min(axis=None, out=None) Return the minimum along a given axis. Refer to `numpy.amin` for full documentation. See Also -------- numpy.amin : equivalent function""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """arr.newbyteorder(new_order='S') Return the array with the same data viewed with a different byte order. Equivalent to:: arr.view(arr.dtype.newbytorder(new_order)) Changes are also made in all fields and sub-arrays of the array data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications above. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_arr : array New array object with the dtype reflecting given change to the byte order.""" return array() def nonzero(self, _): """a.nonzero() Return the indices of the elements that are non-zero. Refer to `numpy.nonzero` for full documentation. See Also -------- numpy.nonzero : equivalent function""" return None def partition(self, kth, axis, kind, order): """a.partition(kth, axis=-1, kind='introselect', order=None) Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- kth : int or sequence of ints Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once. axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort. Notes ----- See ``np.partition`` for notes on the different algorithms. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> a.partition(a, 3) >>> a array([2, 1, 3, 4]) >>> a.partition((1, 3)) array([1, 2, 3, 4])""" return None def prod(self, axis=None, dtype=None, out=None): """a.prod(axis=None, dtype=None, out=None) Return the product of the array elements over the given axis Refer to `numpy.prod` for full documentation. See Also -------- numpy.prod : equivalent function""" return None def ptp(self, axis=None, out=None): """a.ptp(axis=None, out=None) Peak to peak (maximum - minimum) value along a given axis. Refer to `numpy.ptp` for full documentation. See Also -------- numpy.ptp : equivalent function""" return None def put(self, indices, values, mode=_raise): """a.put(indices, values, mode='raise') Set ``a.flat[n] = values[n]`` for all `n` in indices. Refer to `numpy.put` for full documentation. See Also -------- numpy.put : equivalent function""" return None def ravel(self, order): """a.ravel([order]) Return a flattened array. Refer to `numpy.ravel` for full documentation. See Also -------- numpy.ravel : equivalent function ndarray.flat : a flat iterator on the array.""" return None real = getset_descriptor() def repeat(self, repeats, axis=None): """a.repeat(repeats, axis=None) Repeat elements of an array. Refer to `numpy.repeat` for full documentation. See Also -------- numpy.repeat : equivalent function""" return None def reshape(self, shape, order=C): """a.reshape(shape, order='C') Returns an array containing the same data with a new shape. Refer to `numpy.reshape` for full documentation. See Also -------- numpy.reshape : equivalent function""" return None def resize(self, new_shape, refcheck): """a.resize(new_shape, refcheck=True) Change shape and size of array in-place. Parameters ---------- new_shape : tuple of ints, or `n` ints Shape of resized array. refcheck : bool, optional If False, reference count will not be checked. Default is True. Returns ------- None Raises ------ ValueError If `a` does not own its own data or references or views to it exist, and the data memory must be changed. SystemError If the `order` keyword argument is specified. This behaviour is a bug in NumPy. See Also -------- resize : Return a new array with the specified shape. Notes ----- This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False. Examples -------- Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]]) >>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]]) Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]]) Referencing an array prevents resizing... >>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ... Unless `refcheck` is False: >>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])""" return None def round(self, decimals=0, out=None): """a.round(decimals=0, out=None) Return `a` with each element rounded to the given number of decimals. Refer to `numpy.around` for full documentation. See Also -------- numpy.around : equivalent function""" return None def searchsorted(self, v, side=left, sorter=None): """a.searchsorted(v, side='left', sorter=None) Find indices where elements of v should be inserted in a to maintain order. For full documentation, see `numpy.searchsorted` See Also -------- numpy.searchsorted : equivalent function""" return None def setfield(self, val, dtype, offset): """a.setfield(val, dtype, offset=0) Put a value into a specified place in a field defined by a data-type. Place `val` into `a`'s field defined by `dtype` and beginning `offset` bytes into the field. Parameters ---------- val : object Value to be placed in field. dtype : dtype object Data-type of the field in which to place `val`. offset : int, optional The number of bytes into the field at which to place `val`. Returns ------- None See Also -------- getfield Examples -------- >>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])""" return None def setflags(self, write, align, uic): """a.setflags(write=None, align=None, uic=None) Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively. These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The UPDATEIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters ---------- write : bool, optional Describes whether or not `a` can be written to. align : bool, optional Describes whether or not `a` is aligned properly for its type. uic : bool, optional Describes whether or not `a` is a copy of another "base" array. Notes ----- Array flags provide information about how the memory area used for the array is to be interpreted. There are 6 Boolean flags in use, only three of which can be changed by the user: UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array. All flags can be accessed using their first (upper case) letter as well as the full name. Examples -------- >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "", line 1, in ValueError: cannot set UPDATEIFCOPY flag to True""" return None shape = getset_descriptor() size = getset_descriptor() def sort(self, axis, kind, order): """a.sort(axis=-1, kind='quicksort', order=None) Sort an array, in-place. Parameters ---------- axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort. Notes ----- See ``sort`` for notes on the different sorting algorithms. Examples -------- >>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]""" return list() def tostring(self, order): """a.tostring(order='C') Construct a Python string containing the raw data bytes in the array. Constructs a Python string showing a copy of the raw contents of data memory. The string can be produced in either 'C' or 'Fortran', or 'Any' order (the default is 'C'-order). 'Any' order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means 'Fortran' order. Parameters ---------- order : {'C', 'F', None}, optional Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array. Returns ------- s : str A Python string exhibiting a copy of `a`'s raw data. Examples -------- >>> x = np.array([[0, 1], [2, 3]]) >>> x.tostring() '\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tostring('C') == x.tostring() True >>> x.tostring('F') '\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'""" return str() def trace(self, offset=0, axis1=0, axis2=1, dtype=None, out=None): """a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) Return the sum along diagonals of the array. Refer to `numpy.trace` for full documentation. See Also -------- numpy.trace : equivalent function""" return None def transpose(self, axes): """a.transpose(*axes) Returns a view of the array with axes transposed. For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. Parameters ---------- axes : None, tuple of ints, or `n` ints * None or no argument: reverses the order of the axes. * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s `i`-th axis becomes `a.transpose()`'s `j`-th axis. * `n` ints: same as an n-tuple of the same ints (this form is intended simply as a "convenience" alternative to the tuple form) Returns ------- out : ndarray View of `a`, with axes suitably permuted. See Also -------- ndarray.T : Array property returning the array transposed. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])""" return ndarray() def var(self, axis=None, dtype=None, out=None, ddof=0): """a.var(axis=None, dtype=None, out=None, ddof=0) Returns the variance of the array elements, along given axis. Refer to `numpy.var` for full documentation. See Also -------- numpy.var : equivalent function""" return None def view(self, dtype, type): """a.view(dtype=None, type=None) New view of array with the same data. Parameters ---------- dtype : data-type or ndarray sub-class, optional Data-type descriptor of the returned view, e.g., float32 or int16. The default, None, results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the ``type`` parameter). type : Python type, optional Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation. Notes ----- ``a.view()`` is used two different ways: ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view of the array's memory with a different data-type. This can cause a reinterpretation of the bytes of memory. ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory. For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of ``a`` (shown by ``print(a)``). It also depends on exactly how ``a`` is stored in memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results. Examples -------- >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) Viewing array data using a different type and dtype: >>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print type(y) Creating a view on a structured array so it can be used in calculations >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.]) Making changes to the view changes the underlying array >>> xv[0,1] = 20 >>> print x [(1, 20) (3, 4)] Using a view to convert an array to a record array: >>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8) Views share data: >>> x[0] = (9, 10) >>> z[0] (9, 10) Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.: >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "", line 1, in ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', '>> np.ndim([[1,2,3],[4,5,6]]) 2 >>> np.ndim(np.array([[1,2,3],[4,5,6]])) 2 >>> np.ndim(1) 0 """ return int() class ndindex: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def ndincr(self, _): """ Increment the multi-dimensional index by one. This method is for backward compatibility only: do not use. """ return None class nditer: __doc__ = str() def copy(self, _): """copy() Get a copy of the iterator in its current state. Examples -------- >>> x = np.arange(10) >>> y = x + 1 >>> it = np.nditer([x, y]) >>> it.next() (array(0), array(1)) >>> it2 = it.copy() >>> it2.next() (array(1), array(2))""" return None def debug_print(self, _): """debug_print() Print the current state of the `nditer` instance and debug info to stdout.""" return None dtypes = getset_descriptor() def enable_external_loop(self, _): """enable_external_loop() When the "external_loop" was not used during construction, but is desired, this modifies the iterator to behave as if the flag was specified.""" return None finished = getset_descriptor() has_delayed_bufalloc = getset_descriptor() has_index = getset_descriptor() has_multi_index = getset_descriptor() index = getset_descriptor() iterationneedsapi = getset_descriptor() iterindex = getset_descriptor() def iternext(self, _): """iternext() Check whether iterations are left, and perform a single internal iteration without returning the result. Used in the C-style pattern do-while pattern. For an example, see `nditer`. Returns ------- iternext : bool Whether or not there are iterations left.""" return None iterrange = getset_descriptor() itersize = getset_descriptor() itviews = getset_descriptor() multi_index = getset_descriptor() ndim = getset_descriptor() def next(self, _): """x.next() -> the next value, or raise StopIteration""" return None nop = getset_descriptor() operands = getset_descriptor() def remove_axis(self, i): """remove_axis(i) Removes axis `i` from the iterator. Requires that the flag "multi_index" be enabled.""" return None def remove_multi_index(self, _): """remove_multi_index() When the "multi_index" flag was specified, this removes it, allowing the internal iteration structure to be optimized further.""" return None def reset(self, _): """reset() Reset the iterator to its initial state.""" return None shape = getset_descriptor() value = getset_descriptor() def negative(x, out=None): """negative(x[, out]) Returns an array with the negative of each element of the original array. Parameters ---------- x : array_like or scalar Input array. Returns ------- y : ndarray or scalar Returned array or scalar: `y = -x`. Examples -------- >>> np.negative([1.,-1.]) array([-1., 1.])""" return ndarray() if False else float() def nested_iters(): """None""" return None newaxis = None def newbuffer(size): """newbuffer(size) Return a new uninitialized buffer object. Parameters ---------- size : int Size in bytes of returned buffer object. Returns ------- newbuffer : buffer object Returned, uninitialized buffer object of `size` bytes.""" return buffer() def nextafter(x1, x2, out): """nextafter(x1, x2[, out]) Return the next representable floating-point value after x1 in the direction of x2 element-wise. Parameters ---------- x1 : array_like Values to find the next representable value of. x2 : array_like The direction where to look for the next representable value of `x1`. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See `doc.ufuncs`. Returns ------- out : array_like The next representable values of `x1` in the direction of `x2`. Examples -------- >>> eps = np.finfo(np.float64).eps >>> np.nextafter(1, 2) == eps + 1 True >>> np.nextafter([1, 2], [2, 1]) == [eps + 1, 2 - eps] array([ True, True], dtype=bool)""" return ndarray() def nonzero(a): """ Return the indices of the elements that are non-zero. Returns a tuple of arrays, one for each dimension of `a`, containing the indices of the non-zero elements in that dimension. The corresponding non-zero values can be obtained with:: a[nonzero(a)] To group the indices by element, rather than dimension, use:: transpose(nonzero(a)) The result of this is always a 2-D array, with a row for each non-zero element. Parameters ---------- a : array_like Input array. Returns ------- tuple_of_arrays : tuple Indices of elements that are non-zero. See Also -------- flatnonzero : Return indices that are non-zero in the flattened version of the input array. ndarray.nonzero : Equivalent ndarray method. count_nonzero : Counts the number of non-zero elements in the input array. Examples -------- >>> x = np.eye(3) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> np.nonzero(x) (array([0, 1, 2]), array([0, 1, 2])) >>> x[np.nonzero(x)] array([ 1., 1., 1.]) >>> np.transpose(np.nonzero(x)) array([[0, 0], [1, 1], [2, 2]]) A common use for ``nonzero`` is to find the indices of an array, where a condition is True. Given an array `a`, the condition `a` > 3 is a boolean array and since False is interpreted as 0, np.nonzero(a > 3) yields the indices of the `a` where the condition is true. >>> a = np.array([[1,2,3],[4,5,6],[7,8,9]]) >>> a > 3 array([[False, False, False], [ True, True, True], [ True, True, True]], dtype=bool) >>> np.nonzero(a > 3) (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2])) The ``nonzero`` method of the boolean array can also be called. >>> (a > 3).nonzero() (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2])) """ return tuple() def not_equal(x1, x2, out=None): """not_equal(x1, x2[, out]) Return (x1 != x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. out : ndarray, optional A placeholder the same shape as `x1` to store the result. See `doc.ufuncs` (Section "Output arguments") for more details. Returns ------- not_equal : ndarray bool, scalar bool For each element in `x1, x2`, return True if `x1` is not equal to `x2` and False otherwise. See Also -------- equal, greater, greater_equal, less, less_equal Examples -------- >>> np.not_equal([1.,2.], [1., 3.]) array([False, True], dtype=bool) >>> np.not_equal([1, 2], [[1, 3],[1, 4]]) array([[False, True], [False, True]], dtype=bool)""" return ndarray() def nper(rate, pmt, pv="end", fv=0, when="end"): """ Compute the number of periodic payments. Parameters ---------- rate : array_like Rate of interest (per period) pmt : array_like Payment pv : array_like Present value fv : array_like, optional Future value when : {{'begin', 1}, {'end', 0}}, {string, int}, optional When payments are due ('begin' (1) or 'end' (0)) Notes ----- The number of periods ``nper`` is computed by solving the equation:: fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate*((1+rate)**nper-1) = 0 but if ``rate = 0`` then:: fv + pv + pmt*nper = 0 Examples -------- If you only had $150/month to pay towards the loan, how long would it take to pay-off a loan of $8,000 at 7% annual interest? >>> print round(np.nper(0.07/12, -150, 8000), 5) 64.07335 So, over 64 months would be required to pay off the loan. The same analysis could be done with several different interest rates and/or payments and/or total amounts to produce an entire table. >>> np.nper(*(np.ogrid[0.07/12: 0.08/12: 0.01/12, ... -150 : -99 : 50 , ... 8000 : 9001 : 1000])) array([[[ 64.07334877, 74.06368256], [ 108.07548412, 127.99022654]], [[ 66.12443902, 76.87897353], [ 114.70165583, 137.90124779]]]) """ return None def npv(rate, values): """ Returns the NPV (Net Present Value) of a cash flow series. Parameters ---------- rate : scalar The discount rate. values : array_like, shape(M, ) The values of the time series of cash flows. The (fixed) time interval between cash flow "events" must be the same as that for which `rate` is given (i.e., if `rate` is per year, then precisely a year is understood to elapse between each cash flow event). By convention, investments or "deposits" are negative, income or "withdrawals" are positive; `values` must begin with the initial investment, thus `values[0]` will typically be negative. Returns ------- out : float The NPV of the input cash flow series `values` at the discount `rate`. Notes ----- Returns the result of: [G]_ .. math :: \sum_{t=0}^{M-1}{\frac{values_t}{(1+rate)^{t}}} References ---------- .. [G] L. J. Gitman, "Principles of Managerial Finance, Brief," 3rd ed., Addison-Wesley, 2003, pg. 346. Examples -------- >>> np.npv(0.281,[-100, 39, 59, 55, 20]) -0.0084785916384548798 (Compare with the Example given for numpy.lib.financial.irr) """ return float() class number: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def obj2sctype(rep=None, default=None): """ Return the scalar dtype or NumPy equivalent of Python type of an object. Parameters ---------- rep : any The object of which the type is returned. default : any, optional If given, this is returned for objects whose types can not be determined. If not given, None is returned for those objects. Returns ------- dtype : dtype or Python type The data type of `rep`. See Also -------- sctype2char, issctype, issubsctype, issubdtype, maximum_sctype Examples -------- >>> np.obj2sctype(np.int32) >>> np.obj2sctype(np.array([1., 2.])) >>> np.obj2sctype(np.array([1.j])) >>> np.obj2sctype(dict) >>> np.obj2sctype('string') >>> np.obj2sctype(1, default=list) """ return dtype() if False else Python() class object: __doc__ = str() class object_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class object_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() ogrid = nd_grid() def ones(shape="C", dtype=None, order="C"): """ Return a new array of given shape and type, filled with ones. Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. Returns ------- out : ndarray Array of ones with the given shape, dtype, and order. See Also -------- zeros, ones_like Examples -------- >>> np.ones(5) array([ 1., 1., 1., 1., 1.]) >>> np.ones((5,), dtype=np.int) array([1, 1, 1, 1, 1]) >>> np.ones((2, 1)) array([[ 1.], [ 1.]]) >>> s = (2,2) >>> np.ones(s) array([[ 1., 1.], [ 1., 1.]]) """ return ndarray() def ones_like(a=True, dtype=None, order="K", subok=True): """ Return an array of ones with the same shape and type as a given array. Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. dtype : data-type, optional .. versionadded:: 1.6.0 Overrides the data type of the result. order : {'C', 'F', 'A', or 'K'}, optional .. versionadded:: 1.6.0 Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. subok : bool, optional. If True, then the newly created array will use the sub-class type of 'a', otherwise it will be a base-class array. Defaults to True. Returns ------- out : ndarray Array of ones with the same shape and type as `a`. See Also -------- zeros_like : Return an array of zeros with shape and type of input. empty_like : Return an empty array with shape and type of input. zeros : Return a new array setting values to zero. ones : Return a new array setting values to one. empty : Return a new uninitialized array. Examples -------- >>> x = np.arange(6) >>> x = x.reshape((2, 3)) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.ones_like(x) array([[1, 1, 1], [1, 1, 1]]) >>> y = np.arange(3, dtype=np.float) >>> y array([ 0., 1., 2.]) >>> np.ones_like(y) array([ 1., 1., 1.]) """ return ndarray() def outer(a, b): """ Compute the outer product of two vectors. Given two vectors, ``a = [a0, a1, ..., aM]`` and ``b = [b0, b1, ..., bN]``, the outer product [1]_ is:: [[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]] Parameters ---------- a : (M,) array_like First input vector. Input is flattened if not already 1-dimensional. b : (N,) array_like Second input vector. Input is flattened if not already 1-dimensional. Returns ------- out : (M, N) ndarray ``out[i, j] = a[i] * b[j]`` See also -------- inner, einsum References ---------- .. [1] : G. H. Golub and C. F. van Loan, *Matrix Computations*, 3rd ed., Baltimore, MD, Johns Hopkins University Press, 1996, pg. 8. Examples -------- Make a (*very* coarse) grid for computing a Mandelbrot set: >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5)) >>> rl array([[-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.]]) >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,))) >>> im array([[ 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j], [ 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j], [ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j], [ 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]]) >>> grid = rl + im >>> grid array([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j], [-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j], [-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j], [-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j], [-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]]) An example using a "vector" of letters: >>> x = np.array(['a', 'b', 'c'], dtype=object) >>> np.outer(x, [1, 2, 3]) array([[a, aa, aaa], [b, bb, bbb], [c, cc, ccc]], dtype=object) """ return M() def packbits(myarray, axis): """packbits(myarray, axis=None) Packs the elements of a binary-valued array into bits in a uint8 array. The result is padded to full bytes by inserting zero bits at the end. Parameters ---------- myarray : array_like An integer type array whose elements should be packed to bits. axis : int, optional The dimension over which bit-packing is done. ``None`` implies packing the flattened array. Returns ------- packed : ndarray Array of type uint8 whose elements represent bits corresponding to the logical (0 or nonzero) value of the input elements. The shape of `packed` has the same number of dimensions as the input (unless `axis` is None, in which case the output is 1-D). See Also -------- unpackbits: Unpacks elements of a uint8 array into a binary-valued output array. Examples -------- >>> a = np.array([[[1,0,1], ... [0,1,0]], ... [[1,1,0], ... [0,0,1]]]) >>> b = np.packbits(a, axis=-1) >>> b array([[[160],[64]],[[192],[32]]], dtype=uint8) Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000, and 32 = 0010 0000.""" return ndarray() def pad(array, pad_width=None, mode=None): """ Pads an array. Parameters ---------- array : array_like of rank N Input array pad_width : {sequence, int} Number of values padded to the edges of each axis. ((before_1, after_1), ... (before_N, after_N)) unique pad widths for each axis. ((before, after),) yields same before and after pad for each axis. (pad,) or int is a shortcut for before = after = pad width for all axes. mode : {str, function} One of the following string values or a user supplied function. 'constant' Pads with a constant value. 'edge' Pads with the edge values of array. 'linear_ramp' Pads with the linear ramp between end_value and the array edge value. 'maximum' Pads with the maximum value of all or part of the vector along each axis. 'mean' Pads with the mean value of all or part of the vector along each axis. 'median' Pads with the median value of all or part of the vector along each axis. 'minimum' Pads with the minimum value of all or part of the vector along each axis. 'reflect' Pads with the reflection of the vector mirrored on the first and last values of the vector along each axis. 'symmetric' Pads with the reflection of the vector mirrored along the edge of the array. 'wrap' Pads with the wrap of the vector along the axis. The first values are used to pad the end and the end values are used to pad the beginning. Padding function, see Notes. stat_length : {sequence, int}, optional Used in 'maximum', 'mean', 'median', and 'minimum'. Number of values at edge of each axis used to calculate the statistic value. ((before_1, after_1), ... (before_N, after_N)) unique statistic lengths for each axis. ((before, after),) yields same before and after statistic lengths for each axis. (stat_length,) or int is a shortcut for before = after = statistic length for all axes. Default is ``None``, to use the entire axis. constant_values : {sequence, int}, optional Used in 'constant'. The values to set the padded values for each axis. ((before_1, after_1), ... (before_N, after_N)) unique pad constants for each axis. ((before, after),) yields same before and after constants for each axis. (constant,) or int is a shortcut for before = after = constant for all axes. Default is 0. end_values : {sequence, int}, optional Used in 'linear_ramp'. The values used for the ending value of the linear_ramp and that will form the edge of the padded array. ((before_1, after_1), ... (before_N, after_N)) unique end values for each axis. ((before, after),) yields same before and after end values for each axis. (constant,) or int is a shortcut for before = after = end value for all axes. Default is 0. reflect_type : str {'even', 'odd'}, optional Used in 'reflect', and 'symmetric'. The 'even' style is the default with an unaltered reflection around the edge value. For the 'odd' style, the extented part of the array is created by subtracting the reflected values from two times the edge value. Returns ------- pad : ndarray Padded array of rank equal to `array` with shape increased according to `pad_width`. Notes ----- .. versionadded:: 1.7.0 For an array with rank greater than 1, some of the padding of later axes is calculated from padding of previous axes. This is easiest to think about with a rank 2 array where the corners of the padded array are calculated by using padded values from the first axis. The padding function, if used, should return a rank 1 array equal in length to the vector argument with padded values replaced. It has the following signature: padding_func(vector, iaxis_pad_width, iaxis, **kwargs) where vector : ndarray A rank 1 array already padded with zeros. Padded values are vector[:pad_tuple[0]] and vector[-pad_tuple[1]:]. iaxis_pad_width : tuple A 2-tuple of ints, iaxis_pad_width[0] represents the number of values padded at the beginning of vector where iaxis_pad_width[1] represents the number of values padded at the end of vector. iaxis : int The axis currently being calculated. kwargs : misc Any keyword arguments the function requires. Examples -------- >>> a = [1, 2, 3, 4, 5] >>> np.lib.pad(a, (2,3), 'constant', constant_values=(4,6)) array([4, 4, 1, 2, 3, 4, 5, 6, 6, 6]) >>> np.lib.pad(a, (2,3), 'edge') array([1, 1, 1, 2, 3, 4, 5, 5, 5, 5]) >>> np.lib.pad(a, (2,3), 'linear_ramp', end_values=(5,-4)) array([ 5, 3, 1, 2, 3, 4, 5, 2, -1, -4]) >>> np.lib.pad(a, (2,), 'maximum') array([5, 5, 1, 2, 3, 4, 5, 5, 5]) >>> np.lib.pad(a, (2,), 'mean') array([3, 3, 1, 2, 3, 4, 5, 3, 3]) >>> np.lib.pad(a, (2,), 'median') array([3, 3, 1, 2, 3, 4, 5, 3, 3]) >>> a = [[1,2], [3,4]] >>> np.lib.pad(a, ((3, 2), (2, 3)), 'minimum') array([[1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [3, 3, 3, 4, 3, 3, 3], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1]]) >>> a = [1, 2, 3, 4, 5] >>> np.lib.pad(a, (2,3), 'reflect') array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2]) >>> np.lib.pad(a, (2,3), 'reflect', reflect_type='odd') array([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]) >>> np.lib.pad(a, (2,3), 'symmetric') array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3]) >>> np.lib.pad(a, (2,3), 'symmetric', reflect_type='odd') array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7]) >>> np.lib.pad(a, (2,3), 'wrap') array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3]) >>> def padwithtens(vector, pad_width, iaxis, kwargs): ... vector[:pad_width[0]] = 10 ... vector[-pad_width[1]:] = 10 ... return vector >>> a = np.arange(6) >>> a = a.reshape((2,3)) >>> np.lib.pad(a, 2, padwithtens) array([[10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 0, 1, 2, 10, 10], [10, 10, 3, 4, 5, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10]]) """ return ndarray() def partition(a, kth=None, axis=-1, kind="introselect", order=None): """ Return a partitioned copy of an array. Creates a copy of the array with its elements rearranged in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array to be sorted. kth : int or sequence of ints Element index to partition by. The kth value of the element will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once. axis : int or None, optional Axis along which to sort. If None, the array is flattened before sorting. The default is -1, which sorts along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : list, optional When `a` is a structured array, this argument specifies which fields to compare first, second, and so on. This list does not need to include all of the fields. Returns ------- partitioned_array : ndarray Array of the same type and shape as `a`. See Also -------- ndarray.partition : Method to sort an array in-place. argpartition : Indirect partition. sort : Full sorting Notes ----- The various selection algorithms are characterized by their average speed, worst case performance, work space size, and whether they are stable. A stable sort keeps items with the same key in the same relative order. The three available algorithms have the following properties: ================= ======= ============= ============ ======= kind speed worst case work space stable ================= ======= ============= ============ ======= 'introselect' 1 O(n) 0 no ================= ======= ============= ============ ======= All the partition algorithms make temporary copies of the data when partitioning along any but the last axis. Consequently, partitioning along the last axis is faster and uses less space than partitioning along any other axis. The sort order for complex numbers is lexicographic. If both the real and imaginary parts are non-nan then the order is determined by the real parts except when they are equal, in which case the order is determined by the imaginary parts. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> np.partition(a, 3) array([2, 1, 3, 4]) >>> np.partition(a, (1, 3)) array([1, 2, 3, 4]) """ return ndarray() def percentile(a, q=False, axis=None, out=None, overwrite_input=False): """ Compute the qth percentile of the data along the specified axis. Returns the qth percentile of the array elements. Parameters ---------- a : array_like Input array or object that can be converted to an array. q : float in range of [0,100] (or sequence of floats) Percentile to compute which must be between 0 and 100 inclusive. axis : int, optional Axis along which the percentiles are computed. The default (None) is to compute the median along a flattened version of the array. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow use of memory of input array `a` for calculations. The input array will be modified by the call to median. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. Note that, if `overwrite_input` is True and the input is not already an array, an error will be raised. Returns ------- pcntile : ndarray A new array holding the result (unless `out` is specified, in which case that array is returned instead). If the input contains integers, or floats of smaller precision than 64, then the output data-type is float64. Otherwise, the output data-type is the same as that of the input. See Also -------- mean, median Notes ----- Given a vector V of length N, the qth percentile of V is the qth ranked value in a sorted copy of V. A weighted average of the two nearest neighbors is used if the normalized ranking does not match q exactly. The same as the median if ``q=50``, the same as the minimum if ``q=0`` and the same as the maximum if ``q=100``. Examples -------- >>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.percentile(a, 50) 3.5 >>> np.percentile(a, 50, axis=0) array([ 6.5, 4.5, 2.5]) >>> np.percentile(a, 50, axis=1) array([ 7., 2.]) >>> m = np.percentile(a, 50, axis=0) >>> out = np.zeros_like(m) >>> np.percentile(a, 50, axis=0, out=m) array([ 6.5, 4.5, 2.5]) >>> m array([ 6.5, 4.5, 2.5]) >>> b = a.copy() >>> np.percentile(b, 50, axis=1, overwrite_input=True) array([ 7., 2.]) >>> assert not np.all(a==b) >>> b = a.copy() >>> np.percentile(b, 50, axis=None, overwrite_input=True) 3.5 """ return ndarray() pi = float() def piecewise(x, condlist, funclist, args, kw): """ Evaluate a piecewise-defined function. Given a set of conditions and corresponding functions, evaluate each function on the input data wherever its condition is true. Parameters ---------- x : ndarray The input domain. condlist : list of bool arrays Each boolean array corresponds to a function in `funclist`. Wherever `condlist[i]` is True, `funclist[i](x)` is used as the output value. Each boolean array in `condlist` selects a piece of `x`, and should therefore be of the same shape as `x`. The length of `condlist` must correspond to that of `funclist`. If one extra function is given, i.e. if ``len(funclist) - len(condlist) == 1``, then that extra function is the default value, used wherever all conditions are false. funclist : list of callables, f(x,*args,**kw), or scalars Each function is evaluated over `x` wherever its corresponding condition is True. It should take an array as input and give an array or a scalar value as output. If, instead of a callable, a scalar is provided then a constant function (``lambda x: scalar``) is assumed. args : tuple, optional Any further arguments given to `piecewise` are passed to the functions upon execution, i.e., if called ``piecewise(..., ..., 1, 'a')``, then each function is called as ``f(x, 1, 'a')``. kw : dict, optional Keyword arguments used in calling `piecewise` are passed to the functions upon execution, i.e., if called ``piecewise(..., ..., lambda=1)``, then each function is called as ``f(x, lambda=1)``. Returns ------- out : ndarray The output is the same shape and type as x and is found by calling the functions in `funclist` on the appropriate portions of `x`, as defined by the boolean arrays in `condlist`. Portions not covered by any condition have undefined values. See Also -------- choose, select, where Notes ----- This is similar to choose or select, except that functions are evaluated on elements of `x` that satisfy the corresponding condition from `condlist`. The result is:: |-- |funclist[0](x[condlist[0]]) out = |funclist[1](x[condlist[1]]) |... |funclist[n2](x[condlist[n2]]) |-- Examples -------- Define the sigma function, which is -1 for ``x < 0`` and +1 for ``x >= 0``. >>> x = np.linspace(-2.5, 2.5, 6) >>> np.piecewise(x, [x < 0, x >= 0], [-1, 1]) array([-1., -1., -1., 1., 1., 1.]) Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for ``x >= 0``. >>> np.piecewise(x, [x < 0, x >= 0], [lambda x: -x, lambda x: x]) array([ 2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) """ return ndarray() def pkgload(): """Load one or more packages into parent package top-level namespace. This function is intended to shorten the need to import many subpackages, say of scipy, constantly with statements such as import scipy.linalg, scipy.fftpack, scipy.etc... Instead, you can say: import scipy scipy.pkgload('linalg','fftpack',...) or scipy.pkgload() to load all of them in one call. If a name which doesn't exist in scipy's namespace is given, a warning is shown. Parameters ---------- *packages : arg-tuple the names (one or more strings) of all the modules one wishes to load into the top-level namespace. verbose= : integer verbosity level [default: -1]. verbose=-1 will suspend also warnings. force= : bool when True, force reloading loaded packages [default: False]. postpone= : bool when True, don't load packages [default: False] """ return None def place(arr, mask, vals): """ Change elements of an array based on conditional and input values. Similar to ``np.copyto(arr, vals, where=mask)``, the difference is that `place` uses the first N elements of `vals`, where N is the number of True values in `mask`, while `copyto` uses the elements where `mask` is True. Note that `extract` does the exact opposite of `place`. Parameters ---------- arr : array_like Array to put data into. mask : array_like Boolean mask array. Must have the same size as `a`. vals : 1-D sequence Values to put into `a`. Only the first N elements are used, where N is the number of True values in `mask`. If `vals` is smaller than N it will be repeated. See Also -------- copyto, put, take, extract Examples -------- >>> arr = np.arange(6).reshape(2, 3) >>> np.place(arr, arr>2, [44, 55]) >>> arr array([[ 0, 1, 2], [44, 55, 44]]) """ return None def pmt(rate, nper, pv="end", fv=0, when="end"): """ Compute the payment against loan principal plus interest. Given: * a present value, `pv` (e.g., an amount borrowed) * a future value, `fv` (e.g., 0) * an interest `rate` compounded once per period, of which there are * `nper` total * and (optional) specification of whether payment is made at the beginning (`when` = {'begin', 1}) or the end (`when` = {'end', 0}) of each period Return: the (fixed) periodic payment. Parameters ---------- rate : array_like Rate of interest (per period) nper : array_like Number of compounding periods pv : array_like Present value fv : array_like (optional) Future value (default = 0) when : {{'begin', 1}, {'end', 0}}, {string, int} When payments are due ('begin' (1) or 'end' (0)) Returns ------- out : ndarray Payment against loan plus interest. If all input is scalar, returns a scalar float. If any input is array_like, returns payment for each input element. If multiple inputs are array_like, they all must have the same shape. Notes ----- The payment is computed by solving the equation:: fv + pv*(1 + rate)**nper + pmt*(1 + rate*when)/rate*((1 + rate)**nper - 1) == 0 or, when ``rate == 0``:: fv + pv + pmt * nper == 0 for ``pmt``. Note that computing a monthly mortgage payment is only one use for this function. For example, pmt returns the periodic deposit one must make to achieve a specified future balance given an initial deposit, a fixed, periodically compounded interest rate, and the total number of periods. References ---------- .. [WRW] Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May). Open Document Format for Office Applications (OpenDocument)v1.2, Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version, Pre-Draft 12. Organization for the Advancement of Structured Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: http://www.oasis-open.org/committees/documents.php ?wg_abbrev=office-formulaOpenDocument-formula-20090508.odt Examples -------- What is the monthly payment needed to pay off a $200,000 loan in 15 years at an annual interest rate of 7.5%? >>> np.pmt(0.075/12, 12*15, 200000) -1854.0247200054619 In order to pay-off (i.e., have a future-value of 0) the $200,000 obtained today, a monthly payment of $1,854.02 would be required. Note that this example illustrates usage of `fv` having a default value of 0. """ return ndarray() def poly(seq_of_zeros): """ Find the coefficients of a polynomial with the given sequence of roots. Returns the coefficients of the polynomial whose leading coefficient is one for the given sequence of zeros (multiple roots must be included in the sequence as many times as their multiplicity; see Examples). A square matrix (or array, which will be treated as a matrix) can also be given, in which case the coefficients of the characteristic polynomial of the matrix are returned. Parameters ---------- seq_of_zeros : array_like, shape (N,) or (N, N) A sequence of polynomial roots, or a square array or matrix object. Returns ------- c : ndarray 1D array of polynomial coefficients from highest to lowest degree: ``c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]`` where c[0] always equals 1. Raises ------ ValueError If input is the wrong shape (the input must be a 1-D or square 2-D array). See Also -------- polyval : Evaluate a polynomial at a point. roots : Return the roots of a polynomial. polyfit : Least squares polynomial fit. poly1d : A one-dimensional polynomial class. Notes ----- Specifying the roots of a polynomial still leaves one degree of freedom, typically represented by an undetermined leading coefficient. [1]_ In the case of this function, that coefficient - the first one in the returned array - is always taken as one. (If for some reason you have one other point, the only automatic way presently to leverage that information is to use ``polyfit``.) The characteristic polynomial, :math:`p_a(t)`, of an `n`-by-`n` matrix **A** is given by :math:`p_a(t) = \mathrm{det}(t\, \mathbf{I} - \mathbf{A})`, where **I** is the `n`-by-`n` identity matrix. [2]_ References ---------- .. [1] M. Sullivan and M. Sullivan, III, "Algebra and Trignometry, Enhanced With Graphing Utilities," Prentice-Hall, pg. 318, 1996. .. [2] G. Strang, "Linear Algebra and Its Applications, 2nd Edition," Academic Press, pg. 182, 1980. Examples -------- Given a sequence of a polynomial's zeros: >>> np.poly((0, 0, 0)) # Multiple root example array([1, 0, 0, 0]) The line above represents z**3 + 0*z**2 + 0*z + 0. >>> np.poly((-1./2, 0, 1./2)) array([ 1. , 0. , -0.25, 0. ]) The line above represents z**3 - z/4 >>> np.poly((np.random.random(1.)[0], 0, np.random.random(1.)[0])) array([ 1. , -0.77086955, 0.08618131, 0. ]) #random Given a square array object: >>> P = np.array([[0, 1./3], [-1./2, 0]]) >>> np.poly(P) array([ 1. , 0. , 0.16666667]) Or a square matrix object: >>> np.poly(np.matrix(P)) array([ 1. , 0. , 0.16666667]) Note how in all cases the leading coefficient is always 1. """ return ndarray() class poly1d: __dict__ = dictproxy() __doc__ = str() __hash__ = None __module__ = str() __weakref__ = getset_descriptor() coeffs = None def deriv(self=1, m=1): """ Return a derivative of this polynomial. Refer to `polyder` for full documentation. See Also -------- polyder : equivalent function """ return None def integ(self=0, m=1, k=0): """ Return an antiderivative (indefinite integral) of this polynomial. Refer to `polyint` for full documentation. See Also -------- polyint : equivalent function """ return None order = None variable = None def polyadd(a1a2): """ Find the sum of two polynomials. Returns the polynomial resulting from the sum of two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree. Parameters ---------- a1, a2 : array_like or poly1d object Input polynomials. Returns ------- out : ndarray or poly1d object The sum of the inputs. If either input is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree. See Also -------- poly1d : A one-dimensional polynomial class. poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval Examples -------- >>> np.polyadd([1, 2], [9, 5, 4]) array([9, 6, 6]) Using poly1d objects: >>> p1 = np.poly1d([1, 2]) >>> p2 = np.poly1d([9, 5, 4]) >>> print p1 1 x + 2 >>> print p2 2 9 x + 5 x + 4 >>> print np.polyadd(p1, p2) 2 9 x + 6 x + 6 """ return ndarray() if False else poly1d() def polyder(p=1, m=1): """ Return the derivative of the specified order of a polynomial. Parameters ---------- p : poly1d or sequence Polynomial to differentiate. A sequence is interpreted as polynomial coefficients, see `poly1d`. m : int, optional Order of differentiation (default: 1) Returns ------- der : poly1d A new polynomial representing the derivative. See Also -------- polyint : Anti-derivative of a polynomial. poly1d : Class for one-dimensional polynomials. Examples -------- The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is: >>> p = np.poly1d([1,1,1,1]) >>> p2 = np.polyder(p) >>> p2 poly1d([3, 2, 1]) which evaluates to: >>> p2(2.) 17.0 We can verify this, approximating the derivative with ``(f(x + h) - f(x))/h``: >>> (p(2. + 0.001) - p(2.)) / 0.001 17.007000999997857 The fourth-order derivative of a 3rd-order polynomial is zero: >>> np.polyder(p, 2) poly1d([6, 2]) >>> np.polyder(p, 3) poly1d([6]) >>> np.polyder(p, 4) poly1d([ 0.]) """ return poly1d() def polydiv(u, v): """ Returns the quotient and remainder of polynomial division. The input arrays are the coefficients (including any coefficients equal to zero) of the "numerator" (dividend) and "denominator" (divisor) polynomials, respectively. Parameters ---------- u : array_like or poly1d Dividend polynomial's coefficients. v : array_like or poly1d Divisor polynomial's coefficients. Returns ------- q : ndarray Coefficients, including those equal to zero, of the quotient. r : ndarray Coefficients, including those equal to zero, of the remainder. See Also -------- poly, polyadd, polyder, polydiv, polyfit, polyint, polymul, polysub, polyval Notes ----- Both `u` and `v` must be 0-d or 1-d (ndim = 0 or 1), but `u.ndim` need not equal `v.ndim`. In other words, all four possible combinations - ``u.ndim = v.ndim = 0``, ``u.ndim = v.ndim = 1``, ``u.ndim = 1, v.ndim = 0``, and ``u.ndim = 0, v.ndim = 1`` - work. Examples -------- .. math:: \frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25 >>> x = np.array([3.0, 5.0, 2.0]) >>> y = np.array([2.0, 1.0]) >>> np.polydiv(x, y) (array([ 1.5 , 1.75]), array([ 0.25])) """ return ndarray() def polyfit(x, y, deg=False, rcond=None, full=False, w=None, cov=False): """ Least squares polynomial fit. Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg` to points `(x, y)`. Returns a vector of coefficients `p` that minimises the squared error. Parameters ---------- x : array_like, shape (M,) x-coordinates of the M sample points ``(x[i], y[i])``. y : array_like, shape (M,) or (M, K) y-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column. deg : int Degree of the fitting polynomial rcond : float, optional Relative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases. full : bool, optional Switch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned. w : array_like, shape (M,), optional weights to apply to the y-coordinates of the sample points. cov : bool, optional Return the estimate and the covariance matrix of the estimate If full is True, then cov is not returned. Returns ------- p : ndarray, shape (M,) or (M, K) Polynomial coefficients, highest power first. If `y` was 2-D, the coefficients for `k`-th data set are in ``p[:,k]``. residuals, rank, singular_values, rcond : present only if `full` = True Residuals of the least-squares fit, the effective rank of the scaled Vandermonde coefficient matrix, its singular values, and the specified value of `rcond`. For more details, see `linalg.lstsq`. V : ndaray, shape (M,M) or (M,M,K) : present only if `full` = False and `cov`=True The covariance matrix of the polynomial coefficient estimates. The diagonal of this matrix are the variance estimates for each coefficient. If y is a 2-d array, then the covariance matrix for the `k`-th data set are in ``V[:,:,k]`` Warns ----- RankWarning The rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full` = False. The warnings can be turned off by >>> import warnings >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- polyval : Computes polynomial values. linalg.lstsq : Computes a least-squares fit. scipy.interpolate.UnivariateSpline : Computes spline fits. Notes ----- The solution minimizes the squared error .. math :: E = \sum_{j=0}^k |p(x_j) - y_j|^2 in the equations:: x[0]**n * p[n] + ... + x[0] * p[1] + p[0] = y[0] x[1]**n * p[n] + ... + x[1] * p[1] + p[0] = y[1] ... x[k]**n * p[n] + ... + x[k] * p[1] + p[0] = y[k] The coefficient matrix of the coefficients `p` is a Vandermonde matrix. `polyfit` issues a `RankWarning` when the least-squares fit is badly conditioned. This implies that the best fit is not well-defined due to numerical error. The results may be improved by lowering the polynomial degree or by replacing `x` by `x` - `x`.mean(). The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious: including contributions from the small singular values can add numerical noise to the result. Note that fitting polynomial coefficients is inherently badly conditioned when the degree of the polynomial is large or the interval of sample points is badly centered. The quality of the fit should always be checked in these cases. When polynomial fits are not satisfactory, splines may be a good alternative. References ---------- .. [1] Wikipedia, "Curve fitting", http://en.wikipedia.org/wiki/Curve_fitting .. [2] Wikipedia, "Polynomial interpolation", http://en.wikipedia.org/wiki/Polynomial_interpolation Examples -------- >>> x = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0]) >>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0]) >>> z = np.polyfit(x, y, 3) >>> z array([ 0.08703704, -0.81349206, 1.69312169, -0.03968254]) It is convenient to use `poly1d` objects for dealing with polynomials: >>> p = np.poly1d(z) >>> p(0.5) 0.6143849206349179 >>> p(3.5) -0.34732142857143039 >>> p(10) 22.579365079365115 High-order polynomials may oscillate wildly: >>> p30 = np.poly1d(np.polyfit(x, y, 30)) /... RankWarning: Polyfit may be poorly conditioned... >>> p30(4) -0.80000000000000204 >>> p30(5) -0.99999999999999445 >>> p30(4.5) -0.10547061179440398 Illustration: >>> import matplotlib.pyplot as plt >>> xp = np.linspace(-2, 6, 100) >>> plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--') [, , ] >>> plt.ylim(-2,2) (-2, 2) >>> plt.show() """ return ndarray() if False else M() def polyint(p=None, m=1, k=None): """ Return an antiderivative (indefinite integral) of a polynomial. The returned order `m` antiderivative `P` of polynomial `p` satisfies :math:`\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1` integration constants `k`. The constants determine the low-order polynomial part .. math:: \frac{k_{m-1}}{0!} x^0 + \ldots + \frac{k_0}{(m-1)!}x^{m-1} of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`. Parameters ---------- p : {array_like, poly1d} Polynomial to differentiate. A sequence is interpreted as polynomial coefficients, see `poly1d`. m : int, optional Order of the antiderivative. (Default: 1) k : {None, list of `m` scalars, scalar}, optional Integration constants. They are given in the order of integration: those corresponding to highest-order terms come first. If ``None`` (default), all constants are assumed to be zero. If `m = 1`, a single scalar can be given instead of a list. See Also -------- polyder : derivative of a polynomial poly1d.integ : equivalent method Examples -------- The defining property of the antiderivative: >>> p = np.poly1d([1,1,1]) >>> P = np.polyint(p) >>> P poly1d([ 0.33333333, 0.5 , 1. , 0. ]) >>> np.polyder(P) == p True The integration constants default to zero, but can be specified: >>> P = np.polyint(p, 3) >>> P(0) 0.0 >>> np.polyder(P)(0) 0.0 >>> np.polyder(P, 2)(0) 0.0 >>> P = np.polyint(p, 3, k=[6,5,3]) >>> P poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ]) Note that 3 = 6 / 2!, and that the constants are given in the order of integrations. Constant of the highest-order polynomial term comes first: >>> np.polyder(P, 2)(0) 6.0 >>> np.polyder(P, 1)(0) 5.0 >>> P(0) 3.0 """ return None def polymul(a1a2): """ Find the product of two polynomials. Finds the polynomial resulting from the multiplication of the two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree. Parameters ---------- a1, a2 : array_like or poly1d object Input polynomials. Returns ------- out : ndarray or poly1d object The polynomial resulting from the multiplication of the inputs. If either inputs is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree. See Also -------- poly1d : A one-dimensional polynomial class. poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval Examples -------- >>> np.polymul([1, 2, 3], [9, 5, 1]) array([ 9, 23, 38, 17, 3]) Using poly1d objects: >>> p1 = np.poly1d([1, 2, 3]) >>> p2 = np.poly1d([9, 5, 1]) >>> print p1 2 1 x + 2 x + 3 >>> print p2 2 9 x + 5 x + 1 >>> print np.polymul(p1, p2) 4 3 2 9 x + 23 x + 38 x + 17 x + 3 """ return ndarray() if False else poly1d() def polysub(a1a2): """ Difference (subtraction) of two polynomials. Given two polynomials `a1` and `a2`, returns ``a1 - a2``. `a1` and `a2` can be either array_like sequences of the polynomials' coefficients (including coefficients equal to zero), or `poly1d` objects. Parameters ---------- a1, a2 : array_like or poly1d Minuend and subtrahend polynomials, respectively. Returns ------- out : ndarray or poly1d Array or `poly1d` object of the difference polynomial's coefficients. See Also -------- polyval, polydiv, polymul, polyadd Examples -------- .. math:: (2 x^2 + 10 x - 2) - (3 x^2 + 10 x -4) = (-x^2 + 2) >>> np.polysub([2, 10, -2], [3, 10, -4]) array([-1, 0, 2]) """ return ndarray() if False else poly1d() def polyval(p, x): """ Evaluate a polynomial at specific values. If `p` is of length N, this function returns the value: ``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]`` If `x` is a sequence, then `p(x)` is returned for each element of `x`. If `x` is another polynomial then the composite polynomial `p(x(t))` is returned. Parameters ---------- p : array_like or poly1d object 1D array of polynomial coefficients (including coefficients equal to zero) from highest degree to the constant term, or an instance of poly1d. x : array_like or poly1d object A number, a 1D array of numbers, or an instance of poly1d, "at" which to evaluate `p`. Returns ------- values : ndarray or poly1d If `x` is a poly1d instance, the result is the composition of the two polynomials, i.e., `x` is "substituted" in `p` and the simplified result is returned. In addition, the type of `x` - array_like or poly1d - governs the type of the output: `x` array_like => `values` array_like, `x` a poly1d object => `values` is also. See Also -------- poly1d: A polynomial class. Notes ----- Horner's scheme [1]_ is used to evaluate the polynomial. Even so, for polynomials of high degree the values may be inaccurate due to rounding errors. Use carefully. References ---------- .. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng. trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand Reinhold Co., 1985, pg. 720. Examples -------- >>> np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1 76 >>> np.polyval([3,0,1], np.poly1d(5)) poly1d([ 76.]) >>> np.polyval(np.poly1d([3,0,1]), 5) 76 >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5)) poly1d([ 76.]) """ return ndarray() if False else poly1d() def power(x1, x2, out=None): """power(x1, x2[, out]) First array elements raised to powers from second array, element-wise. Raise each base in `x1` to the positionally-corresponding power in `x2`. `x1` and `x2` must be broadcastable to the same shape. Parameters ---------- x1 : array_like The bases. x2 : array_like The exponents. Returns ------- y : ndarray The bases in `x1` raised to the exponents in `x2`. Examples -------- Cube each element in a list. >>> x1 = range(6) >>> x1 [0, 1, 2, 3, 4, 5] >>> np.power(x1, 3) array([ 0, 1, 8, 27, 64, 125]) Raise the bases to different exponents. >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0] >>> np.power(x1, x2) array([ 0., 1., 8., 27., 16., 5.]) The effect of broadcasting. >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]]) >>> x2 array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]]) >>> np.power(x1, x2) array([[ 0, 1, 8, 27, 16, 5], [ 0, 1, 8, 27, 16, 5]])""" return ndarray() def ppmt(rate, per, nper, pv="end", fv=0.0, when="end"): """ Compute the payment against loan principal. Parameters ---------- rate : array_like Rate of interest (per period) per : array_like, int Amount paid against the loan changes. The `per` is the period of interest. nper : array_like Number of compounding periods pv : array_like Present value fv : array_like, optional Future value when : {{'begin', 1}, {'end', 0}}, {string, int} When payments are due ('begin' (1) or 'end' (0)) See Also -------- pmt, pv, ipmt """ return None print_function = instance() def prod(a=False, axis=None, dtype=None, out=None, keepdims=False): """ Return the product of array elements over a given axis. Parameters ---------- a : array_like Input data. axis : None or int or tuple of ints, optional Axis or axes along which a product is performed. The default (`axis` = `None`) is perform a product over all the dimensions of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is a tuple of ints, a product is performed on multiple axes, instead of a single axis or all the axes as before. dtype : data-type, optional The data-type of the returned array, as well as of the accumulator in which the elements are multiplied. By default, if `a` is of integer type, `dtype` is the default platform integer. (Note: if the type of `a` is unsigned, then so is `dtype`.) Otherwise, the dtype is the same as that of `a`. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- product_along_axis : ndarray, see `dtype` parameter above. An array shaped as `a` but with the specified axis removed. Returns a reference to `out` if specified. See Also -------- ndarray.prod : equivalent method numpy.doc.ufuncs : Section "Output arguments" Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. That means that, on a 32-bit platform: >>> x = np.array([536870910, 536870910, 536870910, 536870910]) >>> np.prod(x) #random 16 Examples -------- By default, calculate the product of all elements: >>> np.prod([1.,2.]) 2.0 Even when the input array is two-dimensional: >>> np.prod([[1.,2.],[3.,4.]]) 24.0 But we can also specify the axis over which to multiply: >>> np.prod([[1.,2.],[3.,4.]], axis=1) array([ 2., 12.]) If the type of `x` is unsigned, then the output type is the unsigned platform integer: >>> x = np.array([1, 2, 3], dtype=np.uint8) >>> np.prod(x).dtype == np.uint True If `x` is of a signed integer type, then the output type is the default platform integer: >>> x = np.array([1, 2, 3], dtype=np.int8) >>> np.prod(x).dtype == np.int True """ return ndarray() def product(a=False, axis=None, dtype=None, out=None, keepdims=False): """ Return the product of array elements over a given axis. See Also -------- prod : equivalent function; see for details. """ return None def promote_types(type1, type2): """promote_types(type1, type2) Returns the data type with the smallest size and smallest scalar kind to which both ``type1`` and ``type2`` may be safely cast. The returned data type is always in native byte order. This function is symmetric and associative. Parameters ---------- type1 : dtype or dtype specifier First data type. type2 : dtype or dtype specifier Second data type. Returns ------- out : dtype The promoted data type. Notes ----- .. versionadded:: 1.6.0 See Also -------- result_type, dtype, can_cast Examples -------- >>> np.promote_types('f4', 'f8') dtype('float64') >>> np.promote_types('i8', 'f4') dtype('float64') >>> np.promote_types('>i8', '>> np.promote_types('i1', 'S8') Traceback (most recent call last): File "", line 1, in TypeError: invalid type promotion""" return dtype() def ptp(a=None, axis=None, out=None): """ Range of values (maximum - minimum) along an axis. The name of the function comes from the acronym for 'peak to peak'. Parameters ---------- a : array_like Input values. axis : int, optional Axis along which to find the peaks. By default, flatten the array. out : array_like Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type of the output values will be cast if necessary. Returns ------- ptp : ndarray A new array holding the result, unless `out` was specified, in which case a reference to `out` is returned. Examples -------- >>> x = np.arange(4).reshape((2,2)) >>> x array([[0, 1], [2, 3]]) >>> np.ptp(x, axis=0) array([2, 2]) >>> np.ptp(x, axis=1) array([1, 1]) """ return ndarray() def put(a, ind, v="raise", mode="raise"): """ Replaces specified elements of an array with given values. The indexing works on the flattened target array. `put` is roughly equivalent to: :: a.flat[ind] = v Parameters ---------- a : ndarray Target array. ind : array_like Target indices, interpreted as integers. v : array_like Values to place in `a` at target indices. If `v` is shorter than `ind` it will be repeated as necessary. mode : {'raise', 'wrap', 'clip'}, optional Specifies how out-of-bounds indices will behave. * 'raise' -- raise an error (default) * 'wrap' -- wrap around * 'clip' -- clip to the range 'clip' mode means that all indices that are too large are replaced by the index that addresses the last element along that axis. Note that this disables indexing with negative numbers. See Also -------- putmask, place Examples -------- >>> a = np.arange(5) >>> np.put(a, [0, 2], [-44, -55]) >>> a array([-44, 1, -55, 3, 4]) >>> a = np.arange(5) >>> np.put(a, 22, -5, mode='clip') >>> a array([ 0, 1, 2, 3, -5]) """ return None def putmask(a, mask, values): """putmask(a, mask, values) Changes elements of an array based on conditional and input values. Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``. If `values` is not the same size as `a` and `mask` then it will repeat. This gives behavior different from ``a[mask] = values``. .. note:: The `putmask` functionality is also provided by `copyto`, which can be significantly faster and in addition is NA-aware (`preservena` keyword). Replacing `putmask` with ``np.copyto(a, values, where=mask)`` is recommended. Parameters ---------- a : array_like Target array. mask : array_like Boolean mask array. It has to be the same shape as `a`. values : array_like Values to put into `a` where `mask` is True. If `values` is smaller than `a` it will be repeated. See Also -------- place, put, take, copyto Examples -------- >>> x = np.arange(6).reshape(2, 3) >>> np.putmask(x, x>2, x**2) >>> x array([[ 0, 1, 2], [ 9, 16, 25]]) If `values` is smaller than `a` it is repeated: >>> x = np.arange(5) >>> np.putmask(x, x>1, [-33, -44]) >>> x array([ 0, 1, -33, -44, -33])""" return None def pv(rate, nper, pmt="end", fv=0.0, when="end"): """ Compute the present value. Given: * a future value, `fv` * an interest `rate` compounded once per period, of which there are * `nper` total * a (fixed) payment, `pmt`, paid either * at the beginning (`when` = {'begin', 1}) or the end (`when` = {'end', 0}) of each period Return: the value now Parameters ---------- rate : array_like Rate of interest (per period) nper : array_like Number of compounding periods pmt : array_like Payment fv : array_like, optional Future value when : {{'begin', 1}, {'end', 0}}, {string, int}, optional When payments are due ('begin' (1) or 'end' (0)) Returns ------- out : ndarray, float Present value of a series of payments or investments. Notes ----- The present value is computed by solving the equation:: fv + pv*(1 + rate)**nper + pmt*(1 + rate*when)/rate*((1 + rate)**nper - 1) = 0 or, when ``rate = 0``:: fv + pv + pmt * nper = 0 for `pv`, which is then returned. References ---------- .. [WRW] Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May). Open Document Format for Office Applications (OpenDocument)v1.2, Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version, Pre-Draft 12. Organization for the Advancement of Structured Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula OpenDocument-formula-20090508.odt Examples -------- What is the present value (e.g., the initial investment) of an investment that needs to total $15692.93 after 10 years of saving $100 every month? Assume the interest rate is 5% (annually) compounded monthly. >>> np.pv(0.05/12, 10*12, -100, 15692.93) -100.00067131625819 By convention, the negative sign represents cash flow out (i.e., money not available today). Thus, to end up with $15,692.93 in 10 years saving $100 a month at 5% annual interest, one's initial deposit should also be $100. If any input is array_like, ``pv`` returns an array of equal shape. Let's compare different interest rates in the example above: >>> a = np.array((0.05, 0.04, 0.03))/12 >>> np.pv(a, 10*12, -100, 15692.93) array([ -100.00067132, -649.26771385, -1273.78633713]) So, to end up with the same $15692.93 under the same $100 per month "savings plan," for annual interest rates of 4% and 3%, one would need initial investments of $649.27 and $1273.79, respectively. """ return ndarray() r_ = RClass() def rad2deg(x, out): """rad2deg(x[, out]) Convert angles from radians to degrees. Parameters ---------- x : array_like Angle in radians. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- y : ndarray The corresponding angle in degrees. See Also -------- deg2rad : Convert angles from degrees to radians. unwrap : Remove large jumps in angle by wrapping. Notes ----- .. versionadded:: 1.3.0 rad2deg(x) is ``180 * x / pi``. Examples -------- >>> np.rad2deg(np.pi/2) 90.0""" return ndarray() def radians(x, out): """radians(x[, out]) Convert angles from degrees to radians. Parameters ---------- x : array_like Input array in degrees. out : ndarray, optional Output array of same shape as `x`. Returns ------- y : ndarray The corresponding radian values. See Also -------- deg2rad : equivalent function Examples -------- Convert a degree array to radians >>> deg = np.arange(12.) * 30. >>> np.radians(deg) array([ 0. , 0.52359878, 1.04719755, 1.57079633, 2.0943951 , 2.61799388, 3.14159265, 3.66519143, 4.1887902 , 4.71238898, 5.23598776, 5.75958653]) >>> out = np.zeros((deg.shape)) >>> ret = np.radians(deg, out) >>> ret is out True""" return ndarray() def rank(a): """ Return the number of dimensions of an array. If `a` is not already an array, a conversion is attempted. Scalars are zero dimensional. Parameters ---------- a : array_like Array whose number of dimensions is desired. If `a` is not an array, a conversion is attempted. Returns ------- number_of_dimensions : int The number of dimensions in the array. See Also -------- ndim : equivalent function ndarray.ndim : equivalent property shape : dimensions of array ndarray.shape : dimensions of array Notes ----- In the old Numeric package, `rank` was the term used for the number of dimensions, but in Numpy `ndim` is used instead. Examples -------- >>> np.rank([1,2,3]) 1 >>> np.rank(np.array([[1,2,3],[4,5,6]])) 2 >>> np.rank(1) 0 """ return int() def rate(nper, pmt, pv, fv=100, when="end", guess=0.1, tol=1e-06, maxiter=100): """ Compute the rate of interest per period. Parameters ---------- nper : array_like Number of compounding periods pmt : array_like Payment pv : array_like Present value fv : array_like Future value when : {{'begin', 1}, {'end', 0}}, {string, int}, optional When payments are due ('begin' (1) or 'end' (0)) guess : float, optional Starting guess for solving the rate of interest tol : float, optional Required tolerance for the solution maxiter : int, optional Maximum iterations in finding the solution Notes ----- The rate of interest is computed by iteratively solving the (non-linear) equation:: fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate * ((1+rate)**nper - 1) = 0 for ``rate``. References ---------- Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May). Open Document Format for Office Applications (OpenDocument)v1.2, Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version, Pre-Draft 12. Organization for the Advancement of Structured Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula OpenDocument-formula-20090508.odt """ return None def ravel(a="C", order="C"): """ Return a flattened array. A 1-D array, containing the elements of the input, is returned. A copy is made only if needed. Parameters ---------- a : array_like Input array. The elements in `a` are read in the order specified by `order`, and packed as a 1-D array. order : {'C','F', 'A', 'K'}, optional The elements of `a` are read using this index order. 'C' means to index the elements in C-like order, with the last axis index changing fastest, back to the first axis index changing slowest. 'F' means to index the elements in Fortran-like index order, with the first index changing fastest, and the last index changing slowest. Note that the 'C' and 'F' options take no account of the memory layout of the underlying array, and only refer to the order of axis indexing. 'A' means to read the elements in Fortran-like index order if `a` is Fortran *contiguous* in memory, C-like order otherwise. 'K' means to read the elements in the order they occur in memory, except for reversing the data when strides are negative. By default, 'C' index order is used. Returns ------- 1d_array : ndarray Output of the same dtype as `a`, and of shape ``(a.size,)``. See Also -------- ndarray.flat : 1-D iterator over an array. ndarray.flatten : 1-D array copy of the elements of an array in row-major order. Notes ----- In C-like (row-major) order, in two dimensions, the row index varies the slowest, and the column index the quickest. This can be generalized to multiple dimensions, where row-major order implies that the index along the first axis varies slowest, and the index along the last quickest. The opposite holds for Fortran-like, or column-major, index ordering. Examples -------- It is equivalent to ``reshape(-1, order=order)``. >>> x = np.array([[1, 2, 3], [4, 5, 6]]) >>> print np.ravel(x) [1 2 3 4 5 6] >>> print x.reshape(-1) [1 2 3 4 5 6] >>> print np.ravel(x, order='F') [1 4 2 5 3 6] When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering: >>> print np.ravel(x.T) [1 4 2 5 3 6] >>> print np.ravel(x.T, order='A') [1 2 3 4 5 6] When ``order`` is 'K', it will preserve orderings that are neither 'C' nor 'F', but won't reverse axes: >>> a = np.arange(3)[::-1]; a array([2, 1, 0]) >>> a.ravel(order='C') array([2, 1, 0]) >>> a.ravel(order='K') array([2, 1, 0]) >>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a array([[[ 0, 2, 4], [ 1, 3, 5]], [[ 6, 8, 10], [ 7, 9, 11]]]) >>> a.ravel(order='C') array([ 0, 2, 4, 1, 3, 5, 6, 8, 10, 7, 9, 11]) >>> a.ravel(order='K') array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) """ return ndarray() def ravel_multi_index(multi_index, dims, mode, order): """ravel_multi_index(multi_index, dims, mode='raise', order='C') Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index. Parameters ---------- multi_index : tuple of array_like A tuple of integer arrays, one array for each dimension. dims : tuple of ints The shape of array into which the indices from ``multi_index`` apply. mode : {'raise', 'wrap', 'clip'}, optional Specifies how out-of-bounds indices are handled. Can specify either one mode or a tuple of modes, one mode per index. * 'raise' -- raise an error (default) * 'wrap' -- wrap around * 'clip' -- clip to the range In 'clip' mode, a negative index which would normally wrap will clip to 0 instead. order : {'C', 'F'}, optional Determines whether the multi-index should be viewed as indexing in C (row-major) order or FORTRAN (column-major) order. Returns ------- raveled_indices : ndarray An array of indices into the flattened version of an array of dimensions ``dims``. See Also -------- unravel_index Notes ----- .. versionadded:: 1.6.0 Examples -------- >>> arr = np.array([[3,6,6],[4,5,1]]) >>> np.ravel_multi_index(arr, (7,6)) array([22, 41, 37]) >>> np.ravel_multi_index(arr, (7,6), order='F') array([31, 41, 13]) >>> np.ravel_multi_index(arr, (4,6), mode='clip') array([22, 23, 19]) >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap')) array([12, 13, 13]) >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9)) 1621""" return ndarray() def real(val): """ Return the real part of the elements of the array. Parameters ---------- val : array_like Input array. Returns ------- out : ndarray Output array. If `val` is real, the type of `val` is used for the output. If `val` has complex elements, the returned type is float. See Also -------- real_if_close, imag, angle Examples -------- >>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.real array([ 1., 3., 5.]) >>> a.real = 9 >>> a array([ 9.+2.j, 9.+4.j, 9.+6.j]) >>> a.real = np.array([9, 8, 7]) >>> a array([ 9.+2.j, 8.+4.j, 7.+6.j]) """ return ndarray() def real_if_close(a=100, tol=100): """ If complex input returns a real array if complex parts are close to zero. "Close to zero" is defined as `tol` * (machine epsilon of the type for `a`). Parameters ---------- a : array_like Input array. tol : float Tolerance in machine epsilons for the complex part of the elements in the array. Returns ------- out : ndarray If `a` is real, the type of `a` is used for the output. If `a` has complex elements, the returned type is float. See Also -------- real, imag, angle Notes ----- Machine epsilon varies from machine to machine and between data types but Python floats on most platforms have a machine epsilon equal to 2.2204460492503131e-16. You can use 'np.finfo(np.float).eps' to print out the machine epsilon for floats. Examples -------- >>> np.finfo(np.float).eps 2.2204460492503131e-16 >>> np.real_if_close([2.1 + 4e-14j], tol=1000) array([ 2.1]) >>> np.real_if_close([2.1 + 4e-13j], tol=1000) array([ 2.1 +4.00000000e-13j]) """ return ndarray() class recarray: T = getset_descriptor() __array_finalize__ = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __dict__ = dictproxy() __doc__ = str() __module__ = str() def all(self, axis=None, out=None): """a.all(axis=None, out=None) Returns True if all elements evaluate to True. Refer to `numpy.all` for full documentation. See Also -------- numpy.all : equivalent function""" return None def any(self, axis=None, out=None): """a.any(axis=None, out=None) Returns True if any of the elements of `a` evaluate to True. Refer to `numpy.any` for full documentation. See Also -------- numpy.any : equivalent function""" return None def argmax(self, axis=None, out=None): """a.argmax(axis=None, out=None) Return indices of the maximum values along the given axis. Refer to `numpy.argmax` for full documentation. See Also -------- numpy.argmax : equivalent function""" return None def argmin(self, axis=None, out=None): """a.argmin(axis=None, out=None) Return indices of the minimum values along the given axis of `a`. Refer to `numpy.argmin` for detailed documentation. See Also -------- numpy.argmin : equivalent function""" return None def argpartition(self, kth, axis=_1, kind=quickselect, order=None): """a.argpartition(kth, axis=-1, kind='quickselect', order=None) Returns the indices that would partition this array. Refer to `numpy.argpartition` for full documentation. .. versionadded:: 1.8.0 See Also -------- numpy.argpartition : equivalent function""" return None def argsort(self, axis=_1, kind=quicksort, order=None): """a.argsort(axis=-1, kind='quicksort', order=None) Returns the indices that would sort this array. Refer to `numpy.argsort` for full documentation. See Also -------- numpy.argsort : equivalent function""" return None def astype(self, dtype, order, casting, subok, copy): """a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) Copy of the array, cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to false, and the `dtype`, `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy. Returns ------- arr_t : ndarray Unless `copy` is False and the other conditions for returning the input array are satisfied (see description for `copy` input paramter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by `dtype`, `order`. Raises ------ ComplexWarning When casting from complex to float or int. To avoid this, one should use ``a.real.astype(t)``. Examples -------- >>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5]) >>> x.astype(int) array([1, 2, 2])""" return ndarray() base = getset_descriptor() def byteswap(self, inplace): """a.byteswap(inplace) Swap the bytes of the array elements Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Parameters ---------- inplace : bool, optional If ``True``, swap bytes in-place, default is ``False``. Returns ------- out : ndarray The byteswapped array. If `inplace` is ``True``, this is a view to self. Examples -------- >>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322'] Arrays of strings are not swapped >>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')""" return ndarray() def choose(self, choices, out=None, mode=_raise): """a.choose(choices, out=None, mode='raise') Use an index array to construct a new array from a set of choices. Refer to `numpy.choose` for full documentation. See Also -------- numpy.choose : equivalent function""" return None def clip(self, a_min, a_max, out=None): """a.clip(a_min, a_max, out=None) Return an array whose values are limited to ``[a_min, a_max]``. Refer to `numpy.clip` for full documentation. See Also -------- numpy.clip : equivalent function""" return None def compress(self, condition, axis=None, out=None): """a.compress(condition, axis=None, out=None) Return selected slices of this array along given axis. Refer to `numpy.compress` for full documentation. See Also -------- numpy.compress : equivalent function""" return None def conj(self, _): """a.conj() Complex-conjugate all elements. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def conjugate(self, _): """a.conjugate() Return the complex conjugate, element-wise. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def copy(self, order): """a.copy(order='C') Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :func:numpy.copy are very similar, but have different default values for their order= arguments.) See also -------- numpy.copy numpy.copyto Examples -------- >>> x = np.array([[1,2,3],[4,5,6]], order='F') >>> y = x.copy() >>> x.fill(0) >>> x array([[0, 0, 0], [0, 0, 0]]) >>> y array([[1, 2, 3], [4, 5, 6]]) >>> y.flags['C_CONTIGUOUS'] True""" return None ctypes = getset_descriptor() def cumprod(self, axis=None, dtype=None, out=None): """a.cumprod(axis=None, dtype=None, out=None) Return the cumulative product of the elements along the given axis. Refer to `numpy.cumprod` for full documentation. See Also -------- numpy.cumprod : equivalent function""" return None def cumsum(self, axis=None, dtype=None, out=None): """a.cumsum(axis=None, dtype=None, out=None) Return the cumulative sum of the elements along the given axis. Refer to `numpy.cumsum` for full documentation. See Also -------- numpy.cumsum : equivalent function""" return None data = getset_descriptor() def diagonal(self, offset=0, axis1=0, axis2=1): """a.diagonal(offset=0, axis1=0, axis2=1) Return specified diagonals. Refer to :func:`numpy.diagonal` for full documentation. See Also -------- numpy.diagonal : equivalent function""" return None def dot(self, b, out=None): """a.dot(b, out=None) Dot product of two arrays. Refer to `numpy.dot` for full documentation. See Also -------- numpy.dot : equivalent function Examples -------- >>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]]) This array method can be conveniently chained: >>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])""" return None dtype = getset_descriptor() def dump(self, file): """a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load. Parameters ---------- file : str A string naming the dump file.""" return None def dumps(self, _): """a.dumps() Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array. Parameters ---------- None""" return None def field(self, attr=None, val=None): """None""" return None def fill(self, value): """a.fill(value) Fill the array with a scalar value. Parameters ---------- value : scalar All elements of `a` will be assigned this value. Examples -------- >>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])""" return None flags = getset_descriptor() flat = getset_descriptor() def flatten(self, order): """a.flatten(order='C') Return a copy of the array collapsed into one dimension. Parameters ---------- order : {'C', 'F', 'A'}, optional Whether to flatten in C (row-major), Fortran (column-major) order, or preserve the C/Fortran ordering from `a`. The default is 'C'. Returns ------- y : ndarray A copy of the input array, flattened to one dimension. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the array. Examples -------- >>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])""" return ndarray() def getfield(self, dtype, offset): """a.getfield(dtype, offset=0) Returns a field of the given array as a certain type. A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes. Parameters ---------- dtype : str or dtype The data type of the view. The dtype size of the view can not be larger than that of the array itself. offset : int Number of bytes to skip before beginning the element view. Examples -------- >>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]]) By choosing an offset of 8 bytes we can select the complex part of the array for our view: >>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])""" return array() imag = getset_descriptor() def item(self, ESCargs): """a.item(*args) Copy an element of an array to a standard Python scalar and return it. Parameters ---------- \*args : Arguments (variable number and type) * none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned. * int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return. * tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array. Returns ------- z : Standard Python scalar object A copy of the specified element of the array as a suitable Python scalar Notes ----- When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned. `item` is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python's optimized math. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3""" return Standard() def itemset(self, ESCargs): """a.itemset(*args) Insert scalar into an array (scalar is cast to array's dtype, if possible) There must be at least 1 argument, and define the last argument as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster than ``a[args] = item``. The item should be a scalar value and `args` must select a single item in the array `a`. Parameters ---------- \*args : Arguments If one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple. Notes ----- Compared to indexing syntax, `itemset` provides some speed increase for placing a scalar into a particular location in an `ndarray`, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using `itemset` (and `item`) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])""" return None itemsize = getset_descriptor() def max(self, axis=None, out=None): """a.max(axis=None, out=None) Return the maximum along a given axis. Refer to `numpy.amax` for full documentation. See Also -------- numpy.amax : equivalent function""" return None def mean(self, axis=None, dtype=None, out=None): """a.mean(axis=None, dtype=None, out=None) Returns the average of the array elements along given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean : equivalent function""" return None def min(self, axis=None, out=None): """a.min(axis=None, out=None) Return the minimum along a given axis. Refer to `numpy.amin` for full documentation. See Also -------- numpy.amin : equivalent function""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """arr.newbyteorder(new_order='S') Return the array with the same data viewed with a different byte order. Equivalent to:: arr.view(arr.dtype.newbytorder(new_order)) Changes are also made in all fields and sub-arrays of the array data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications above. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_arr : array New array object with the dtype reflecting given change to the byte order.""" return array() def nonzero(self, _): """a.nonzero() Return the indices of the elements that are non-zero. Refer to `numpy.nonzero` for full documentation. See Also -------- numpy.nonzero : equivalent function""" return None def partition(self, kth, axis, kind, order): """a.partition(kth, axis=-1, kind='introselect', order=None) Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- kth : int or sequence of ints Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once. axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort. Notes ----- See ``np.partition`` for notes on the different algorithms. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> a.partition(a, 3) >>> a array([2, 1, 3, 4]) >>> a.partition((1, 3)) array([1, 2, 3, 4])""" return None def prod(self, axis=None, dtype=None, out=None): """a.prod(axis=None, dtype=None, out=None) Return the product of the array elements over the given axis Refer to `numpy.prod` for full documentation. See Also -------- numpy.prod : equivalent function""" return None def ptp(self, axis=None, out=None): """a.ptp(axis=None, out=None) Peak to peak (maximum - minimum) value along a given axis. Refer to `numpy.ptp` for full documentation. See Also -------- numpy.ptp : equivalent function""" return None def put(self, indices, values, mode=_raise): """a.put(indices, values, mode='raise') Set ``a.flat[n] = values[n]`` for all `n` in indices. Refer to `numpy.put` for full documentation. See Also -------- numpy.put : equivalent function""" return None def ravel(self, order): """a.ravel([order]) Return a flattened array. Refer to `numpy.ravel` for full documentation. See Also -------- numpy.ravel : equivalent function ndarray.flat : a flat iterator on the array.""" return None real = getset_descriptor() def repeat(self, repeats, axis=None): """a.repeat(repeats, axis=None) Repeat elements of an array. Refer to `numpy.repeat` for full documentation. See Also -------- numpy.repeat : equivalent function""" return None def reshape(self, shape, order=C): """a.reshape(shape, order='C') Returns an array containing the same data with a new shape. Refer to `numpy.reshape` for full documentation. See Also -------- numpy.reshape : equivalent function""" return None def resize(self, new_shape, refcheck): """a.resize(new_shape, refcheck=True) Change shape and size of array in-place. Parameters ---------- new_shape : tuple of ints, or `n` ints Shape of resized array. refcheck : bool, optional If False, reference count will not be checked. Default is True. Returns ------- None Raises ------ ValueError If `a` does not own its own data or references or views to it exist, and the data memory must be changed. SystemError If the `order` keyword argument is specified. This behaviour is a bug in NumPy. See Also -------- resize : Return a new array with the specified shape. Notes ----- This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False. Examples -------- Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]]) >>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]]) Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]]) Referencing an array prevents resizing... >>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ... Unless `refcheck` is False: >>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])""" return None def round(self, decimals=0, out=None): """a.round(decimals=0, out=None) Return `a` with each element rounded to the given number of decimals. Refer to `numpy.around` for full documentation. See Also -------- numpy.around : equivalent function""" return None def searchsorted(self, v, side=left, sorter=None): """a.searchsorted(v, side='left', sorter=None) Find indices where elements of v should be inserted in a to maintain order. For full documentation, see `numpy.searchsorted` See Also -------- numpy.searchsorted : equivalent function""" return None def setfield(self, val, dtype, offset): """a.setfield(val, dtype, offset=0) Put a value into a specified place in a field defined by a data-type. Place `val` into `a`'s field defined by `dtype` and beginning `offset` bytes into the field. Parameters ---------- val : object Value to be placed in field. dtype : dtype object Data-type of the field in which to place `val`. offset : int, optional The number of bytes into the field at which to place `val`. Returns ------- None See Also -------- getfield Examples -------- >>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])""" return None def setflags(self, write, align, uic): """a.setflags(write=None, align=None, uic=None) Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively. These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The UPDATEIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters ---------- write : bool, optional Describes whether or not `a` can be written to. align : bool, optional Describes whether or not `a` is aligned properly for its type. uic : bool, optional Describes whether or not `a` is a copy of another "base" array. Notes ----- Array flags provide information about how the memory area used for the array is to be interpreted. There are 6 Boolean flags in use, only three of which can be changed by the user: UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array. All flags can be accessed using their first (upper case) letter as well as the full name. Examples -------- >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "", line 1, in ValueError: cannot set UPDATEIFCOPY flag to True""" return None shape = getset_descriptor() size = getset_descriptor() def sort(self, axis, kind, order): """a.sort(axis=-1, kind='quicksort', order=None) Sort an array, in-place. Parameters ---------- axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort. Notes ----- See ``sort`` for notes on the different sorting algorithms. Examples -------- >>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]""" return list() def tostring(self, order): """a.tostring(order='C') Construct a Python string containing the raw data bytes in the array. Constructs a Python string showing a copy of the raw contents of data memory. The string can be produced in either 'C' or 'Fortran', or 'Any' order (the default is 'C'-order). 'Any' order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means 'Fortran' order. Parameters ---------- order : {'C', 'F', None}, optional Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array. Returns ------- s : str A Python string exhibiting a copy of `a`'s raw data. Examples -------- >>> x = np.array([[0, 1], [2, 3]]) >>> x.tostring() '\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tostring('C') == x.tostring() True >>> x.tostring('F') '\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'""" return str() def trace(self, offset=0, axis1=0, axis2=1, dtype=None, out=None): """a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) Return the sum along diagonals of the array. Refer to `numpy.trace` for full documentation. See Also -------- numpy.trace : equivalent function""" return None def transpose(self, axes): """a.transpose(*axes) Returns a view of the array with axes transposed. For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. Parameters ---------- axes : None, tuple of ints, or `n` ints * None or no argument: reverses the order of the axes. * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s `i`-th axis becomes `a.transpose()`'s `j`-th axis. * `n` ints: same as an n-tuple of the same ints (this form is intended simply as a "convenience" alternative to the tuple form) Returns ------- out : ndarray View of `a`, with axes suitably permuted. See Also -------- ndarray.T : Array property returning the array transposed. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])""" return ndarray() def var(self, axis=None, dtype=None, out=None, ddof=0): """a.var(axis=None, dtype=None, out=None, ddof=0) Returns the variance of the array elements, along given axis. Refer to `numpy.var` for full documentation. See Also -------- numpy.var : equivalent function""" return None def view(self=None, dtype=None, type=None): """None""" return None def rec_fromcsv(fnamekwargs): """ Load ASCII data stored in a comma-separated file. The returned array is a record array (if ``usemask=False``, see `recarray`) or a masked record array (if ``usemask=True``, see `ma.mrecords.MaskedRecords`). Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function to load ASCII data. """ return None def rec_fromtxt(fnamekwargs): """ Load ASCII data from a file and return it in a record array. If ``usemask=False`` a standard `recarray` is returned, if ``usemask=True`` a MaskedRecords array is returned. Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function Notes ----- By default, `dtype` is None, which means that the data-type of the output array will be determined from the data. """ return None def reciprocal(x, out=None): """reciprocal(x[, out]) Return the reciprocal of the argument, element-wise. Calculates ``1/x``. Parameters ---------- x : array_like Input array. Returns ------- y : ndarray Return array. Notes ----- .. note:: This function is not designed to work with integers. For integer arguments with absolute value larger than 1 the result is always zero because of the way Python handles integer division. For integer zero the result is an overflow. Examples -------- >>> np.reciprocal(2.) 0.5 >>> np.reciprocal([1, 2., 3.33]) array([ 1. , 0.5 , 0.3003003])""" return ndarray() class record: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() def getfield(self, _): """None""" return None imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() def pprint(self, _): """Pretty-print all fields.""" return None real = getset_descriptor() def setfield(self, _): """None""" return None shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def remainder(x1, x2, out): """remainder(x1, x2[, out]) Return element-wise remainder of division. Computes ``x1 - floor(x1 / x2) * x2``. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. Returns ------- y : ndarray The remainder of the quotient ``x1/x2``, element-wise. Returns a scalar if both `x1` and `x2` are scalars. See Also -------- divide, floor Notes ----- Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of) integers. Examples -------- >>> np.remainder([4, 7], [2, 3]) array([0, 1]) >>> np.remainder(np.arange(7), 5) array([0, 1, 2, 3, 4, 0, 1])""" return ndarray() def repeat(a, repeats=None, axis=None): """ Repeat elements of an array. Parameters ---------- a : array_like Input array. repeats : {int, array of ints} The number of repetitions for each element. `repeats` is broadcasted to fit the shape of the given axis. axis : int, optional The axis along which to repeat values. By default, use the flattened input array, and return a flat output array. Returns ------- repeated_array : ndarray Output array which has the same shape as `a`, except along the given axis. See Also -------- tile : Tile an array. Examples -------- >>> x = np.array([[1,2],[3,4]]) >>> np.repeat(x, 2) array([1, 1, 2, 2, 3, 3, 4, 4]) >>> np.repeat(x, 3, axis=1) array([[1, 1, 1, 2, 2, 2], [3, 3, 3, 4, 4, 4]]) >>> np.repeat(x, [1, 2], axis=0) array([[1, 2], [3, 4], [3, 4]]) """ return ndarray() def require(a=None, dtype=None, requirements=None): """ Return an ndarray of the provided type that satisfies requirements. This function is useful to be sure that an array with the correct flags is returned for passing to compiled code (perhaps through ctypes). Parameters ---------- a : array_like The object to be converted to a type-and-requirement-satisfying array. dtype : data-type The required data-type, the default data-type is float64). requirements : str or list of str The requirements list can be any of the following * 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array * 'ALIGNED' ('A') - ensure a data-type aligned array * 'WRITEABLE' ('W') - ensure a writable array * 'OWNDATA' ('O') - ensure an array that owns its own data See Also -------- asarray : Convert input to an ndarray. asanyarray : Convert to an ndarray, but pass through ndarray subclasses. ascontiguousarray : Convert input to a contiguous array. asfortranarray : Convert input to an ndarray with column-major memory order. ndarray.flags : Information about the memory layout of the array. Notes ----- The returned array will be guaranteed to have the listed requirements by making a copy if needed. Examples -------- >>> x = np.arange(6).reshape(2,3) >>> x.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : False WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F']) >>> y.flags C_CONTIGUOUS : False F_CONTIGUOUS : True OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False """ return None def reshape(a, newshape="C", order="C"): """ Gives a new shape to an array without changing its data. Parameters ---------- a : array_like Array to be reshaped. newshape : int or tuple of ints The new shape should be compatible with the original shape. If an integer, then the result will be a 1-D array of that length. One shape dimension can be -1. In this case, the value is inferred from the length of the array and remaining dimensions. order : {'C', 'F', 'A'}, optional Read the elements of `a` using this index order, and place the elements into the reshaped array using this index order. 'C' means to read / write the elements using C-like index order, with the last axis index changing fastest, back to the first axis index changing slowest. 'F' means to read / write the elements using Fortran-like index order, with the first index changing fastest, and the last index changing slowest. Note that the 'C' and 'F' options take no account of the memory layout of the underlying array, and only refer to the order of indexing. 'A' means to read / write the elements in Fortran-like index order if `a` is Fortran *contiguous* in memory, C-like order otherwise. Returns ------- reshaped_array : ndarray This will be a new view object if possible; otherwise, it will be a copy. Note there is no guarantee of the *memory layout* (C- or Fortran- contiguous) of the returned array. See Also -------- ndarray.reshape : Equivalent method. Notes ----- It is not always possible to change the shape of an array without copying the data. If you want an error to be raise if the data is copied, you should assign the new shape to the shape attribute of the array:: >>> a = np.zeros((10, 2)) # A transpose make the array non-contiguous >>> b = a.T # Taking a view makes it possible to modify the shape without modifying the # initial object. >>> c = b.view() >>> c.shape = (20) AttributeError: incompatible shape for a non-contiguous array The `order` keyword gives the index ordering both for *fetching* the values from `a`, and then *placing* the values into the output array. For example, let's say you have an array: >>> a = np.arange(6).reshape((3, 2)) >>> a array([[0, 1], [2, 3], [4, 5]]) You can think of reshaping as first raveling the array (using the given index order), then inserting the elements from the raveled array into the new array using the same kind of index ordering as was used for the raveling. >>> np.reshape(a, (2, 3)) # C-like index ordering array([[0, 1, 2], [3, 4, 5]]) >>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape array([[0, 1, 2], [3, 4, 5]]) >>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering array([[0, 4, 3], [2, 1, 5]]) >>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F') array([[0, 4, 3], [2, 1, 5]]) Examples -------- >>> a = np.array([[1,2,3], [4,5,6]]) >>> np.reshape(a, 6) array([1, 2, 3, 4, 5, 6]) >>> np.reshape(a, 6, order='F') array([1, 4, 2, 5, 3, 6]) >>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2 array([[1, 2], [3, 4], [5, 6]]) """ return ndarray() def resize(a, new_shape): """ Return a new array with the specified shape. If the new array is larger than the original array, then the new array is filled with repeated copies of `a`. Note that this behavior is different from a.resize(new_shape) which fills with zeros instead of repeated copies of `a`. Parameters ---------- a : array_like Array to be resized. new_shape : int or tuple of int Shape of resized array. Returns ------- reshaped_array : ndarray The new array is formed from the data in the old array, repeated if necessary to fill out the required number of elements. The data are repeated in the order that they are stored in memory. See Also -------- ndarray.resize : resize an array in-place. Examples -------- >>> a=np.array([[0,1],[2,3]]) >>> np.resize(a,(1,4)) array([[0, 1, 2, 3]]) >>> np.resize(a,(2,4)) array([[0, 1, 2, 3], [0, 1, 2, 3]]) """ return ndarray() def restoredot(): """Restore `dot`, `vdot`, and `innerproduct` to the default non-BLAS implementations. Typically, the user will only need to call this when troubleshooting and installation problem, reproducing the conditions of a build without an accelerated BLAS, or when being very careful about benchmarking linear algebra operations. See Also -------- alterdot : `restoredot` undoes the effects of `alterdot`.""" return None def result_type(arrays_and_dtypes): """result_type(*arrays_and_dtypes) Returns the type that results from applying the NumPy type promotion rules to the arguments. Type promotion in NumPy works similarly to the rules in languages like C++, with some slight differences. When both scalars and arrays are used, the array's type takes precedence and the actual value of the scalar is taken into account. For example, calculating 3*a, where a is an array of 32-bit floats, intuitively should result in a 32-bit float output. If the 3 is a 32-bit integer, the NumPy rules indicate it can't convert losslessly into a 32-bit float, so a 64-bit float should be the result type. By examining the value of the constant, '3', we see that it fits in an 8-bit integer, which can be cast losslessly into the 32-bit float. Parameters ---------- arrays_and_dtypes : list of arrays and dtypes The operands of some operation whose result type is needed. Returns ------- out : dtype The result type. See also -------- dtype, promote_types, min_scalar_type, can_cast Notes ----- .. versionadded:: 1.6.0 The specific algorithm used is as follows. Categories are determined by first checking which of boolean, integer (int/uint), or floating point (float/complex) the maximum kind of all the arrays and the scalars are. If there are only scalars or the maximum category of the scalars is higher than the maximum category of the arrays, the data types are combined with :func:`promote_types` to produce the return value. Otherwise, `min_scalar_type` is called on each array, and the resulting data types are all combined with :func:`promote_types` to produce the return value. The set of int values is not a subset of the uint values for types with the same number of bits, something not reflected in :func:`min_scalar_type`, but handled as a special case in `result_type`. Examples -------- >>> np.result_type(3, np.arange(7, dtype='i1')) dtype('int8') >>> np.result_type('i4', 'c8') dtype('complex128') >>> np.result_type(3.0, -2) dtype('float64')""" return dtype() def right_shift(x1, x2, out=None): """right_shift(x1, x2[, out]) Shift the bits of an integer to the right. Bits are shifted to the right by removing `x2` bits at the right of `x1`. Since the internal representation of numbers is in binary format, this operation is equivalent to dividing `x1` by ``2**x2``. Parameters ---------- x1 : array_like, int Input values. x2 : array_like, int Number of bits to remove at the right of `x1`. Returns ------- out : ndarray, int Return `x1` with bits shifted `x2` times to the right. See Also -------- left_shift : Shift the bits of an integer to the left. binary_repr : Return the binary representation of the input number as a string. Examples -------- >>> np.binary_repr(10) '1010' >>> np.right_shift(10, 1) 5 >>> np.binary_repr(5) '101' >>> np.right_shift(10, [1,2,3]) array([5, 2, 1])""" return ndarray() def rint(x, out=None): """rint(x[, out]) Round elements of the array to the nearest integer. Parameters ---------- x : array_like Input array. Returns ------- out : {ndarray, scalar} Output array is same shape and type as `x`. See Also -------- ceil, floor, trunc Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.rint(a) array([-2., -2., -0., 0., 2., 2., 2.])""" return ndarray() def roll(a, shift=None, axis=None): """ Roll array elements along a given axis. Elements that roll beyond the last position are re-introduced at the first. Parameters ---------- a : array_like Input array. shift : int The number of places by which elements are shifted. axis : int, optional The axis along which elements are shifted. By default, the array is flattened before shifting, after which the original shape is restored. Returns ------- res : ndarray Output array, with the same shape as `a`. See Also -------- rollaxis : Roll the specified axis backwards, until it lies in a given position. Examples -------- >>> x = np.arange(10) >>> np.roll(x, 2) array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]) >>> x2 = np.reshape(x, (2,5)) >>> x2 array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) >>> np.roll(x2, 1) array([[9, 0, 1, 2, 3], [4, 5, 6, 7, 8]]) >>> np.roll(x2, 1, axis=0) array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]) >>> np.roll(x2, 1, axis=1) array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]) """ return ndarray() def rollaxis(a, axis=0, start=0): """ Roll the specified axis backwards, until it lies in a given position. Parameters ---------- a : ndarray Input array. axis : int The axis to roll backwards. The positions of the other axes do not change relative to one another. start : int, optional The axis is rolled until it lies before this position. The default, 0, results in a "complete" roll. Returns ------- res : ndarray Output array. See Also -------- roll : Roll the elements of an array by a number of positions along a given axis. Examples -------- >>> a = np.ones((3,4,5,6)) >>> np.rollaxis(a, 3, 1).shape (3, 6, 4, 5) >>> np.rollaxis(a, 2).shape (5, 3, 4, 6) >>> np.rollaxis(a, 1, 4).shape (3, 5, 6, 4) """ return ndarray() def roots(p): """ Return the roots of a polynomial with coefficients given in p. The values in the rank-1 array `p` are coefficients of a polynomial. If the length of `p` is n+1 then the polynomial is described by:: p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n] Parameters ---------- p : array_like Rank-1 array of polynomial coefficients. Returns ------- out : ndarray An array containing the complex roots of the polynomial. Raises ------ ValueError When `p` cannot be converted to a rank-1 array. See also -------- poly : Find the coefficients of a polynomial with a given sequence of roots. polyval : Evaluate a polynomial at a point. polyfit : Least squares polynomial fit. poly1d : A one-dimensional polynomial class. Notes ----- The algorithm relies on computing the eigenvalues of the companion matrix [1]_. References ---------- .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7. Examples -------- >>> coeff = [3.2, 2, 1] >>> np.roots(coeff) array([-0.3125+0.46351241j, -0.3125-0.46351241j]) """ return ndarray() def rot90(m=1, k=1): """ Rotate an array by 90 degrees in the counter-clockwise direction. The first two dimensions are rotated; therefore, the array must be at least 2-D. Parameters ---------- m : array_like Array of two or more dimensions. k : integer Number of times the array is rotated by 90 degrees. Returns ------- y : ndarray Rotated array. See Also -------- fliplr : Flip an array horizontally. flipud : Flip an array vertically. Examples -------- >>> m = np.array([[1,2],[3,4]], int) >>> m array([[1, 2], [3, 4]]) >>> np.rot90(m) array([[2, 4], [1, 3]]) >>> np.rot90(m, 2) array([[4, 3], [2, 1]]) """ return ndarray() def round_(a=None, decimals=0, out=None): """ Round an array to the given number of decimals. Refer to `around` for full documentation. See Also -------- around : equivalent function """ return None def round_(a=None, decimals=0, out=None): """ Round an array to the given number of decimals. Refer to `around` for full documentation. See Also -------- around : equivalent function """ return None def vstack(tup): """ Stack arrays in sequence vertically (row wise). Take a sequence of arrays and stack them vertically to make a single array. Rebuild arrays divided by `vsplit`. Parameters ---------- tup : sequence of ndarrays Tuple containing arrays to be stacked. The arrays must have the same shape along all but the first axis. Returns ------- stacked : ndarray The array formed by stacking the given arrays. See Also -------- hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third dimension). concatenate : Join a sequence of arrays together. vsplit : Split array into a list of multiple sub-arrays vertically. Notes ----- Equivalent to ``np.concatenate(tup, axis=0)`` if `tup` contains arrays that are at least 2-dimensional. Examples -------- >>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.vstack((a,b)) array([[1, 2, 3], [2, 3, 4]]) >>> a = np.array([[1], [2], [3]]) >>> b = np.array([[2], [3], [4]]) >>> np.vstack((a,b)) array([[1], [2], [3], [2], [3], [4]]) """ return ndarray() s_ = IndexExpression() def safe_eval(source): """ Protected string evaluation. Evaluate a string containing a Python literal expression without allowing the execution of arbitrary non-literal code. Parameters ---------- source : str The string to evaluate. Returns ------- obj : object The result of evaluating `source`. Raises ------ SyntaxError If the code has invalid Python syntax, or if it contains non-literal code. Examples -------- >>> np.safe_eval('1') 1 >>> np.safe_eval('[1, 2, 3]') [1, 2, 3] >>> np.safe_eval('{"foo": ("bar", 10.0)}') {'foo': ('bar', 10.0)} >>> np.safe_eval('import os') Traceback (most recent call last): ... SyntaxError: invalid syntax >>> np.safe_eval('open("/home/user/.ssh/id_dsa").read()') Traceback (most recent call last): ... SyntaxError: Unsupported source construct: compiler.ast.CallFunc """ return object() def save(file, arr): """ Save an array to a binary file in NumPy ``.npy`` format. Parameters ---------- file : file or str File or filename to which the data is saved. If file is a file-object, then the filename is unchanged. If file is a string, a ``.npy`` extension will be appended to the file name if it does not already have one. arr : array_like Array data to be saved. See Also -------- savez : Save several arrays into a ``.npz`` archive savetxt, load Notes ----- For a description of the ``.npy`` format, see `format`. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = np.arange(10) >>> np.save(outfile, x) >>> outfile.seek(0) # Only needed here to simulate closing & reopening file >>> np.load(outfile) array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) """ return None def savetxt(fname, X="# ", fmt="%.18e", delimiter=" ", newline=" ", header="", footer="", comments="# "): """ Save an array to a text file. Parameters ---------- fname : filename or file handle If the filename ends in ``.gz``, the file is automatically saved in compressed gzip format. `loadtxt` understands gzipped files transparently. X : array_like Data to be saved to a text file. fmt : str or sequence of strs, optional A single format (%10.5f), a sequence of formats, or a multi-format string, e.g. 'Iteration %d -- %10.5f', in which case `delimiter` is ignored. For complex `X`, the legal options for `fmt` are: a) a single specifier, `fmt='%.4e'`, resulting in numbers formatted like `' (%s+%sj)' % (fmt, fmt)` b) a full string specifying every real and imaginary part, e.g. `' %.4e %+.4j %.4e %+.4j %.4e %+.4j'` for 3 columns c) a list of specifiers, one per column - in this case, the real and imaginary part must have separate specifiers, e.g. `['%.3e + %.3ej', '(%.15e%+.15ej)']` for 2 columns delimiter : str, optional Character separating columns. newline : str, optional .. versionadded:: 1.5.0 header : str, optional String that will be written at the beginning of the file. .. versionadded:: 1.7.0 footer : str, optional String that will be written at the end of the file. .. versionadded:: 1.7.0 comments : str, optional String that will be prepended to the ``header`` and ``footer`` strings, to mark them as comments. Default: '# ', as expected by e.g. ``numpy.loadtxt``. .. versionadded:: 1.7.0 Character separating lines. See Also -------- save : Save an array to a binary file in NumPy ``.npy`` format savez : Save several arrays into a ``.npz`` compressed archive Notes ----- Further explanation of the `fmt` parameter (``%[flag]width[.precision]specifier``): flags: ``-`` : left justify ``+`` : Forces to preceed result with + or -. ``0`` : Left pad the number with zeros instead of space (see width). width: Minimum number of characters to be printed. The value is not truncated if it has more characters. precision: - For integer specifiers (eg. ``d,i,o,x``), the minimum number of digits. - For ``e, E`` and ``f`` specifiers, the number of digits to print after the decimal point. - For ``g`` and ``G``, the maximum number of significant digits. - For ``s``, the maximum number of characters. specifiers: ``c`` : character ``d`` or ``i`` : signed decimal integer ``e`` or ``E`` : scientific notation with ``e`` or ``E``. ``f`` : decimal floating point ``g,G`` : use the shorter of ``e,E`` or ``f`` ``o`` : signed octal ``s`` : string of characters ``u`` : unsigned decimal integer ``x,X`` : unsigned hexadecimal integer This explanation of ``fmt`` is not complete, for an exhaustive specification see [1]_. References ---------- .. [1] `Format Specification Mini-Language `_, Python Documentation. Examples -------- >>> x = y = z = np.arange(0.0,5.0,1.0) >>> np.savetxt('test.out', x, delimiter=',') # X is an array >>> np.savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays >>> np.savetxt('test.out', x, fmt='%1.4e') # use exponential notation """ return None def savez(file, args, kwds): """ Save several arrays into a single file in uncompressed ``.npz`` format. If arguments are passed in with no keywords, the corresponding variable names, in the .npz file, are 'arr_0', 'arr_1', etc. If keyword arguments are given, the corresponding variable names, in the ``.npz`` file will match the keyword names. Parameters ---------- file : str or file Either the file name (string) or an open file (file-like object) where the data will be saved. If file is a string, the ``.npz`` extension will be appended to the file name if it is not already there. args : Arguments, optional Arrays to save to the file. Since it is not possible for Python to know the names of the arrays outside `savez`, the arrays will be saved with names "arr_0", "arr_1", and so on. These arguments can be any expression. kwds : Keyword arguments, optional Arrays to save to the file. Arrays will be saved in the file with the keyword names. Returns ------- None See Also -------- save : Save a single array to a binary file in NumPy format. savetxt : Save an array to a file as plain text. savez_compressed : Save several arrays into a compressed .npz file format Notes ----- The ``.npz`` file format is a zipped archive of files named after the variables they contain. The archive is not compressed and each file in the archive contains one variable in ``.npy`` format. For a description of the ``.npy`` format, see `format`. When opening the saved ``.npz`` file with `load` a `NpzFile` object is returned. This is a dictionary-like object which can be queried for its list of arrays (with the ``.files`` attribute), and for the arrays themselves. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = np.arange(10) >>> y = np.sin(x) Using `savez` with \*args, the arrays are saved with default names. >>> np.savez(outfile, x, y) >>> outfile.seek(0) # Only needed here to simulate closing & reopening file >>> npzfile = np.load(outfile) >>> npzfile.files ['arr_1', 'arr_0'] >>> npzfile['arr_0'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) Using `savez` with \**kwds, the arrays are saved with the keyword names. >>> outfile = TemporaryFile() >>> np.savez(outfile, x=x, y=y) >>> outfile.seek(0) >>> npzfile = np.load(outfile) >>> npzfile.files ['y', 'x'] >>> npzfile['x'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) """ return None def savez_compressed(file, args, kwds): """ Save several arrays into a single file in compressed ``.npz`` format. If keyword arguments are given, then filenames are taken from the keywords. If arguments are passed in with no keywords, then stored file names are arr_0, arr_1, etc. Parameters ---------- file : str File name of .npz file. args : Arguments Function arguments. kwds : Keyword arguments Keywords. See Also -------- numpy.savez : Save several arrays into an uncompressed .npz file format """ return None def sctype2char(sctype): """ Return the string representation of a scalar dtype. Parameters ---------- sctype : scalar dtype or object If a scalar dtype, the corresponding string character is returned. If an object, `sctype2char` tries to infer its scalar type and then return the corresponding string character. Returns ------- typechar : str The string character corresponding to the scalar type. Raises ------ ValueError If `sctype` is an object for which the type can not be inferred. See Also -------- obj2sctype, issctype, issubsctype, mintypecode Examples -------- >>> for sctype in [np.int32, np.float, np.complex, np.string_, np.ndarray]: ... print np.sctype2char(sctype) l d D S O >>> x = np.array([1., 2-1.j]) >>> np.sctype2char(x) 'D' >>> np.sctype2char(list) 'O' """ return str() sctypeDict = dict() sctypeNA = dict() sctypes = dict() def searchsorted(a, v=None, side="left", sorter=None): """ Find indices where elements should be inserted to maintain order. Find the indices into a sorted array `a` such that, if the corresponding elements in `v` were inserted before the indices, the order of `a` would be preserved. Parameters ---------- a : 1-D array_like Input array. If `sorter` is None, then it must be sorted in ascending order, otherwise `sorter` must be an array of indices that sort it. v : array_like Values to insert into `a`. side : {'left', 'right'}, optional If 'left', the index of the first suitable location found is given. If 'right', return the last such index. If there is no suitable index, return either 0 or N (where N is the length of `a`). sorter : 1-D array_like, optional .. versionadded:: 1.7.0 Optional array of integer indices that sort array a into ascending order. They are typically the result of argsort. Returns ------- indices : array of ints Array of insertion points with the same shape as `v`. See Also -------- sort : Return a sorted copy of an array. histogram : Produce histogram from 1-D data. Notes ----- Binary search is used to find the required insertion points. As of Numpy 1.4.0 `searchsorted` works with real/complex arrays containing `nan` values. The enhanced sort order is documented in `sort`. Examples -------- >>> np.searchsorted([1,2,3,4,5], 3) 2 >>> np.searchsorted([1,2,3,4,5], 3, side='right') 3 >>> np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3]) array([0, 5, 1, 2]) """ return array() def select(condlist, choicelist=0, default=0): """ Return an array drawn from elements in choicelist, depending on conditions. Parameters ---------- condlist : list of bool ndarrays The list of conditions which determine from which array in `choicelist` the output elements are taken. When multiple conditions are satisfied, the first one encountered in `condlist` is used. choicelist : list of ndarrays The list of arrays from which the output elements are taken. It has to be of the same length as `condlist`. default : scalar, optional The element inserted in `output` when all conditions evaluate to False. Returns ------- output : ndarray The output at position m is the m-th element of the array in `choicelist` where the m-th element of the corresponding array in `condlist` is True. See Also -------- where : Return elements from one of two arrays depending on condition. take, choose, compress, diag, diagonal Examples -------- >>> x = np.arange(10) >>> condlist = [x<3, x>5] >>> choicelist = [x, x**2] >>> np.select(condlist, choicelist) array([ 0, 1, 2, 0, 0, 0, 36, 49, 64, 81]) """ return ndarray() def set_numeric_ops(op1=func1, op2=func2, more_args=None): """set_numeric_ops(op1=func1, op2=func2, ...) Set numerical operators for array objects. Parameters ---------- op1, op2, ... : callable Each ``op = func`` pair describes an operator to be replaced. For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace addition by modulus 5 addition. Returns ------- saved_ops : list of callables A list of all operators, stored before making replacements. Notes ----- .. WARNING:: Use with care! Incorrect usage may lead to memory errors. A function replacing an operator cannot make use of that operator. For example, when replacing add, you may not use ``+``. Instead, directly call ufuncs. Examples -------- >>> def add_mod5(x, y): ... return np.add(x, y) % 5 ... >>> old_funcs = np.set_numeric_ops(add=add_mod5) >>> x = np.arange(12).reshape((3, 4)) >>> x + x array([[0, 2, 4, 1], [3, 0, 2, 4], [1, 3, 0, 2]]) >>> ignore = np.set_numeric_ops(**old_funcs) # restore operators""" return list() def set_printoptions(precision=None, threshold=None, edgeitems=None, linewidth=None, suppress=None, nanstr=None, infstr=None, formatter=None): """ Set printing options. These options determine the way floating point numbers, arrays and other NumPy objects are displayed. Parameters ---------- precision : int, optional Number of digits of precision for floating point output (default 8). threshold : int, optional Total number of array elements which trigger summarization rather than full repr (default 1000). edgeitems : int, optional Number of array items in summary at beginning and end of each dimension (default 3). linewidth : int, optional The number of characters per line for the purpose of inserting line breaks (default 75). suppress : bool, optional Whether or not suppress printing of small floating point values using scientific notation (default False). nanstr : str, optional String representation of floating point not-a-number (default nan). infstr : str, optional String representation of floating point infinity (default inf). formatter : dict of callables, optional If not None, the keys should indicate the type(s) that the respective formatting function applies to. Callables should return a string. Types that are not specified (by their corresponding keys) are handled by the default formatters. Individual types for which a formatter can be set are:: - 'bool' - 'int' - 'timedelta' : a `numpy.timedelta64` - 'datetime' : a `numpy.datetime64` - 'float' - 'longfloat' : 128-bit floats - 'complexfloat' - 'longcomplexfloat' : composed of two 128-bit floats - 'numpy_str' : types `numpy.string_` and `numpy.unicode_` - 'str' : all other strings Other keys that can be used to set a group of types at once are:: - 'all' : sets all types - 'int_kind' : sets 'int' - 'float_kind' : sets 'float' and 'longfloat' - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat' - 'str_kind' : sets 'str' and 'numpystr' See Also -------- get_printoptions, set_string_function, array2string Notes ----- `formatter` is always reset with a call to `set_printoptions`. Examples -------- Floating point precision can be set: >>> np.set_printoptions(precision=4) >>> print np.array([1.123456789]) [ 1.1235] Long arrays can be summarised: >>> np.set_printoptions(threshold=5) >>> print np.arange(10) [0 1 2 ..., 7 8 9] Small results can be suppressed: >>> eps = np.finfo(float).eps >>> x = np.arange(4.) >>> x**2 - (x + eps)**2 array([ -4.9304e-32, -4.4409e-16, 0.0000e+00, 0.0000e+00]) >>> np.set_printoptions(suppress=True) >>> x**2 - (x + eps)**2 array([-0., -0., 0., 0.]) A custom formatter can be used to display array elements as desired: >>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)}) >>> x = np.arange(3) >>> x array([int: 0, int: -1, int: -2]) >>> np.set_printoptions() # formatter gets reset >>> x array([0, 1, 2]) To put back the default options, you can use: >>> np.set_printoptions(edgeitems=3,infstr='inf', ... linewidth=75, nanstr='nan', precision=8, ... suppress=False, threshold=1000, formatter=None) """ return None def set_string_function(f=True, repr=True): """ Set a Python function to be used when pretty printing arrays. Parameters ---------- f : function or None Function to be used to pretty print arrays. The function should expect a single array argument and return a string of the representation of the array. If None, the function is reset to the default NumPy function to print arrays. repr : bool, optional If True (default), the function for pretty printing (``__repr__``) is set, if False the function that returns the default string representation (``__str__``) is set. See Also -------- set_printoptions, get_printoptions Examples -------- >>> def pprint(arr): ... return 'HA! - What are you going to do now?' ... >>> np.set_string_function(pprint) >>> a = np.arange(10) >>> a HA! - What are you going to do now? >>> print a [0 1 2 3 4 5 6 7 8 9] We can reset the function to the default: >>> np.set_string_function(None) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) `repr` affects either pretty printing or normal string representation. Note that ``__repr__`` is still affected by setting ``__str__`` because the width of each array element in the returned string becomes equal to the length of the result of ``__str__()``. >>> x = np.arange(4) >>> np.set_string_function(lambda x:'random', repr=False) >>> x.__str__() 'random' >>> x.__repr__() 'array([ 0, 1, 2, 3])' """ return None def setbufsize(): """ Set the size of the buffer used in ufuncs. Parameters ---------- size : int Size of buffer. """ return None def setdiff1d(ar1, ar2=False, assume_unique=False): """ Find the set difference of two arrays. Return the sorted, unique values in `ar1` that are not in `ar2`. Parameters ---------- ar1 : array_like Input array. ar2 : array_like Input comparison array. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setdiff1d : ndarray Sorted 1D array of values in `ar1` that are not in `ar2`. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4, 1]) >>> b = np.array([3, 4, 5, 6]) >>> np.setdiff1d(a, b) array([1, 2]) """ return ndarray() def seterr(all=None, divide=None, over=None, under=None, invalid=None): """ Set how floating-point errors are handled. Note that operations on integer scalar types (such as `int16`) are handled like floating point, and are affected by these settings. Parameters ---------- all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Set treatment for all types of floating-point errors at once: - ignore: Take no action when the exception occurs. - warn: Print a `RuntimeWarning` (via the Python `warnings` module). - raise: Raise a `FloatingPointError`. - call: Call a function specified using the `seterrcall` function. - print: Print a warning directly to ``stdout``. - log: Record error in a Log object specified by `seterrcall`. The default is not to change the current behavior. divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for division by zero. over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for floating-point overflow. under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for floating-point underflow. invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for invalid floating-point operation. Returns ------- old_settings : dict Dictionary containing the old settings. See also -------- seterrcall : Set a callback function for the 'call' mode. geterr, geterrcall, errstate Notes ----- The floating-point exceptions are defined in the IEEE 754 standard [1]: - Division by zero: infinite result obtained from finite numbers. - Overflow: result too large to be expressed. - Underflow: result so close to zero that some precision was lost. - Invalid operation: result is not an expressible number, typically indicates that a NaN was produced. .. [1] http://en.wikipedia.org/wiki/IEEE_754 Examples -------- >>> old_settings = np.seterr(all='ignore') #seterr to known value >>> np.seterr(over='raise') {'over': 'ignore', 'divide': 'ignore', 'invalid': 'ignore', 'under': 'ignore'} >>> np.seterr(all='ignore') # reset to default {'over': 'raise', 'divide': 'ignore', 'invalid': 'ignore', 'under': 'ignore'} >>> np.int16(32000) * np.int16(3) 30464 >>> old_settings = np.seterr(all='warn', over='raise') >>> np.int16(32000) * np.int16(3) Traceback (most recent call last): File "", line 1, in FloatingPointError: overflow encountered in short_scalars >>> old_settings = np.seterr(all='print') >>> np.geterr() {'over': 'print', 'divide': 'print', 'invalid': 'print', 'under': 'print'} >>> np.int16(32000) * np.int16(3) Warning: overflow encountered in short_scalars 30464 """ return dict() def seterrcall(func): """ Set the floating-point error callback function or log object. There are two ways to capture floating-point error messages. The first is to set the error-handler to 'call', using `seterr`. Then, set the function to call using this function. The second is to set the error-handler to 'log', using `seterr`. Floating-point errors then trigger a call to the 'write' method of the provided object. Parameters ---------- func : callable f(err, flag) or object with write method Function to call upon floating-point errors ('call'-mode) or object whose 'write' method is used to log such message ('log'-mode). The call function takes two arguments. The first is the type of error (one of "divide", "over", "under", or "invalid"), and the second is the status flag. The flag is a byte, whose least-significant bits indicate the status:: [0 0 0 0 invalid over under invalid] In other words, ``flags = divide + 2*over + 4*under + 8*invalid``. If an object is provided, its write method should take one argument, a string. Returns ------- h : callable, log instance or None The old error handler. See Also -------- seterr, geterr, geterrcall Examples -------- Callback upon error: >>> def err_handler(type, flag): ... print "Floating point error (%s), with flag %s" % (type, flag) ... >>> saved_handler = np.seterrcall(err_handler) >>> save_err = np.seterr(all='call') >>> np.array([1, 2, 3]) / 0.0 Floating point error (divide by zero), with flag 1 array([ Inf, Inf, Inf]) >>> np.seterrcall(saved_handler) >>> np.seterr(**save_err) {'over': 'call', 'divide': 'call', 'invalid': 'call', 'under': 'call'} Log error message: >>> class Log(object): ... def write(self, msg): ... print "LOG: %s" % msg ... >>> log = Log() >>> saved_handler = np.seterrcall(log) >>> save_err = np.seterr(all='log') >>> np.array([1, 2, 3]) / 0.0 LOG: Warning: divide by zero encountered in divide array([ Inf, Inf, Inf]) >>> np.seterrcall(saved_handler) <__main__.Log object at 0x...> >>> np.seterr(**save_err) {'over': 'log', 'divide': 'log', 'invalid': 'log', 'under': 'log'} """ return callable() if False else None() def seterrobj(errobj): """seterrobj(errobj) Set the object that defines floating-point error handling. The error object contains all information that defines the error handling behavior in Numpy. `seterrobj` is used internally by the other functions that set error handling behavior (`seterr`, `seterrcall`). Parameters ---------- errobj : list The error object, a list containing three elements: [internal numpy buffer size, error mask, error callback function]. The error mask is a single integer that holds the treatment information on all four floating point errors. The information for each error type is contained in three bits of the integer. If we print it in base 8, we can see what treatment is set for "invalid", "under", "over", and "divide" (in that order). The printed string can be interpreted with * 0 : 'ignore' * 1 : 'warn' * 2 : 'raise' * 3 : 'call' * 4 : 'print' * 5 : 'log' See Also -------- geterrobj, seterr, geterr, seterrcall, geterrcall getbufsize, setbufsize Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> old_errobj = np.geterrobj() # first get the defaults >>> old_errobj [10000, 0, None] >>> def err_handler(type, flag): ... print "Floating point error (%s), with flag %s" % (type, flag) ... >>> new_errobj = [20000, 12, err_handler] >>> np.seterrobj(new_errobj) >>> np.base_repr(12, 8) # int for divide=4 ('print') and over=1 ('warn') '14' >>> np.geterr() {'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'} >>> np.geterrcall() is err_handler True""" return None def setxor1d(ar1, ar2=False, assume_unique=False): """ Find the set exclusive-or of two arrays. Return the sorted, unique values that are in only one (not both) of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setxor1d : ndarray Sorted 1D array of unique values that are in only one of the input arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4]) >>> b = np.array([2, 3, 5, 7, 5]) >>> np.setxor1d(a,b) array([1, 4, 5, 7]) """ return ndarray() def shape(a): """ Return the shape of an array. Parameters ---------- a : array_like Input array. Returns ------- shape : tuple of ints The elements of the shape tuple give the lengths of the corresponding array dimensions. See Also -------- alen ndarray.shape : Equivalent array method. Examples -------- >>> np.shape(np.eye(3)) (3, 3) >>> np.shape([[1, 2]]) (1, 2) >>> np.shape([0]) (1,) >>> np.shape(0) () >>> a = np.array([(1, 2), (3, 4)], dtype=[('x', 'i4'), ('y', 'i4')]) >>> np.shape(a) (2,) >>> a.shape (2,) """ return tuple() class int16: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def show(): """None""" return None def sign(x, out=None): """sign(x[, out]) Returns an element-wise indication of the sign of a number. The `sign` function returns ``-1 if x < 0, 0 if x==0, 1 if x > 0``. Parameters ---------- x : array_like Input values. Returns ------- y : ndarray The sign of `x`. Examples -------- >>> np.sign([-5., 4.5]) array([-1., 1.]) >>> np.sign(0) 0""" return ndarray() def signbit(x, out): """signbit(x[, out]) Returns element-wise True where signbit is set (less than zero). Parameters ---------- x : array_like The input value(s). out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See `doc.ufuncs`. Returns ------- result : ndarray of bool Output array, or reference to `out` if that was supplied. Examples -------- >>> np.signbit(-1.2) True >>> np.signbit(np.array([1, -2.3, 2.1])) array([False, True, False], dtype=bool)""" return ndarray() class signedinteger: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def sin(x, out=None): """sin(x[, out]) Trigonometric sine, element-wise. Parameters ---------- x : array_like Angle, in radians (:math:`2 \pi` rad equals 360 degrees). Returns ------- y : array_like The sine of each element of x. See Also -------- arcsin, sinh, cos Notes ----- The sine is one of the fundamental functions of trigonometry (the mathematical study of triangles). Consider a circle of radius 1 centered on the origin. A ray comes in from the :math:`+x` axis, makes an angle at the origin (measured counter-clockwise from that axis), and departs from the origin. The :math:`y` coordinate of the outgoing ray's intersection with the unit circle is the sine of that angle. It ranges from -1 for :math:`x=3\pi / 2` to +1 for :math:`\pi / 2.` The function has zeroes where the angle is a multiple of :math:`\pi`. Sines of angles between :math:`\pi` and :math:`2\pi` are negative. The numerous properties of the sine and related functions are included in any standard trigonometry text. Examples -------- Print sine of one angle: >>> np.sin(np.pi/2.) 1.0 Print sines of an array of angles given in degrees: >>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. ) array([ 0. , 0.5 , 0.70710678, 0.8660254 , 1. ]) Plot the sine function: >>> import matplotlib.pylab as plt >>> x = np.linspace(-np.pi, np.pi, 201) >>> plt.plot(x, np.sin(x)) >>> plt.xlabel('Angle [rad]') >>> plt.ylabel('sin(x)') >>> plt.axis('tight') >>> plt.show()""" return ndarray() def sinc(x): """ Return the sinc function. The sinc function is :math:`\sin(\pi x)/(\pi x)`. Parameters ---------- x : ndarray Array (possibly multi-dimensional) of values for which to to calculate ``sinc(x)``. Returns ------- out : ndarray ``sinc(x)``, which has the same shape as the input. Notes ----- ``sinc(0)`` is the limit value 1. The name sinc is short for "sine cardinal" or "sinus cardinalis". The sinc function is used in various signal processing applications, including in anti-aliasing, in the construction of a Lanczos resampling filter, and in interpolation. For bandlimited interpolation of discrete-time signals, the ideal interpolation kernel is proportional to the sinc function. References ---------- .. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SincFunction.html .. [2] Wikipedia, "Sinc function", http://en.wikipedia.org/wiki/Sinc_function Examples -------- >>> x = np.linspace(-4, 4, 41) >>> np.sinc(x) array([ -3.89804309e-17, -4.92362781e-02, -8.40918587e-02, -8.90384387e-02, -5.84680802e-02, 3.89804309e-17, 6.68206631e-02, 1.16434881e-01, 1.26137788e-01, 8.50444803e-02, -3.89804309e-17, -1.03943254e-01, -1.89206682e-01, -2.16236208e-01, -1.55914881e-01, 3.89804309e-17, 2.33872321e-01, 5.04551152e-01, 7.56826729e-01, 9.35489284e-01, 1.00000000e+00, 9.35489284e-01, 7.56826729e-01, 5.04551152e-01, 2.33872321e-01, 3.89804309e-17, -1.55914881e-01, -2.16236208e-01, -1.89206682e-01, -1.03943254e-01, -3.89804309e-17, 8.50444803e-02, 1.26137788e-01, 1.16434881e-01, 6.68206631e-02, 3.89804309e-17, -5.84680802e-02, -8.90384387e-02, -8.40918587e-02, -4.92362781e-02, -3.89804309e-17]) >>> plt.plot(x, np.sinc(x)) [] >>> plt.title("Sinc Function") >>> plt.ylabel("Amplitude") >>> plt.xlabel("X") >>> plt.show() It works in 2-D as well: >>> x = np.linspace(-4, 4, 401) >>> xx = np.outer(x, x) >>> plt.imshow(np.sinc(xx)) """ return ndarray() class float32: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class complex64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def sinh(x, out): """sinh(x[, out]) Hyperbolic sine, element-wise. Equivalent to ``1/2 * (np.exp(x) - np.exp(-x))`` or ``-1j * np.sin(1j*x)``. Parameters ---------- x : array_like Input array. out : ndarray, optional Output array of same shape as `x`. Returns ------- y : ndarray The corresponding hyperbolic sine values. Raises ------ ValueError: invalid return array shape if `out` is provided and `out.shape` != `x.shape` (See Examples) Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972, pg. 83. Examples -------- >>> np.sinh(0) 0.0 >>> np.sinh(np.pi*1j/2) 1j >>> np.sinh(np.pi*1j) # (exact value is 0) 1.2246063538223773e-016j >>> # Discrepancy due to vagaries of floating point arithmetic. >>> # Example of providing the optional output parameter >>> out2 = np.sinh([0.1], out1) >>> out2 is out1 True >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.sinh(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: invalid return array shape""" return ndarray() def size(a=None, axis=None): """ Return the number of elements along a given axis. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which the elements are counted. By default, give the total number of elements. Returns ------- element_count : int Number of elements along the specified axis. See Also -------- shape : dimensions of array ndarray.shape : dimensions of array ndarray.size : number of elements in array Examples -------- >>> a = np.array([[1,2,3],[4,5,6]]) >>> np.size(a) 6 >>> np.size(a,1) 3 >>> np.size(a,0) 2 """ return int() def sometrue(a=False, axis=None, out=None, keepdims=False): """ Check whether some values are true. Refer to `any` for full documentation. See Also -------- any : equivalent function """ return None def sort(a=None, axis=-1, kind="quicksort", order=None): """ Return a sorted copy of an array. Parameters ---------- a : array_like Array to be sorted. axis : int or None, optional Axis along which to sort. If None, the array is flattened before sorting. The default is -1, which sorts along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : list, optional When `a` is a structured array, this argument specifies which fields to compare first, second, and so on. This list does not need to include all of the fields. Returns ------- sorted_array : ndarray Array of the same type and shape as `a`. See Also -------- ndarray.sort : Method to sort an array in-place. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in a sorted array. partition : Partial sort. Notes ----- The various sorting algorithms are characterized by their average speed, worst case performance, work space size, and whether they are stable. A stable sort keeps items with the same key in the same relative order. The three available algorithms have the following properties: =========== ======= ============= ============ ======= kind speed worst case work space stable =========== ======= ============= ============ ======= 'quicksort' 1 O(n^2) 0 no 'mergesort' 2 O(n*log(n)) ~n/2 yes 'heapsort' 3 O(n*log(n)) 0 no =========== ======= ============= ============ ======= All the sort algorithms make temporary copies of the data when sorting along any but the last axis. Consequently, sorting along the last axis is faster and uses less space than sorting along any other axis. The sort order for complex numbers is lexicographic. If both the real and imaginary parts are non-nan then the order is determined by the real parts except when they are equal, in which case the order is determined by the imaginary parts. Previous to numpy 1.4.0 sorting real and complex arrays containing nan values led to undefined behaviour. In numpy versions >= 1.4.0 nan values are sorted to the end. The extended sort order is: * Real: [R, nan] * Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj] where R is a non-nan real value. Complex values with the same nan placements are sorted according to the non-nan part if it exists. Non-nan values are sorted as before. Examples -------- >>> a = np.array([[1,4],[3,1]]) >>> np.sort(a) # sort along the last axis array([[1, 4], [1, 3]]) >>> np.sort(a, axis=None) # sort the flattened array array([1, 1, 3, 4]) >>> np.sort(a, axis=0) # sort along the first axis array([[1, 1], [3, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> dtype = [('name', 'S10'), ('height', float), ('age', int)] >>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38), ... ('Galahad', 1.7, 38)] >>> a = np.array(values, dtype=dtype) # create a structured array >>> np.sort(a, order='height') # doctest: +SKIP array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41), ('Lancelot', 1.8999999999999999, 38)], dtype=[('name', '|S10'), ('height', '>> np.sort(a, order=['age', 'height']) # doctest: +SKIP array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38), ('Arthur', 1.8, 41)], dtype=[('name', '|S10'), ('height', '>> np.sort_complex([5, 3, 6, 2, 1]) array([ 1.+0.j, 2.+0.j, 3.+0.j, 5.+0.j, 6.+0.j]) >>> np.sort_complex([1 + 2j, 2 - 1j, 3 - 2j, 3 - 3j, 3 + 5j]) array([ 1.+2.j, 2.-1.j, 3.-3.j, 3.-2.j, 3.+5.j]) """ return complex() def source(object="", output=""): """ Print or write to a file the source code for a Numpy object. The source code is only returned for objects written in Python. Many functions and classes are defined in C and will therefore not return useful information. Parameters ---------- object : numpy object Input object. This can be any object (function, class, module, ...). output : file object, optional If `output` not supplied then source code is printed to screen (sys.stdout). File object must be created with either write 'w' or append 'a' modes. See Also -------- lookfor, info Examples -------- >>> np.source(np.interp) #doctest: +SKIP In file: /usr/lib/python2.6/dist-packages/numpy/lib/function_base.py def interp(x, xp, fp, left=None, right=None): ___.... (full docstring printed)___ if isinstance(x, (float, int, number)): return compiled_interp([x], xp, fp, left, right).item() else: return compiled_interp(x, xp, fp, left, right) The source code is only returned for objects written in Python. >>> np.source(np.array) #doctest: +SKIP Not available for this object. """ return None def spacing(x, out=None): """spacing(x[, out]) Return the distance between x and the nearest adjacent number. Parameters ---------- x1 : array_like Values to find the spacing of. Returns ------- out : array_like The spacing of values of `x1`. Notes ----- It can be considered as a generalization of EPS: ``spacing(np.float64(1)) == np.finfo(np.float64).eps``, and there should not be any representable number between ``x + spacing(x)`` and x for any finite x. Spacing of +- inf and nan is nan. Examples -------- >>> np.spacing(1) == np.finfo(np.float64).eps True""" return ndarray() def split(ary, indices_or_sections=0, axis=0): """ Split an array into multiple sub-arrays. Parameters ---------- ary : ndarray Array to be divided into sub-arrays. indices_or_sections : int or 1-D array If `indices_or_sections` is an integer, N, the array will be divided into N equal arrays along `axis`. If such a split is not possible, an error is raised. If `indices_or_sections` is a 1-D array of sorted integers, the entries indicate where along `axis` the array is split. For example, ``[2, 3]`` would, for ``axis=0``, result in - ary[:2] - ary[2:3] - ary[3:] If an index exceeds the dimension of the array along `axis`, an empty sub-array is returned correspondingly. axis : int, optional The axis along which to split, default is 0. Returns ------- sub-arrays : list of ndarrays A list of sub-arrays. Raises ------ ValueError If `indices_or_sections` is given as an integer, but a split does not result in equal division. See Also -------- array_split : Split an array into multiple sub-arrays of equal or near-equal size. Does not raise an exception if an equal division cannot be made. hsplit : Split array into multiple sub-arrays horizontally (column-wise). vsplit : Split array into multiple sub-arrays vertically (row wise). dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). concatenate : Join arrays together. hstack : Stack arrays in sequence horizontally (column wise). vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third dimension). Examples -------- >>> x = np.arange(9.0) >>> np.split(x, 3) [array([ 0., 1., 2.]), array([ 3., 4., 5.]), array([ 6., 7., 8.])] >>> x = np.arange(8.0) >>> np.split(x, [3, 5, 6, 10]) [array([ 0., 1., 2.]), array([ 3., 4.]), array([ 5.]), array([ 6., 7.]), array([], dtype=float64)] """ return list() def sqrt(x, out): """sqrt(x[, out]) Return the positive square-root of an array, element-wise. Parameters ---------- x : array_like The values whose square-roots are required. out : ndarray, optional Alternate array object in which to put the result; if provided, it must have the same shape as `x` Returns ------- y : ndarray An array of the same shape as `x`, containing the positive square-root of each element in `x`. If any element in `x` is complex, a complex array is returned (and the square-roots of negative reals are calculated). If all of the elements in `x` are real, so is `y`, with negative elements returning ``nan``. If `out` was provided, `y` is a reference to it. See Also -------- lib.scimath.sqrt A version which returns complex numbers when given negative reals. Notes ----- *sqrt* has--consistent with common convention--as its branch cut the real "interval" [`-inf`, 0), and is continuous from above on it. (A branch cut is a curve in the complex plane across which a given complex function fails to be continuous.) Examples -------- >>> np.sqrt([1,4,9]) array([ 1., 2., 3.]) >>> np.sqrt([4, -1, -3+4J]) array([ 2.+0.j, 0.+1.j, 1.+2.j]) >>> np.sqrt([4, -1, numpy.inf]) array([ 2., NaN, Inf])""" return ndarray() def square(x, out=None): """square(x[, out]) Return the element-wise square of the input. Parameters ---------- x : array_like Input data. Returns ------- out : ndarray Element-wise `x*x`, of the same shape and dtype as `x`. Returns scalar if `x` is a scalar. See Also -------- numpy.linalg.matrix_power sqrt power Examples -------- >>> np.square([-1j, 1]) array([-1.-0.j, 1.+0.j])""" return ndarray() def squeeze(a=None, axis=None): """ Remove single-dimensional entries from the shape of an array. Parameters ---------- a : array_like Input data. axis : None or int or tuple of ints, optional .. versionadded:: 1.7.0 Selects a subset of the single-dimensional entries in the shape. If an axis is selected with shape entry greater than one, an error is raised. Returns ------- squeezed : ndarray The input array, but with with all or a subset of the dimensions of length 1 removed. This is always `a` itself or a view into `a`. Examples -------- >>> x = np.array([[[0], [1], [2]]]) >>> x.shape (1, 3, 1) >>> np.squeeze(x).shape (3,) >>> np.squeeze(x, axis=(2,)).shape (1, 3) """ return ndarray() def std(a=False, axis=None, dtype=None, out=None, ddof=0, keepdims=False): """ Compute the standard deviation along the specified axis. Returns the standard deviation, a measure of the spread of a distribution, of the array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis. Parameters ---------- a : array_like Calculate the standard deviation of these values. axis : int, optional Axis along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array. dtype : dtype, optional Type to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary. ddof : int, optional Means Delta Degrees of Freedom. The divisor used in calculations is ``N - ddof``, where ``N`` represents the number of elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- standard_deviation : ndarray, see dtype parameter above. If `out` is None, return a new array containing the standard deviation, otherwise return a reference to the output array. See Also -------- var, mean, nanmean, nanstd, nanvar numpy.doc.ufuncs : Section "Output arguments" Notes ----- The standard deviation is the square root of the average of the squared deviations from the mean, i.e., ``std = sqrt(mean(abs(x - x.mean())**2))``. The average squared deviation is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of the infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with ``ddof=1``, it will not be an unbiased estimate of the standard deviation per se. Note that, for complex numbers, `std` takes the absolute value before squaring, so that the result is always real and nonnegative. For floating-point input, the *std* is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> np.std(a) 1.1180339887498949 >>> np.std(a, axis=0) array([ 1., 1.]) >>> np.std(a, axis=1) array([ 0.5, 0.5]) In single precision, std() can be inaccurate: >>> a = np.zeros((2,512*512), dtype=np.float32) >>> a[0,:] = 1.0 >>> a[1,:] = 0.1 >>> np.std(a) 0.45172946707416706 Computing the standard deviation in float64 is more accurate: >>> np.std(a, dtype=np.float64) 0.44999999925552653 """ return ndarray() class str: __doc__ = str() def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None def capitalize(self, _): """S.capitalize() -> string Return a copy of the string S with only its first character capitalized.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> string Return S centered in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> object Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> object Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that is able to handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> string Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def format(self, args, kwargs): """S.format(*args, **kwargs) -> string Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. uppercase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None def join(self, iterable): """S.join(iterable) -> string Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> string Return S left-justified in a string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> string Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> string or unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None def replace(self, old, new, count): """S.replace(old, new[, count]) -> string Return a copy of string S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> string Return S right-justified in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> string or unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None def strip(self, chars): """S.strip([chars]) -> string or unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> string Return a copy of the string S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> string Return a titlecased version of S, i.e. words start with uppercase characters, all remaining cased characters have lowercase.""" return None def translate(self, table, deletechars): """S.translate(table [,deletechars]) -> string Return a copy of the string S, where all characters occurring in the optional argument deletechars are removed, and the remaining characters have been mapped through the given translation table, which must be a string of length 256 or None. If the table argument is None, no translation is applied and the operation simply removes the characters in deletechars.""" return None def upper(self, _): """S.upper() -> string Return a copy of the string S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> string Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None class string_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None base = getset_descriptor() def capitalize(self, _): """S.capitalize() -> string Return a copy of the string S with only its first character capitalized.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> string Return S centered in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def conj(self, _): """None""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None data = getset_descriptor() def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> object Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None dtype = getset_descriptor() def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> object Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that is able to handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> string Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None flags = getset_descriptor() flat = getset_descriptor() def format(self, args, kwargs): """S.format(*args, **kwargs) -> string Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None imag = getset_descriptor() def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. uppercase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None itemsize = getset_descriptor() def join(self, iterable): """S.join(iterable) -> string Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> string Return S left-justified in a string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> string Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> string or unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None real = getset_descriptor() def replace(self, old, new, count): """S.replace(old, new[, count]) -> string Return a copy of string S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> string Return S right-justified in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> string or unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None shape = getset_descriptor() size = getset_descriptor() def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None strides = getset_descriptor() def strip(self, chars): """S.strip([chars]) -> string or unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> string Return a copy of the string S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> string Return a titlecased version of S, i.e. words start with uppercase characters, all remaining cased characters have lowercase.""" return None def translate(self, table, deletechars): """S.translate(table [,deletechars]) -> string Return a copy of the string S, where all characters occurring in the optional argument deletechars are removed, and the remaining characters have been mapped through the given translation table, which must be a string of length 256 or None. If the table argument is None, no translation is applied and the operation simply removes the characters in deletechars.""" return None def upper(self, _): """S.upper() -> string Return a copy of the string S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> string Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None class string_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None base = getset_descriptor() def capitalize(self, _): """S.capitalize() -> string Return a copy of the string S with only its first character capitalized.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> string Return S centered in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def conj(self, _): """None""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None data = getset_descriptor() def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> object Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None dtype = getset_descriptor() def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> object Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that is able to handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> string Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None flags = getset_descriptor() flat = getset_descriptor() def format(self, args, kwargs): """S.format(*args, **kwargs) -> string Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None imag = getset_descriptor() def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. uppercase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None itemsize = getset_descriptor() def join(self, iterable): """S.join(iterable) -> string Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> string Return S left-justified in a string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> string Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> string or unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None real = getset_descriptor() def replace(self, old, new, count): """S.replace(old, new[, count]) -> string Return a copy of string S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> string Return S right-justified in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> string or unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None shape = getset_descriptor() size = getset_descriptor() def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None strides = getset_descriptor() def strip(self, chars): """S.strip([chars]) -> string or unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> string Return a copy of the string S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> string Return a titlecased version of S, i.e. words start with uppercase characters, all remaining cased characters have lowercase.""" return None def translate(self, table, deletechars): """S.translate(table [,deletechars]) -> string Return a copy of the string S, where all characters occurring in the optional argument deletechars are removed, and the remaining characters have been mapped through the given translation table, which must be a string of length 256 or None. If the table argument is None, no translation is applied and the operation simply removes the characters in deletechars.""" return None def upper(self, _): """S.upper() -> string Return a copy of the string S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> string Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None class string_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None base = getset_descriptor() def capitalize(self, _): """S.capitalize() -> string Return a copy of the string S with only its first character capitalized.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> string Return S centered in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def conj(self, _): """None""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None data = getset_descriptor() def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> object Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None dtype = getset_descriptor() def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> object Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that is able to handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> string Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None flags = getset_descriptor() flat = getset_descriptor() def format(self, args, kwargs): """S.format(*args, **kwargs) -> string Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None imag = getset_descriptor() def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. uppercase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None itemsize = getset_descriptor() def join(self, iterable): """S.join(iterable) -> string Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> string Return S left-justified in a string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> string Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> string or unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None real = getset_descriptor() def replace(self, old, new, count): """S.replace(old, new[, count]) -> string Return a copy of string S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> string Return S right-justified in a string of length width. Padding is done using the specified fill character (default is a space)""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> string or unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None shape = getset_descriptor() size = getset_descriptor() def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in the string S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None strides = getset_descriptor() def strip(self, chars): """S.strip([chars]) -> string or unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is unicode, S will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> string Return a copy of the string S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> string Return a titlecased version of S, i.e. words start with uppercase characters, all remaining cased characters have lowercase.""" return None def translate(self, table, deletechars): """S.translate(table [,deletechars]) -> string Return a copy of the string S, where all characters occurring in the optional argument deletechars are removed, and the remaining characters have been mapped through the given translation table, which must be a string of length 256 or None. If the table argument is None, no translation is applied and the operation simply removes the characters in deletechars.""" return None def upper(self, _): """S.upper() -> string Return a copy of the string S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> string Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None def subtract(x1, x2, out=None): """subtract(x1, x2[, out]) Subtract arguments, element-wise. Parameters ---------- x1, x2 : array_like The arrays to be subtracted from each other. Returns ------- y : ndarray The difference of `x1` and `x2`, element-wise. Returns a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to ``x1 - x2`` in terms of array broadcasting. Examples -------- >>> np.subtract(1.0, 4.0) -3.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.subtract(x1, x2) array([[ 0., 0., 0.], [ 3., 3., 3.], [ 6., 6., 6.]])""" return ndarray() def sum(a=False, axis=None, dtype=None, out=None, keepdims=False): """ Sum of array elements over a given axis. Parameters ---------- a : array_like Elements to sum. axis : None or int or tuple of ints, optional Axis or axes along which a sum is performed. The default (`axis` = `None`) is perform a sum over all the dimensions of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is a tuple of ints, a sum is performed on multiple axes, instead of a single axis or all the axes as before. dtype : dtype, optional The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of `a` is used. An exception is when `a` has an integer type with less precision than the default platform integer. In that case, the default platform integer is used instead. out : ndarray, optional Array into which the output is placed. By default, a new array is created. If `out` is given, it must be of the appropriate shape (the shape of `a` with `axis` removed, i.e., ``numpy.delete(a.shape, axis)``). Its type is preserved. See `doc.ufuncs` (Section "Output arguments") for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- sum_along_axis : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if `axis` is None, a scalar is returned. If an output array is specified, a reference to `out` is returned. See Also -------- ndarray.sum : Equivalent method. cumsum : Cumulative sum of array elements. trapz : Integration of array values using the composite trapezoidal rule. mean, average Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. Examples -------- >>> np.sum([0.5, 1.5]) 2.0 >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32) 1 >>> np.sum([[0, 1], [0, 5]]) 6 >>> np.sum([[0, 1], [0, 5]], axis=0) array([0, 6]) >>> np.sum([[0, 1], [0, 5]], axis=1) array([1, 5]) If the accumulator is too small, overflow occurs: >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8) -128 """ return ndarray() def swapaxes(a, axis1, axis2): """ Interchange two axes of an array. Parameters ---------- a : array_like Input array. axis1 : int First axis. axis2 : int Second axis. Returns ------- a_swapped : ndarray If `a` is an ndarray, then a view of `a` is returned; otherwise a new array is created. Examples -------- >>> x = np.array([[1,2,3]]) >>> np.swapaxes(x,0,1) array([[1], [2], [3]]) >>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]]) >>> x array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> np.swapaxes(x,0,2) array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]]) """ return ndarray() def take(a, indices="raise", axis=None, out=None, mode="raise"): """ Take elements from an array along an axis. This function does the same thing as "fancy" indexing (indexing arrays using arrays); however, it can be easier to use if you need elements along a given axis. Parameters ---------- a : array_like The source array. indices : array_like The indices of the values to extract. .. versionadded:: 1.8.0 Also allow scalars for indices. axis : int, optional The axis over which to select values. By default, the flattened input array is used. out : ndarray, optional If provided, the result will be placed in this array. It should be of the appropriate shape and dtype. mode : {'raise', 'wrap', 'clip'}, optional Specifies how out-of-bounds indices will behave. * 'raise' -- raise an error (default) * 'wrap' -- wrap around * 'clip' -- clip to the range 'clip' mode means that all indices that are too large are replaced by the index that addresses the last element along that axis. Note that this disables indexing with negative numbers. Returns ------- subarray : ndarray The returned array has the same type as `a`. See Also -------- ndarray.take : equivalent method Examples -------- >>> a = [4, 3, 5, 7, 6, 8] >>> indices = [0, 1, 4] >>> np.take(a, indices) array([4, 3, 6]) In this example if `a` is an ndarray, "fancy" indexing can be used. >>> a = np.array(a) >>> a[indices] array([4, 3, 6]) If `indices` is not one dimensional, the output also has these dimensions. >>> np.take(a, [[0, 1], [2, 3]]) array([[4, 3], [5, 7]]) """ return ndarray() def tan(x, out): """tan(x[, out]) Compute tangent element-wise. Equivalent to ``np.sin(x)/np.cos(x)`` element-wise. Parameters ---------- x : array_like Input array. out : ndarray, optional Output array of same shape as `x`. Returns ------- y : ndarray The corresponding tangent values. Raises ------ ValueError: invalid return array shape if `out` is provided and `out.shape` != `x.shape` (See Examples) Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972. Examples -------- >>> from math import pi >>> np.tan(np.array([-pi,pi/2,pi])) array([ 1.22460635e-16, 1.63317787e+16, -1.22460635e-16]) >>> >>> # Example of providing the optional output parameter illustrating >>> # that what is returned is a reference to said parameter >>> out2 = np.cos([0.1], out1) >>> out2 is out1 True >>> >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.cos(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: invalid return array shape""" return ndarray() def tanh(x, out): """tanh(x[, out]) Compute hyperbolic tangent element-wise. Equivalent to ``np.sinh(x)/np.cosh(x)`` or ``-1j * np.tan(1j*x)``. Parameters ---------- x : array_like Input array. out : ndarray, optional Output array of same shape as `x`. Returns ------- y : ndarray The corresponding hyperbolic tangent values. Raises ------ ValueError: invalid return array shape if `out` is provided and `out.shape` != `x.shape` (See Examples) Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- .. [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972, pg. 83. http://www.math.sfu.ca/~cbm/aands/ .. [2] Wikipedia, "Hyperbolic function", http://en.wikipedia.org/wiki/Hyperbolic_function Examples -------- >>> np.tanh((0, np.pi*1j, np.pi*1j/2)) array([ 0. +0.00000000e+00j, 0. -1.22460635e-16j, 0. +1.63317787e+16j]) >>> # Example of providing the optional output parameter illustrating >>> # that what is returned is a reference to said parameter >>> out2 = np.tanh([0.1], out1) >>> out2 is out1 True >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.tanh(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: invalid return array shape""" return ndarray() def tensordot(a, b=2, axes=2): """ Compute tensor dot product along specified axes for arrays >= 1-D. Given two tensors (arrays of dimension greater than or equal to one), `a` and `b`, and an array_like object containing two array_like objects, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s elements (components) over the axes specified by ``a_axes`` and ``b_axes``. The third argument can be a single non-negative integer_like scalar, ``N``; if it is such, then the last ``N`` dimensions of `a` and the first ``N`` dimensions of `b` are summed over. Parameters ---------- a, b : array_like, len(shape) >= 1 Tensors to "dot". axes : variable type * integer_like scalar Number of axes to sum over (applies to both arrays); or * (2,) array_like, both elements array_like of the same length List of axes to be summed over, first sequence applying to `a`, second to `b`. See Also -------- dot, einsum Notes ----- When there is more than one axis to sum over - and they are not the last (first) axes of `a` (`b`) - the argument `axes` should consist of two sequences of the same length, with the first axis to sum over given first in both sequences, the second axis second, and so forth. Examples -------- A "traditional" example: >>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> c = np.tensordot(a,b, axes=([1,0],[0,1])) >>> c.shape (5, 2) >>> c array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> # A slower but equivalent way of computing the same... >>> d = np.zeros((5,2)) >>> for i in range(5): ... for j in range(2): ... for k in range(3): ... for n in range(4): ... d[i,j] += a[k,n,i] * b[n,k,j] >>> c == d array([[ True, True], [ True, True], [ True, True], [ True, True], [ True, True]], dtype=bool) An extended example taking advantage of the overloading of + and \*: >>> a = np.array(range(1, 9)) >>> a.shape = (2, 2, 2) >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object) >>> A.shape = (2, 2) >>> a; A array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]) array([[a, b], [c, d]], dtype=object) >>> np.tensordot(a, A) # third argument default is 2 array([abbcccdddd, aaaaabbbbbbcccccccdddddddd], dtype=object) >>> np.tensordot(a, A, 1) array([[[acc, bdd], [aaacccc, bbbdddd]], [[aaaaacccccc, bbbbbdddddd], [aaaaaaacccccccc, bbbbbbbdddddddd]]], dtype=object) >>> np.tensordot(a, A, 0) # "Left for reader" (result too long to incl.) array([[[[[a, b], [c, d]], ... >>> np.tensordot(a, A, (0, 1)) array([[[abbbbb, cddddd], [aabbbbbb, ccdddddd]], [[aaabbbbbbb, cccddddddd], [aaaabbbbbbbb, ccccdddddddd]]], dtype=object) >>> np.tensordot(a, A, (2, 1)) array([[[abb, cdd], [aaabbbb, cccdddd]], [[aaaaabbbbbb, cccccdddddd], [aaaaaaabbbbbbbb, cccccccdddddddd]]], dtype=object) >>> np.tensordot(a, A, ((0, 1), (0, 1))) array([abbbcccccddddddd, aabbbbccccccdddddddd], dtype=object) >>> np.tensordot(a, A, ((2, 1), (1, 0))) array([acccbbdddd, aaaaacccccccbbbbbbdddddddd], dtype=object) """ return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() def tile(A, reps): """ Construct an array by repeating A the number of times given by reps. If `reps` has length ``d``, the result will have dimension of ``max(d, A.ndim)``. If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication, or shape (1, 1, 3) for 3-D replication. If this is not the desired behavior, promote `A` to d-dimensions manually before calling this function. If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it. Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as (1, 1, 2, 2). Parameters ---------- A : array_like The input array. reps : array_like The number of repetitions of `A` along each axis. Returns ------- c : ndarray The tiled output array. See Also -------- repeat : Repeat elements of an array. Examples -------- >>> a = np.array([0, 1, 2]) >>> np.tile(a, 2) array([0, 1, 2, 0, 1, 2]) >>> np.tile(a, (2, 2)) array([[0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 1, 2]]) >>> np.tile(a, (2, 1, 2)) array([[[0, 1, 2, 0, 1, 2]], [[0, 1, 2, 0, 1, 2]]]) >>> b = np.array([[1, 2], [3, 4]]) >>> np.tile(b, 2) array([[1, 2, 1, 2], [3, 4, 3, 4]]) >>> np.tile(b, (2, 1)) array([[1, 2], [3, 4], [1, 2], [3, 4]]) """ return ndarray() class timedelta64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def trace(a=None, offset=0, axis1=0, axis2=1, dtype=None, out=None): """ Return the sum along diagonals of the array. If `a` is 2-D, the sum along its diagonal with the given offset is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i. If `a` has more than two dimensions, then the axes specified by axis1 and axis2 are used to determine the 2-D sub-arrays whose traces are returned. The shape of the resulting array is the same as that of `a` with `axis1` and `axis2` removed. Parameters ---------- a : array_like Input array, from which the diagonals are taken. offset : int, optional Offset of the diagonal from the main diagonal. Can be both positive and negative. Defaults to 0. axis1, axis2 : int, optional Axes to be used as the first and second axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults are the first two axes of `a`. dtype : dtype, optional Determines the data-type of the returned array and of the accumulator where the elements are summed. If dtype has the value None and `a` is of integer type of precision less than the default integer precision, then the default integer precision is used. Otherwise, the precision is the same as that of `a`. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. Returns ------- sum_along_diagonals : ndarray If `a` is 2-D, the sum along the diagonal is returned. If `a` has larger dimensions, then an array of sums along diagonals is returned. See Also -------- diag, diagonal, diagflat Examples -------- >>> np.trace(np.eye(3)) 3.0 >>> a = np.arange(8).reshape((2,2,2)) >>> np.trace(a) array([6, 8]) >>> a = np.arange(24).reshape((2,2,2,3)) >>> np.trace(a).shape (2, 3) """ return ndarray() def transpose(a=None, axes=None): """ Permute the dimensions of an array. Parameters ---------- a : array_like Input array. axes : list of ints, optional By default, reverse the dimensions, otherwise permute the axes according to the values given. Returns ------- p : ndarray `a` with its axes permuted. A view is returned whenever possible. See Also -------- rollaxis Examples -------- >>> x = np.arange(4).reshape((2,2)) >>> x array([[0, 1], [2, 3]]) >>> np.transpose(x) array([[0, 2], [1, 3]]) >>> x = np.ones((1, 2, 3)) >>> np.transpose(x, (1, 0, 2)).shape (2, 1, 3) """ return ndarray() def trapz(y=-1, x=None, dx=1.0, axis=-1): """ Integrate along the given axis using the composite trapezoidal rule. Integrate `y` (`x`) along given axis. Parameters ---------- y : array_like Input array to integrate. x : array_like, optional If `x` is None, then spacing between all `y` elements is `dx`. dx : scalar, optional If `x` is None, spacing given by `dx` is assumed. Default is 1. axis : int, optional Specify the axis. Returns ------- trapz : float Definite integral as approximated by trapezoidal rule. See Also -------- sum, cumsum Notes ----- Image [2]_ illustrates trapezoidal rule -- y-axis locations of points will be taken from `y` array, by default x-axis distances between points will be 1.0, alternatively they can be provided with `x` array or with `dx` scalar. Return value will be equal to combined area under the red lines. References ---------- .. [1] Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule .. [2] Illustration image: http://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png Examples -------- >>> np.trapz([1,2,3]) 4.0 >>> np.trapz([1,2,3], x=[4,6,8]) 8.0 >>> np.trapz([1,2,3], dx=2) 8.0 >>> a = np.arange(6).reshape(2, 3) >>> a array([[0, 1, 2], [3, 4, 5]]) >>> np.trapz(a, axis=0) array([ 1.5, 2.5, 3.5]) >>> np.trapz(a, axis=1) array([ 2., 8.]) """ return float() def tri(N=typefloat(), M=None, k=0, dtype=typefloat()): """ An array with ones at and below the given diagonal and zeros elsewhere. Parameters ---------- N : int Number of rows in the array. M : int, optional Number of columns in the array. By default, `M` is taken equal to `N`. k : int, optional The sub-diagonal at and below which the array is filled. `k` = 0 is the main diagonal, while `k` < 0 is below it, and `k` > 0 is above. The default is 0. dtype : dtype, optional Data type of the returned array. The default is float. Returns ------- tri : ndarray of shape (N, M) Array with its lower triangle filled with ones and zero elsewhere; in other words ``T[i,j] == 1`` for ``i <= j + k``, 0 otherwise. Examples -------- >>> np.tri(3, 5, 2, dtype=int) array([[1, 1, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 1, 1]]) >>> np.tri(3, 5, -1) array([[ 0., 0., 0., 0., 0.], [ 1., 0., 0., 0., 0.], [ 1., 1., 0., 0., 0.]]) """ return ndarray() def tril(m=0, k=0): """ Lower triangle of an array. Return a copy of an array with elements above the `k`-th diagonal zeroed. Parameters ---------- m : array_like, shape (M, N) Input array. k : int, optional Diagonal above which to zero elements. `k = 0` (the default) is the main diagonal, `k < 0` is below it and `k > 0` is above. Returns ------- tril : ndarray, shape (M, N) Lower triangle of `m`, of same shape and data-type as `m`. See Also -------- triu : same thing, only for the upper triangle Examples -------- >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 0, 0, 0], [ 4, 0, 0], [ 7, 8, 0], [10, 11, 12]]) """ return ndarray() def tril_indices(n=0, k=0): """ Return the indices for the lower-triangle of an (n, n) array. Parameters ---------- n : int The row dimension of the square arrays for which the returned indices will be valid. k : int, optional Diagonal offset (see `tril` for details). Returns ------- inds : tuple of arrays The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array. See also -------- triu_indices : similar function, for upper-triangular. mask_indices : generic function accepting an arbitrary mask function. tril, triu Notes ----- .. versionadded:: 1.4.0 Examples -------- Compute two different sets of indices to access 4x4 arrays, one for the lower triangular part starting at the main diagonal, and one starting two diagonals further right: >>> il1 = np.tril_indices(4) >>> il2 = np.tril_indices(4, 2) Here is how they can be used with a sample array: >>> a = np.arange(16).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) Both for indexing: >>> a[il1] array([ 0, 4, 5, 8, 9, 10, 12, 13, 14, 15]) And for assigning values: >>> a[il1] = -1 >>> a array([[-1, 1, 2, 3], [-1, -1, 6, 7], [-1, -1, -1, 11], [-1, -1, -1, -1]]) These cover almost the whole array (two diagonals right of the main one): >>> a[il2] = -10 >>> a array([[-10, -10, -10, 3], [-10, -10, -10, -10], [-10, -10, -10, -10], [-10, -10, -10, -10]]) """ return tuple() def tril_indices__from(arr=0, k=0): """ Return the indices for the lower-triangle of arr. See `tril_indices` for full details. Parameters ---------- arr : array_like The indices will be valid for square arrays whose dimensions are the same as arr. k : int, optional Diagonal offset (see `tril` for details). See Also -------- tril_indices, tril Notes ----- .. versionadded:: 1.4.0 """ return None def trim_zeros(filt="fb", trim="fb"): """ Trim the leading and/or trailing zeros from a 1-D array or sequence. Parameters ---------- filt : 1-D array or sequence Input array. trim : str, optional A string with 'f' representing trim from front and 'b' to trim from back. Default is 'fb', trim zeros from both front and back of the array. Returns ------- trimmed : 1-D array or sequence The result of trimming the input. The input data type is preserved. Examples -------- >>> a = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0)) >>> np.trim_zeros(a) array([1, 2, 3, 0, 2, 1]) >>> np.trim_zeros(a, 'b') array([0, 0, 0, 1, 2, 3, 0, 2, 1]) The input data type is preserved, list/tuple in means list/tuple out. >>> np.trim_zeros([0, 1, 2, 0]) [1, 2] """ return _1_D() if False else sequence() def triu(m=0, k=0): """ Upper triangle of an array. Return a copy of a matrix with the elements below the `k`-th diagonal zeroed. Please refer to the documentation for `tril` for further details. See Also -------- tril : lower triangle of an array Examples -------- >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 1, 2, 3], [ 4, 5, 6], [ 0, 8, 9], [ 0, 0, 12]]) """ return None def triu_indices(n=0, k=0): """ Return the indices for the upper-triangle of an (n, n) array. Parameters ---------- n : int The size of the arrays for which the returned indices will be valid. k : int, optional Diagonal offset (see `triu` for details). Returns ------- inds : tuple, shape(2) of ndarrays, shape(`n`) The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array. Can be used to slice a ndarray of shape(`n`, `n`). See also -------- tril_indices : similar function, for lower-triangular. mask_indices : generic function accepting an arbitrary mask function. triu, tril Notes ----- .. versionadded:: 1.4.0 Examples -------- Compute two different sets of indices to access 4x4 arrays, one for the upper triangular part starting at the main diagonal, and one starting two diagonals further right: >>> iu1 = np.triu_indices(4) >>> iu2 = np.triu_indices(4, 2) Here is how they can be used with a sample array: >>> a = np.arange(16).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) Both for indexing: >>> a[iu1] array([ 0, 1, 2, 3, 5, 6, 7, 10, 11, 15]) And for assigning values: >>> a[iu1] = -1 >>> a array([[-1, -1, -1, -1], [ 4, -1, -1, -1], [ 8, 9, -1, -1], [12, 13, 14, -1]]) These cover only a small part of the whole array (two diagonals right of the main one): >>> a[iu2] = -10 >>> a array([[ -1, -1, -10, -10], [ 4, -1, -1, -10], [ 8, 9, -1, -1], [ 12, 13, 14, -1]]) """ return tuple() def triu_indices__from(arr=0, k=0): """ Return the indices for the upper-triangle of a (N, N) array. See `triu_indices` for full details. Parameters ---------- arr : ndarray, shape(N, N) The indices will be valid for square arrays. k : int, optional Diagonal offset (see `triu` for details). Returns ------- triu_indices_from : tuple, shape(2) of ndarray, shape(N) Indices for the upper-triangle of `arr`. See Also -------- triu_indices, triu Notes ----- .. versionadded:: 1.4.0 """ return tuple() def true_divide(x1, x2, out=None): """true_divide(x1, x2[, out]) Returns a true division of the inputs, element-wise. Instead of the Python traditional 'floor division', this returns a true division. True division adjusts the output type to present the best answer, regardless of input types. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. Returns ------- out : ndarray Result is scalar if both inputs are scalar, ndarray otherwise. Notes ----- The floor division operator ``//`` was added in Python 2.2 making ``//`` and ``/`` equivalent operators. The default floor division operation of ``/`` can be replaced by true division with ``from __future__ import division``. In Python 3.0, ``//`` is the floor division operator and ``/`` the true division operator. The ``true_divide(x1, x2)`` function is equivalent to true division in Python. Examples -------- >>> x = np.arange(5) >>> np.true_divide(x, 4) array([ 0. , 0.25, 0.5 , 0.75, 1. ]) >>> x/4 array([0, 0, 0, 0, 1]) >>> x//4 array([0, 0, 0, 0, 1]) >>> from __future__ import division >>> x/4 array([ 0. , 0.25, 0.5 , 0.75, 1. ]) >>> x//4 array([0, 0, 0, 0, 1])""" return ndarray() def trunc(x, out=None): """trunc(x[, out]) Return the truncated value of the input, element-wise. The truncated value of the scalar `x` is the nearest integer `i` which is closer to zero than `x` is. In short, the fractional part of the signed number `x` is discarded. Parameters ---------- x : array_like Input data. Returns ------- y : {ndarray, scalar} The truncated value of each element in `x`. See Also -------- ceil, floor, rint Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.trunc(a) array([-1., -1., -0., 0., 1., 1., 2.])""" return ndarray() typeDict = dict() typeNA = dict() typecodes = dict() def typename(char): """ Return a description for the given data type code. Parameters ---------- char : str Data type code. Returns ------- out : str Description of the input data type code. See Also -------- dtype, typecodes Examples -------- >>> typechars = ['S1', '?', 'B', 'D', 'G', 'F', 'I', 'H', 'L', 'O', 'Q', ... 'S', 'U', 'V', 'b', 'd', 'g', 'f', 'i', 'h', 'l', 'q'] >>> for typechar in typechars: ... print typechar, ' : ', np.typename(typechar) ... S1 : character ? : bool B : unsigned char D : complex double precision G : complex long double precision F : complex single precision I : unsigned integer H : unsigned short L : unsigned long integer O : object Q : unsigned long long integer S : string U : unicode V : void b : signed char d : double precision g : long precision f : single precision i : integer h : short l : long integer q : long long integer """ return str() class uint8: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class ufunc: __doc__ = str() __name__ = str() def accumulate(self, array, axis, dtype, out): """accumulate(array, axis=0, dtype=None, out=None) Accumulate the result of applying the operator to all elements. For a one-dimensional array, accumulate produces results equivalent to:: r = np.empty(len(A)) t = op.identity # op = the ufunc being applied to A's elements for i in range(len(A)): t = op(t, A[i]) r[i] = t return r For example, add.accumulate() is equivalent to np.cumsum(). For a multi-dimensional array, accumulate is applied along only one axis (axis zero by default; see Examples below) so repeated use is necessary if one wants to accumulate over multiple axes. Parameters ---------- array : array_like The array to act on. axis : int, optional The axis along which to apply the accumulation; default is zero. dtype : data-type code, optional The data-type used to represent the intermediate results. Defaults to the data-type of the output array if such is provided, or the the data-type of the input array if no output array is provided. out : ndarray, optional A location into which the result is stored. If not provided a freshly-allocated array is returned. Returns ------- r : ndarray The accumulated values. If `out` was supplied, `r` is a reference to `out`. Examples -------- 1-D array examples: >>> np.add.accumulate([2, 3, 5]) array([ 2, 5, 10]) >>> np.multiply.accumulate([2, 3, 5]) array([ 2, 6, 30]) 2-D array examples: >>> I = np.eye(2) >>> I array([[ 1., 0.], [ 0., 1.]]) Accumulate along axis 0 (rows), down columns: >>> np.add.accumulate(I, 0) array([[ 1., 0.], [ 1., 1.]]) >>> np.add.accumulate(I) # no axis specified = axis zero array([[ 1., 0.], [ 1., 1.]]) Accumulate along axis 1 (columns), through rows: >>> np.add.accumulate(I, 1) array([[ 1., 1.], [ 0., 1.]])""" return ndarray() def at(self, a, indices, b): """at(a, indices, b=None) Performs unbuffered in place operation on operand 'a' for elements specified by 'indices'. For addition ufunc, this method is equivalent to `a[indices] += b`, except that results are accumulated for elements that are indexed more than once. For example, `a[[0,0]] += 1` will only increment the first element once because of buffering, whereas `add.at(a, [0,0], 1)` will increment the first element twice. Parameters ---------- a : array_like The array to perform in place operation on. indices : array_like or tuple Array like index object or slice object for indexing into first operand. If first operand has multiple dimensions, indices can be a tuple of array like index objects or slice objects. b : array_like Second operand for ufuncs requiring two operands. Operand must be broadcastable over first operand after indexing or slicing. Examples -------- Set items 0 and 1 to their negative values: >>> a = np.array([1, 2, 3, 4]) >>> np.negative.at(a, [0, 1]) >>> print(a) array([-1, -2, 3, 4]) :: Increment items 0 and 1, and increment item 2 twice: >>> a = np.array([1, 2, 3, 4]) >>> np.add.at(a, [0, 1, 2, 2], 1) >>> print(a) array([2, 3, 5, 4]) :: Add items 0 and 1 in first array to second array, and store results in first array: >>> a = np.array([1, 2, 3, 4]) >>> b = np.array([1, 2]) >>> np.add.at(a, [0, 1], b) >>> print(a) array([2, 4, 3, 4])""" return None identity = getset_descriptor() nargs = getset_descriptor() nin = getset_descriptor() nout = getset_descriptor() ntypes = getset_descriptor() def outer(self, A, B): """outer(A, B) Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`. Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of ``op.outer(A, B)`` is an array of dimension M + N such that: .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] = op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}]) For `A` and `B` one-dimensional, this is equivalent to:: r = empty(len(A),len(B)) for i in range(len(A)): for j in range(len(B)): r[i,j] = op(A[i], B[j]) # op = ufunc in question Parameters ---------- A : array_like First array B : array_like Second array Returns ------- r : ndarray Output array See Also -------- numpy.outer Examples -------- >>> np.multiply.outer([1, 2, 3], [4, 5, 6]) array([[ 4, 5, 6], [ 8, 10, 12], [12, 15, 18]]) A multi-dimensional example: >>> A = np.array([[1, 2, 3], [4, 5, 6]]) >>> A.shape (2, 3) >>> B = np.array([[1, 2, 3, 4]]) >>> B.shape (1, 4) >>> C = np.multiply.outer(A, B) >>> C.shape; C (2, 3, 1, 4) array([[[[ 1, 2, 3, 4]], [[ 2, 4, 6, 8]], [[ 3, 6, 9, 12]]], [[[ 4, 8, 12, 16]], [[ 5, 10, 15, 20]], [[ 6, 12, 18, 24]]]])""" return ndarray() def reduce(self, a, axis, dtype, out, keepdims): """reduce(a, axis=0, dtype=None, out=None, keepdims=False) Reduces `a`'s dimension by one, by applying ufunc along one axis. Let :math:`a.shape = (N_0, ..., N_i, ..., N_{M-1})`. Then :math:`ufunc.reduce(a, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` = the result of iterating `j` over :math:`range(N_i)`, cumulatively applying ufunc to each :math:`a[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`. For a one-dimensional array, reduce produces results equivalent to: :: r = op.identity # op = ufunc for i in range(len(A)): r = op(r, A[i]) return r For example, add.reduce() is equivalent to sum(). Parameters ---------- a : array_like The array to act on. axis : None or int or tuple of ints, optional Axis or axes along which a reduction is performed. The default (`axis` = 0) is perform a reduction over the first dimension of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is `None`, a reduction is performed over all the axes. If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. For operations which are either not commutative or not associative, doing a reduction over multiple axes is not well-defined. The ufuncs do not currently raise an exception in this case, but will likely do so in the future. dtype : data-type code, optional The type used to represent the intermediate results. Defaults to the data-type of the output array if this is provided, or the data-type of the input array if no output array is provided. out : ndarray, optional A location into which the result is stored. If not provided, a freshly-allocated array is returned. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- r : ndarray The reduced array. If `out` was supplied, `r` is a reference to it. Examples -------- >>> np.multiply.reduce([2,3,5]) 30 A multi-dimensional array example: >>> X = np.arange(8).reshape((2,2,2)) >>> X array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> np.add.reduce(X, 0) array([[ 4, 6], [ 8, 10]]) >>> np.add.reduce(X) # confirm: default axis value is 0 array([[ 4, 6], [ 8, 10]]) >>> np.add.reduce(X, 1) array([[ 2, 4], [10, 12]]) >>> np.add.reduce(X, 2) array([[ 1, 5], [ 9, 13]])""" return ndarray() def reduceat(self, a, indices, axis, dtype, out): """reduceat(a, indices, axis=0, dtype=None, out=None) Performs a (local) reduce with specified slices over a single axis. For i in ``range(len(indices))``, `reduceat` computes ``ufunc.reduce(a[indices[i]:indices[i+1]])``, which becomes the i-th generalized "row" parallel to `axis` in the final result (i.e., in a 2-D array, for example, if `axis = 0`, it becomes the i-th row, but if `axis = 1`, it becomes the i-th column). There are two exceptions to this: * when ``i = len(indices) - 1`` (so for the last index), ``indices[i+1] = a.shape[axis]``. * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is simply ``a[indices[i]]``. The shape of the output depends on the size of `indices`, and may be larger than `a` (this happens if ``len(indices) > a.shape[axis]``). Parameters ---------- a : array_like The array to act on. indices : array_like Paired indices, comma separated (not colon), specifying slices to reduce. axis : int, optional The axis along which to apply the reduceat. dtype : data-type code, optional The type used to represent the intermediate results. Defaults to the data type of the output array if this is provided, or the data type of the input array if no output array is provided. out : ndarray, optional A location into which the result is stored. If not provided a freshly-allocated array is returned. Returns ------- r : ndarray The reduced values. If `out` was supplied, `r` is a reference to `out`. Notes ----- A descriptive example: If `a` is 1-D, the function `ufunc.accumulate(a)` is the same as ``ufunc.reduceat(a, indices)[::2]`` where `indices` is ``range(len(array) - 1)`` with a zero placed in every other element: ``indices = zeros(2 * len(a) - 1)``, ``indices[1::2] = range(1, len(a))``. Don't be fooled by this attribute's name: `reduceat(a)` is not necessarily smaller than `a`. Examples -------- To take the running sum of four successive values: >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2] array([ 6, 10, 14, 18]) A 2-D example: >>> x = np.linspace(0, 15, 16).reshape(4,4) >>> x array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 12., 13., 14., 15.]]) :: # reduce such that the result has the following five rows: # [row1 + row2 + row3] # [row4] # [row2] # [row3] # [row1 + row2 + row3 + row4] >>> np.add.reduceat(x, [0, 3, 1, 2, 0]) array([[ 12., 15., 18., 21.], [ 12., 13., 14., 15.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 24., 28., 32., 36.]]) :: # reduce such that result has the following two columns: # [col1 * col2 * col3, col4] >>> np.multiply.reduceat(x, [0, 3], 1) array([[ 0., 3.], [ 120., 7.], [ 720., 11.], [ 2184., 15.]])""" return ndarray() signature = getset_descriptor() types = getset_descriptor() class uint64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint16: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint32: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint8: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint32: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class uint64: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class unicode: __doc__ = str() def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None def capitalize(self, _): """S.capitalize() -> unicode Return a capitalized version of S, i.e. make the first character have upper case and the rest lower case.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> unicode Return S centered in a Unicode string of length width. Padding is done using the specified fill character (default is a space)""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in Unicode string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> string or unicode Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> string or unicode Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> unicode Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def format(self, args, kwargs): """S.format(*args, **kwargs) -> unicode Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdecimal(self, _): """S.isdecimal() -> bool Return True if there are only decimal characters in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isnumeric(self, _): """S.isnumeric() -> bool Return True if there are only numeric characters in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. upper- and titlecase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None def join(self, iterable): """S.join(iterable) -> unicode Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> int Return S left-justified in a Unicode string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> unicode Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None def replace(self, old, new, count): """S.replace(old, new[, count]) -> unicode Return a copy of S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> unicode Return S right-justified in a Unicode string of length width. Padding is done using the specified fill character (default is a space).""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None def strip(self, chars): """S.strip([chars]) -> unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> unicode Return a copy of S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> unicode Return a titlecased version of S, i.e. words start with title case characters, all remaining cased characters have lower case.""" return None def translate(self, table): """S.translate(table) -> unicode Return a copy of the string S, where all characters have been mapped through the given translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, Unicode strings or None. Unmapped characters are left untouched. Characters mapped to None are deleted.""" return None def upper(self, _): """S.upper() -> unicode Return a copy of S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> unicode Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None class unicode_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None base = getset_descriptor() def capitalize(self, _): """S.capitalize() -> unicode Return a capitalized version of S, i.e. make the first character have upper case and the rest lower case.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> unicode Return S centered in a Unicode string of length width. Padding is done using the specified fill character (default is a space)""" return None def conj(self, _): """None""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in Unicode string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None data = getset_descriptor() def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> string or unicode Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None dtype = getset_descriptor() def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> string or unicode Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> unicode Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None flags = getset_descriptor() flat = getset_descriptor() def format(self, args, kwargs): """S.format(*args, **kwargs) -> unicode Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None imag = getset_descriptor() def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdecimal(self, _): """S.isdecimal() -> bool Return True if there are only decimal characters in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isnumeric(self, _): """S.isnumeric() -> bool Return True if there are only numeric characters in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. upper- and titlecase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None itemsize = getset_descriptor() def join(self, iterable): """S.join(iterable) -> unicode Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> int Return S left-justified in a Unicode string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> unicode Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None real = getset_descriptor() def replace(self, old, new, count): """S.replace(old, new[, count]) -> unicode Return a copy of S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> unicode Return S right-justified in a Unicode string of length width. Padding is done using the specified fill character (default is a space).""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None shape = getset_descriptor() size = getset_descriptor() def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None strides = getset_descriptor() def strip(self, chars): """S.strip([chars]) -> unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> unicode Return a copy of S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> unicode Return a titlecased version of S, i.e. words start with title case characters, all remaining cased characters have lower case.""" return None def translate(self, table): """S.translate(table) -> unicode Return a copy of the string S, where all characters have been mapped through the given translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, Unicode strings or None. Unmapped characters are left untouched. Characters mapped to None are deleted.""" return None def upper(self, _): """S.upper() -> unicode Return a copy of S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> unicode Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None class unicode_: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None def _formatter_field_name_split(self, _): """None""" return None def _formatter_parser(self, _): """None""" return None base = getset_descriptor() def capitalize(self, _): """S.capitalize() -> unicode Return a capitalized version of S, i.e. make the first character have upper case and the rest lower case.""" return None def center(self, width, fillchar): """S.center(width[, fillchar]) -> unicode Return S centered in a Unicode string of length width. Padding is done using the specified fill character (default is a space)""" return None def conj(self, _): """None""" return None def count(self, sub, start, end): """S.count(sub[, start[, end]]) -> int Return the number of non-overlapping occurrences of substring sub in Unicode string S[start:end]. Optional arguments start and end are interpreted as in slice notation.""" return None data = getset_descriptor() def decode(self, encoding, errors): """S.decode([encoding[,errors]]) -> string or unicode Decodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeDecodeError. Other possible values are 'ignore' and 'replace' as well as any other name registered with codecs.register_error that is able to handle UnicodeDecodeErrors.""" return None dtype = getset_descriptor() def encode(self, encoding, errors): """S.encode([encoding[,errors]]) -> string or unicode Encodes S using the codec registered for encoding. encoding defaults to the default encoding. errors may be given to set a different error handling scheme. Default is 'strict' meaning that encoding errors raise a UnicodeEncodeError. Other possible values are 'ignore', 'replace' and 'xmlcharrefreplace' as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.""" return None def endswith(self, suffix, start, end): """S.endswith(suffix[, start[, end]]) -> bool Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.""" return None def expandtabs(self, tabsize): """S.expandtabs([tabsize]) -> unicode Return a copy of S where all tab characters are expanded using spaces. If tabsize is not given, a tab size of 8 characters is assumed.""" return None def find(self, sub, start, end): """S.find(sub [,start [,end]]) -> int Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None flags = getset_descriptor() flat = getset_descriptor() def format(self, args, kwargs): """S.format(*args, **kwargs) -> unicode Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces ('{' and '}').""" return None imag = getset_descriptor() def index(self, sub, start, end): """S.index(sub [,start [,end]]) -> int Like S.find() but raise ValueError when the substring is not found.""" return None def isalnum(self, _): """S.isalnum() -> bool Return True if all characters in S are alphanumeric and there is at least one character in S, False otherwise.""" return None def isalpha(self, _): """S.isalpha() -> bool Return True if all characters in S are alphabetic and there is at least one character in S, False otherwise.""" return None def isdecimal(self, _): """S.isdecimal() -> bool Return True if there are only decimal characters in S, False otherwise.""" return None def isdigit(self, _): """S.isdigit() -> bool Return True if all characters in S are digits and there is at least one character in S, False otherwise.""" return None def islower(self, _): """S.islower() -> bool Return True if all cased characters in S are lowercase and there is at least one cased character in S, False otherwise.""" return None def isnumeric(self, _): """S.isnumeric() -> bool Return True if there are only numeric characters in S, False otherwise.""" return None def isspace(self, _): """S.isspace() -> bool Return True if all characters in S are whitespace and there is at least one character in S, False otherwise.""" return None def istitle(self, _): """S.istitle() -> bool Return True if S is a titlecased string and there is at least one character in S, i.e. upper- and titlecase characters may only follow uncased characters and lowercase characters only cased ones. Return False otherwise.""" return None def isupper(self, _): """S.isupper() -> bool Return True if all cased characters in S are uppercase and there is at least one cased character in S, False otherwise.""" return None itemsize = getset_descriptor() def join(self, iterable): """S.join(iterable) -> unicode Return a string which is the concatenation of the strings in the iterable. The separator between elements is S.""" return None def ljust(self, width, fillchar): """S.ljust(width[, fillchar]) -> int Return S left-justified in a Unicode string of length width. Padding is done using the specified fill character (default is a space).""" return None def lower(self, _): """S.lower() -> unicode Return a copy of the string S converted to lowercase.""" return None def lstrip(self, chars): """S.lstrip([chars]) -> unicode Return a copy of the string S with leading whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() def partition(self, sep): """S.partition(sep) -> (head, sep, tail) Search for the separator sep in S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return S and two empty strings.""" return None real = getset_descriptor() def replace(self, old, new, count): """S.replace(old, new[, count]) -> unicode Return a copy of S with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.""" return None def rfind(self, sub, start, end): """S.rfind(sub [,start [,end]]) -> int Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 on failure.""" return None def rindex(self, sub, start, end): """S.rindex(sub [,start [,end]]) -> int Like S.rfind() but raise ValueError when the substring is not found.""" return None def rjust(self, width, fillchar): """S.rjust(width[, fillchar]) -> unicode Return S right-justified in a Unicode string of length width. Padding is done using the specified fill character (default is a space).""" return None def rpartition(self, sep): """S.rpartition(sep) -> (head, sep, tail) Search for the separator sep in S, starting at the end of S, and return the part before it, the separator itself, and the part after it. If the separator is not found, return two empty strings and S.""" return None def rsplit(self, sep, maxsplit): """S.rsplit([sep [,maxsplit]]) -> list of strings Return a list of the words in S, using sep as the delimiter string, starting at the end of the string and working to the front. If maxsplit is given, at most maxsplit splits are done. If sep is not specified, any whitespace string is a separator.""" return None def rstrip(self, chars): """S.rstrip([chars]) -> unicode Return a copy of the string S with trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None shape = getset_descriptor() size = getset_descriptor() def split(self, sep, maxsplit): """S.split([sep [,maxsplit]]) -> list of strings Return a list of the words in S, using sep as the delimiter string. If maxsplit is given, at most maxsplit splits are done. If sep is not specified or is None, any whitespace string is a separator and empty strings are removed from the result.""" return None def splitlines(self, keepends=False): """S.splitlines(keepends=False) -> list of strings Return a list of the lines in S, breaking at line boundaries. Line breaks are not included in the resulting list unless keepends is given and true.""" return None def startswith(self, prefix, start, end): """S.startswith(prefix[, start[, end]]) -> bool Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.""" return None strides = getset_descriptor() def strip(self, chars): """S.strip([chars]) -> unicode Return a copy of the string S with leading and trailing whitespace removed. If chars is given and not None, remove characters in chars instead. If chars is a str, it will be converted to unicode before stripping""" return None def swapcase(self, _): """S.swapcase() -> unicode Return a copy of S with uppercase characters converted to lowercase and vice versa.""" return None def title(self, _): """S.title() -> unicode Return a titlecased version of S, i.e. words start with title case characters, all remaining cased characters have lower case.""" return None def translate(self, table): """S.translate(table) -> unicode Return a copy of the string S, where all characters have been mapped through the given translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, Unicode strings or None. Unmapped characters are left untouched. Characters mapped to None are deleted.""" return None def upper(self, _): """S.upper() -> unicode Return a copy of S converted to uppercase.""" return None def zfill(self, width): """S.zfill(width) -> unicode Pad a numeric string S with zeros on the left, to fill a field of the specified width. The string S is never truncated.""" return None def union1d(ar1ar2): """ Find the union of two arrays. Return the unique, sorted array of values that are in either of the two input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. They are flattened if they are not already 1D. Returns ------- union1d : ndarray Unique, sorted union of the input arrays. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.union1d([-1, 0, 1], [-2, 0, 2]) array([-2, -1, 0, 1, 2]) """ return ndarray() def unique(ar=False, return_index=False, return_inverse=False): """ Find the unique elements of an array. Returns the sorted unique elements of an array. There are two optional outputs in addition to the unique elements: the indices of the input array that give the unique values, and the indices of the unique array that reconstruct the input array. Parameters ---------- ar : array_like Input array. This will be flattened if it is not already 1-D. return_index : bool, optional If True, also return the indices of `ar` that result in the unique array. return_inverse : bool, optional If True, also return the indices of the unique array that can be used to reconstruct `ar`. Returns ------- unique : ndarray The sorted unique values. unique_indices : ndarray, optional The indices of the first occurrences of the unique values in the (flattened) original array. Only provided if `return_index` is True. unique_inverse : ndarray, optional The indices to reconstruct the (flattened) original array from the unique array. Only provided if `return_inverse` is True. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.unique([1, 1, 2, 2, 3, 3]) array([1, 2, 3]) >>> a = np.array([[1, 1], [2, 3]]) >>> np.unique(a) array([1, 2, 3]) Return the indices of the original array that give the unique values: >>> a = np.array(['a', 'b', 'b', 'c', 'a']) >>> u, indices = np.unique(a, return_index=True) >>> u array(['a', 'b', 'c'], dtype='|S1') >>> indices array([0, 1, 3]) >>> a[indices] array(['a', 'b', 'c'], dtype='|S1') Reconstruct the input array from the unique values: >>> a = np.array([1, 2, 6, 4, 2, 3, 2]) >>> u, indices = np.unique(a, return_inverse=True) >>> u array([1, 2, 3, 4, 6]) >>> indices array([0, 1, 4, 3, 1, 2, 1]) >>> u[indices] array([1, 2, 6, 4, 2, 3, 2]) """ return ndarray() def unpackbits(myarray, axis): """unpackbits(myarray, axis=None) Unpacks elements of a uint8 array into a binary-valued output array. Each element of `myarray` represents a bit-field that should be unpacked into a binary-valued output array. The shape of the output array is either 1-D (if `axis` is None) or the same shape as the input array with unpacking done along the axis specified. Parameters ---------- myarray : ndarray, uint8 type Input array. axis : int, optional Unpacks along this axis. Returns ------- unpacked : ndarray, uint8 type The elements are binary-valued (0 or 1). See Also -------- packbits : Packs the elements of a binary-valued array into bits in a uint8 array. Examples -------- >>> a = np.array([[2], [7], [23]], dtype=np.uint8) >>> a array([[ 2], [ 7], [23]], dtype=uint8) >>> b = np.unpackbits(a, axis=1) >>> b array([[0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)""" return ndarray() def unravel_index(indices, dims, order): """unravel_index(indices, dims, order='C') Converts a flat index or array of flat indices into a tuple of coordinate arrays. Parameters ---------- indices : array_like An integer array whose elements are indices into the flattened version of an array of dimensions ``dims``. Before version 1.6.0, this function accepted just one index value. dims : tuple of ints The shape of the array to use for unraveling ``indices``. order : {'C', 'F'}, optional .. versionadded:: 1.6.0 Determines whether the indices should be viewed as indexing in C (row-major) order or FORTRAN (column-major) order. Returns ------- unraveled_coords : tuple of ndarray Each array in the tuple has the same shape as the ``indices`` array. See Also -------- ravel_multi_index Examples -------- >>> np.unravel_index([22, 41, 37], (7,6)) (array([3, 6, 6]), array([4, 5, 1])) >>> np.unravel_index([31, 41, 13], (7,6), order='F') (array([3, 6, 6]), array([4, 5, 1])) >>> np.unravel_index(1621, (6,7,8,9)) (3, 1, 4, 1)""" return tuple() class unsignedinteger: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def unwrap(p=-1, discont=3.14159265359, axis=-1): """ Unwrap by changing deltas between values to 2*pi complement. Unwrap radian phase `p` by changing absolute jumps greater than `discont` to their 2*pi complement along the given axis. Parameters ---------- p : array_like Input array. discont : float, optional Maximum discontinuity between values, default is ``pi``. axis : int, optional Axis along which unwrap will operate, default is the last axis. Returns ------- out : ndarray Output array. See Also -------- rad2deg, deg2rad Notes ----- If the discontinuity in `p` is smaller than ``pi``, but larger than `discont`, no unwrapping is done because taking the 2*pi complement would only make the discontinuity larger. Examples -------- >>> phase = np.linspace(0, np.pi, num=5) >>> phase[3:] += np.pi >>> phase array([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531]) >>> np.unwrap(phase) array([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ]) """ return ndarray() class uint16: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def vander(x=None, N=None): """ Generate a Van der Monde matrix. The columns of the output matrix are decreasing powers of the input vector. Specifically, the `i`-th output column is the input vector raised element-wise to the power of ``N - i - 1``. Such a matrix with a geometric progression in each row is named for Alexandre-Theophile Vandermonde. Parameters ---------- x : array_like 1-D input array. N : int, optional Order of (number of columns in) the output. If `N` is not specified, a square array is returned (``N = len(x)``). Returns ------- out : ndarray Van der Monde matrix of order `N`. The first column is ``x^(N-1)``, the second ``x^(N-2)`` and so forth. Examples -------- >>> x = np.array([1, 2, 3, 5]) >>> N = 3 >>> np.vander(x, N) array([[ 1, 1, 1], [ 4, 2, 1], [ 9, 3, 1], [25, 5, 1]]) >>> np.column_stack([x**(N-1-i) for i in range(N)]) array([[ 1, 1, 1], [ 4, 2, 1], [ 9, 3, 1], [25, 5, 1]]) >>> x = np.array([1, 2, 3, 5]) >>> np.vander(x) array([[ 1, 1, 1, 1], [ 8, 4, 2, 1], [ 27, 9, 3, 1], [125, 25, 5, 1]]) The determinant of a square Vandermonde matrix is the product of the differences between the values of the input vector: >>> np.linalg.det(np.vander(x)) 48.000000000000043 >>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1) 48 """ return ndarray() def var(a=False, axis=None, dtype=None, out=None, ddof=0, keepdims=False): """ Compute the variance along the specified axis. Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis. Parameters ---------- a : array_like Array containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the variance is computed. The default is to compute the variance of the flattened array. dtype : data-type, optional Type to use in computing the variance. For arrays of integer type the default is `float32`; for arrays of float types it is the same as the array type. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary. ddof : int, optional "Delta Degrees of Freedom": the divisor used in the calculation is ``N - ddof``, where ``N`` represents the number of elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- variance : ndarray, see dtype parameter above If ``out=None``, returns a new array containing the variance; otherwise, a reference to the output array is returned. See Also -------- std , mean, nanmean, nanstd, nanvar numpy.doc.ufuncs : Section "Output arguments" Notes ----- The variance is the average of the squared deviations from the mean, i.e., ``var = mean(abs(x - x.mean())**2)``. The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of a hypothetical infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative. For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32` (see example below). Specifying a higher-accuracy accumulator using the ``dtype`` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1,2],[3,4]]) >>> np.var(a) 1.25 >>> np.var(a, axis=0) array([ 1., 1.]) >>> np.var(a, axis=1) array([ 0.25, 0.25]) In single precision, var() can be inaccurate: >>> a = np.zeros((2,512*512), dtype=np.float32) >>> a[0,:] = 1.0 >>> a[1,:] = 0.1 >>> np.var(a) 0.20405951142311096 Computing the variance in float64 is more accurate: >>> np.var(a, dtype=np.float64) 0.20249999932997387 >>> ((1-0.55)**2 + (0.1-0.55)**2)/2 0.20250000000000001 """ return ndarray() def vdot(a, b): """vdot(a, b) Return the dot product of two vectors. The vdot(`a`, `b`) function handles complex numbers differently than dot(`a`, `b`). If the first argument is complex the complex conjugate of the first argument is used for the calculation of the dot product. Note that `vdot` handles multidimensional arrays differently than `dot`: it does *not* perform a matrix product, but flattens input arguments to 1-D vectors first. Consequently, it should only be used for vectors. Parameters ---------- a : array_like If `a` is complex the complex conjugate is taken before calculation of the dot product. b : array_like Second argument to the dot product. Returns ------- output : ndarray Dot product of `a` and `b`. Can be an int, float, or complex depending on the types of `a` and `b`. See Also -------- dot : Return the dot product without using the complex conjugate of the first argument. Examples -------- >>> a = np.array([1+2j,3+4j]) >>> b = np.array([5+6j,7+8j]) >>> np.vdot(a, b) (70-8j) >>> np.vdot(b, a) (70+8j) Note that higher-dimensional arrays are flattened! >>> a = np.array([[1, 4], [5, 6]]) >>> b = np.array([[4, 1], [2, 2]]) >>> np.vdot(a, b) 30 >>> np.vdot(b, a) 30 >>> 1*4 + 4*1 + 5*2 + 6*2 30""" return ndarray() class vectorize: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _get_ufunc_and_otypes(self, ufunc, otypes): """Return (ufunc, otypes).""" return None def _vectorize_call(self, _): """Vectorized call to `func` over positional `args`.""" return None class void: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() def getfield(self, _): """None""" return None imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() def setfield(self, _): """None""" return None shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() class void: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() def getfield(self, _): """None""" return None imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return dtype() real = getset_descriptor() def setfield(self, _): """None""" return None shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def vsplit(): """ Split an array into multiple sub-arrays vertically (row-wise). Please refer to the ``split`` documentation. ``vsplit`` is equivalent to ``split`` with `axis=0` (default), the array is always split along the first axis regardless of the array dimension. See Also -------- split : Split an array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(16.0).reshape(4, 4) >>> x array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 12., 13., 14., 15.]]) >>> np.vsplit(x, 2) [array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.]]), array([[ 8., 9., 10., 11.], [ 12., 13., 14., 15.]])] >>> np.vsplit(x, np.array([3, 6])) [array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.]]), array([[ 12., 13., 14., 15.]]), array([], dtype=float64)] With a higher dimensional array the split is still along the first axis. >>> x = np.arange(8.0).reshape(2, 2, 2) >>> x array([[[ 0., 1.], [ 2., 3.]], [[ 4., 5.], [ 6., 7.]]]) >>> np.vsplit(x, 2) [array([[[ 0., 1.], [ 2., 3.]]]), array([[[ 4., 5.], [ 6., 7.]]])] """ return None def vstack(tup): """ Stack arrays in sequence vertically (row wise). Take a sequence of arrays and stack them vertically to make a single array. Rebuild arrays divided by `vsplit`. Parameters ---------- tup : sequence of ndarrays Tuple containing arrays to be stacked. The arrays must have the same shape along all but the first axis. Returns ------- stacked : ndarray The array formed by stacking the given arrays. See Also -------- hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third dimension). concatenate : Join a sequence of arrays together. vsplit : Split array into a list of multiple sub-arrays vertically. Notes ----- Equivalent to ``np.concatenate(tup, axis=0)`` if `tup` contains arrays that are at least 2-dimensional. Examples -------- >>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.vstack((a,b)) array([[1, 2, 3], [2, 3, 4]]) >>> a = np.array([[1], [2], [3]]) >>> b = np.array([[2], [3], [4]]) >>> np.vstack((a,b)) array([[1], [2], [3], [2], [3], [4]]) """ return ndarray() def where(condition, x=None, y=None): """where(condition, [x, y]) Return elements, either from `x` or `y`, depending on `condition`. If only `condition` is given, return ``condition.nonzero()``. Parameters ---------- condition : array_like, bool When True, yield `x`, otherwise yield `y`. x, y : array_like, optional Values from which to choose. `x` and `y` need to have the same shape as `condition`. Returns ------- out : ndarray or tuple of ndarrays If both `x` and `y` are specified, the output array contains elements of `x` where `condition` is True, and elements from `y` elsewhere. If only `condition` is given, return the tuple ``condition.nonzero()``, the indices where `condition` is True. See Also -------- nonzero, choose Notes ----- If `x` and `y` are given and input arrays are 1-D, `where` is equivalent to:: [xv if c else yv for (c,xv,yv) in zip(condition,x,y)] Examples -------- >>> np.where([[True, False], [True, True]], ... [[1, 2], [3, 4]], ... [[9, 8], [7, 6]]) array([[1, 8], [3, 4]]) >>> np.where([[0, 1], [1, 0]]) (array([0, 1]), array([1, 0])) >>> x = np.arange(9.).reshape(3, 3) >>> np.where( x > 5 ) (array([2, 2, 2]), array([0, 1, 2])) >>> x[np.where( x > 3.0 )] # Note: result is 1D. array([ 4., 5., 6., 7., 8.]) >>> np.where(x < 5, x, -1) # Note: broadcasting. array([[ 0., 1., 2.], [ 3., 4., -1.], [-1., -1., -1.]]) Find the indices of elements of `x` that are in `goodvalues`. >>> goodvalues = [3, 4, 7] >>> ix = np.in1d(x.ravel(), goodvalues).reshape(x.shape) >>> ix array([[False, False, False], [ True, True, False], [False, True, False]], dtype=bool) >>> np.where(ix) (array([1, 1, 2]), array([0, 1, 1]))""" return ndarray() if False else tuple() def who(vardict=None): """ Print the Numpy arrays in the given dictionary. If there is no dictionary passed in or `vardict` is None then returns Numpy arrays in the globals() dictionary (all Numpy arrays in the namespace). Parameters ---------- vardict : dict, optional A dictionary possibly containing ndarrays. Default is globals(). Returns ------- out : None Returns 'None'. Notes ----- Prints out the name, shape, bytes and type of all of the ndarrays present in `vardict`. Examples -------- >>> a = np.arange(10) >>> b = np.ones(20) >>> np.who() Name Shape Bytes Type =========================================================== a 10 40 int32 b 20 160 float64 Upper bound on total bytes = 200 >>> d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str', ... 'idx':5} >>> np.who(d) Name Shape Bytes Type =========================================================== y 3 24 float64 x 2 16 float64 Upper bound on total bytes = 40 """ return None() def zeros(shape, dtype, order): """zeros(shape, dtype=float, order='C') Return a new array of given shape and type, filled with zeros. Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. Returns ------- out : ndarray Array of zeros with the given shape, dtype, and order. See Also -------- zeros_like : Return an array of zeros with shape and type of input. ones_like : Return an array of ones with shape and type of input. empty_like : Return an empty array with shape and type of input. ones : Return a new array setting values to one. empty : Return a new uninitialized array. Examples -------- >>> np.zeros(5) array([ 0., 0., 0., 0., 0.]) >>> np.zeros((5,), dtype=numpy.int) array([0, 0, 0, 0, 0]) >>> np.zeros((2, 1)) array([[ 0.], [ 0.]]) >>> s = (2,2) >>> np.zeros(s) array([[ 0., 0.], [ 0., 0.]]) >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype array([(0, 0), (0, 0)], dtype=[('x', '>> x = np.arange(6) >>> x = x.reshape((2, 3)) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.zeros_like(x) array([[0, 0, 0], [0, 0, 0]]) >>> y = np.arange(3, dtype=np.float) >>> y array([ 0., 1., 2.]) >>> np.zeros_like(y) array([ 0., 0., 0.]) """ return ndarray() class ctypeslib: class PyCArrayType: __bases__ = tuple() __basicsize__ = int() __dict__ = dictproxy() __dictoffset__ = int() __doc__ = str() __flags__ = int() __itemsize__ = int() __module__ = str() __mro__ = tuple() __name__ = str() __weakrefoffset__ = int() def _from_address(self, integer): """C.from_address(integer) -> C instance access a C instance at the specified address""" return None def _from_buffer(self, object, offset=0): """C.from_buffer(object, offset=0) -> C instance create a C instance from a writeable buffer""" return None def _from_buffer_copy(self, object, offset=0): """C.from_buffer_copy(object, offset=0) -> C instance create a C instance from a readable buffer""" return None def _from_param(self, _): """Convert a Python object into a function call parameter.""" return None def in_dll(self, dll, name): """C.in_dll(dll, name) -> C instance access a C instance in a dll""" return None def mro(self, _): """mro() -> list return a type's method resolution order""" return None __all__ = list() __builtins__ = dict() __doc__ = str() __file__ = str() __name__ = str() __package__ = None class dtype: __doc__ = str() alignment = member_descriptor() base = getset_descriptor() byteorder = member_descriptor() char = member_descriptor() descr = getset_descriptor() fields = getset_descriptor() flags = member_descriptor() hasobject = getset_descriptor() isalignedstruct = getset_descriptor() isbuiltin = getset_descriptor() isnative = getset_descriptor() itemsize = member_descriptor() kind = member_descriptor() metadata = getset_descriptor() name = getset_descriptor() names = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new dtype with a different byte order. Changes are also made in all fields and sub-arrays of the data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications below. The default value ('S') results in swapping the current byte order. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The code does a case-insensitive check on the first letter of `new_order` for these alternatives. For example, any of '>' or 'B' or 'b' or 'brian' are valid to specify big-endian. Returns ------- new_dtype : dtype New dtype object with the given change to the byte order. Notes ----- Changes are also made in all fields and sub-arrays of the data type. Examples -------- >>> import sys >>> sys_is_le = sys.byteorder == 'little' >>> native_code = sys_is_le and '<' or '>' >>> swapped_code = sys_is_le and '>' or '<' >>> native_dt = np.dtype(native_code+'i2') >>> swapped_dt = np.dtype(swapped_code+'i2') >>> native_dt.newbyteorder('S') == swapped_dt True >>> native_dt.newbyteorder() == swapped_dt True >>> native_dt == swapped_dt.newbyteorder('S') True >>> native_dt == swapped_dt.newbyteorder('=') True >>> native_dt == swapped_dt.newbyteorder('N') True >>> native_dt == native_dt.newbyteorder('|') True >>> np.dtype('>> np.dtype('>> np.dtype('>i2') == native_dt.newbyteorder('>') True >>> np.dtype('>i2') == native_dt.newbyteorder('B') True""" return dtype() num = member_descriptor() shape = getset_descriptor() str = getset_descriptor() subdtype = getset_descriptor() type = member_descriptor() _flagdict = dict() _flagnames = list() def _flags__fromnum(self, _): """None""" return None def _ndptr(self, _): """None""" return None def c_void_p(self, _): """None""" return None def _num__fromflags(self, _): """None""" return None _pointer_type_cache = dict() _typecodes = dict() absolute_import = instance() def array(self, object, dtype, copy, order, subok, ndmin): """array(object, dtype=None, copy=True, order=None, subok=False, ndmin=0) Create an array. Parameters ---------- object : array_like An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence. dtype : data-type, optional The desired data-type for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. This argument can only be used to 'upcast' the array. For downcasting, use the .astype(t) method. copy : bool, optional If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (`dtype`, `order`, etc.). order : {'C', 'F', 'A'}, optional Specify the order of the array. If order is 'C' (default), then the array will be in C-contiguous order (last-index varies the fastest). If order is 'F', then the returned array will be in Fortran-contiguous order (first-index varies the fastest). If order is 'A', then the returned array may be in any order (either C-, Fortran-contiguous, or even discontiguous). subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (default). ndmin : int, optional Specifies the minimum number of dimensions that the resulting array should have. Ones will be pre-pended to the shape as needed to meet this requirement. Returns ------- out : ndarray An array object satisfying the specified requirements. See Also -------- empty, empty_like, zeros, zeros_like, ones, ones_like, fill Examples -------- >>> np.array([1, 2, 3]) array([1, 2, 3]) Upcasting: >>> np.array([1, 2, 3.0]) array([ 1., 2., 3.]) More than one dimension: >>> np.array([[1, 2], [3, 4]]) array([[1, 2], [3, 4]]) Minimum dimensions 2: >>> np.array([1, 2, 3], ndmin=2) array([[1, 2, 3]]) Type provided: >>> np.array([1, 2, 3], dtype=complex) array([ 1.+0.j, 2.+0.j, 3.+0.j]) Data-type consisting of more than one element: >>> x = np.array([(1,2),(3,4)],dtype=[('a','>> x['a'] array([1, 3]) Creating an array from sub-classes: >>> np.array(np.mat('1 2; 3 4')) array([[1, 2], [3, 4]]) >>> np.array(np.mat('1 2; 3 4'), subok=True) matrix([[1, 2], [3, 4]])""" return ndarray() def as_array(self, obj=None, shape=None): """Create a numpy array from a ctypes array or a ctypes POINTER. The numpy array shares the memory with the ctypes object. The size parameter must be given if converting from a ctypes POINTER. The size parameter is ignored if converting from a ctypes array """ return None def as_ctypes(self, _): """Create and return a ctypes object from a numpy array. Actually anything that exposes the __array_interface__ is accepted.""" return None def c_long(self, _): """None""" return None code = str() def ctypes_load_library(self): """`ctypes_load_library` is deprecated, use `load_library` instead!""" return None def deprecate(self): """ Issues a DeprecationWarning, adds warning to `old_name`'s docstring, rebinds ``old_name.__name__`` and returns the new function object. This function may also be used as a decorator. Parameters ---------- func : function The function to be deprecated. old_name : str, optional The name of the function to be deprecated. Default is None, in which case the name of `func` is used. new_name : str, optional The new name for the function. Default is None, in which case the deprecation message is that `old_name` is deprecated. If given, the deprecation message is that `old_name` is deprecated and `new_name` should be used instead. message : str, optional Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- old_func : function The deprecated function. Examples -------- Note that ``olduint`` returns a value after printing Deprecation Warning: >>> olduint = np.deprecate(np.uint) >>> olduint(6) /usr/lib/python2.5/site-packages/numpy/lib/utils.py:114: DeprecationWarning: uint32 is deprecated warnings.warn(str1, DeprecationWarning) 6 """ return None division = instance() class flagsobj: __doc__ = None aligned = getset_descriptor() behaved = getset_descriptor() c_contiguous = getset_descriptor() carray = getset_descriptor() contiguous = getset_descriptor() f_contiguous = getset_descriptor() farray = getset_descriptor() fnc = getset_descriptor() forc = getset_descriptor() fortran = getset_descriptor() num = getset_descriptor() owndata = getset_descriptor() updateifcopy = getset_descriptor() writeable = getset_descriptor() class integer: T = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = None base = getset_descriptor() def conj(self, _): """None""" return None data = getset_descriptor() dtype = getset_descriptor() flags = getset_descriptor() flat = getset_descriptor() imag = getset_descriptor() itemsize = getset_descriptor() nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * 'S' - swap dtype from current to opposite endian * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order.""" return None real = getset_descriptor() shape = getset_descriptor() size = getset_descriptor() strides = getset_descriptor() def load_library(self, _): """None""" return None class ndarray: T = getset_descriptor() __array_finalize__ = getset_descriptor() __array_interface__ = getset_descriptor() __array_priority__ = getset_descriptor() __array_struct__ = getset_descriptor() __doc__ = str() def all(self, axis=None, out=None): """a.all(axis=None, out=None) Returns True if all elements evaluate to True. Refer to `numpy.all` for full documentation. See Also -------- numpy.all : equivalent function""" return None def any(self, axis=None, out=None): """a.any(axis=None, out=None) Returns True if any of the elements of `a` evaluate to True. Refer to `numpy.any` for full documentation. See Also -------- numpy.any : equivalent function""" return None def argmax(self, axis=None, out=None): """a.argmax(axis=None, out=None) Return indices of the maximum values along the given axis. Refer to `numpy.argmax` for full documentation. See Also -------- numpy.argmax : equivalent function""" return None def argmin(self, axis=None, out=None): """a.argmin(axis=None, out=None) Return indices of the minimum values along the given axis of `a`. Refer to `numpy.argmin` for detailed documentation. See Also -------- numpy.argmin : equivalent function""" return None def argpartition(self, kth, axis=_1, kind=quickselect, order=None): """a.argpartition(kth, axis=-1, kind='quickselect', order=None) Returns the indices that would partition this array. Refer to `numpy.argpartition` for full documentation. .. versionadded:: 1.8.0 See Also -------- numpy.argpartition : equivalent function""" return None def argsort(self, axis=_1, kind=quicksort, order=None): """a.argsort(axis=-1, kind='quicksort', order=None) Returns the indices that would sort this array. Refer to `numpy.argsort` for full documentation. See Also -------- numpy.argsort : equivalent function""" return None def astype(self, dtype, order, casting, subok, copy): """a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) Copy of the array, cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to false, and the `dtype`, `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy. Returns ------- arr_t : ndarray Unless `copy` is False and the other conditions for returning the input array are satisfied (see description for `copy` input paramter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by `dtype`, `order`. Raises ------ ComplexWarning When casting from complex to float or int. To avoid this, one should use ``a.real.astype(t)``. Examples -------- >>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5]) >>> x.astype(int) array([1, 2, 2])""" return ndarray() base = getset_descriptor() def byteswap(self, inplace): """a.byteswap(inplace) Swap the bytes of the array elements Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Parameters ---------- inplace : bool, optional If ``True``, swap bytes in-place, default is ``False``. Returns ------- out : ndarray The byteswapped array. If `inplace` is ``True``, this is a view to self. Examples -------- >>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322'] Arrays of strings are not swapped >>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')""" return ndarray() def choose(self, choices, out=None, mode=_raise): """a.choose(choices, out=None, mode='raise') Use an index array to construct a new array from a set of choices. Refer to `numpy.choose` for full documentation. See Also -------- numpy.choose : equivalent function""" return None def clip(self, a_min, a_max, out=None): """a.clip(a_min, a_max, out=None) Return an array whose values are limited to ``[a_min, a_max]``. Refer to `numpy.clip` for full documentation. See Also -------- numpy.clip : equivalent function""" return None def compress(self, condition, axis=None, out=None): """a.compress(condition, axis=None, out=None) Return selected slices of this array along given axis. Refer to `numpy.compress` for full documentation. See Also -------- numpy.compress : equivalent function""" return None def conj(self, _): """a.conj() Complex-conjugate all elements. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def conjugate(self, _): """a.conjugate() Return the complex conjugate, element-wise. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function""" return None def copy(self, order): """a.copy(order='C') Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :func:numpy.copy are very similar, but have different default values for their order= arguments.) See also -------- numpy.copy numpy.copyto Examples -------- >>> x = np.array([[1,2,3],[4,5,6]], order='F') >>> y = x.copy() >>> x.fill(0) >>> x array([[0, 0, 0], [0, 0, 0]]) >>> y array([[1, 2, 3], [4, 5, 6]]) >>> y.flags['C_CONTIGUOUS'] True""" return None ctypes = getset_descriptor() def cumprod(self, axis=None, dtype=None, out=None): """a.cumprod(axis=None, dtype=None, out=None) Return the cumulative product of the elements along the given axis. Refer to `numpy.cumprod` for full documentation. See Also -------- numpy.cumprod : equivalent function""" return None def cumsum(self, axis=None, dtype=None, out=None): """a.cumsum(axis=None, dtype=None, out=None) Return the cumulative sum of the elements along the given axis. Refer to `numpy.cumsum` for full documentation. See Also -------- numpy.cumsum : equivalent function""" return None data = getset_descriptor() def diagonal(self, offset=0, axis1=0, axis2=1): """a.diagonal(offset=0, axis1=0, axis2=1) Return specified diagonals. Refer to :func:`numpy.diagonal` for full documentation. See Also -------- numpy.diagonal : equivalent function""" return None def dot(self, b, out=None): """a.dot(b, out=None) Dot product of two arrays. Refer to `numpy.dot` for full documentation. See Also -------- numpy.dot : equivalent function Examples -------- >>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]]) This array method can be conveniently chained: >>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])""" return None dtype = getset_descriptor() def dump(self, file): """a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load. Parameters ---------- file : str A string naming the dump file.""" return None def dumps(self, _): """a.dumps() Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array. Parameters ---------- None""" return None def fill(self, value): """a.fill(value) Fill the array with a scalar value. Parameters ---------- value : scalar All elements of `a` will be assigned this value. Examples -------- >>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])""" return None flags = getset_descriptor() flat = getset_descriptor() def flatten(self, order): """a.flatten(order='C') Return a copy of the array collapsed into one dimension. Parameters ---------- order : {'C', 'F', 'A'}, optional Whether to flatten in C (row-major), Fortran (column-major) order, or preserve the C/Fortran ordering from `a`. The default is 'C'. Returns ------- y : ndarray A copy of the input array, flattened to one dimension. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the array. Examples -------- >>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])""" return ndarray() def getfield(self, dtype, offset): """a.getfield(dtype, offset=0) Returns a field of the given array as a certain type. A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes. Parameters ---------- dtype : str or dtype The data type of the view. The dtype size of the view can not be larger than that of the array itself. offset : int Number of bytes to skip before beginning the element view. Examples -------- >>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]]) By choosing an offset of 8 bytes we can select the complex part of the array for our view: >>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])""" return array() imag = getset_descriptor() def item(self, ESCargs): """a.item(*args) Copy an element of an array to a standard Python scalar and return it. Parameters ---------- \*args : Arguments (variable number and type) * none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned. * int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return. * tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array. Returns ------- z : Standard Python scalar object A copy of the specified element of the array as a suitable Python scalar Notes ----- When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned. `item` is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python's optimized math. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3""" return Standard() def itemset(self, ESCargs): """a.itemset(*args) Insert scalar into an array (scalar is cast to array's dtype, if possible) There must be at least 1 argument, and define the last argument as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster than ``a[args] = item``. The item should be a scalar value and `args` must select a single item in the array `a`. Parameters ---------- \*args : Arguments If one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple. Notes ----- Compared to indexing syntax, `itemset` provides some speed increase for placing a scalar into a particular location in an `ndarray`, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using `itemset` (and `item`) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])""" return None itemsize = getset_descriptor() def max(self, axis=None, out=None): """a.max(axis=None, out=None) Return the maximum along a given axis. Refer to `numpy.amax` for full documentation. See Also -------- numpy.amax : equivalent function""" return None def mean(self, axis=None, dtype=None, out=None): """a.mean(axis=None, dtype=None, out=None) Returns the average of the array elements along given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean : equivalent function""" return None def min(self, axis=None, out=None): """a.min(axis=None, out=None) Return the minimum along a given axis. Refer to `numpy.amin` for full documentation. See Also -------- numpy.amin : equivalent function""" return None nbytes = getset_descriptor() ndim = getset_descriptor() def newbyteorder(self, new_order): """arr.newbyteorder(new_order='S') Return the array with the same data viewed with a different byte order. Equivalent to:: arr.view(arr.dtype.newbytorder(new_order)) Changes are also made in all fields and sub-arrays of the array data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications above. `new_order` codes can be any of:: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_arr : array New array object with the dtype reflecting given change to the byte order.""" return array() def nonzero(self, _): """a.nonzero() Return the indices of the elements that are non-zero. Refer to `numpy.nonzero` for full documentation. See Also -------- numpy.nonzero : equivalent function""" return None def partition(self, kth, axis, kind, order): """a.partition(kth, axis=-1, kind='introselect', order=None) Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- kth : int or sequence of ints Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once. axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort. Notes ----- See ``np.partition`` for notes on the different algorithms. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> a.partition(a, 3) >>> a array([2, 1, 3, 4]) >>> a.partition((1, 3)) array([1, 2, 3, 4])""" return None def prod(self, axis=None, dtype=None, out=None): """a.prod(axis=None, dtype=None, out=None) Return the product of the array elements over the given axis Refer to `numpy.prod` for full documentation. See Also -------- numpy.prod : equivalent function""" return None def ptp(self, axis=None, out=None): """a.ptp(axis=None, out=None) Peak to peak (maximum - minimum) value along a given axis. Refer to `numpy.ptp` for full documentation. See Also -------- numpy.ptp : equivalent function""" return None def put(self, indices, values, mode=_raise): """a.put(indices, values, mode='raise') Set ``a.flat[n] = values[n]`` for all `n` in indices. Refer to `numpy.put` for full documentation. See Also -------- numpy.put : equivalent function""" return None def ravel(self, order): """a.ravel([order]) Return a flattened array. Refer to `numpy.ravel` for full documentation. See Also -------- numpy.ravel : equivalent function ndarray.flat : a flat iterator on the array.""" return None real = getset_descriptor() def repeat(self, repeats, axis=None): """a.repeat(repeats, axis=None) Repeat elements of an array. Refer to `numpy.repeat` for full documentation. See Also -------- numpy.repeat : equivalent function""" return None def reshape(self, shape, order=C): """a.reshape(shape, order='C') Returns an array containing the same data with a new shape. Refer to `numpy.reshape` for full documentation. See Also -------- numpy.reshape : equivalent function""" return None def resize(self, new_shape, refcheck): """a.resize(new_shape, refcheck=True) Change shape and size of array in-place. Parameters ---------- new_shape : tuple of ints, or `n` ints Shape of resized array. refcheck : bool, optional If False, reference count will not be checked. Default is True. Returns ------- None Raises ------ ValueError If `a` does not own its own data or references or views to it exist, and the data memory must be changed. SystemError If the `order` keyword argument is specified. This behaviour is a bug in NumPy. See Also -------- resize : Return a new array with the specified shape. Notes ----- This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False. Examples -------- Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]]) >>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]]) Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]]) Referencing an array prevents resizing... >>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ... Unless `refcheck` is False: >>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])""" return None def round(self, decimals=0, out=None): """a.round(decimals=0, out=None) Return `a` with each element rounded to the given number of decimals. Refer to `numpy.around` for full documentation. See Also -------- numpy.around : equivalent function""" return None def searchsorted(self, v, side=left, sorter=None): """a.searchsorted(v, side='left', sorter=None) Find indices where elements of v should be inserted in a to maintain order. For full documentation, see `numpy.searchsorted` See Also -------- numpy.searchsorted : equivalent function""" return None def setfield(self, val, dtype, offset): """a.setfield(val, dtype, offset=0) Put a value into a specified place in a field defined by a data-type. Place `val` into `a`'s field defined by `dtype` and beginning `offset` bytes into the field. Parameters ---------- val : object Value to be placed in field. dtype : dtype object Data-type of the field in which to place `val`. offset : int, optional The number of bytes into the field at which to place `val`. Returns ------- None See Also -------- getfield Examples -------- >>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])""" return None def setflags(self, write, align, uic): """a.setflags(write=None, align=None, uic=None) Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively. These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The UPDATEIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters ---------- write : bool, optional Describes whether or not `a` can be written to. align : bool, optional Describes whether or not `a` is aligned properly for its type. uic : bool, optional Describes whether or not `a` is a copy of another "base" array. Notes ----- Array flags provide information about how the memory area used for the array is to be interpreted. There are 6 Boolean flags in use, only three of which can be changed by the user: UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array. All flags can be accessed using their first (upper case) letter as well as the full name. Examples -------- >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "", line 1, in ValueError: cannot set UPDATEIFCOPY flag to True""" return None shape = getset_descriptor() size = getset_descriptor() def sort(self, axis, kind, order): """a.sort(axis=-1, kind='quicksort', order=None) Sort an array, in-place. Parameters ---------- axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : list, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. Not all fields need be specified. See Also -------- numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort. Notes ----- See ``sort`` for notes on the different sorting algorithms. Examples -------- >>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]""" return list() def tostring(self, order): """a.tostring(order='C') Construct a Python string containing the raw data bytes in the array. Constructs a Python string showing a copy of the raw contents of data memory. The string can be produced in either 'C' or 'Fortran', or 'Any' order (the default is 'C'-order). 'Any' order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means 'Fortran' order. Parameters ---------- order : {'C', 'F', None}, optional Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array. Returns ------- s : str A Python string exhibiting a copy of `a`'s raw data. Examples -------- >>> x = np.array([[0, 1], [2, 3]]) >>> x.tostring() '\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tostring('C') == x.tostring() True >>> x.tostring('F') '\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'""" return str() def trace(self, offset=0, axis1=0, axis2=1, dtype=None, out=None): """a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) Return the sum along diagonals of the array. Refer to `numpy.trace` for full documentation. See Also -------- numpy.trace : equivalent function""" return None def transpose(self, axes): """a.transpose(*axes) Returns a view of the array with axes transposed. For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. Parameters ---------- axes : None, tuple of ints, or `n` ints * None or no argument: reverses the order of the axes. * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s `i`-th axis becomes `a.transpose()`'s `j`-th axis. * `n` ints: same as an n-tuple of the same ints (this form is intended simply as a "convenience" alternative to the tuple form) Returns ------- out : ndarray View of `a`, with axes suitably permuted. See Also -------- ndarray.T : Array property returning the array transposed. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])""" return ndarray() def var(self, axis=None, dtype=None, out=None, ddof=0): """a.var(axis=None, dtype=None, out=None, ddof=0) Returns the variance of the array elements, along given axis. Refer to `numpy.var` for full documentation. See Also -------- numpy.var : equivalent function""" return None def view(self, dtype, type): """a.view(dtype=None, type=None) New view of array with the same data. Parameters ---------- dtype : data-type or ndarray sub-class, optional Data-type descriptor of the returned view, e.g., float32 or int16. The default, None, results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the ``type`` parameter). type : Python type, optional Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation. Notes ----- ``a.view()`` is used two different ways: ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view of the array's memory with a different data-type. This can cause a reinterpretation of the bytes of memory. ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory. For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of ``a`` (shown by ``print(a)``). It also depends on exactly how ``a`` is stored in memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results. Examples -------- >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) Viewing array data using a different type and dtype: >>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print type(y) Creating a view on a structured array so it can be used in calculations >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.]) Making changes to the view changes the underlying array >>> xv[0,1] = 20 >>> print x [(1, 20) (3, 4)] Using a view to convert an array to a record array: >>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8) Views share data: >>> x[0] = (9, 10) >>> z[0] (9, 10) Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.: >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "", line 1, in ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', '>> clib.somefunc.argtypes = [np.ctypeslib.ndpointer(dtype=np.float64, ... ndim=1, ... flags='C_CONTIGUOUS')] ... #doctest: +SKIP >>> clib.somefunc(np.array([1, 2, 3], dtype=np.float64)) ... #doctest: +SKIP """ return ndpointer() def prep_array(self, _): """Given a ctypes array type, construct and attach an __array_interface__ property to it if it does not yet have one. """ return None def prep_pointer(self, _): """Given a ctypes pointer object, construct and attach an __array_interface__ property to it if it does not yet have one. """ return None def prep_simple(self, _): """Given a ctypes simple type, construct and attach an __array_interface__ property to it if it does not yet have one. """ return None print_function = instance() simple_types = list() def c_double(self, _): """None""" return None types = tuple() class lib: class scimath: __all__ = list() __builtins__ = dict() __doc__ = str() __file__ = str() __name__ = str() __package__ = None def _fix_int_lt_zero(self, x): """Convert `x` to double if it has real, negative components. Otherwise, output is just the array version of the input (via asarray). Parameters ---------- x : array_like Returns ------- array Examples -------- >>> np.lib.scimath._fix_int_lt_zero([1,2]) array([1, 2]) >>> np.lib.scimath._fix_int_lt_zero([-1,2]) array([-1., 2.]) """ return None def _fix_real_abs_gt_1(self, x): """Convert `x` to complex if it has real components x_i with abs(x_i)>1. Otherwise, output is just the array version of the input (via asarray). Parameters ---------- x : array_like Returns ------- array Examples -------- >>> np.lib.scimath._fix_real_abs_gt_1([0,1]) array([0, 1]) >>> np.lib.scimath._fix_real_abs_gt_1([0,2]) array([ 0.+0.j, 2.+0.j]) """ return None def _fix_real_lt_zero(self, x): """Convert `x` to complex if it has real, negative components. Otherwise, output is just the array version of the input (via asarray). Parameters ---------- x : array_like Returns ------- array Examples -------- >>> np.lib.scimath._fix_real_lt_zero([1,2]) array([1, 2]) >>> np.lib.scimath._fix_real_lt_zero([-1,2]) array([-1.+0.j, 2.+0.j]) """ return None _ln2 = float64() def _tocomplex(self, arr): """Convert its input `arr` to a complex array. The input is returned as a complex array of the smallest type that will fit the original data: types like single, byte, short, etc. become csingle, while others become cdouble. A copy of the input is always made. Parameters ---------- arr : array Returns ------- array An array with the same input data as the input but in complex form. Examples -------- First, consider an input of type short: >>> a = np.array([1,2,3],np.short) >>> ac = np.lib.scimath._tocomplex(a); ac array([ 1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64) >>> ac.dtype dtype('complex64') If the input is of type double, the output is correspondingly of the complex double type as well: >>> b = np.array([1,2,3],np.double) >>> bc = np.lib.scimath._tocomplex(b); bc array([ 1.+0.j, 2.+0.j, 3.+0.j]) >>> bc.dtype dtype('complex128') Note that even if the input was complex to begin with, a copy is still made, since the astype() method always copies: >>> c = np.array([1,2,3],np.csingle) >>> cc = np.lib.scimath._tocomplex(c); cc array([ 1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64) >>> c *= 2; c array([ 2.+0.j, 4.+0.j, 6.+0.j], dtype=complex64) >>> cc array([ 1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64) """ return None absolute_import = instance() def any(self, a=False, axis=None, out=None, keepdims=False): """ Test whether any array element along a given axis evaluates to True. Returns single boolean unless `axis` is not ``None`` Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : None or int or tuple of ints, optional Axis or axes along which a logical OR reduction is performed. The default (`axis` = `None`) is perform a logical OR over all the dimensions of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if it is of type float, then it will remain so, returning 1.0 for True and 0.0 for False, regardless of the type of `a`). See `doc.ufuncs` (Section "Output arguments") for details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- any : bool or ndarray A new boolean or `ndarray` is returned unless `out` is specified, in which case a reference to `out` is returned. See Also -------- ndarray.any : equivalent method all : Test whether all elements along a given axis evaluate to True. Notes ----- Not a Number (NaN), positive infinity and negative infinity evaluate to `True` because these are not equal to zero. Examples -------- >>> np.any([[True, False], [True, True]]) True >>> np.any([[True, False], [False, False]], axis=0) array([ True, False], dtype=bool) >>> np.any([-1, 0, 5]) True >>> np.any(np.nan) True >>> o=np.array([False]) >>> z=np.any([-1, 4, 5], out=o) >>> z, o (array([ True], dtype=bool), array([ True], dtype=bool)) >>> # Check now that z is a reference to o >>> z is o True >>> id(z), id(o) # identity of z and o # doctest: +SKIP (191614240, 191614240) """ return bool() if False else ndarray() def arccos(self, x): """ Compute the inverse cosine of x. Return the "principal value" (for a description of this, see `numpy.arccos`) of the inverse cosine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[0, \pi]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arccos is (are) required. Returns ------- out : ndarray or scalar The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arccos Notes ----- For an arccos() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arccos`. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.arccos(1) # a scalar is returned 0.0 >>> np.emath.arccos([1,2]) array([ 0.-0.j , 0.+1.317j]) """ return ndarray() if False else float() def arcsin(self, x): """ Compute the inverse sine of x. Return the "principal value" (for a description of this, see `numpy.arcsin`) of the inverse sine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[-\pi/2, \pi/2]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arcsin is (are) required. Returns ------- out : ndarray or scalar The inverse sine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arcsin Notes ----- For an arcsin() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arcsin`. Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.arcsin(0) 0.0 >>> np.emath.arcsin([0,1]) array([ 0. , 1.5708]) """ return ndarray() if False else float() def arctanh(self, x): """ Compute the inverse hyperbolic tangent of `x`. Return the "principal value" (for a description of this, see `numpy.arctanh`) of `arctanh(x)`. For real `x` such that `abs(x) < 1`, this is a real number. If `abs(x) > 1`, or if `x` is complex, the result is complex. Finally, `x = 1` returns``inf`` and `x=-1` returns ``-inf``. Parameters ---------- x : array_like The value(s) whose arctanh is (are) required. Returns ------- out : ndarray or scalar The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was a scalar so is `out`, otherwise an array is returned. See Also -------- numpy.arctanh Notes ----- For an arctanh() that returns ``NAN`` when real `x` is not in the interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does return +/-inf for `x = +/-1`). Examples -------- >>> np.set_printoptions(precision=4) >>> np.emath.arctanh(np.matrix(np.eye(2))) array([[ Inf, 0.], [ 0., Inf]]) >>> np.emath.arctanh([1j]) array([ 0.+0.7854j]) """ return ndarray() if False else float() def asarray(self, a=None, dtype=None, order=None): """ Convert the input to an array. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F'}, optional Whether to use row-major ('C') or column-major ('F' for FORTRAN) memory representation. Defaults to 'C'. Returns ------- out : ndarray Array interpretation of `a`. No copy is performed if the input is already an ndarray. If `a` is a subclass of ndarray, a base class ndarray is returned. See Also -------- asanyarray : Similar function which passes through subclasses. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. asarray_chkfinite : Similar function which checks input for NaNs and Infs. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array: >>> a = [1, 2] >>> np.asarray(a) array([1, 2]) Existing arrays are not copied: >>> a = np.array([1, 2]) >>> np.asarray(a) is a True If `dtype` is set, array is copied only if dtype does not match: >>> a = np.array([1, 2], dtype=np.float32) >>> np.asarray(a, dtype=np.float32) is a True >>> np.asarray(a, dtype=np.float64) is a False Contrary to `asanyarray`, ndarray subclasses are not passed through: >>> issubclass(np.matrix, np.ndarray) True >>> a = np.matrix([[1, 2]]) >>> np.asarray(a) is a False >>> np.asanyarray(a) is a True """ return ndarray() division = instance() def isreal(self, x): """ Returns a bool array, where True if input element is real. If element has complex type with zero complex part, the return value for that element is True. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray, bool Boolean array of same shape as `x`. See Also -------- iscomplex isrealobj : Return True if x is not a complex type. Examples -------- >>> np.isreal([1+1j, 1+0j, 4.5, 3, 2, 2j]) array([False, True, True, True, True, False], dtype=bool) """ return ndarray() def log(self, x): """ Compute the natural logarithm of `x`. Return the "principal value" (for a description of this, see `numpy.log`) of :math:`log_e(x)`. For real `x > 0`, this is a real number (``log(0)`` returns ``-inf`` and ``log(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like The value(s) whose log is (are) required. Returns ------- out : ndarray or scalar The log of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.log Notes ----- For a log() that returns ``NAN`` when real `x < 0`, use `numpy.log` (note, however, that otherwise `numpy.log` and this `log` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- >>> np.emath.log(np.exp(1)) 1.0 Negative arguments are handled "correctly" (recall that ``exp(log(x)) == x`` does *not* hold for real ``x < 0``): >>> np.emath.log(-np.exp(1)) == (1 + np.pi * 1j) True """ return ndarray() if False else float() def log10(self, x): """ Compute the logarithm base 10 of `x`. Return the "principal value" (for a description of this, see `numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose log base 10 is (are) required. Returns ------- out : ndarray or scalar The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.log10 Notes ----- For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10` (note, however, that otherwise `numpy.log10` and this `log10` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- (We set the printing precision so the example can be auto-tested) >>> np.set_printoptions(precision=4) >>> np.emath.log10(10**1) 1.0 >>> np.emath.log10([-10**1, -10**2, 10**2]) array([ 1.+1.3644j, 2.+1.3644j, 2.+0.j ]) """ return ndarray() if False else float() def log2(self, x): """ Compute the logarithm base 2 of `x`. Return the "principal value" (for a description of this, see `numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like The value(s) whose log base 2 is (are) required. Returns ------- out : ndarray or scalar The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.log2 Notes ----- For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2` (note, however, that otherwise `numpy.log2` and this `log2` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- We set the printing precision so the example can be auto-tested: >>> np.set_printoptions(precision=4) >>> np.emath.log2(8) 3.0 >>> np.emath.log2([-4, -8, 8]) array([ 2.+4.5324j, 3.+4.5324j, 3.+0.j ]) """ return ndarray() if False else float() def logn(self, n, x): """ Take log base n of x. If `x` contains negative inputs, the answer is computed and returned in the complex domain. Parameters ---------- n : int The base in which the log is taken. x : array_like The value(s) whose log base `n` is (are) required. Returns ------- out : ndarray or scalar The log base `n` of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. Examples -------- >>> np.set_printoptions(precision=4) >>> np.lib.scimath.logn(2, [4, 8]) array([ 2., 3.]) >>> np.lib.scimath.logn(2, [-4, -8, 8]) array([ 2.+4.5324j, 3.+4.5324j, 3.+0.j ]) """ return ndarray() if False else float() def power(self, x, p): """ Return x to the power p, (x**p). If `x` contains negative values, the output is converted to the complex domain. Parameters ---------- x : array_like The input value(s). p : array_like of ints The power(s) to which `x` is raised. If `x` contains multiple values, `p` has to either be a scalar, or contain the same number of values as `x`. In the latter case, the result is ``x[0]**p[0], x[1]**p[1], ...``. Returns ------- out : ndarray or scalar The result of ``x**p``. If `x` and `p` are scalars, so is `out`, otherwise an array is returned. See Also -------- numpy.power Examples -------- >>> np.set_printoptions(precision=4) >>> np.lib.scimath.power([2, 4], 2) array([ 4, 16]) >>> np.lib.scimath.power([2, 4], -2) array([ 0.25 , 0.0625]) >>> np.lib.scimath.power([-2, 4], 2) array([ 4.+0.j, 16.+0.j]) """ return ndarray() if False else float() print_function = instance() def sqrt(self, x): """ Compute the square root of x. For negative input elements, a complex value is returned (unlike `numpy.sqrt` which returns NaN). Parameters ---------- x : array_like The input value(s). Returns ------- out : ndarray or scalar The square root of `x`. If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.sqrt Examples -------- For real, non-negative inputs this works just like `numpy.sqrt`: >>> np.lib.scimath.sqrt(1) 1.0 >>> np.lib.scimath.sqrt([1, 4]) array([ 1., 2.]) But it automatically handles negative inputs: >>> np.lib.scimath.sqrt(-1) (0.0+1.0j) >>> np.lib.scimath.sqrt([-1,4]) array([ 0.+1.j, 2.+0.j]) """ return ndarray() if False else float() class fft: class NoseTester: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _get_custom_doctester(self, _): """ Return instantiated plugin for doctests Allows subclassing of this class to override doctester A return value of None means use the nose builtin doctest plugin """ return None def _show_system_info(self, _): """None""" return None def _test_argv(self, label, verbose, extra_argv): """ Generate argv for nosetest command Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional see ``test`` docstring verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- argv : list command line arguments that will be passed to nose """ return list() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() excludes = list() def prepare_test_args(self=False, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False): """ Run tests for module using nose. This method does the heavy lifting for the `test` method. It takes all the same arguments, for details see `test`. See Also -------- test """ return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() __builtins__ = dict() __doc__ = str() __file__ = str() __name__ = str() __package__ = str() __path__ = list() absolute_import = instance() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() division = instance() def fft(self, a=-1, n=None, axis=-1): """ Compute the one-dimensional discrete Fourier Transform. This function computes the one-dimensional *n*-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT]. Parameters ---------- a : array_like Input array, can be complex. n : int, optional Length of the transformed axis of the output. If `n` is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If `n` is not given, the length of the input (along the axis specified by `axis`) is used. axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. Raises ------ IndexError if `axes` is larger than the last axis of `a`. See Also -------- numpy.fft : for definition of the DFT and conventions used. ifft : The inverse of `fft`. fft2 : The two-dimensional FFT. fftn : The *n*-dimensional FFT. rfftn : The *n*-dimensional FFT of real input. fftfreq : Frequency bins for given FFT parameters. Notes ----- FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when `n` is a power of 2, and the transform is therefore most efficient for these sizes. The DFT is defined, with the conventions used in this implementation, in the documentation for the `numpy.fft` module. References ---------- .. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the machine calculation of complex Fourier series," *Math. Comput.* 19: 297-301. Examples -------- >>> np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8)) array([ -3.44505240e-16 +1.14383329e-17j, 8.00000000e+00 -5.71092652e-15j, 2.33482938e-16 +1.22460635e-16j, 1.64863782e-15 +1.77635684e-15j, 9.95839695e-17 +2.33482938e-16j, 0.00000000e+00 +1.66837030e-15j, 1.14383329e-17 +1.22460635e-16j, -1.64863782e-15 +1.77635684e-15j]) >>> import matplotlib.pyplot as plt >>> t = np.arange(256) >>> sp = np.fft.fft(np.sin(t)) >>> freq = np.fft.fftfreq(t.shape[-1]) >>> plt.plot(freq, sp.real, freq, sp.imag) [, ] >>> plt.show() In this example, real input has an FFT which is Hermitian, i.e., symmetric in the real part and anti-symmetric in the imaginary part, as described in the `numpy.fft` documentation. """ return complex() def fft2(self, a="(-2, -1)", s=None, axes="(-2, -1)"): """ Compute the 2-dimensional discrete Fourier Transform This function computes the *n*-dimensional discrete Fourier Transform over any axes in an *M*-dimensional array by means of the Fast Fourier Transform (FFT). By default, the transform is computed over the last two axes of the input array, i.e., a 2-dimensional FFT. Parameters ---------- a : array_like Input array, can be complex s : sequence of ints, optional Shape (length of each transformed axis) of the output (`s[0]` refers to axis 0, `s[1]` to axis 1, etc.). This corresponds to `n` for `fft(x, n)`. Along each axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. if `s` is not given, the shape of the input (along the axes specified by `axes`) is used. axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last two axes are used. A repeated index in `axes` means the transform over that axis is performed multiple times. A one-element sequence means that a one-dimensional FFT is performed. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or the last two axes if `axes` is not given. Raises ------ ValueError If `s` and `axes` have different length, or `axes` not given and ``len(s) != 2``. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- numpy.fft : Overall view of discrete Fourier transforms, with definitions and conventions used. ifft2 : The inverse two-dimensional FFT. fft : The one-dimensional FFT. fftn : The *n*-dimensional FFT. fftshift : Shifts zero-frequency terms to the center of the array. For two-dimensional input, swaps first and third quadrants, and second and fourth quadrants. Notes ----- `fft2` is just `fftn` with a different default for `axes`. The output, analogously to `fft`, contains the term for zero frequency in the low-order corner of the transformed axes, the positive frequency terms in the first half of these axes, the term for the Nyquist frequency in the middle of the axes and the negative frequency terms in the second half of the axes, in order of decreasingly negative frequency. See `fftn` for details and a plotting example, and `numpy.fft` for definitions and conventions used. Examples -------- >>> a = np.mgrid[:5, :5][0] >>> np.fft.fft2(a) array([[ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 5.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 10.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 15.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 20.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]]) """ return complex() def fftfreq(self, n=1.0, d=1.0): """ Return the Discrete Fourier Transform sample frequencies. The returned float array `f` contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second. Given a window length `n` and a sample spacing `d`:: f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd Parameters ---------- n : int Window length. d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1. Returns ------- f : ndarray Array of length `n` containing the sample frequencies. Examples -------- >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float) >>> fourier = np.fft.fft(signal) >>> n = signal.size >>> timestep = 0.1 >>> freq = np.fft.fftfreq(n, d=timestep) >>> freq array([ 0. , 1.25, 2.5 , 3.75, -5. , -3.75, -2.5 , -1.25]) """ return ndarray() def fftn(self, a=None, s=None, axes=None): """ Compute the N-dimensional discrete Fourier Transform. This function computes the *N*-dimensional discrete Fourier Transform over any number of axes in an *M*-dimensional array by means of the Fast Fourier Transform (FFT). Parameters ---------- a : array_like Input array, can be complex. s : sequence of ints, optional Shape (length of each transformed axis) of the output (`s[0]` refers to axis 0, `s[1]` to axis 1, etc.). This corresponds to `n` for `fft(x, n)`. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. if `s` is not given, the shape of the input (along the axes specified by `axes`) is used. axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last ``len(s)`` axes are used, or all axes if `s` is also not specified. Repeated indices in `axes` means that the transform over that axis is performed multiple times. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` and `a`, as explained in the parameters section above. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- numpy.fft : Overall view of discrete Fourier transforms, with definitions and conventions used. ifftn : The inverse of `fftn`, the inverse *n*-dimensional FFT. fft : The one-dimensional FFT, with definitions and conventions used. rfftn : The *n*-dimensional FFT of real input. fft2 : The two-dimensional FFT. fftshift : Shifts zero-frequency terms to centre of array Notes ----- The output, analogously to `fft`, contains the term for zero frequency in the low-order corner of all axes, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency. See `numpy.fft` for details, definitions and conventions used. Examples -------- >>> a = np.mgrid[:3, :3, :3][0] >>> np.fft.fftn(a, axes=(1, 2)) array([[[ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]], [[ 9.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]], [[ 18.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]]]) >>> np.fft.fftn(a, (2, 2), axes=(0, 1)) array([[[ 2.+0.j, 2.+0.j, 2.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]], [[-2.+0.j, -2.+0.j, -2.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]]]) >>> import matplotlib.pyplot as plt >>> [X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12, ... 2 * np.pi * np.arange(200) / 34) >>> S = np.sin(X) + np.cos(Y) + np.random.uniform(0, 1, X.shape) >>> FS = np.fft.fftn(S) >>> plt.imshow(np.log(np.abs(np.fft.fftshift(FS))**2)) >>> plt.show() """ return complex() def fftshift(self, x=None, axes=None): """ Shift the zero-frequency component to the center of the spectrum. This function swaps half-spaces for all axes listed (defaults to all). Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even. Parameters ---------- x : array_like Input array. axes : int or shape tuple, optional Axes over which to shift. Default is None, which shifts all axes. Returns ------- y : ndarray The shifted array. See Also -------- ifftshift : The inverse of `fftshift`. Examples -------- >>> freqs = np.fft.fftfreq(10, 0.1) >>> freqs array([ 0., 1., 2., 3., 4., -5., -4., -3., -2., -1.]) >>> np.fft.fftshift(freqs) array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.]) Shift the zero-frequency component only along the second axis: >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) >>> freqs array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) >>> np.fft.fftshift(freqs, axes=(1,)) array([[ 2., 0., 1.], [-4., 3., 4.], [-1., -3., -2.]]) """ return ndarray() def hfft(self, a=-1, n=None, axis=-1): """ Compute the FFT of a signal whose spectrum has Hermitian symmetry. Parameters ---------- a : array_like The input array. n : int, optional The length of the FFT. axis : int, optional The axis over which to compute the FFT, assuming Hermitian symmetry of the spectrum. Default is the last axis. Returns ------- out : ndarray The transformed input. See also -------- rfft : Compute the one-dimensional FFT for real input. ihfft : The inverse of `hfft`. Notes ----- `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the opposite case: here the signal is real in the frequency domain and has Hermite symmetry in the time domain. So here it's `hfft` for which you must supply the length of the result if it is to be odd: ``ihfft(hfft(a), len(a)) == a``, within numerical accuracy. Examples -------- >>> signal = np.array([[1, 1.j], [-1.j, 2]]) >>> np.conj(signal.T) - signal # check Hermitian symmetry array([[ 0.-0.j, 0.+0.j], [ 0.+0.j, 0.-0.j]]) >>> freq_spectrum = np.fft.hfft(signal) >>> freq_spectrum array([[ 1., 1.], [ 2., -2.]]) """ return ndarray() def ifft(self, a=-1, n=None, axis=-1): """ Compute the one-dimensional inverse discrete Fourier Transform. This function computes the inverse of the one-dimensional *n*-point discrete Fourier transform computed by `fft`. In other words, ``ifft(fft(a)) == a`` to within numerical accuracy. For a general description of the algorithm and definitions, see `numpy.fft`. The input should be ordered in the same way as is returned by `fft`, i.e., ``a[0]`` should contain the zero frequency term, ``a[1:n/2+1]`` should contain the positive-frequency terms, and ``a[n/2+1:]`` should contain the negative-frequency terms, in order of decreasingly negative frequency. See `numpy.fft` for details. Parameters ---------- a : array_like Input array, can be complex. n : int, optional Length of the transformed axis of the output. If `n` is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If `n` is not given, the length of the input (along the axis specified by `axis`) is used. See notes about padding issues. axis : int, optional Axis over which to compute the inverse DFT. If not given, the last axis is used. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. Raises ------ IndexError If `axes` is larger than the last axis of `a`. See Also -------- numpy.fft : An introduction, with definitions and general explanations. fft : The one-dimensional (forward) FFT, of which `ifft` is the inverse ifft2 : The two-dimensional inverse FFT. ifftn : The n-dimensional inverse FFT. Notes ----- If the input parameter `n` is larger than the size of the input, the input is padded by appending zeros at the end. Even though this is the common approach, it might lead to surprising results. If a different padding is desired, it must be performed before calling `ifft`. Examples -------- >>> np.fft.ifft([0, 4, 0, 0]) array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) Create and plot a band-limited signal with random phases: >>> import matplotlib.pyplot as plt >>> t = np.arange(400) >>> n = np.zeros((400,), dtype=complex) >>> n[40:60] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20,))) >>> s = np.fft.ifft(n) >>> plt.plot(t, s.real, 'b-', t, s.imag, 'r--') [, ] >>> plt.legend(('real', 'imaginary')) >>> plt.show() """ return complex() def ifft2(self, a="(-2, -1)", s=None, axes="(-2, -1)"): """ Compute the 2-dimensional inverse discrete Fourier Transform. This function computes the inverse of the 2-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). In other words, ``ifft2(fft2(a)) == a`` to within numerical accuracy. By default, the inverse transform is computed over the last two axes of the input array. The input, analogously to `ifft`, should be ordered in the same way as is returned by `fft2`, i.e. it should have the term for zero frequency in the low-order corner of the two axes, the positive frequency terms in the first half of these axes, the term for the Nyquist frequency in the middle of the axes and the negative frequency terms in the second half of both axes, in order of decreasingly negative frequency. Parameters ---------- a : array_like Input array, can be complex. s : sequence of ints, optional Shape (length of each axis) of the output (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). This corresponds to `n` for ``ifft(x, n)``. Along each axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. if `s` is not given, the shape of the input (along the axes specified by `axes`) is used. See notes for issue on `ifft` zero padding. axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last two axes are used. A repeated index in `axes` means the transform over that axis is performed multiple times. A one-element sequence means that a one-dimensional FFT is performed. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or the last two axes if `axes` is not given. Raises ------ ValueError If `s` and `axes` have different length, or `axes` not given and ``len(s) != 2``. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- numpy.fft : Overall view of discrete Fourier transforms, with definitions and conventions used. fft2 : The forward 2-dimensional FFT, of which `ifft2` is the inverse. ifftn : The inverse of the *n*-dimensional FFT. fft : The one-dimensional FFT. ifft : The one-dimensional inverse FFT. Notes ----- `ifft2` is just `ifftn` with a different default for `axes`. See `ifftn` for details and a plotting example, and `numpy.fft` for definition and conventions used. Zero-padding, analogously with `ifft`, is performed by appending zeros to the input along the specified dimension. Although this is the common approach, it might lead to surprising results. If another form of zero padding is desired, it must be performed before `ifft2` is called. Examples -------- >>> a = 4 * np.eye(4) >>> np.fft.ifft2(a) array([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j], [ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j], [ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]]) """ return complex() def ifftn(self, a=None, s=None, axes=None): """ Compute the N-dimensional inverse discrete Fourier Transform. This function computes the inverse of the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). In other words, ``ifftn(fftn(a)) == a`` to within numerical accuracy. For a description of the definitions and conventions used, see `numpy.fft`. The input, analogously to `ifft`, should be ordered in the same way as is returned by `fftn`, i.e. it should have the term for zero frequency in all axes in the low-order corner, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency. Parameters ---------- a : array_like Input array, can be complex. s : sequence of ints, optional Shape (length of each transformed axis) of the output (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). This corresponds to ``n`` for ``ifft(x, n)``. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. if `s` is not given, the shape of the input (along the axes specified by `axes`) is used. See notes for issue on `ifft` zero padding. axes : sequence of ints, optional Axes over which to compute the IFFT. If not given, the last ``len(s)`` axes are used, or all axes if `s` is also not specified. Repeated indices in `axes` means that the inverse transform over that axis is performed multiple times. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` or `a`, as explained in the parameters section above. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- numpy.fft : Overall view of discrete Fourier transforms, with definitions and conventions used. fftn : The forward *n*-dimensional FFT, of which `ifftn` is the inverse. ifft : The one-dimensional inverse FFT. ifft2 : The two-dimensional inverse FFT. ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning of array. Notes ----- See `numpy.fft` for definitions and conventions used. Zero-padding, analogously with `ifft`, is performed by appending zeros to the input along the specified dimension. Although this is the common approach, it might lead to surprising results. If another form of zero padding is desired, it must be performed before `ifftn` is called. Examples -------- >>> a = np.eye(4) >>> np.fft.ifftn(np.fft.fftn(a, axes=(0,)), axes=(1,)) array([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]]) Create and plot an image with band-limited frequency content: >>> import matplotlib.pyplot as plt >>> n = np.zeros((200,200), dtype=complex) >>> n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20))) >>> im = np.fft.ifftn(n).real >>> plt.imshow(im) >>> plt.show() """ return complex() def ifftshift(self, x=None, axes=None): """ The inverse of fftshift. Parameters ---------- x : array_like Input array. axes : int or shape tuple, optional Axes over which to calculate. Defaults to None, which shifts all axes. Returns ------- y : ndarray The shifted array. See Also -------- fftshift : Shift zero-frequency component to the center of the spectrum. Examples -------- >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) >>> freqs array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) >>> np.fft.ifftshift(np.fft.fftshift(freqs)) array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) """ return ndarray() def ihfft(self, a=-1, n=None, axis=-1): """ Compute the inverse FFT of a signal whose spectrum has Hermitian symmetry. Parameters ---------- a : array_like Input array. n : int, optional Length of the inverse FFT. axis : int, optional Axis over which to compute the inverse FFT, assuming Hermitian symmetry of the spectrum. Default is the last axis. Returns ------- out : ndarray The transformed input. See also -------- hfft, irfft Notes ----- `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the opposite case: here the signal is real in the frequency domain and has Hermite symmetry in the time domain. So here it's `hfft` for which you must supply the length of the result if it is to be odd: ``ihfft(hfft(a), len(a)) == a``, within numerical accuracy. """ return ndarray() def irfft(self, a=-1, n=None, axis=-1): """ Compute the inverse of the n-point DFT for real input. This function computes the inverse of the one-dimensional *n*-point discrete Fourier Transform of real input computed by `rfft`. In other words, ``irfft(rfft(a), len(a)) == a`` to within numerical accuracy. (See Notes below for why ``len(a)`` is necessary here.) The input is expected to be in the form returned by `rfft`, i.e. the real zero-frequency term followed by the complex positive frequency terms in order of increasing frequency. Since the discrete Fourier Transform of real input is Hermite-symmetric, the negative frequency terms are taken to be the complex conjugates of the corresponding positive frequency terms. Parameters ---------- a : array_like The input array. n : int, optional Length of the transformed axis of the output. For `n` output points, ``n//2+1`` input points are necessary. If the input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. If `n` is not given, it is determined from the length of the input (along the axis specified by `axis`). axis : int, optional Axis over which to compute the inverse FFT. Returns ------- out : ndarray The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. The length of the transformed axis is `n`, or, if `n` is not given, ``2*(m-1)`` where `m` is the length of the transformed axis of the input. To get an odd number of output points, `n` must be specified. Raises ------ IndexError If `axis` is larger than the last axis of `a`. See Also -------- numpy.fft : For definition of the DFT and conventions used. rfft : The one-dimensional FFT of real input, of which `irfft` is inverse. fft : The one-dimensional FFT. irfft2 : The inverse of the two-dimensional FFT of real input. irfftn : The inverse of the *n*-dimensional FFT of real input. Notes ----- Returns the real valued `n`-point inverse discrete Fourier transform of `a`, where `a` contains the non-negative frequency terms of a Hermite-symmetric sequence. `n` is the length of the result, not the input. If you specify an `n` such that `a` must be zero-padded or truncated, the extra/removed values will be added/removed at high frequencies. One can thus resample a series to `m` points via Fourier interpolation by: ``a_resamp = irfft(rfft(a), m)``. Examples -------- >>> np.fft.ifft([1, -1j, -1, 1j]) array([ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]) >>> np.fft.irfft([1, -1j, -1]) array([ 0., 1., 0., 0.]) Notice how the last term in the input to the ordinary `ifft` is the complex conjugate of the second term, and the output has zero imaginary part everywhere. When calling `irfft`, the negative frequencies are not specified, and the output array is purely real. """ return ndarray() def irfft2(self, a="(-2, -1)", s=None, axes="(-2, -1)"): """ Compute the 2-dimensional inverse FFT of a real array. Parameters ---------- a : array_like The input array s : sequence of ints, optional Shape of the inverse FFT. axes : sequence of ints, optional The axes over which to compute the inverse fft. Default is the last two axes. Returns ------- out : ndarray The result of the inverse real 2-D FFT. See Also -------- irfftn : Compute the inverse of the N-dimensional FFT of real input. Notes ----- This is really `irfftn` with different defaults. For more details see `irfftn`. """ return ndarray() def irfftn(self, a=None, s=None, axes=None): """ Compute the inverse of the N-dimensional FFT of real input. This function computes the inverse of the N-dimensional discrete Fourier Transform for real input over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). In other words, ``irfftn(rfftn(a), a.shape) == a`` to within numerical accuracy. (The ``a.shape`` is necessary like ``len(a)`` is for `irfft`, and for the same reason.) The input should be ordered in the same way as is returned by `rfftn`, i.e. as for `irfft` for the final transformation axis, and as for `ifftn` along all the other axes. Parameters ---------- a : array_like Input array. s : sequence of ints, optional Shape (length of each transformed axis) of the output (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the number of input points used along this axis, except for the last axis, where ``s[-1]//2+1`` points of the input are used. Along any axis, if the shape indicated by `s` is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. If `s` is not given, the shape of the input (along the axes specified by `axes`) is used. axes : sequence of ints, optional Axes over which to compute the inverse FFT. If not given, the last `len(s)` axes are used, or all axes if `s` is also not specified. Repeated indices in `axes` means that the inverse transform over that axis is performed multiple times. Returns ------- out : ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` or `a`, as explained in the parameters section above. The length of each transformed axis is as given by the corresponding element of `s`, or the length of the input in every axis except for the last one if `s` is not given. In the final transformed axis the length of the output when `s` is not given is ``2*(m-1)`` where `m` is the length of the final transformed axis of the input. To get an odd number of output points in the final axis, `s` must be specified. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- rfftn : The forward n-dimensional FFT of real input, of which `ifftn` is the inverse. fft : The one-dimensional FFT, with definitions and conventions used. irfft : The inverse of the one-dimensional FFT of real input. irfft2 : The inverse of the two-dimensional FFT of real input. Notes ----- See `fft` for definitions and conventions used. See `rfft` for definitions and conventions used for real input. Examples -------- >>> a = np.zeros((3, 2, 2)) >>> a[0, 0, 0] = 3 * 2 * 2 >>> np.fft.irfftn(a) array([[[ 1., 1.], [ 1., 1.]], [[ 1., 1.], [ 1., 1.]], [[ 1., 1.], [ 1., 1.]]]) """ return ndarray() print_function = instance() def rfft(self, a=-1, n=None, axis=-1): """ Compute the one-dimensional discrete Fourier Transform for real input. This function computes the one-dimensional *n*-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT). Parameters ---------- a : array_like Input array n : int, optional Number of points along transformation axis in the input to use. If `n` is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If `n` is not given, the length of the input (along the axis specified by `axis`) is used. axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. If `n` is even, the length of the transformed axis is ``(n/2)+1``. If `n` is odd, the length is ``(n+1)/2``. Raises ------ IndexError If `axis` is larger than the last axis of `a`. See Also -------- numpy.fft : For definition of the DFT and conventions used. irfft : The inverse of `rfft`. fft : The one-dimensional FFT of general (complex) input. fftn : The *n*-dimensional FFT. rfftn : The *n*-dimensional FFT of real input. Notes ----- When the DFT is computed for purely real input, the output is Hermite-symmetric, i.e. the negative frequency terms are just the complex conjugates of the corresponding positive-frequency terms, and the negative-frequency terms are therefore redundant. This function does not compute the negative frequency terms, and the length of the transformed axis of the output is therefore ``n//2+1``. When ``A = rfft(a)`` and fs is the sampling frequency, ``A[0]`` contains the zero-frequency term 0*fs, which is real due to Hermitian symmetry. If `n` is even, ``A[-1]`` contains the term representing both positive and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely real. If `n` is odd, there is no term at fs/2; ``A[-1]`` contains the largest positive frequency (fs/2*(n-1)/n), and is complex in the general case. If the input `a` contains an imaginary part, it is silently discarded. Examples -------- >>> np.fft.fft([0, 1, 0, 0]) array([ 1.+0.j, 0.-1.j, -1.+0.j, 0.+1.j]) >>> np.fft.rfft([0, 1, 0, 0]) array([ 1.+0.j, 0.-1.j, -1.+0.j]) Notice how the final element of the `fft` output is the complex conjugate of the second element, for real input. For `rfft`, this symmetry is exploited to compute only the non-negative frequency terms. """ return complex() def rfft2(self, a="(-2, -1)", s=None, axes="(-2, -1)"): """ Compute the 2-dimensional FFT of a real array. Parameters ---------- a : array Input array, taken to be real. s : sequence of ints, optional Shape of the FFT. axes : sequence of ints, optional Axes over which to compute the FFT. Returns ------- out : ndarray The result of the real 2-D FFT. See Also -------- rfftn : Compute the N-dimensional discrete Fourier Transform for real input. Notes ----- This is really just `rfftn` with different default behavior. For more details see `rfftn`. """ return ndarray() def rfftfreq(self, n=1.0, d=1.0): """ Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). The returned float array `f` contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second. Given a window length `n` and a sample spacing `d`:: f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`) the Nyquist frequency component is considered to be positive. Parameters ---------- n : int Window length. d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1. Returns ------- f : ndarray Array of length ``n//2 + 1`` containing the sample frequencies. Examples -------- >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float) >>> fourier = np.fft.rfft(signal) >>> n = signal.size >>> sample_rate = 100 >>> freq = np.fft.fftfreq(n, d=1./sample_rate) >>> freq array([ 0., 10., 20., 30., 40., -50., -40., -30., -20., -10.]) >>> freq = np.fft.rfftfreq(n, d=1./sample_rate) >>> freq array([ 0., 10., 20., 30., 40., 50.]) """ return ndarray() def rfftn(self, a=None, s=None, axes=None): """ Compute the N-dimensional discrete Fourier Transform for real input. This function computes the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional real array by means of the Fast Fourier Transform (FFT). By default, all axes are transformed, with the real transform performed over the last axis, while the remaining transforms are complex. Parameters ---------- a : array_like Input array, taken to be real. s : sequence of ints, optional Shape (length along each transformed axis) to use from the input. (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). The final element of `s` corresponds to `n` for ``rfft(x, n)``, while for the remaining axes, it corresponds to `n` for ``fft(x, n)``. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. if `s` is not given, the shape of the input (along the axes specified by `axes`) is used. axes : sequence of ints, optional Axes over which to compute the FFT. If not given, the last ``len(s)`` axes are used, or all axes if `s` is also not specified. Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` and `a`, as explained in the parameters section above. The length of the last axis transformed will be ``s[-1]//2+1``, while the remaining transformed axes will have lengths according to `s`, or unchanged from the input. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- irfftn : The inverse of `rfftn`, i.e. the inverse of the n-dimensional FFT of real input. fft : The one-dimensional FFT, with definitions and conventions used. rfft : The one-dimensional FFT of real input. fftn : The n-dimensional FFT. rfft2 : The two-dimensional FFT of real input. Notes ----- The transform for real input is performed over the last transformation axis, as by `rfft`, then the transform over the remaining axes is performed as by `fftn`. The order of the output is as for `rfft` for the final transformation axis, and as for `fftn` for the remaining transformation axes. See `fft` for details, definitions and conventions used. Examples -------- >>> a = np.ones((2, 2, 2)) >>> np.fft.rfftn(a) array([[[ 8.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]], [[ 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]]]) >>> np.fft.rfftn(a, axes=(2, 0)) array([[[ 4.+0.j, 0.+0.j], [ 4.+0.j, 0.+0.j]], [[ 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j]]]) """ return complex() def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() class linalg: class LinAlgError: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() args = getset_descriptor() message = getset_descriptor() class NoseTester: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _get_custom_doctester(self, _): """ Return instantiated plugin for doctests Allows subclassing of this class to override doctester A return value of None means use the nose builtin doctest plugin """ return None def _show_system_info(self, _): """None""" return None def _test_argv(self, label, verbose, extra_argv): """ Generate argv for nosetest command Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional see ``test`` docstring verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- argv : list command line arguments that will be passed to nose """ return list() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() excludes = list() def prepare_test_args(self=False, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False): """ Run tests for module using nose. This method does the heavy lifting for the `test` method. It takes all the same arguments, for details see `test`. See Also -------- test """ return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() __builtins__ = dict() __doc__ = str() __file__ = str() __name__ = str() __package__ = str() __path__ = list() absolute_import = instance() def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() def cholesky(self, a): """ Cholesky decomposition. Return the Cholesky decomposition, `L * L.H`, of the square matrix `a`, where `L` is lower-triangular and .H is the conjugate transpose operator (which is the ordinary transpose if `a` is real-valued). `a` must be Hermitian (symmetric if real-valued) and positive-definite. Only `L` is actually returned. Parameters ---------- a : (..., M, M) array_like Hermitian (symmetric if all elements are real), positive-definite input matrix. Returns ------- L : (..., M, M) array_like Upper or lower-triangular Cholesky factor of `a`. Returns a matrix object if `a` is a matrix object. Raises ------ LinAlgError If the decomposition fails, for example, if `a` is not positive-definite. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. The Cholesky decomposition is often used as a fast way of solving .. math:: A \mathbf{x} = \mathbf{b} (when `A` is both Hermitian/symmetric and positive-definite). First, we solve for :math:`\mathbf{y}` in .. math:: L \mathbf{y} = \mathbf{b}, and then for :math:`\mathbf{x}` in .. math:: L.H \mathbf{x} = \mathbf{y}. Examples -------- >>> A = np.array([[1,-2j],[2j,5]]) >>> A array([[ 1.+0.j, 0.-2.j], [ 0.+2.j, 5.+0.j]]) >>> L = np.linalg.cholesky(A) >>> L array([[ 1.+0.j, 0.+0.j], [ 0.+2.j, 1.+0.j]]) >>> np.dot(L, L.T.conj()) # verify that L * L.H = A array([[ 1.+0.j, 0.-2.j], [ 0.+2.j, 5.+0.j]]) >>> A = [[1,-2j],[2j,5]] # what happens if A is only array_like? >>> np.linalg.cholesky(A) # an ndarray object is returned array([[ 1.+0.j, 0.+0.j], [ 0.+2.j, 1.+0.j]]) >>> # But a matrix object is returned if A is a matrix object >>> LA.cholesky(np.matrix(A)) matrix([[ 1.+0.j, 0.+0.j], [ 0.+2.j, 1.+0.j]]) """ return more_args() def cond(self, x=None, p=None): """ Compute the condition number of a matrix. This function is capable of returning the condition number using one of seven different norms, depending on the value of `p` (see Parameters below). Parameters ---------- x : (M, N) array_like The matrix whose condition number is sought. p : {None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional Order of the norm: ===== ============================ p norm for matrices ===== ============================ None 2-norm, computed directly using the ``SVD`` 'fro' Frobenius norm inf max(sum(abs(x), axis=1)) -inf min(sum(abs(x), axis=1)) 1 max(sum(abs(x), axis=0)) -1 min(sum(abs(x), axis=0)) 2 2-norm (largest sing. value) -2 smallest singular value ===== ============================ inf means the numpy.inf object, and the Frobenius norm is the root-of-sum-of-squares norm. Returns ------- c : {float, inf} The condition number of the matrix. May be infinite. See Also -------- numpy.linalg.norm Notes ----- The condition number of `x` is defined as the norm of `x` times the norm of the inverse of `x` [1]_; the norm can be the usual L2-norm (root-of-sum-of-squares) or one of a number of other matrix norms. References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, Orlando, FL, Academic Press, Inc., 1980, pg. 285. Examples -------- >>> from numpy import linalg as LA >>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]]) >>> a array([[ 1, 0, -1], [ 0, 1, 0], [ 1, 0, 1]]) >>> LA.cond(a) 1.4142135623730951 >>> LA.cond(a, 'fro') 3.1622776601683795 >>> LA.cond(a, np.inf) 2.0 >>> LA.cond(a, -np.inf) 1.0 >>> LA.cond(a, 1) 2.0 >>> LA.cond(a, -1) 1.0 >>> LA.cond(a, 2) 1.4142135623730951 >>> LA.cond(a, -2) 0.70710678118654746 >>> min(LA.svd(a, compute_uv=0))*min(LA.svd(LA.inv(a), compute_uv=0)) 0.70710678118654746 """ return None def det(self, a): """ Compute the determinant of an array. Parameters ---------- a : (..., M, M) array_like Input array to compute determinants for. Returns ------- det : (...) array_like Determinant of `a`. See Also -------- slogdet : Another way to representing the determinant, more suitable for large matrices where underflow/overflow may occur. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. The determinant is computed via LU factorization using the LAPACK routine z/dgetrf. Examples -------- The determinant of a 2-D array [[a, b], [c, d]] is ad - bc: >>> a = np.array([[1, 2], [3, 4]]) >>> np.linalg.det(a) -2.0 Computing determinants for a stack of matrices: >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ]) >>> a.shape (2, 2, 2 >>> np.linalg.det(a) array([-2., -3., -8.]) """ return more_args() division = instance() def eig(self, a): """ Compute the eigenvalues and right eigenvectors of a square array. Parameters ---------- a : (..., M, M) array Matrices for which the eigenvalues and right eigenvectors will be computed Returns ------- w : (..., M) array The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be always be of complex type. When `a` is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs v : (..., M, M) array The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]``. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eigvalsh : eigenvalues of a symmetric or Hermitian (conjugate symmetric) array. eigvals : eigenvalues of a non-symmetric array. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. This is implemented using the _geev LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. The number `w` is an eigenvalue of `a` if there exists a vector `v` such that ``dot(a,v) = w * v``. Thus, the arrays `a`, `w`, and `v` satisfy the equations ``dot(a[:,:], v[:,i]) = w[i] * v[:,i]`` for :math:`i \in \{0,...,M-1\}`. The array `v` of eigenvectors may not be of maximum rank, that is, some of the columns may be linearly dependent, although round-off error may obscure that fact. If the eigenvalues are all different, then theoretically the eigenvectors are linearly independent. Likewise, the (complex-valued) matrix of eigenvectors `v` is unitary if the matrix `a` is normal, i.e., if ``dot(a, a.H) = dot(a.H, a)``, where `a.H` denotes the conjugate transpose of `a`. Finally, it is emphasized that `v` consists of the *right* (as in right-hand side) eigenvectors of `a`. A vector `y` satisfying ``dot(y.T, a) = z * y.T`` for some number `z` is called a *left* eigenvector of `a`, and, in general, the left and right eigenvectors of a matrix are not necessarily the (perhaps conjugate) transposes of each other. References ---------- G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, Various pp. Examples -------- >>> from numpy import linalg as LA (Almost) trivial example with real e-values and e-vectors. >>> w, v = LA.eig(np.diag((1, 2, 3))) >>> w; v array([ 1., 2., 3.]) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) Real matrix possessing complex e-values and e-vectors; note that the e-values are complex conjugates of each other. >>> w, v = LA.eig(np.array([[1, -1], [1, 1]])) >>> w; v array([ 1. + 1.j, 1. - 1.j]) array([[ 0.70710678+0.j , 0.70710678+0.j ], [ 0.00000000-0.70710678j, 0.00000000+0.70710678j]]) Complex-valued matrix with real e-values (but complex-valued e-vectors); note that a.conj().T = a, i.e., a is Hermitian. >>> a = np.array([[1, 1j], [-1j, 1]]) >>> w, v = LA.eig(a) >>> w; v array([ 2.00000000e+00+0.j, 5.98651912e-36+0.j]) # i.e., {2, 0} array([[ 0.00000000+0.70710678j, 0.70710678+0.j ], [ 0.70710678+0.j , 0.00000000+0.70710678j]]) Be careful about round-off error! >>> a = np.array([[1 + 1e-9, 0], [0, 1 - 1e-9]]) >>> # Theor. e-values are 1 +/- 1e-9 >>> w, v = LA.eig(a) >>> w; v array([ 1., 1.]) array([[ 1., 0.], [ 0., 1.]]) """ return None def eigh(self, a="L", UPLO="L"): """ Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix. Returns two objects, a 1-D array containing the eigenvalues of `a`, and a 2-D square array or matrix (depending on the input type) of the corresponding eigenvectors (in columns). Parameters ---------- A : (..., M, M) array Hermitian/Symmetric matrices whose eigenvalues and eigenvectors are to be computed. UPLO : {'L', 'U'}, optional Specifies whether the calculation is done with the lower triangular part of `a` ('L', default) or the upper triangular part ('U'). Returns ------- w : (..., M) ndarray The eigenvalues, not necessarily ordered. v : {(..., M, M) ndarray, (..., M, M) matrix} The column ``v[:, i]`` is the normalized eigenvector corresponding to the eigenvalue ``w[i]``. Will return a matrix object if `a` is a matrix object. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eigvalsh : eigenvalues of symmetric or Hermitian arrays. eig : eigenvalues and right eigenvectors for non-symmetric arrays. eigvals : eigenvalues of non-symmetric arrays. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. The eigenvalues/eigenvectors are computed using LAPACK routines _ssyevd, _heevd The eigenvalues of real symmetric or complex Hermitian matrices are always real. [1]_ The array `v` of (column) eigenvectors is unitary and `a`, `w`, and `v` satisfy the equations ``dot(a, v[:, i]) = w[i] * v[:, i]``. References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pg. 222. Examples -------- >>> from numpy import linalg as LA >>> a = np.array([[1, -2j], [2j, 5]]) >>> a array([[ 1.+0.j, 0.-2.j], [ 0.+2.j, 5.+0.j]]) >>> w, v = LA.eigh(a) >>> w; v array([ 0.17157288, 5.82842712]) array([[-0.92387953+0.j , -0.38268343+0.j ], [ 0.00000000+0.38268343j, 0.00000000-0.92387953j]]) >>> np.dot(a, v[:, 0]) - w[0] * v[:, 0] # verify 1st e-val/vec pair array([2.77555756e-17 + 0.j, 0. + 1.38777878e-16j]) >>> np.dot(a, v[:, 1]) - w[1] * v[:, 1] # verify 2nd e-val/vec pair array([ 0.+0.j, 0.+0.j]) >>> A = np.matrix(a) # what happens if input is a matrix object >>> A matrix([[ 1.+0.j, 0.-2.j], [ 0.+2.j, 5.+0.j]]) >>> w, v = LA.eigh(A) >>> w; v array([ 0.17157288, 5.82842712]) matrix([[-0.92387953+0.j , -0.38268343+0.j ], [ 0.00000000+0.38268343j, 0.00000000-0.92387953j]]) """ return more_args() def eigvals(self, a): """ Compute the eigenvalues of a general matrix. Main difference between `eigvals` and `eig`: the eigenvectors aren't returned. Parameters ---------- a : (..., M, M) array_like A complex- or real-valued matrix whose eigenvalues will be computed. Returns ------- w : (..., M,) ndarray The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eig : eigenvalues and right eigenvectors of general arrays eigvalsh : eigenvalues of symmetric or Hermitian arrays. eigh : eigenvalues and eigenvectors of symmetric/Hermitian arrays. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. This is implemented using the _geev LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays. Examples -------- Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, `Q`, and on the right by `Q.T` (the transpose of `Q`), preserves the eigenvalues of the "middle" matrix. In other words, if `Q` is orthogonal, then ``Q * A * Q.T`` has the same eigenvalues as ``A``: >>> from numpy import linalg as LA >>> x = np.random.random() >>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]]) >>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :]) (1.0, 1.0, 0.0) Now multiply a diagonal matrix by Q on one side and by Q.T on the other: >>> D = np.diag((-1,1)) >>> LA.eigvals(D) array([-1., 1.]) >>> A = np.dot(Q, D) >>> A = np.dot(A, Q.T) >>> LA.eigvals(A) array([ 1., -1.]) """ return more_args() def eigvalsh(self, a="L", UPLO="L"): """ Compute the eigenvalues of a Hermitian or real symmetric matrix. Main difference from eigh: the eigenvectors are not computed. Parameters ---------- a : (..., M, M) array_like A complex- or real-valued matrix whose eigenvalues are to be computed. UPLO : {'L', 'U'}, optional Same as `lower`, with 'L' for lower and 'U' for upper triangular. Deprecated. Returns ------- w : (..., M,) ndarray The eigenvalues, not necessarily ordered, each repeated according to its multiplicity. Raises ------ LinAlgError If the eigenvalue computation does not converge. See Also -------- eigh : eigenvalues and eigenvectors of symmetric/Hermitian arrays. eigvals : eigenvalues of general real or complex arrays. eig : eigenvalues and right eigenvectors of general real or complex arrays. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. The eigenvalues are computed using LAPACK routines _ssyevd, _heevd Examples -------- >>> from numpy import linalg as LA >>> a = np.array([[1, -2j], [2j, 5]]) >>> LA.eigvalsh(a) array([ 0.17157288+0.j, 5.82842712+0.j]) """ return more_args() def inv(self, a): """ Compute the (multiplicative) inverse of a matrix. Given a square matrix `a`, return the matrix `ainv` satisfying ``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])``. Parameters ---------- a : (..., M, M) array_like Matrix to be inverted. Returns ------- ainv : (..., M, M) ndarray or matrix (Multiplicative) inverse of the matrix `a`. Raises ------ LinAlgError If `a` is not square or inversion fails. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. Examples -------- >>> from numpy.linalg import inv >>> a = np.array([[1., 2.], [3., 4.]]) >>> ainv = inv(a) >>> np.allclose(np.dot(a, ainv), np.eye(2)) True >>> np.allclose(np.dot(ainv, a), np.eye(2)) True If a is a matrix object, then the return value is a matrix as well: >>> ainv = inv(np.matrix(a)) >>> ainv matrix([[-2. , 1. ], [ 1.5, -0.5]]) Inverses of several matrices can be computed at once: >>> a = np.array([[[1., 2.], [3., 4.]], [[1, 3], [3, 5]]]) >>> inv(a) array([[[-2. , 1. ], [ 1.5, -0.5]], [[-5. , 2. ], [ 3. , -1. ]]]) """ return more_args() if False else matrix() def lstsq(self, a, b=-1, rcond=-1): """ Return the least-squares solution to a linear matrix equation. Solves the equation `a x = b` by computing a vector `x` that minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may be under-, well-, or over- determined (i.e., the number of linearly independent rows of `a` can be less than, equal to, or greater than its number of linearly independent columns). If `a` is square and of full rank, then `x` (but for round-off error) is the "exact" solution of the equation. Parameters ---------- a : (M, N) array_like "Coefficient" matrix. b : {(M,), (M, K)} array_like Ordinate or "dependent variable" values. If `b` is two-dimensional, the least-squares solution is calculated for each of the `K` columns of `b`. rcond : float, optional Cut-off ratio for small singular values of `a`. Singular values are set to zero if they are smaller than `rcond` times the largest singular value of `a`. Returns ------- x : {(N,), (N, K)} ndarray Least-squares solution. If `b` is two-dimensional, the solutions are in the `K` columns of `x`. residuals : {(), (1,), (K,)} ndarray Sums of residuals; squared Euclidean 2-norm for each column in ``b - a*x``. If the rank of `a` is < N or > M, this is an empty array. If `b` is 1-dimensional, this is a (1,) shape array. Otherwise the shape is (K,). rank : int Rank of matrix `a`. s : (min(M, N),) ndarray Singular values of `a`. Raises ------ LinAlgError If computation does not converge. Notes ----- If `b` is a matrix, then all array results are returned as matrices. Examples -------- Fit a line, ``y = mx + c``, through some noisy data-points: >>> x = np.array([0, 1, 2, 3]) >>> y = np.array([-1, 0.2, 0.9, 2.1]) By examining the coefficients, we see that the line should have a gradient of roughly 1 and cut the y-axis at, more or less, -1. We can rewrite the line equation as ``y = Ap``, where ``A = [[x 1]]`` and ``p = [[m], [c]]``. Now use `lstsq` to solve for `p`: >>> A = np.vstack([x, np.ones(len(x))]).T >>> A array([[ 0., 1.], [ 1., 1.], [ 2., 1.], [ 3., 1.]]) >>> m, c = np.linalg.lstsq(A, y)[0] >>> print m, c 1.0 -0.95 Plot the data along with the fitted line: >>> import matplotlib.pyplot as plt >>> plt.plot(x, y, 'o', label='Original data', markersize=10) >>> plt.plot(x, m*x + c, 'r', label='Fitted line') >>> plt.legend() >>> plt.show() """ return N() def matrix_power(self, M, n): """ Raise a square matrix to the (integer) power `n`. For positive integers `n`, the power is computed by repeated matrix squarings and matrix multiplications. If ``n == 0``, the identity matrix of the same shape as M is returned. If ``n < 0``, the inverse is computed and then raised to the ``abs(n)``. Parameters ---------- M : ndarray or matrix object Matrix to be "powered." Must be square, i.e. ``M.shape == (m, m)``, with `m` a positive integer. n : int The exponent can be any integer or long integer, positive, negative, or zero. Returns ------- M**n : ndarray or matrix object The return value is the same shape and type as `M`; if the exponent is positive or zero then the type of the elements is the same as those of `M`. If the exponent is negative the elements are floating-point. Raises ------ LinAlgError If the matrix is not numerically invertible. See Also -------- matrix Provides an equivalent function as the exponentiation operator (``**``, not ``^``). Examples -------- >>> from numpy import linalg as LA >>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit >>> LA.matrix_power(i, 3) # should = -i array([[ 0, -1], [ 1, 0]]) >>> LA.matrix_power(np.matrix(i), 3) # matrix arg returns matrix matrix([[ 0, -1], [ 1, 0]]) >>> LA.matrix_power(i, 0) array([[1, 0], [0, 1]]) >>> LA.matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements array([[ 0., 1.], [-1., 0.]]) Somewhat more sophisticated example >>> q = np.zeros((4, 4)) >>> q[0:2, 0:2] = -i >>> q[2:4, 2:4] = i >>> q # one of the three quarternion units not equal to 1 array([[ 0., -1., 0., 0.], [ 1., 0., 0., 0.], [ 0., 0., 0., 1.], [ 0., 0., -1., 0.]]) >>> LA.matrix_power(q, 2) # = -np.eye(4) array([[-1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., -1.]]) """ return ndarray() if False else matrix() def matrix_rank(self, M=None, tol=None): """ Return matrix rank of array using SVD method Rank of the array is the number of SVD singular values of the array that are greater than `tol`. Parameters ---------- M : {(M,), (M, N)} array_like array of <=2 dimensions tol : {None, float}, optional threshold below which SVD values are considered zero. If `tol` is None, and ``S`` is an array with singular values for `M`, and ``eps`` is the epsilon value for datatype of ``S``, then `tol` is set to ``S.max() * max(M.shape) * eps``. Notes ----- The default threshold to detect rank deficiency is a test on the magnitude of the singular values of `M`. By default, we identify singular values less than ``S.max() * max(M.shape) * eps`` as indicating rank deficiency (with the symbols defined above). This is the algorithm MATLAB uses [1]. It also appears in *Numerical recipes* in the discussion of SVD solutions for linear least squares [2]. This default threshold is designed to detect rank deficiency accounting for the numerical errors of the SVD computation. Imagine that there is a column in `M` that is an exact (in floating point) linear combination of other columns in `M`. Computing the SVD on `M` will not produce a singular value exactly equal to 0 in general: any difference of the smallest SVD value from 0 will be caused by numerical imprecision in the calculation of the SVD. Our threshold for small SVD values takes this numerical imprecision into account, and the default threshold will detect such numerical rank deficiency. The threshold may declare a matrix `M` rank deficient even if the linear combination of some columns of `M` is not exactly equal to another column of `M` but only numerically very close to another column of `M`. We chose our default threshold because it is in wide use. Other thresholds are possible. For example, elsewhere in the 2007 edition of *Numerical recipes* there is an alternative threshold of ``S.max() * np.finfo(M.dtype).eps / 2. * np.sqrt(m + n + 1.)``. The authors describe this threshold as being based on "expected roundoff error" (p 71). The thresholds above deal with floating point roundoff error in the calculation of the SVD. However, you may have more information about the sources of error in `M` that would make you consider other tolerance values to detect *effective* rank deficiency. The most useful measure of the tolerance depends on the operations you intend to use on your matrix. For example, if your data come from uncertain measurements with uncertainties greater than floating point epsilon, choosing a tolerance near that uncertainty may be preferable. The tolerance may be absolute if the uncertainties are absolute rather than relative. References ---------- .. [1] MATLAB reference documention, "Rank" http://www.mathworks.com/help/techdoc/ref/rank.html .. [2] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, "Numerical Recipes (3rd edition)", Cambridge University Press, 2007, page 795. Examples -------- >>> from numpy.linalg import matrix_rank >>> matrix_rank(np.eye(4)) # Full rank matrix 4 >>> I=np.eye(4); I[-1,-1] = 0. # rank deficient matrix >>> matrix_rank(I) 3 >>> matrix_rank(np.ones((4,))) # 1 dimension - rank 1 unless all 0 1 >>> matrix_rank(np.zeros((4,))) 0 """ return None def norm(self, x=None, ord=None, axis=None): """ Matrix or vector norm. This function is able to return one of seven different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ``ord`` parameter. Parameters ---------- x : array_like Input array. If `axis` is None, `x` must be 1-D or 2-D. ord : {non-zero int, inf, -inf, 'fro'}, optional Order of the norm (see table under ``Notes``). inf means numpy's `inf` object. axis : {int, 2-tuple of ints, None}, optional If `axis` is an integer, it specifies the axis of `x` along which to compute the vector norms. If `axis` is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. If `axis` is None then either a vector norm (when `x` is 1-D) or a matrix norm (when `x` is 2-D) is returned. Returns ------- n : float or ndarray Norm of the matrix or vector(s). Notes ----- For values of ``ord <= 0``, the result is, strictly speaking, not a mathematical 'norm', but it may still be useful for various numerical purposes. The following norms can be calculated: ===== ============================ ========================== ord norm for matrices norm for vectors ===== ============================ ========================== None Frobenius norm 2-norm 'fro' Frobenius norm -- inf max(sum(abs(x), axis=1)) max(abs(x)) -inf min(sum(abs(x), axis=1)) min(abs(x)) 0 -- sum(x != 0) 1 max(sum(abs(x), axis=0)) as below -1 min(sum(abs(x), axis=0)) as below 2 2-norm (largest sing. value) as below -2 smallest singular value as below other -- sum(abs(x)**ord)**(1./ord) ===== ============================ ========================== The Frobenius norm is given by [1]_: :math:`||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}` References ---------- .. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*, Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15 Examples -------- >>> from numpy import linalg as LA >>> a = np.arange(9) - 4 >>> a array([-4, -3, -2, -1, 0, 1, 2, 3, 4]) >>> b = a.reshape((3, 3)) >>> b array([[-4, -3, -2], [-1, 0, 1], [ 2, 3, 4]]) >>> LA.norm(a) 7.745966692414834 >>> LA.norm(b) 7.745966692414834 >>> LA.norm(b, 'fro') 7.745966692414834 >>> LA.norm(a, np.inf) 4 >>> LA.norm(b, np.inf) 9 >>> LA.norm(a, -np.inf) 0 >>> LA.norm(b, -np.inf) 2 >>> LA.norm(a, 1) 20 >>> LA.norm(b, 1) 7 >>> LA.norm(a, -1) -4.6566128774142013e-010 >>> LA.norm(b, -1) 6 >>> LA.norm(a, 2) 7.745966692414834 >>> LA.norm(b, 2) 7.3484692283495345 >>> LA.norm(a, -2) nan >>> LA.norm(b, -2) 1.8570331885190563e-016 >>> LA.norm(a, 3) 5.8480354764257312 >>> LA.norm(a, -3) nan Using the `axis` argument to compute vector norms: >>> c = np.array([[ 1, 2, 3], ... [-1, 1, 4]]) >>> LA.norm(c, axis=0) array([ 1.41421356, 2.23606798, 5. ]) >>> LA.norm(c, axis=1) array([ 3.74165739, 4.24264069]) >>> LA.norm(c, ord=1, axis=1) array([6, 6]) Using the `axis` argument to compute matrix norms: >>> m = np.arange(8).reshape(2,2,2) >>> LA.norm(m, axis=(1,2)) array([ 3.74165739, 11.22497216]) >>> LA.norm(m[0, :, :]), LA.norm(m[1, :, :]) (3.7416573867739413, 11.224972160321824) """ return float() if False else ndarray() def pinv(self, a=1e-15, rcond=1e-15): """ Compute the (Moore-Penrose) pseudo-inverse of a matrix. Calculate the generalized inverse of a matrix using its singular-value decomposition (SVD) and including all *large* singular values. Parameters ---------- a : (M, N) array_like Matrix to be pseudo-inverted. rcond : float Cutoff for small singular values. Singular values smaller (in modulus) than `rcond` * largest_singular_value (again, in modulus) are set to zero. Returns ------- B : (N, M) ndarray The pseudo-inverse of `a`. If `a` is a `matrix` instance, then so is `B`. Raises ------ LinAlgError If the SVD computation does not converge. Notes ----- The pseudo-inverse of a matrix A, denoted :math:`A^+`, is defined as: "the matrix that 'solves' [the least-squares problem] :math:`Ax = b`," i.e., if :math:`\bar{x}` is said solution, then :math:`A^+` is that matrix such that :math:`\bar{x} = A^+b`. It can be shown that if :math:`Q_1 \Sigma Q_2^T = A` is the singular value decomposition of A, then :math:`A^+ = Q_2 \Sigma^+ Q_1^T`, where :math:`Q_{1,2}` are orthogonal matrices, :math:`\Sigma` is a diagonal matrix consisting of A's so-called singular values, (followed, typically, by zeros), and then :math:`\Sigma^+` is simply the diagonal matrix consisting of the reciprocals of A's singular values (again, followed by zeros). [1]_ References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pp. 139-142. Examples -------- The following example checks that ``a * a+ * a == a`` and ``a+ * a * a+ == a+``: >>> a = np.random.randn(9, 6) >>> B = np.linalg.pinv(a) >>> np.allclose(a, np.dot(a, np.dot(B, a))) True >>> np.allclose(B, np.dot(B, np.dot(a, B))) True """ return N() print_function = instance() def qr(self, a="reduced", mode="reduced"): """ Compute the qr factorization of a matrix. Factor the matrix `a` as *qr*, where `q` is orthonormal and `r` is upper-triangular. Parameters ---------- a : array_like, shape (M, N) Matrix to be factored. mode : {'reduced', 'complete', 'r', 'raw', 'full', 'economic'}, optional If K = min(M, N), then 'reduced' : returns q, r with dimensions (M, K), (K, N) (default) 'complete' : returns q, r with dimensions (M, M), (M, N) 'r' : returns r only with dimensions (K, N) 'raw' : returns h, tau with dimensions (N, M), (K,) 'full' : alias of 'reduced', deprecated 'economic' : returns h from 'raw', deprecated. The options 'reduced', 'complete, and 'raw' are new in numpy 1.8, see the notes for more information. The default is 'reduced' and to maintain backward compatibility with earlier versions of numpy both it and the old default 'full' can be omitted. Note that array h returned in 'raw' mode is transposed for calling Fortran. The 'economic' mode is deprecated. The modes 'full' and 'economic' may be passed using only the first letter for backwards compatibility, but all others must be spelled out. See the Notes for more explanation. Returns ------- q : ndarray of float or complex, optional A matrix with orthonormal columns. When mode = 'complete' the result is an orthogonal/unitary matrix depending on whether or not a is real/complex. The determinant may be either +/- 1 in that case. r : ndarray of float or complex, optional The upper-triangular matrix. (h, tau) : ndarrays of np.double or np.cdouble, optional The array h contains the Householder reflectors that generate q along with r. The tau array contains scaling factors for the reflectors. In the deprecated 'economic' mode only h is returned. Raises ------ LinAlgError If factoring fails. Notes ----- This is an interface to the LAPACK routines dgeqrf, zgeqrf, dorgqr, and zungqr. For more information on the qr factorization, see for example: http://en.wikipedia.org/wiki/QR_factorization Subclasses of `ndarray` are preserved except for the 'raw' mode. So if `a` is of type `matrix`, all the return values will be matrices too. New 'reduced', 'complete', and 'raw' options for mode were added in Numpy 1.8 and the old option 'full' was made an alias of 'reduced'. In addition the options 'full' and 'economic' were deprecated. Because 'full' was the previous default and 'reduced' is the new default, backward compatibility can be maintained by letting `mode` default. The 'raw' option was added so that LAPACK routines that can multiply arrays by q using the Householder reflectors can be used. Note that in this case the returned arrays are of type np.double or np.cdouble and the h array is transposed to be FORTRAN compatible. No routines using the 'raw' return are currently exposed by numpy, but some are available in lapack_lite and just await the necessary work. Examples -------- >>> a = np.random.randn(9, 6) >>> q, r = np.linalg.qr(a) >>> np.allclose(a, np.dot(q, r)) # a does equal qr True >>> r2 = np.linalg.qr(a, mode='r') >>> r3 = np.linalg.qr(a, mode='economic') >>> np.allclose(r, r2) # mode='r' returns the same r as mode='full' True >>> # But only triu parts are guaranteed equal when mode='economic' >>> np.allclose(r, np.triu(r3[:6,:6], k=0)) True Example illustrating a common use of `qr`: solving of least squares problems What are the least-squares-best `m` and `y0` in ``y = y0 + mx`` for the following data: {(0,1), (1,0), (1,2), (2,1)}. (Graph the points and you'll see that it should be y0 = 0, m = 1.) The answer is provided by solving the over-determined matrix equation ``Ax = b``, where:: A = array([[0, 1], [1, 1], [1, 1], [2, 1]]) x = array([[y0], [m]]) b = array([[1], [0], [2], [1]]) If A = qr such that q is orthonormal (which is always possible via Gram-Schmidt), then ``x = inv(r) * (q.T) * b``. (In numpy practice, however, we simply use `lstsq`.) >>> A = np.array([[0, 1], [1, 1], [1, 1], [2, 1]]) >>> A array([[0, 1], [1, 1], [1, 1], [2, 1]]) >>> b = np.array([1, 0, 2, 1]) >>> q, r = LA.qr(A) >>> p = np.dot(q.T, b) >>> np.dot(LA.inv(r), p) array([ 1.1e-16, 1.0e+00]) """ return ndarray() if False else complex() def slogdet(self, a): """ Compute the sign and (natural) logarithm of the determinant of an array. If an array has a very small or very large determinant, than a call to `det` may overflow or underflow. This routine is more robust against such issues, because it computes the logarithm of the determinant rather than the determinant itself. Parameters ---------- a : (..., M, M) array_like Input array, has to be a square 2-D array. Returns ------- sign : (...) array_like A number representing the sign of the determinant. For a real matrix, this is 1, 0, or -1. For a complex matrix, this is a complex number with absolute value 1 (i.e., it is on the unit circle), or else 0. logdet : (...) array_like The natural log of the absolute value of the determinant. If the determinant is zero, then `sign` will be 0 and `logdet` will be -Inf. In all cases, the determinant is equal to ``sign * np.exp(logdet)``. See Also -------- det Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. The determinant is computed via LU factorization using the LAPACK routine z/dgetrf. .. versionadded:: 1.6.0. Examples -------- The determinant of a 2-D array ``[[a, b], [c, d]]`` is ``ad - bc``: >>> a = np.array([[1, 2], [3, 4]]) >>> (sign, logdet) = np.linalg.slogdet(a) >>> (sign, logdet) (-1, 0.69314718055994529) >>> sign * np.exp(logdet) -2.0 Computing log-determinants for a stack of matrices: >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ]) >>> a.shape (3, 2, 2) >>> sign, logdet = np.linalg.slogdet(a) >>> (sign, logdet) (array([-1., -1., -1.]), array([ 0.69314718, 1.09861229, 2.07944154])) >>> sign * np.exp(logdet) array([-2., -3., -8.]) This routine succeeds where ordinary `det` does not: >>> np.linalg.det(np.eye(500) * 0.1) 0.0 >>> np.linalg.slogdet(np.eye(500) * 0.1) (1, -1151.2925464970228) """ return more_args() def solve(self, a, b): """ Solve a linear matrix equation, or system of linear scalar equations. Computes the "exact" solution, `x`, of the well-determined, i.e., full rank, linear matrix equation `ax = b`. Parameters ---------- a : (..., M, M) array_like Coefficient matrix. b : {(..., M,), (..., M, K)}, array_like Ordinate or "dependent variable" values. Returns ------- x : {(..., M,), (..., M, K)} ndarray Solution to the system a x = b. Returned shape is identical to `b`. Raises ------ LinAlgError If `a` is singular or not square. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. The solutions are computed using LAPACK routine _gesv `a` must be square and of full-rank, i.e., all rows (or, equivalently, columns) must be linearly independent; if either is not true, use `lstsq` for the least-squares best "solution" of the system/equation. References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pg. 22. Examples -------- Solve the system of equations ``3 * x0 + x1 = 9`` and ``x0 + 2 * x1 = 8``: >>> a = np.array([[3,1], [1,2]]) >>> b = np.array([9,8]) >>> x = np.linalg.solve(a, b) >>> x array([ 2., 3.]) Check that the solution is correct: >>> np.allclose(np.dot(a, x), b) True """ return more_args() def svd(self, a=1, full_matrices=1, compute_uv=1): """ Singular Value Decomposition. Factors the matrix `a` as ``u * np.diag(s) * v``, where `u` and `v` are unitary and `s` is a 1-d array of `a`'s singular values. Parameters ---------- a : (..., M, N) array_like A real or complex matrix of shape (`M`, `N`) . full_matrices : bool, optional If True (default), `u` and `v` have the shapes (`M`, `M`) and (`N`, `N`), respectively. Otherwise, the shapes are (`M`, `K`) and (`K`, `N`), respectively, where `K` = min(`M`, `N`). compute_uv : bool, optional Whether or not to compute `u` and `v` in addition to `s`. True by default. Returns ------- u : { (..., M, M), (..., M, K) } array Unitary matrices. The actual shape depends on the value of ``full_matrices``. Only returned when ``compute_uv`` is True. s : (..., K) array The singular values for every matrix, sorted in descending order. v : { (..., N, N), (..., K, N) } array Unitary matrices. The actual shape depends on the value of ``full_matrices``. Only returned when ``compute_uv`` is True. Raises ------ LinAlgError If SVD computation does not converge. Notes ----- Broadcasting rules apply, see the `numpy.linalg` documentation for details. The decomposition is performed using LAPACK routine _gesdd The SVD is commonly written as ``a = U S V.H``. The `v` returned by this function is ``V.H`` and ``u = U``. If ``U`` is a unitary matrix, it means that it satisfies ``U.H = inv(U)``. The rows of `v` are the eigenvectors of ``a.H a``. The columns of `u` are the eigenvectors of ``a a.H``. For row ``i`` in `v` and column ``i`` in `u`, the corresponding eigenvalue is ``s[i]**2``. If `a` is a `matrix` object (as opposed to an `ndarray`), then so are all the return values. Examples -------- >>> a = np.random.randn(9, 6) + 1j*np.random.randn(9, 6) Reconstruction based on full SVD: >>> U, s, V = np.linalg.svd(a, full_matrices=True) >>> U.shape, V.shape, s.shape ((9, 9), (6, 6), (6,)) >>> S = np.zeros((9, 6), dtype=complex) >>> S[:6, :6] = np.diag(s) >>> np.allclose(a, np.dot(U, np.dot(S, V))) True Reconstruction based on reduced SVD: >>> U, s, V = np.linalg.svd(a, full_matrices=False) >>> U.shape, V.shape, s.shape ((9, 6), (6, 6), (6,)) >>> S = np.diag(s) >>> np.allclose(a, np.dot(U, np.dot(S, V))) True """ return None def tensorinv(self, a=2, ind=2): """ Compute the 'inverse' of an N-dimensional array. The result is an inverse for `a` relative to the tensordot operation ``tensordot(a, b, ind)``, i. e., up to floating-point accuracy, ``tensordot(tensorinv(a), a, ind)`` is the "identity" tensor for the tensordot operation. Parameters ---------- a : array_like Tensor to 'invert'. Its shape must be 'square', i. e., ``prod(a.shape[:ind]) == prod(a.shape[ind:])``. ind : int, optional Number of first indices that are involved in the inverse sum. Must be a positive integer, default is 2. Returns ------- b : ndarray `a`'s tensordot inverse, shape ``a.shape[:ind] + a.shape[ind:]``. Raises ------ LinAlgError If `a` is singular or not 'square' (in the above sense). See Also -------- tensordot, tensorsolve Examples -------- >>> a = np.eye(4*6) >>> a.shape = (4, 6, 8, 3) >>> ainv = np.linalg.tensorinv(a, ind=2) >>> ainv.shape (8, 3, 4, 6) >>> b = np.random.randn(4, 6) >>> np.allclose(np.tensordot(ainv, b), np.linalg.tensorsolve(a, b)) True >>> a = np.eye(4*6) >>> a.shape = (24, 8, 3) >>> ainv = np.linalg.tensorinv(a, ind=1) >>> ainv.shape (8, 3, 24) >>> b = np.random.randn(24) >>> np.allclose(np.tensordot(ainv, b, 1), np.linalg.tensorsolve(a, b)) True """ return ndarray() def tensorsolve(self, a, b=None, axes=None): """ Solve the tensor equation ``a x = b`` for x. It is assumed that all indices of `x` are summed over in the product, together with the rightmost indices of `a`, as is done in, for example, ``tensordot(a, x, axes=len(b.shape))``. Parameters ---------- a : array_like Coefficient tensor, of shape ``b.shape + Q``. `Q`, a tuple, equals the shape of that sub-tensor of `a` consisting of the appropriate number of its rightmost indices, and must be such that ``prod(Q) == prod(b.shape)`` (in which sense `a` is said to be 'square'). b : array_like Right-hand tensor, which can be of any shape. axes : tuple of ints, optional Axes in `a` to reorder to the right, before inversion. If None (default), no reordering is done. Returns ------- x : ndarray, shape Q Raises ------ LinAlgError If `a` is singular or not 'square' (in the above sense). See Also -------- tensordot, tensorinv, einsum Examples -------- >>> a = np.eye(2*3*4) >>> a.shape = (2*3, 4, 2, 3, 4) >>> b = np.random.randn(2*3, 4) >>> x = np.linalg.tensorsolve(a, b) >>> x.shape (2, 3, 4) >>> np.allclose(np.tensordot(a, x, axes=3), b) True """ return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() class testing: class IgnoreException: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() args = getset_descriptor() message = getset_descriptor() class TestCase: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _addSkip(self, _): """None""" return None def _baseAssertEqual(self, first, second=None, msg=None): """The default assertEqual implementation, not type specific.""" return None _classSetupFailed = bool() def _deprecate(self, _): """None""" return None _diffThreshold = int() def _formatMessage(self, _): """Honour the longMessage attribute when generating failure messages. If longMessage is False this means: * Use only an explicit message if it is provided * Otherwise use the standard message for the assert If longMessage is True: * Use the standard message * If an explicit message is provided, plus ' : ' and the explicit message """ return None def _getAssertEqualityFunc(self, _): """Get a detailed comparison function for the types of the two args. Returns: A callable accepting (first, second, msg=None) that will raise a failure exception if first != second with a useful human readable error message for those types. """ return None def _truncateMessage(self, _): """None""" return None def addCleanup(self, _): """Add a function, with arguments, to be called when the test is completed. Functions added are called on a LIFO basis and are called after tearDown on test failure or success. Cleanup items are called even if setUp fails (unlike tearDown).""" return None def addTypeEqualityFunc(self, _): """Add a type specific assertEqual style function to compare a type. This method is for use by TestCase subclasses that need to register their own type equality functions to provide nicer error messages. Args: typeobj: The data type to call this function on when both values are of the same type in assertEqual(). function: The callable taking two arguments and an optional msg= argument that raises self.failureException with a useful error message when the two arguments are not equal. """ return None def assertAlmostEqual(self, first, second=None, places=None, msg=None, delta=None): """Fail if the two objects are unequal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the between the two objects is more than the given delta. Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit). If the two objects compare equal then they will automatically compare almost equal. """ return None def assertAlmostEqual(self, first, second=None, places=None, msg=None, delta=None): """Fail if the two objects are unequal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the between the two objects is more than the given delta. Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit). If the two objects compare equal then they will automatically compare almost equal. """ return None def assertDictContainsSubset(self, expected, actual=None, msg=None): """Checks whether actual is a superset of expected.""" return None def assertDictEqual(self, d1, d2=None, msg=None): """None""" return None def assertEqual(self, first, second=None, msg=None): """Fail if the two objects are unequal as determined by the '==' operator. """ return None def assertEqual(self, first, second=None, msg=None): """Fail if the two objects are unequal as determined by the '==' operator. """ return None def assertFalse(self, expr=None, msg=None): """Check that the expression is false.""" return None def assertGreater(self, a, b=None, msg=None): """Just like self.assertTrue(a > b), but with a nicer default message.""" return None def assertGreaterEqual(self, a, b=None, msg=None): """Just like self.assertTrue(a >= b), but with a nicer default message.""" return None def assertIn(self, member, container=None, msg=None): """Just like self.assertTrue(a in b), but with a nicer default message.""" return None def assertIs(self, expr1, expr2=None, msg=None): """Just like self.assertTrue(a is b), but with a nicer default message.""" return None def assertIsInstance(self, obj, cls=None, msg=None): """Same as self.assertTrue(isinstance(obj, cls)), with a nicer default message.""" return None def assertIsNone(self, obj=None, msg=None): """Same as self.assertTrue(obj is None), with a nicer default message.""" return None def assertIsNot(self, expr1, expr2=None, msg=None): """Just like self.assertTrue(a is not b), but with a nicer default message.""" return None def assertIsNotNone(self, obj=None, msg=None): """Included for symmetry with assertIsNone.""" return None def assertItemsEqual(self, expected_seq, actual_seq=None, msg=None): """An unordered sequence specific comparison. It asserts that actual_seq and expected_seq have the same element counts. Equivalent to:: self.assertEqual(Counter(iter(actual_seq)), Counter(iter(expected_seq))) Asserts that each element has the same count in both sequences. Example: - [0, 1, 1] and [1, 0, 1] compare equal. - [0, 0, 1] and [0, 1] compare unequal. """ return None def assertLess(self, a, b=None, msg=None): """Just like self.assertTrue(a < b), but with a nicer default message.""" return None def assertLessEqual(self, a, b=None, msg=None): """Just like self.assertTrue(a <= b), but with a nicer default message.""" return None def assertListEqual(self, list1, list2=None, msg=None): """A list-specific equality assertion. Args: list1: The first list to compare. list2: The second list to compare. msg: Optional message to use on failure instead of a list of differences. """ return None def assertMultiLineEqual(self, first, second=None, msg=None): """Assert that two multi-line strings are equal.""" return None def assertNotAlmostEqual(self, first, second=None, places=None, msg=None, delta=None): """Fail if the two objects are equal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the between the two objects is less than the given delta. Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit). Objects that are equal automatically fail. """ return None def assertNotAlmostEqual(self, first, second=None, places=None, msg=None, delta=None): """Fail if the two objects are equal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the between the two objects is less than the given delta. Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit). Objects that are equal automatically fail. """ return None def assertNotEqual(self, first, second=None, msg=None): """Fail if the two objects are equal as determined by the '!=' operator. """ return None def assertNotEqual(self, first, second=None, msg=None): """Fail if the two objects are equal as determined by the '!=' operator. """ return None def assertNotIn(self, member, container=None, msg=None): """Just like self.assertTrue(a not in b), but with a nicer default message.""" return None def assertNotIsInstance(self, obj, cls=None, msg=None): """Included for symmetry with assertIsInstance.""" return None def assertNotRegexpMatches(self, text, unexpected_regexp=None, msg=None): """Fail the test if the text matches the regular expression.""" return None def assertRaises(self, excClass=None, callableObj=None): """Fail unless an exception of class excClass is raised by callableObj when invoked with arguments args and keyword arguments kwargs. If a different type of exception is raised, it will not be caught, and the test case will be deemed to have suffered an error, exactly as for an unexpected exception. If called with callableObj omitted or None, will return a context object used like this:: with self.assertRaises(SomeException): do_something() The context manager keeps a reference to the exception as the 'exception' attribute. This allows you to inspect the exception after the assertion:: with self.assertRaises(SomeException) as cm: do_something() the_exception = cm.exception self.assertEqual(the_exception.error_code, 3) """ return None def assertRaisesRegexp(self, expected_exception, expected_regexp=None, callable_obj=None): """Asserts that the message in a raised exception matches a regexp. Args: expected_exception: Exception class expected to be raised. expected_regexp: Regexp (re pattern object or string) expected to be found in error message. callable_obj: Function to be called. args: Extra args. kwargs: Extra kwargs. """ return None def assertRegexpMatches(self, text, expected_regexp=None, msg=None): """Fail the test unless the text matches the regular expression.""" return None def assertSequenceEqual(self, seq1, seq2=None, msg=None, seq_type=None): """An equality assertion for ordered sequences (like lists and tuples). For the purposes of this function, a valid ordered sequence type is one which can be indexed, has a length, and has an equality operator. Args: seq1: The first sequence to compare. seq2: The second sequence to compare. seq_type: The expected datatype of the sequences, or None if no datatype should be enforced. msg: Optional message to use on failure instead of a list of differences. """ return None def assertSetEqual(self, set1, set2=None, msg=None): """A set-specific equality assertion. Args: set1: The first set to compare. set2: The second set to compare. msg: Optional message to use on failure instead of a list of differences. assertSetEqual uses ducktyping to support different types of sets, and is optimized for sets specifically (parameters must support a difference method). """ return None def assertTrue(self, expr=None, msg=None): """Check that the expression is true.""" return None def assertTupleEqual(self, tuple1, tuple2=None, msg=None): """A tuple-specific equality assertion. Args: tuple1: The first tuple to compare. tuple2: The second tuple to compare. msg: Optional message to use on failure instead of a list of differences. """ return None def assertTrue(self, expr=None, msg=None): """Check that the expression is true.""" return None def countTestCases(self, _): """None""" return None def debug(self, _): """Run the test without collecting errors in a TestResult""" return None def defaultTestResult(self, _): """None""" return None def doCleanups(self, _): """Execute all cleanup functions. Normally called for you after tearDown.""" return None def fail(self=None, msg=None): """Fail immediately, with the given message.""" return None def deprecated_func(self): """None""" return None def deprecated_func(self): """None""" return None def deprecated_func(self): """None""" return None def deprecated_func(self): """None""" return None def deprecated_func(self): """None""" return None def deprecated_func(self): """None""" return None def deprecated_func(self): """None""" return None def id(self, _): """None""" return None longMessage = bool() maxDiff = int() def run(self=None, result=None): """None""" return None def setUp(self, _): """Hook method for setting up the test fixture before exercising it.""" return None def setUpClass(self, _): """Hook method for setting up class fixture before running tests in the class.""" return None def shortDescription(self, _): """Returns a one-line description of the test, or None if no description has been provided. The default implementation of this method returns the first line of the specified test method's docstring. """ return None def skipTest(self, _): """Skip this test.""" return None def tearDown(self, _): """Hook method for deconstructing the test fixture after testing it.""" return None def tearDownClass(self, _): """Hook method for deconstructing the class fixture after running all tests in the class.""" return None class NoseTester: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _get_custom_doctester(self, _): """ Return instantiated plugin for doctests Allows subclassing of this class to override doctester A return value of None means use the nose builtin doctest plugin """ return None def _show_system_info(self, _): """None""" return None def _test_argv(self, label, verbose, extra_argv): """ Generate argv for nosetest command Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional see ``test`` docstring verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- argv : list command line arguments that will be passed to nose """ return list() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() excludes = list() def prepare_test_args(self=False, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False): """ Run tests for module using nose. This method does the heavy lifting for the `test` method. It takes all the same arguments, for details see `test`. See Also -------- test """ return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() __builtins__ = dict() __doc__ = str() __file__ = str() __name__ = str() __package__ = str() __path__ = list() absolute_import = instance() def assert_(self, val="", msg=""): """ Assert that works in release mode. The Python built-in ``assert`` does not work when executing code in optimized mode (the ``-O`` flag) - no byte-code is generated for it. For documentation on usage, refer to the Python documentation. """ return None def assert_allclose(self, actual, desired=True, rtol=1e-07, atol=0, err_msg="", verbose=True): """ Raise an assertion if two objects are not equal up to desired tolerance. The test is equivalent to ``allclose(actual, desired, rtol, atol)``. It compares the difference between `actual` and `desired` to ``atol + rtol * abs(desired)``. Parameters ---------- actual : array_like Array obtained. desired : array_like Array desired. rtol : float, optional Relative tolerance. atol : float, optional Absolute tolerance. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired are not equal up to specified precision. See Also -------- assert_array_almost_equal_nulp, assert_array_max_ulp Examples -------- >>> x = [1e-5, 1e-3, 1e-1] >>> y = np.arccos(np.cos(x)) >>> assert_allclose(x, y, rtol=1e-5, atol=0) """ return None def assert_almost_equal(self, actual, desired=True, decimal=7, err_msg="", verbose=True): """ Raise an assertion if two items are not equal up to desired precision. .. note:: It is recommended to use one of `assert_allclose`, `assert_array_almost_equal_nulp` or `assert_array_max_ulp` instead of this function for more consistent floating point comparisons. The test is equivalent to ``abs(desired-actual) < 0.5 * 10**(-decimal)``. Given two objects (numbers or ndarrays), check that all elements of these objects are almost equal. An exception is raised at conflicting values. For ndarrays this delegates to assert_array_almost_equal Parameters ---------- actual : array_like The object to check. desired : array_like The expected object. decimal : int, optional Desired precision, default is 7. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired are not equal up to specified precision. See Also -------- assert_allclose: Compare two array_like objects for equality with desired relative and/or absolute precision. assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal Examples -------- >>> import numpy.testing as npt >>> npt.assert_almost_equal(2.3333333333333, 2.33333334) >>> npt.assert_almost_equal(2.3333333333333, 2.33333334, decimal=10) ... : Items are not equal: ACTUAL: 2.3333333333333002 DESIRED: 2.3333333399999998 >>> npt.assert_almost_equal(np.array([1.0,2.3333333333333]), ... np.array([1.0,2.33333334]), decimal=9) ... : Arrays are not almost equal (mismatch 50.0%) x: array([ 1. , 2.33333333]) y: array([ 1. , 2.33333334]) """ return None def assert_approx_equal(self, actual, desired=True, significant=7, err_msg="", verbose=True): """ Raise an assertion if two items are not equal up to significant digits. .. note:: It is recommended to use one of `assert_allclose`, `assert_array_almost_equal_nulp` or `assert_array_max_ulp` instead of this function for more consistent floating point comparisons. Given two numbers, check that they are approximately equal. Approximately equal is defined as the number of significant digits that agree. Parameters ---------- actual : scalar The object to check. desired : scalar The expected object. significant : int, optional Desired precision, default is 7. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired are not equal up to specified precision. See Also -------- assert_allclose: Compare two array_like objects for equality with desired relative and/or absolute precision. assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal Examples -------- >>> np.testing.assert_approx_equal(0.12345677777777e-20, 0.1234567e-20) >>> np.testing.assert_approx_equal(0.12345670e-20, 0.12345671e-20, significant=8) >>> np.testing.assert_approx_equal(0.12345670e-20, 0.12345672e-20, significant=8) ... : Items are not equal to 8 significant digits: ACTUAL: 1.234567e-021 DESIRED: 1.2345672000000001e-021 the evaluated condition that raises the exception is >>> abs(0.12345670e-20/1e-21 - 0.12345672e-20/1e-21) >= 10**-(8-1) True """ return None def assert_array_almost_equal(self, x, y=True, decimal=6, err_msg="", verbose=True): """ Raise an assertion if two objects are not equal up to desired precision. .. note:: It is recommended to use one of `assert_allclose`, `assert_array_almost_equal_nulp` or `assert_array_max_ulp` instead of this function for more consistent floating point comparisons. The test verifies identical shapes and verifies values with ``abs(desired-actual) < 0.5 * 10**(-decimal)``. Given two array_like objects, check that the shape is equal and all elements of these objects are almost equal. An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions. Parameters ---------- x : array_like The actual object to check. y : array_like The desired, expected object. decimal : int, optional Desired precision, default is 6. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired are not equal up to specified precision. See Also -------- assert_allclose: Compare two array_like objects for equality with desired relative and/or absolute precision. assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal Examples -------- the first assert does not raise an exception >>> np.testing.assert_array_almost_equal([1.0,2.333,np.nan], [1.0,2.333,np.nan]) >>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan], ... [1.0,2.33339,np.nan], decimal=5) ... : AssertionError: Arrays are not almost equal (mismatch 50.0%) x: array([ 1. , 2.33333, NaN]) y: array([ 1. , 2.33339, NaN]) >>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan], ... [1.0,2.33333, 5], decimal=5) : ValueError: Arrays are not almost equal x: array([ 1. , 2.33333, NaN]) y: array([ 1. , 2.33333, 5. ]) """ return None def assert_array_almost_equal_nulp(self, x, y=1, nulp=1): """ Compare two arrays relatively to their spacing. This is a relatively robust method to compare two arrays whose amplitude is variable. Parameters ---------- x, y : array_like Input arrays. nulp : int, optional The maximum number of unit in the last place for tolerance (see Notes). Default is 1. Returns ------- None Raises ------ AssertionError If the spacing between `x` and `y` for one or more elements is larger than `nulp`. See Also -------- assert_array_max_ulp : Check that all items of arrays differ in at most N Units in the Last Place. spacing : Return the distance between x and the nearest adjacent number. Notes ----- An assertion is raised if the following condition is not met:: abs(x - y) <= nulps * spacing(max(abs(x), abs(y))) Examples -------- >>> x = np.array([1., 1e-10, 1e-20]) >>> eps = np.finfo(x.dtype).eps >>> np.testing.assert_array_almost_equal_nulp(x, x*eps/2 + x) >>> np.testing.assert_array_almost_equal_nulp(x, x*eps + x) ------------------------------------------------------------ Traceback (most recent call last): ... AssertionError: X and Y are not equal to 1 ULP (max is 2) """ return None def assert_array_equal(self, x, y=True, err_msg="", verbose=True): """ Raise an assertion if two array_like objects are not equal. Given two array_like objects, check that the shape is equal and all elements of these objects are equal. An exception is raised at shape mismatch or conflicting values. In contrast to the standard usage in numpy, NaNs are compared like numbers, no assertion is raised if both objects have NaNs in the same positions. The usual caution for verifying equality with floating point numbers is advised. Parameters ---------- x : array_like The actual object to check. y : array_like The desired, expected object. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired objects are not equal. See Also -------- assert_allclose: Compare two array_like objects for equality with desired relative and/or absolute precision. assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal Examples -------- The first assert does not raise an exception: >>> np.testing.assert_array_equal([1.0,2.33333,np.nan], ... [np.exp(0),2.33333, np.nan]) Assert fails with numerical inprecision with floats: >>> np.testing.assert_array_equal([1.0,np.pi,np.nan], ... [1, np.sqrt(np.pi)**2, np.nan]) ... : AssertionError: Arrays are not equal (mismatch 50.0%) x: array([ 1. , 3.14159265, NaN]) y: array([ 1. , 3.14159265, NaN]) Use `assert_allclose` or one of the nulp (number of floating point values) functions for these cases instead: >>> np.testing.assert_allclose([1.0,np.pi,np.nan], ... [1, np.sqrt(np.pi)**2, np.nan], ... rtol=1e-10, atol=0) """ return None def assert_array_less(self, x, y=True, err_msg="", verbose=True): """ Raise an assertion if two array_like objects are not ordered by less than. Given two array_like objects, check that the shape is equal and all elements of the first object are strictly smaller than those of the second object. An exception is raised at shape mismatch or incorrectly ordered values. Shape mismatch does not raise if an object has zero dimension. In contrast to the standard usage in numpy, NaNs are compared, no assertion is raised if both objects have NaNs in the same positions. Parameters ---------- x : array_like The smaller object to check. y : array_like The larger object to compare. err_msg : string The error message to be printed in case of failure. verbose : bool If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired objects are not equal. See Also -------- assert_array_equal: tests objects for equality assert_array_almost_equal: test objects for equality up to precision Examples -------- >>> np.testing.assert_array_less([1.0, 1.0, np.nan], [1.1, 2.0, np.nan]) >>> np.testing.assert_array_less([1.0, 1.0, np.nan], [1, 2.0, np.nan]) ... : Arrays are not less-ordered (mismatch 50.0%) x: array([ 1., 1., NaN]) y: array([ 1., 2., NaN]) >>> np.testing.assert_array_less([1.0, 4.0], 3) ... : Arrays are not less-ordered (mismatch 50.0%) x: array([ 1., 4.]) y: array(3) >>> np.testing.assert_array_less([1.0, 2.0, 3.0], [4]) ... : Arrays are not less-ordered (shapes (3,), (1,) mismatch) x: array([ 1., 2., 3.]) y: array([4]) """ return None def assert_array_max_ulp(self, a, b=None, maxulp=1, dtype=None): """ Check that all items of arrays differ in at most N Units in the Last Place. Parameters ---------- a, b : array_like Input arrays to be compared. maxulp : int, optional The maximum number of units in the last place that elements of `a` and `b` can differ. Default is 1. dtype : dtype, optional Data-type to convert `a` and `b` to if given. Default is None. Returns ------- ret : ndarray Array containing number of representable floating point numbers between items in `a` and `b`. Raises ------ AssertionError If one or more elements differ by more than `maxulp`. See Also -------- assert_array_almost_equal_nulp : Compare two arrays relatively to their spacing. Examples -------- >>> a = np.linspace(0., 1., 100) >>> res = np.testing.assert_array_max_ulp(a, np.arcsin(np.sin(a))) """ return ndarray() def assert_equal(self, actual, desired=True, err_msg="", verbose=True): """ Raise an assertion if two objects are not equal. Given two objects (scalars, lists, tuples, dictionaries or numpy arrays), check that all elements of these objects are equal. An exception is raised at the first conflicting values. Parameters ---------- actual : array_like The object to check. desired : array_like The expected object. err_msg : str, optional The error message to be printed in case of failure. verbose : bool, optional If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired are not equal. Examples -------- >>> np.testing.assert_equal([4,5], [4,6]) ... : Items are not equal: item=1 ACTUAL: 5 DESIRED: 6 """ return None def assert_no_warnings(self, func, ESCargs, ESCESCkwargs): """ Fail if the given callable produces any warnings. Parameters ---------- func : callable The callable to test. \*args : Arguments Arguments passed to `func`. \*\*kwargs : Kwargs Keyword arguments passed to `func`. Returns ------- The value returned by `func`. """ return None def assert__raises(self): """ assert_raises(exception_class, callable, *args, **kwargs) Fail unless an exception of class exception_class is thrown by callable when invoked with arguments args and keyword arguments kwargs. If a different type of exception is thrown, it will not be caught, and the test case will be deemed to have suffered an error, exactly as for an unexpected exception. """ return None def assert_string_equal(self, actual, desired): """ Test if two strings are equal. If the given strings are equal, `assert_string_equal` does nothing. If they are not equal, an AssertionError is raised, and the diff between the strings is shown. Parameters ---------- actual : str The string to test for equality against the expected string. desired : str The expected string. Examples -------- >>> np.testing.assert_string_equal('abc', 'abc') >>> np.testing.assert_string_equal('abc', 'abcd') Traceback (most recent call last): File "", line 1, in ... AssertionError: Differences in strings: - abc+ abcd? + """ return None def assert_warns(self, warning__class, func, ESCargs, ESCESCkwargs): """ Fail unless the given callable throws the specified warning. A warning of class warning_class should be thrown by the callable when invoked with arguments args and keyword arguments kwargs. If a different type of warning is thrown, it will not be caught, and the test case will be deemed to have suffered an error. Parameters ---------- warning_class : class The class defining the warning that `func` is expected to throw. func : callable The callable to test. \*args : Arguments Arguments passed to `func`. \*\*kwargs : Kwargs Keyword arguments passed to `func`. Returns ------- The value returned by `func`. """ return None def build_err_msg(self, arrays, err_msg="('ACTUAL', 'DESIRED')", header="Items are not equal:", verbose=True, names="('ACTUAL', 'DESIRED')"): """None""" return None def decorate_methods(cls, decorator=None, testmatch=None): """ Apply a decorator to all methods in a class matching a regular expression. The given decorator is applied to all public methods of `cls` that are matched by the regular expression `testmatch` (``testmatch.search(methodname)``). Methods that are private, i.e. start with an underscore, are ignored. Parameters ---------- cls : class Class whose methods to decorate. decorator : function Decorator to apply to methods testmatch : compiled regexp or str, optional The regular expression. Default value is None, in which case the nose default (``re.compile(r'(?:^|[\b_\.%s-])[Tt]est' % os.sep)``) is used. If `testmatch` is a string, it is compiled to a regular expression first. """ return None division = instance() def importall(self, _): """ `importall` is DEPRECATED and will be removed in numpy 1.9.0 Try recursively to import all subpackages under package. """ return None def jiffies(self, _proc_pid_stat="/proc/405/stat", _load_time="[]"): """ Return number of jiffies (1/100ths of a second) that this process has been scheduled in user mode. See man 5 proc. """ return None def measure(self, code_str=None, times=1, label=None): """ Return elapsed time for executing code in the namespace of the caller. The supplied code string is compiled with the Python builtin ``compile``. The precision of the timing is 10 milli-seconds. If the code will execute fast on this timescale, it can be executed many times to get reasonable timing accuracy. Parameters ---------- code_str : str The code to be timed. times : int, optional The number of times the code is executed. Default is 1. The code is only compiled once. label : str, optional A label to identify `code_str` with. This is passed into ``compile`` as the second argument (for run-time error messages). Returns ------- elapsed : float Total elapsed time in seconds for executing `code_str` `times` times. Examples -------- >>> etime = np.testing.measure('for i in range(1000): np.sqrt(i**2)', ... times=times) >>> print "Time for a single execution : ", etime / times, "s" Time for a single execution : 0.005 s """ return float() def memusage(self, _proc_pid_stat="/proc/405/stat"): """ Return virtual memory size in bytes of the running python. """ return None def print_assert_equal(self, test_string, actual, desired): """ Test if two objects are equal, and print an error message if test fails. The test is performed with ``actual == desired``. Parameters ---------- test_string : str The message supplied to AssertionError. actual : object The object to test for equality against `desired`. desired : object The expected result. Examples -------- >>> np.testing.print_assert_equal('Test XYZ of func xyz', [0, 1], [0, 1]) >>> np.testing.print_assert_equal('Test XYZ of func xyz', [0, 1], [0, 2]) Traceback (most recent call last): ... AssertionError: Test XYZ of func xyz failed ACTUAL: [0, 1] DESIRED: [0, 2] """ return None print_function = instance() def _raises(self): """None""" return None def rand(self): """Returns an array of random numbers with the given shape. This only uses the standard library, so it is useful for testing purposes. """ return None def run_module_suite(self, file_to_run=None): """None""" return None def rundocs(self, filename=None, raise_on_error=True): """ Run doctests found in the given file. By default `rundocs` raises an AssertionError on failure. Parameters ---------- filename : str The path to the file for which the doctests are run. raise_on_error : bool Whether to raise an AssertionError when a doctest fails. Default is True. Notes ----- The doctests can be run by the user/developer by adding the ``doctests`` argument to the ``test()`` call. For example, to run all tests (including doctests) for `numpy.lib`: >>> np.lib.test(doctests=True) #doctest: +SKIP """ return None def runstring(self, _): """None""" return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() verbose = int() class random: class RandomState: __doc__ = str() def beta(self, a, b, size): """ beta(a, b, size=None) The Beta distribution over ``[0, 1]``. The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function .. math:: f(x; a,b) = \frac{1}{B(\alpha, \beta)} x^{\alpha - 1} (1 - x)^{\beta - 1}, where the normalisation, B, is the beta function, .. math:: B(\alpha, \beta) = \int_0^1 t^{\alpha - 1} (1 - t)^{\beta - 1} dt. It is often seen in Bayesian inference and order statistics. Parameters ---------- a : float Alpha, non-negative. b : float Beta, non-negative. size : tuple of ints, optional The number of samples to draw. The output is packed according to the size given. Returns ------- out : ndarray Array of the given shape, containing values drawn from a Beta distribution. """ return ndarray() def binomial(self, n, p, size): """ binomial(n, p, size=None) Draw samples from a binomial distribution. Samples are drawn from a Binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. (n may be input as a float, but it is truncated to an integer in use) Parameters ---------- n : float (but truncated to an integer) parameter, >= 0. p : float parameter, >= 0 and <=1. size : {tuple, int} Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} where the values are all integers in [0, n]. See Also -------- scipy.stats.distributions.binom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Binomial distribution is .. math:: P(N) = \binom{n}{N}p^N(1-p)^{n-N}, where :math:`n` is the number of trials, :math:`p` is the probability of success, and :math:`N` is the number of successes. When estimating the standard error of a proportion in a population by using a random sample, the normal distribution works well unless the product p*n <=5, where p = population proportion estimate, and n = number of samples, in which case the binomial distribution is used instead. For example, a sample of 15 people shows 4 who are left handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4, so the binomial distribution should be used in this case. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics with R", Springer-Verlag, 2002. .. [2] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill, Fifth Edition, 2002. .. [3] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [4] Weisstein, Eric W. "Binomial Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/BinomialDistribution.html .. [5] Wikipedia, "Binomial-distribution", http://en.wikipedia.org/wiki/Binomial_distribution Examples -------- Draw samples from the distribution: >>> n, p = 10, .5 # number of trials, probability of each trial >>> s = np.random.binomial(n, p, 1000) # result of flipping a coin 10 times, tested 1000 times. A real world example. A company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of 0.1. All nine wells fail. What is the probability of that happening? Let's do 20,000 trials of the model, and count the number that generate zero positive results. >>> sum(np.random.binomial(9,0.1,20000)==0)/20000. answer = 0.38885, or 38%. """ return ndarray() def bytes(self, length): """ bytes(length) Return random bytes. Parameters ---------- length : int Number of random bytes. Returns ------- out : str String of length `length`. Examples -------- >>> np.random.bytes(10) ' eh\x85\x022SZ\xbf\xa4' #random """ return str() def chisquare(self, df, size): """ chisquare(df, size=None) Draw samples from a chi-square distribution. When `df` independent random variables, each with standard normal distributions (mean 0, variance 1), are squared and summed, the resulting distribution is chi-square (see Notes). This distribution is often used in hypothesis testing. Parameters ---------- df : int Number of degrees of freedom. size : tuple of ints, int, optional Size of the returned array. By default, a scalar is returned. Returns ------- output : ndarray Samples drawn from the distribution, packed in a `size`-shaped array. Raises ------ ValueError When `df` <= 0 or when an inappropriate `size` (e.g. ``size=-1``) is given. Notes ----- The variable obtained by summing the squares of `df` independent, standard normally distributed random variables: .. math:: Q = \sum_{i=0}^{\mathtt{df}} X^2_i is chi-square distributed, denoted .. math:: Q \sim \chi^2_k. The probability density function of the chi-squared distribution is .. math:: p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}, where :math:`\Gamma` is the gamma function, .. math:: \Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt. References ---------- `NIST/SEMATECH e-Handbook of Statistical Methods `_ Examples -------- >>> np.random.chisquare(2,4) array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) """ return ndarray() def choice(self, a, size, replace, p): """ choice(a, size=None, replace=True, p=None) Generates a random sample from a given 1-D array .. versionadded:: 1.7.0 Parameters ----------- a : 1-D array-like or int If an ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if a was np.arange(n) size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. replace : boolean, optional Whether the sample is with or without replacement p : 1-D array-like, optional The probabilities associated with each entry in a. If not given the sample assumes a uniform distribtion over all entries in a. Returns -------- samples : 1-D ndarray, shape (size,) The generated random samples Raises ------- ValueError If a is an int and less than zero, if a or p are not 1-dimensional, if a is an array-like of size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size See Also --------- randint, shuffle, permutation Examples --------- Generate a uniform random sample from np.arange(5) of size 3: >>> np.random.choice(5, 3) array([0, 3, 4]) >>> #This is equivalent to np.random.randint(0,5,3) Generate a non-uniform random sample from np.arange(5) of size 3: >>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0]) array([3, 3, 0]) Generate a uniform random sample from np.arange(5) of size 3 without replacement: >>> np.random.choice(5, 3, replace=False) array([3,1,0]) >>> #This is equivalent to np.random.shuffle(np.arange(5))[:3] Generate a non-uniform random sample from np.arange(5) of size 3 without replacement: >>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0]) array([2, 3, 0]) Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance: >>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher'] >>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3]) array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], dtype='|S11') """ return _1_D() def dirichlet(self, alpha, size): """ dirichlet(alpha, size=None) Draw samples from the Dirichlet distribution. Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. Dirichlet pdf is the conjugate prior of a multinomial in Bayesian inference. Parameters ---------- alpha : array Parameter of the distribution (k dimension for sample of dimension k). size : array Number of samples to draw. Returns ------- samples : ndarray, The drawn samples, of shape (alpha.ndim, size). Notes ----- .. math:: X \approx \prod_{i=1}^{k}{x^{\alpha_i-1}_i} Uses the following property for computation: for each dimension, draw a random sample y_i from a standard gamma generator of shape `alpha_i`, then :math:`X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, \ldots, y_n)` is Dirichlet distributed. References ---------- .. [1] David McKay, "Information Theory, Inference and Learning Algorithms," chapter 23, http://www.inference.phy.cam.ac.uk/mackay/ .. [2] Wikipedia, "Dirichlet distribution", http://en.wikipedia.org/wiki/Dirichlet_distribution Examples -------- Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces. >>> s = np.random.dirichlet((10, 5, 3), 20).transpose() >>> plt.barh(range(20), s[0]) >>> plt.barh(range(20), s[1], left=s[0], color='g') >>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r') >>> plt.title("Lengths of Strings") """ return ndarray() def exponential(self, scale, size): """ exponential(scale=1.0, size=None) Exponential distribution. Its probability density function is .. math:: f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}), for ``x > 0`` and 0 elsewhere. :math:`\beta` is the scale parameter, which is the inverse of the rate parameter :math:`\lambda = 1/\beta`. The rate parameter is an alternative, widely used parameterization of the exponential distribution [3]_. The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [1]_, or the time between page requests to Wikipedia [2]_. Parameters ---------- scale : float The scale parameter, :math:`\beta = 1/\lambda`. size : tuple of ints Number of samples to draw. The output is shaped according to `size`. References ---------- .. [1] Peyton Z. Peebles Jr., "Probability, Random Variables and Random Signal Principles", 4th ed, 2001, p. 57. .. [2] "Poisson Process", Wikipedia, http://en.wikipedia.org/wiki/Poisson_process .. [3] "Exponential Distribution, Wikipedia, http://en.wikipedia.org/wiki/Exponential_distribution """ return None def f(self, dfnum, dfden, size): """ f(dfnum, dfden, size=None) Draw samples from a F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters should be greater than zero. The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates. Parameters ---------- dfnum : float Degrees of freedom in numerator. Should be greater than zero. dfden : float Degrees of freedom in denominator. Should be greater than zero. size : {tuple, int}, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. By default only one sample is returned. Returns ------- samples : {ndarray, scalar} Samples from the Fisher distribution. See Also -------- scipy.stats.distributions.f : probability density function, distribution or cumulative density function, etc. Notes ----- The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable `dfnum` is the number of samples minus one, the between-groups degrees of freedom, while `dfden` is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups. References ---------- .. [1] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill, Fifth Edition, 2002. .. [2] Wikipedia, "F-distribution", http://en.wikipedia.org/wiki/F-distribution Examples -------- An example from Glantz[1], pp 47-40. Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children's blood glucose levels? Calculating the F statistic from the data gives a value of 36.01. Draw samples from the distribution: >>> dfnum = 1. # between group degrees of freedom >>> dfden = 48. # within groups degrees of freedom >>> s = np.random.f(dfnum, dfden, 1000) The lower bound for the top 1% of the samples is : >>> sort(s)[-10] 7.61988120985 So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level. """ return ndarray() def gamma(self, shape, scale, size): """ gamma(shape, scale=1.0, size=None) Draw samples from a Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, `shape` (sometimes designated "k") and `scale` (sometimes designated "theta"), where both parameters are > 0. Parameters ---------- shape : scalar > 0 The shape of the gamma distribution. scale : scalar > 0, optional The scale of the gamma distribution. Default is equal to 1. size : shape_tuple, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- out : ndarray, float Returns one sample unless `size` parameter is specified. See Also -------- scipy.stats.distributions.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma-distribution", http://en.wikipedia.org/wiki/Gamma-distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 2. # mean and dispersion >>> s = np.random.gamma(shape, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> y = bins**(shape-1)*(np.exp(-bins/scale) / ... (sps.gamma(shape)*scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') >>> plt.show() """ return ndarray() def geometric(self, p, size): """ geometric(p, size=None) Draw samples from the geometric distribution. Bernoulli trials are experiments with one of two outcomes: success or failure (an example of such an experiment is flipping a coin). The geometric distribution models the number of trials that must be run in order to achieve success. It is therefore supported on the positive integers, ``k = 1, 2, ...``. The probability mass function of the geometric distribution is .. math:: f(k) = (1 - p)^{k - 1} p where `p` is the probability of success of an individual trial. Parameters ---------- p : float The probability of success of an individual trial. size : tuple of ints Number of values to draw from the distribution. The output is shaped according to `size`. Returns ------- out : ndarray Samples from the geometric distribution, shaped according to `size`. Examples -------- Draw ten thousand values from the geometric distribution, with the probability of an individual success equal to 0.35: >>> z = np.random.geometric(p=0.35, size=10000) How many trials succeeded after a single run? >>> (z == 1).sum() / 10000. 0.34889999999999999 #random """ return ndarray() def get_state(self, _): """ get_state() Return a tuple representing the internal state of the generator. For more details, see `set_state`. Returns ------- out : tuple(str, ndarray of 624 uints, int, int, float) The returned tuple has the following items: 1. the string 'MT19937'. 2. a 1-D array of 624 unsigned integer keys. 3. an integer ``pos``. 4. an integer ``has_gauss``. 5. a float ``cached_gaussian``. See Also -------- set_state Notes ----- `set_state` and `get_state` are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing. """ return None def gumbel(self, loc, scale, size): """ gumbel(loc=0.0, scale=1.0, size=None) Gumbel distribution. Draw samples from a Gumbel distribution with specified location and scale. For more information on the Gumbel distribution, see Notes and References below. Parameters ---------- loc : float The location of the mode of the distribution. scale : float The scale parameter of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- out : ndarray The samples See Also -------- scipy.stats.gumbel_l scipy.stats.gumbel_r scipy.stats.genextreme probability density function, distribution, or cumulative density function, etc. for each of the above weibull Notes ----- The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value Type I) distribution is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The Gumbel is a special case of the Extreme Value Type I distribution for maximums from distributions with "exponential-like" tails. The probability density for the Gumbel distribution is .. math:: p(x) = \frac{e^{-(x - \mu)/ \beta}}{\beta} e^{ -e^{-(x - \mu)/ \beta}}, where :math:`\mu` is the mode, a location parameter, and :math:`\beta` is the scale parameter. The Gumbel (named for German mathematician Emil Julius Gumbel) was used very early in the hydrology literature, for modeling the occurrence of flood events. It is also used for modeling maximum wind speed and rainfall rates. It is a "fat-tailed" distribution - the probability of an event in the tail of the distribution is larger than if one used a Gaussian, hence the surprisingly frequent occurrence of 100-year floods. Floods were initially modeled as a Gaussian process, which underestimated the frequency of extreme events. It is one of a class of extreme value distributions, the Generalized Extreme Value (GEV) distributions, which also includes the Weibull and Frechet. The function has a mean of :math:`\mu + 0.57721\beta` and a variance of :math:`\frac{\pi^2}{6}\beta^2`. References ---------- Gumbel, E. J., *Statistics of Extremes*, New York: Columbia University Press, 1958. Reiss, R.-D. and Thomas, M., *Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields*, Basel: Birkhauser Verlag, 2001. Examples -------- Draw samples from the distribution: >>> mu, beta = 0, 0.1 # location and scale >>> s = np.random.gumbel(mu, beta, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, normed=True) >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp( -np.exp( -(bins - mu) /beta) ), ... linewidth=2, color='r') >>> plt.show() Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian: >>> means = [] >>> maxima = [] >>> for i in range(0,1000) : ... a = np.random.normal(mu, beta, 1000) ... means.append(a.mean()) ... maxima.append(a.max()) >>> count, bins, ignored = plt.hist(maxima, 30, normed=True) >>> beta = np.std(maxima)*np.pi/np.sqrt(6) >>> mu = np.mean(maxima) - 0.57721*beta >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp(-np.exp(-(bins - mu)/beta)), ... linewidth=2, color='r') >>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi)) ... * np.exp(-(bins - mu)**2 / (2 * beta**2)), ... linewidth=2, color='g') >>> plt.show() """ return ndarray() def hypergeometric(self, ngood, nbad, nsample, size): """ hypergeometric(ngood, nbad, nsample, size=None) Draw samples from a Hypergeometric distribution. Samples are drawn from a Hypergeometric distribution with specified parameters, ngood (ways to make a good selection), nbad (ways to make a bad selection), and nsample = number of items sampled, which is less than or equal to the sum ngood + nbad. Parameters ---------- ngood : int or array_like Number of ways to make a good selection. Must be nonnegative. nbad : int or array_like Number of ways to make a bad selection. Must be nonnegative. nsample : int or array_like Number of items sampled. Must be at least 1 and at most ``ngood + nbad``. size : int or tuple of int Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : ndarray or scalar The values are all integers in [0, n]. See Also -------- scipy.stats.distributions.hypergeom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Hypergeometric distribution is .. math:: P(x) = \frac{\binom{m}{n}\binom{N-m}{n-x}}{\binom{N}{n}}, where :math:`0 \le x \le m` and :math:`n+m-N \le x \le n` for P(x) the probability of x successes, n = ngood, m = nbad, and N = number of samples. Consider an urn with black and white marbles in it, ngood of them black and nbad are white. If you draw nsample balls without replacement, then the Hypergeometric distribution describes the distribution of black balls in the drawn sample. Note that this distribution is very similar to the Binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the Binomial. References ---------- .. [1] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [2] Weisstein, Eric W. "Hypergeometric Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HypergeometricDistribution.html .. [3] Wikipedia, "Hypergeometric-distribution", http://en.wikipedia.org/wiki/Hypergeometric-distribution Examples -------- Draw samples from the distribution: >>> ngood, nbad, nsamp = 100, 2, 10 # number of good, number of bad, and number of samples >>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000) >>> hist(s) # note that it is very unlikely to grab both bad items Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color? >>> s = np.random.hypergeometric(15, 15, 15, 100000) >>> sum(s>=12)/100000. + sum(s<=3)/100000. # answer = 0.003 ... pretty unlikely! """ return ndarray() if False else float() def laplace(self, loc, scale): """ laplace(loc=0.0, scale=1.0, size=None) Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables. Parameters ---------- loc : float The position, :math:`\mu`, of the distribution peak. scale : float :math:`\lambda`, the exponential decay. Notes ----- It has the probability density function .. math:: f(x; \mu, \lambda) = \frac{1}{2\lambda} \exp\left(-\frac{|x - \mu|}{\lambda}\right). The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in Economics and Health sciences, this distribution seems to model the data better than the standard Gaussian distribution References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972. .. [2] The Laplace distribution and generalizations By Samuel Kotz, Tomasz J. Kozubowski, Krzysztof Podgorski, Birkhauser, 2001. .. [3] Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LaplaceDistribution.html .. [4] Wikipedia, "Laplace distribution", http://en.wikipedia.org/wiki/Laplace_distribution Examples -------- Draw samples from the distribution >>> loc, scale = 0., 1. >>> s = np.random.laplace(loc, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, normed=True) >>> x = np.arange(-8., 8., .01) >>> pdf = np.exp(-abs(x-loc/scale))/(2.*scale) >>> plt.plot(x, pdf) Plot Gaussian for comparison: >>> g = (1/(scale * np.sqrt(2 * np.pi)) * ... np.exp( - (x - loc)**2 / (2 * scale**2) )) >>> plt.plot(x,g) """ return None def logistic(self, loc, scale, size): """ logistic(loc=0.0, scale=1.0, size=None) Draw samples from a Logistic distribution. Samples are drawn from a Logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0). Parameters ---------- loc : float scale : float > 0. size : {tuple, int} Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} where the values are all integers in [0, n]. See Also -------- scipy.stats.distributions.logistic : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Logistic distribution is .. math:: P(x) = P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2}, where :math:`\mu` = location and :math:`s` = scale. The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable. References ---------- .. [1] Reiss, R.-D. and Thomas M. (2001), Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields, Birkhauser Verlag, Basel, pp 132-133. .. [2] Weisstein, Eric W. "Logistic Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LogisticDistribution.html .. [3] Wikipedia, "Logistic-distribution", http://en.wikipedia.org/wiki/Logistic-distribution Examples -------- Draw samples from the distribution: >>> loc, scale = 10, 1 >>> s = np.random.logistic(loc, scale, 10000) >>> count, bins, ignored = plt.hist(s, bins=50) # plot against distribution >>> def logist(x, loc, scale): ... return exp((loc-x)/scale)/(scale*(1+exp((loc-x)/scale))**2) >>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\ ... logist(bins, loc, scale).max()) >>> plt.show() """ return ndarray() def lognormal(self, mean, sigma, size): """ lognormal(mean=0.0, sigma=1.0, size=None) Return samples drawn from a log-normal distribution. Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from. Parameters ---------- mean : float Mean value of the underlying normal distribution sigma : float, > 0. Standard deviation of the underlying normal distribution size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : ndarray or float The desired samples. An array of the same shape as `size` if given, if `size` is None a float is returned. See Also -------- scipy.stats.lognorm : probability density function, distribution, cumulative density function, etc. Notes ----- A variable `x` has a log-normal distribution if `log(x)` is normally distributed. The probability density function for the log-normal distribution is: .. math:: p(x) = \frac{1}{\sigma x \sqrt{2\pi}} e^{(-\frac{(ln(x)-\mu)^2}{2\sigma^2})} where :math:`\mu` is the mean and :math:`\sigma` is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the *product* of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the *sum* of a large number of independent, identically-distributed variables. References ---------- Limpert, E., Stahel, W. A., and Abbt, M., "Log-normal Distributions across the Sciences: Keys and Clues," *BioScience*, Vol. 51, No. 5, May, 2001. http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf Reiss, R.D. and Thomas, M., *Statistical Analysis of Extreme Values*, Basel: Birkhauser Verlag, 2001, pp. 31-32. Examples -------- Draw samples from the distribution: >>> mu, sigma = 3., 1. # mean and standard deviation >>> s = np.random.lognormal(mu, sigma, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='mid') >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, linewidth=2, color='r') >>> plt.axis('tight') >>> plt.show() Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function. >>> # Generate a thousand samples: each is the product of 100 random >>> # values, drawn from a normal distribution. >>> b = [] >>> for i in range(1000): ... a = 10. + np.random.random(100) ... b.append(np.product(a)) >>> b = np.array(b) / np.min(b) # scale values to be positive >>> count, bins, ignored = plt.hist(b, 100, normed=True, align='center') >>> sigma = np.std(np.log(b)) >>> mu = np.mean(np.log(b)) >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, color='r', linewidth=2) >>> plt.show() """ return ndarray() if False else float() def logseries(self, loc, scale, size): """ logseries(p, size=None) Draw samples from a Logarithmic Series distribution. Samples are drawn from a Log Series distribution with specified parameter, p (probability, 0 < p < 1). Parameters ---------- loc : float scale : float > 0. size : {tuple, int} Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} where the values are all integers in [0, n]. See Also -------- scipy.stats.distributions.logser : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Log Series distribution is .. math:: P(k) = \frac{-p^k}{k \ln(1-p)}, where p = probability. The Log Series distribution is frequently used to represent species richness and occurrence, first proposed by Fisher, Corbet, and Williams in 1943 [2]. It may also be used to model the numbers of occupants seen in cars [3]. References ---------- .. [1] Buzas, Martin A.; Culver, Stephen J., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9). .. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58. .. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small Data Sets, CRC Press, 1994. .. [4] Wikipedia, "Logarithmic-distribution", http://en.wikipedia.org/wiki/Logarithmic-distribution Examples -------- Draw samples from the distribution: >>> a = .6 >>> s = np.random.logseries(a, 10000) >>> count, bins, ignored = plt.hist(s) # plot against distribution >>> def logseries(k, p): ... return -p**k/(k*log(1-p)) >>> plt.plot(bins, logseries(bins, a)*count.max()/ logseries(bins, a).max(), 'r') >>> plt.show() """ return ndarray() def multinomial(self, n, pvals, size): """ multinomial(n, pvals, size=None) Draw samples from a multinomial distribution. The multinomial distribution is a multivariate generalisation of the binomial distribution. Take an experiment with one of ``p`` possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents `n` such experiments. Its values, ``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the outcome was ``i``. Parameters ---------- n : int Number of experiments. pvals : sequence of floats, length p Probabilities of each of the ``p`` different outcomes. These should sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as ``sum(pvals[:-1]) <= 1)``. size : tuple of ints Given a `size` of ``(M, N, K)``, then ``M*N*K`` samples are drawn, and the output shape becomes ``(M, N, K, p)``, since each sample has shape ``(p,)``. Examples -------- Throw a dice 20 times: >>> np.random.multinomial(20, [1/6.]*6, size=1) array([[4, 1, 7, 5, 2, 1]]) It landed 4 times on 1, once on 2, etc. Now, throw the dice 20 times, and 20 times again: >>> np.random.multinomial(20, [1/6.]*6, size=2) array([[3, 4, 3, 3, 4, 3], [2, 4, 3, 4, 0, 7]]) For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc. A loaded dice is more likely to land on number 6: >>> np.random.multinomial(100, [1/7.]*5) array([13, 16, 13, 16, 42]) """ return None def multivariate_normal(self, mean, cov, size): """ multivariate_normal(mean, cov[, size]) Draw random samples from a multivariate normal distribution. The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Such a distribution is specified by its mean and covariance matrix. These parameters are analogous to the mean (average or "center") and variance (standard deviation, or "width," squared) of the one-dimensional normal distribution. Parameters ---------- mean : 1-D array_like, of length N Mean of the N-dimensional distribution. cov : 2-D array_like, of shape (N, N) Covariance matrix of the distribution. Must be symmetric and positive semi-definite for "physically meaningful" results. size : int or tuple of ints, optional Given a shape of, for example, ``(m,n,k)``, ``m*n*k`` samples are generated, and packed in an `m`-by-`n`-by-`k` arrangement. Because each sample is `N`-dimensional, the output shape is ``(m,n,k,N)``. If no shape is specified, a single (`N`-D) sample is returned. Returns ------- out : ndarray The drawn samples, of shape *size*, if that was provided. If not, the shape is ``(N,)``. In other words, each entry ``out[i,j,...,:]`` is an N-dimensional value drawn from the distribution. Notes ----- The mean is a coordinate in N-dimensional space, which represents the location where samples are most likely to be generated. This is analogous to the peak of the bell curve for the one-dimensional or univariate normal distribution. Covariance indicates the level to which two variables vary together. From the multivariate normal distribution, we draw N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]`. The covariance matrix element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance of :math:`x_i` (i.e. its "spread"). Instead of specifying the full covariance matrix, popular approximations include: - Spherical covariance (*cov* is a multiple of the identity matrix) - Diagonal covariance (*cov* has non-negative elements, and only on the diagonal) This geometrical property can be seen in two dimensions by plotting generated data-points: >>> mean = [0,0] >>> cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis >>> import matplotlib.pyplot as plt >>> x,y = np.random.multivariate_normal(mean,cov,5000).T >>> plt.plot(x,y,'x'); plt.axis('equal'); plt.show() Note that the covariance matrix must be non-negative definite. References ---------- Papoulis, A., *Probability, Random Variables, and Stochastic Processes*, 3rd ed., New York: McGraw-Hill, 1991. Duda, R. O., Hart, P. E., and Stork, D. G., *Pattern Classification*, 2nd ed., New York: Wiley, 2001. Examples -------- >>> mean = (1,2) >>> cov = [[1,0],[1,0]] >>> x = np.random.multivariate_normal(mean,cov,(3,3)) >>> x.shape (3, 3, 2) The following is probably true, given that 0.6 is roughly twice the standard deviation: >>> print list( (x[0,0,:] - mean) < 0.6 ) [True, True] """ return ndarray() def negative_binomial(self, n, p, size): """ negative_binomial(n, p, size=None) Draw samples from a negative_binomial distribution. Samples are drawn from a negative_Binomial distribution with specified parameters, `n` trials and `p` probability of success where `n` is an integer > 0 and `p` is in the interval [0, 1]. Parameters ---------- n : int Parameter, > 0. p : float Parameter, >= 0 and <=1. size : int or tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : int or ndarray of ints Drawn samples. Notes ----- The probability density for the Negative Binomial distribution is .. math:: P(N;n,p) = \binom{N+n-1}{n-1}p^{n}(1-p)^{N}, where :math:`n-1` is the number of successes, :math:`p` is the probability of success, and :math:`N+n-1` is the number of trials. The negative binomial distribution gives the probability of n-1 successes and N failures in N+n-1 trials, and success on the (N+n)th trial. If one throws a die repeatedly until the third time a "1" appears, then the probability distribution of the number of non-"1"s that appear before the third "1" is a negative binomial distribution. References ---------- .. [1] Weisstein, Eric W. "Negative Binomial Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NegativeBinomialDistribution.html .. [2] Wikipedia, "Negative binomial distribution", http://en.wikipedia.org/wiki/Negative_binomial_distribution Examples -------- Draw samples from the distribution: A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.? >>> s = np.random.negative_binomial(1, 0.1, 100000) >>> for i in range(1, 11): ... probability = sum(s= 1. nonc : float Non-centrality, should be > 0. size : int or tuple of ints Shape of the output. Notes ----- The probability density function for the noncentral Chi-square distribution is .. math:: P(x;df,nonc) = \sum^{\infty}_{i=0} \frac{e^{-nonc/2}(nonc/2)^{i}}{i!}P_{Y_{df+2i}}(x), where :math:`Y_{q}` is the Chi-square with q degrees of freedom. In Delhi (2007), it is noted that the noncentral chi-square is useful in bombing and coverage problems, the probability of killing the point target given by the noncentral chi-squared distribution. References ---------- .. [1] Delhi, M.S. Holla, "On a noncentral chi-square distribution in the analysis of weapon systems effectiveness", Metrika, Volume 15, Number 1 / December, 1970. .. [2] Wikipedia, "Noncentral chi-square distribution" http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution Examples -------- Draw values from the distribution and plot the histogram >>> import matplotlib.pyplot as plt >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000), ... bins=200, normed=True) >>> plt.show() Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare. >>> plt.figure() >>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000), ... bins=np.arange(0., 25, .1), normed=True) >>> values2 = plt.hist(np.random.chisquare(3, 100000), ... bins=np.arange(0., 25, .1), normed=True) >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob') >>> plt.show() Demonstrate how large values of non-centrality lead to a more symmetric distribution. >>> plt.figure() >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000), ... bins=200, normed=True) >>> plt.show() """ return None def noncentral_f(self, dfnum, dfden, nonc, size): """ noncentral_f(dfnum, dfden, nonc, size=None) Draw samples from the noncentral F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters > 1. `nonc` is the non-centrality parameter. Parameters ---------- dfnum : int Parameter, should be > 1. dfden : int Parameter, should be > 1. nonc : float Parameter, should be >= 0. size : int or tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : scalar or ndarray Drawn samples. Notes ----- When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic. References ---------- Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html Wikipedia, "Noncentral F distribution", http://en.wikipedia.org/wiki/Noncentral_F-distribution Examples -------- In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We'll plot the two probability distributions for comparison. >>> dfnum = 3 # between group deg of freedom >>> dfden = 20 # within groups degrees of freedom >>> nonc = 3.0 >>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000) >>> NF = np.histogram(nc_vals, bins=50, normed=True) >>> c_vals = np.random.f(dfnum, dfden, 1000000) >>> F = np.histogram(c_vals, bins=50, normed=True) >>> plt.plot(F[1][1:], F[0]) >>> plt.plot(NF[1][1:], NF[0]) >>> plt.show() """ return float() if False else ndarray() def normal(self, loc, scale, size): """ normal(loc=0.0, scale=1.0, size=None) Draw random samples from a normal (Gaussian) distribution. The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [2]_, is often called the bell curve because of its characteristic shape (see the example below). The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [2]_. Parameters ---------- loc : float Mean ("centre") of the distribution. scale : float Standard deviation (spread or "width") of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. See Also -------- scipy.stats.distributions.norm : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gaussian distribution is .. math:: p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }} e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} }, where :math:`\mu` is the mean and :math:`\sigma` the standard deviation. The square of the standard deviation, :math:`\sigma^2`, is called the variance. The function has its peak at the mean, and its "spread" increases with the standard deviation (the function reaches 0.607 times its maximum at :math:`x + \sigma` and :math:`x - \sigma` [2]_). This implies that `numpy.random.normal` is more likely to return samples lying close to the mean, rather than those far away. References ---------- .. [1] Wikipedia, "Normal distribution", http://en.wikipedia.org/wiki/Normal_distribution .. [2] P. R. Peebles Jr., "Central Limit Theorem" in "Probability, Random Variables and Random Signal Principles", 4th ed., 2001, pp. 51, 51, 125. Examples -------- Draw samples from the distribution: >>> mu, sigma = 0, 0.1 # mean and standard deviation >>> s = np.random.normal(mu, sigma, 1000) Verify the mean and the variance: >>> abs(mu - np.mean(s)) < 0.01 True >>> abs(sigma - np.std(s, ddof=1)) < 0.01 True Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, normed=True) >>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * ... np.exp( - (bins - mu)**2 / (2 * sigma**2) ), ... linewidth=2, color='r') >>> plt.show() """ return None def pareto(self, shape, size): """ pareto(a, size=None) Draw samples from a Pareto II or Lomax distribution with specified shape. The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding the location parameter m, see below. The smallest value of the Lomax distribution is zero while for the classical Pareto distribution it is m, where the standard Pareto distribution has location m=1. Lomax can also be considered as a simplified version of the Generalized Pareto distribution (available in SciPy), with the scale set to one and the location set to zero. The Pareto distribution must be greater than zero, and is unbounded above. It is also known as the "80-20 rule". In this distribution, 80 percent of the weights are in the lowest 20 percent of the range, while the other 20 percent fill the remaining 80 percent of the range. Parameters ---------- shape : float, > 0. Shape of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. See Also -------- scipy.stats.distributions.lomax.pdf : probability density function, distribution or cumulative density function, etc. scipy.stats.distributions.genpareto.pdf : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Pareto distribution is .. math:: p(x) = \frac{am^a}{x^{a+1}} where :math:`a` is the shape and :math:`m` the location The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution useful in many real world problems. Outside the field of economics it is generally referred to as the Bradford distribution. Pareto developed the distribution to describe the distribution of wealth in an economy. It has also found use in insurance, web page access statistics, oil field sizes, and many other problems, including the download frequency for projects in Sourceforge [1]. It is one of the so-called "fat-tailed" distributions. References ---------- .. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of Sourceforge projects. .. [2] Pareto, V. (1896). Course of Political Economy. Lausanne. .. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme Values, Birkhauser Verlag, Basel, pp 23-30. .. [4] Wikipedia, "Pareto distribution", http://en.wikipedia.org/wiki/Pareto_distribution Examples -------- Draw samples from the distribution: >>> a, m = 3., 1. # shape and mode >>> s = np.random.pareto(a, 1000) + m Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='center') >>> fit = a*m**a/bins**(a+1) >>> plt.plot(bins, max(count)*fit/max(fit),linewidth=2, color='r') >>> plt.show() """ return None def permutation(self, x): """ permutation(x) Randomly permute a sequence, or return a permuted range. If `x` is a multi-dimensional array, it is only shuffled along its first index. Parameters ---------- x : int or array_like If `x` is an integer, randomly permute ``np.arange(x)``. If `x` is an array, make a copy and shuffle the elements randomly. Returns ------- out : ndarray Permuted sequence or array range. Examples -------- >>> np.random.permutation(10) array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6]) >>> np.random.permutation([1, 4, 9, 12, 15]) array([15, 1, 9, 4, 12]) >>> arr = np.arange(9).reshape((3, 3)) >>> np.random.permutation(arr) array([[6, 7, 8], [0, 1, 2], [3, 4, 5]]) """ return ndarray() def poisson(self, lam, size): """ poisson(lam=1.0, size=None) Draw samples from a Poisson distribution. The Poisson distribution is the limit of the Binomial distribution for large N. Parameters ---------- lam : float Expectation of interval, should be >= 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Notes ----- The Poisson distribution .. math:: f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!} For events with an expected separation :math:`\lambda` the Poisson distribution :math:`f(k; \lambda)` describes the probability of :math:`k` events occurring within the observed interval :math:`\lambda`. Because the output is limited to the range of the C long type, a ValueError is raised when `lam` is within 10 sigma of the maximum representable value. References ---------- .. [1] Weisstein, Eric W. "Poisson Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html .. [2] Wikipedia, "Poisson distribution", http://en.wikipedia.org/wiki/Poisson_distribution Examples -------- Draw samples from the distribution: >>> import numpy as np >>> s = np.random.poisson(5, 10000) Display histogram of the sample: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 14, normed=True) >>> plt.show() """ return None poisson_lam_max = float64() def power(self, a, size): """ power(a, size=None) Draws samples in [0, 1] from a power distribution with positive exponent a - 1. Also known as the power function distribution. Parameters ---------- a : float parameter, > 0 size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} The returned samples lie in [0, 1]. Raises ------ ValueError If a<1. Notes ----- The probability density function is .. math:: P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0. The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution. It is used, for example, in modeling the over-reporting of insurance claims. References ---------- .. [1] Christian Kleiber, Samuel Kotz, "Statistical size distributions in economics and actuarial sciences", Wiley, 2003. .. [2] Heckert, N. A. and Filliben, James J. (2003). NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions", National Institute of Standards and Technology Handbook Series, June 2003. http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf Examples -------- Draw samples from the distribution: >>> a = 5. # shape >>> samples = 1000 >>> s = np.random.power(a, samples) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, bins=30) >>> x = np.linspace(0, 1, 100) >>> y = a*x**(a-1.) >>> normed_y = samples*np.diff(bins)[0]*y >>> plt.plot(x, normed_y) >>> plt.show() Compare the power function distribution to the inverse of the Pareto. >>> from scipy import stats >>> rvs = np.random.power(5, 1000000) >>> rvsp = np.random.pareto(5, 1000000) >>> xx = np.linspace(0,1,100) >>> powpdf = stats.powerlaw.pdf(xx,5) >>> plt.figure() >>> plt.hist(rvs, bins=50, normed=True) >>> plt.plot(xx,powpdf,'r-') >>> plt.title('np.random.power(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, normed=True) >>> plt.plot(xx,powpdf,'r-') >>> plt.title('inverse of 1 + np.random.pareto(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, normed=True) >>> plt.plot(xx,powpdf,'r-') >>> plt.title('inverse of stats.pareto(5)') """ return ndarray() def rand(self, d0d1more_argsdn): """ rand(d0, d1, ..., dn) Random values in a given shape. Create an array of the given shape and propagate it with random samples from a uniform distribution over ``[0, 1)``. Parameters ---------- d0, d1, ..., dn : int, optional The dimensions of the returned array, should all be positive. If no argument is given a single Python float is returned. Returns ------- out : ndarray, shape ``(d0, d1, ..., dn)`` Random values. See Also -------- random Notes ----- This is a convenience function. If you want an interface that takes a shape-tuple as the first argument, refer to np.random.random_sample . Examples -------- >>> np.random.rand(3,2) array([[ 0.14022471, 0.96360618], #random [ 0.37601032, 0.25528411], #random [ 0.49313049, 0.94909878]]) #random """ return None def randint(self, low, high, size): """ randint(low, high=None, size=None) Return random integers from `low` (inclusive) to `high` (exclusive). Return random integers from the "discrete uniform" distribution in the "half-open" interval [`low`, `high`). If `high` is None (the default), then results are from [0, `low`). Parameters ---------- low : int Lowest (signed) integer to be drawn from the distribution (unless ``high=None``, in which case this parameter is the *highest* such integer). high : int, optional If provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if ``high=None``). size : int or tuple of ints, optional Output shape. Default is None, in which case a single int is returned. Returns ------- out : int or ndarray of ints `size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided. See Also -------- random.random_integers : similar to `randint`, only for the closed interval [`low`, `high`], and 1 is the lowest value if `high` is omitted. In particular, this other one is the one to use to generate uniformly distributed discrete non-integers. Examples -------- >>> np.random.randint(2, size=10) array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) >>> np.random.randint(1, size=10) array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) Generate a 2 x 4 array of ints between 0 and 4, inclusive: >>> np.random.randint(5, size=(2, 4)) array([[4, 0, 2, 1], [3, 2, 2, 0]]) """ return int() if False else ndarray() def randn(self, d0d1more_argsdn): """ randn(d0, d1, ..., dn) Return a sample (or samples) from the "standard normal" distribution. If positive, int_like or int-convertible arguments are provided, `randn` generates an array of shape ``(d0, d1, ..., dn)``, filled with random floats sampled from a univariate "normal" (Gaussian) distribution of mean 0 and variance 1 (if any of the :math:`d_i` are floats, they are first converted to integers by truncation). A single float randomly sampled from the distribution is returned if no argument is provided. This is a convenience function. If you want an interface that takes a tuple as the first argument, use `numpy.random.standard_normal` instead. Parameters ---------- d0, d1, ..., dn : int, optional The dimensions of the returned array, should be all positive. If no argument is given a single Python float is returned. Returns ------- Z : ndarray or float A ``(d0, d1, ..., dn)``-shaped array of floating-point samples from the standard normal distribution, or a single such float if no parameters were supplied. See Also -------- random.standard_normal : Similar, but takes a tuple as its argument. Notes ----- For random samples from :math:`N(\mu, \sigma^2)`, use: ``sigma * np.random.randn(...) + mu`` Examples -------- >>> np.random.randn() 2.1923875335537315 #random Two-by-four array of samples from N(3, 6.25): >>> 2.5 * np.random.randn(2, 4) + 3 array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], #random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) #random """ return ndarray() if False else float() def random_integers(self, low, high, size): """ random_integers(low, high=None, size=None) Return random integers between `low` and `high`, inclusive. Return random integers from the "discrete uniform" distribution in the closed interval [`low`, `high`]. If `high` is None (the default), then results are from [1, `low`]. Parameters ---------- low : int Lowest (signed) integer to be drawn from the distribution (unless ``high=None``, in which case this parameter is the *highest* such integer). high : int, optional If provided, the largest (signed) integer to be drawn from the distribution (see above for behavior if ``high=None``). size : int or tuple of ints, optional Output shape. Default is None, in which case a single int is returned. Returns ------- out : int or ndarray of ints `size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided. See Also -------- random.randint : Similar to `random_integers`, only for the half-open interval [`low`, `high`), and 0 is the lowest value if `high` is omitted. Notes ----- To sample from N evenly spaced floating-point numbers between a and b, use:: a + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.) Examples -------- >>> np.random.random_integers(5) 4 >>> type(np.random.random_integers(5)) >>> np.random.random_integers(5, size=(3.,2.)) array([[5, 4], [3, 3], [4, 5]]) Choose five random numbers from the set of five evenly-spaced numbers between 0 and 2.5, inclusive (*i.e.*, from the set :math:`{0, 5/8, 10/8, 15/8, 20/8}`): >>> 2.5 * (np.random.random_integers(5, size=(5,)) - 1) / 4. array([ 0.625, 1.25 , 0.625, 0.625, 2.5 ]) Roll two six sided dice 1000 times and sum the results: >>> d1 = np.random.random_integers(1, 6, 1000) >>> d2 = np.random.random_integers(1, 6, 1000) >>> dsums = d1 + d2 Display results as a histogram: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(dsums, 11, normed=True) >>> plt.show() """ return int() if False else ndarray() def random_sample(self, size): """ random_sample(size=None) Return random floats in the half-open interval [0.0, 1.0). Results are from the "continuous uniform" distribution over the stated interval. To sample :math:`Unif[a, b), b > a` multiply the output of `random_sample` by `(b-a)` and add `a`:: (b - a) * random_sample() + a Parameters ---------- size : int or tuple of ints, optional Defines the shape of the returned array of random floats. If None (the default), returns a single float. Returns ------- out : float or ndarray of floats Array of random floats of shape `size` (unless ``size=None``, in which case a single float is returned). Examples -------- >>> np.random.random_sample() 0.47108547995356098 >>> type(np.random.random_sample()) >>> np.random.random_sample((5,)) array([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) Three-by-two array of random numbers from [-5, 0): >>> 5 * np.random.random_sample((3, 2)) - 5 array([[-3.99149989, -0.52338984], [-2.99091858, -0.79479508], [-1.23204345, -1.75224494]]) """ return float() if False else ndarray() def rayleigh(self, scale, size): """ rayleigh(scale=1.0, size=None) Draw samples from a Rayleigh distribution. The :math:`\chi` and Weibull distributions are generalizations of the Rayleigh. Parameters ---------- scale : scalar Scale, also equals the mode. Should be >= 0. size : int or tuple of ints, optional Shape of the output. Default is None, in which case a single value is returned. Notes ----- The probability density function for the Rayleigh distribution is .. math:: P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}} The Rayleigh distribution arises if the wind speed and wind direction are both gaussian variables, then the vector wind velocity forms a Rayleigh distribution. The Rayleigh distribution is used to model the expected output from wind turbines. References ---------- .. [1] Brighton Webs Ltd., Rayleigh Distribution, http://www.brighton-webs.co.uk/distributions/rayleigh.asp .. [2] Wikipedia, "Rayleigh distribution" http://en.wikipedia.org/wiki/Rayleigh_distribution Examples -------- Draw values from the distribution and plot the histogram >>> values = hist(np.random.rayleigh(3, 100000), bins=200, normed=True) Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters? >>> meanvalue = 1 >>> modevalue = np.sqrt(2 / np.pi) * meanvalue >>> s = np.random.rayleigh(modevalue, 1000000) The percentage of waves larger than 3 meters is: >>> 100.*sum(s>3)/1000000. 0.087300000000000003 """ return None def seed(self, seed): """ seed(seed=None) Seed the generator. This method is called when `RandomState` is initialized. It can be called again to re-seed the generator. For details, see `RandomState`. Parameters ---------- seed : int or array_like, optional Seed for `RandomState`. See Also -------- RandomState """ return None def set_state(self, state): """ set_state(state) Set the internal state of the generator from a tuple. For use if one has reason to manually (re-)set the internal state of the "Mersenne Twister"[1]_ pseudo-random number generating algorithm. Parameters ---------- state : tuple(str, ndarray of 624 uints, int, int, float) The `state` tuple has the following items: 1. the string 'MT19937', specifying the Mersenne Twister algorithm. 2. a 1-D array of 624 unsigned integers ``keys``. 3. an integer ``pos``. 4. an integer ``has_gauss``. 5. a float ``cached_gaussian``. Returns ------- out : None Returns 'None' on success. See Also -------- get_state Notes ----- `set_state` and `get_state` are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing. For backwards compatibility, the form (str, array of 624 uints, int) is also accepted although it is missing some information about the cached Gaussian value: ``state = ('MT19937', keys, pos)``. References ---------- .. [1] M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator," *ACM Trans. on Modeling and Computer Simulation*, Vol. 8, No. 1, pp. 3-30, Jan. 1998. """ return None def shuffle(self, x): """ shuffle(x) Modify a sequence in-place by shuffling its contents. Parameters ---------- x : array_like The array or list to be shuffled. Returns ------- None Examples -------- >>> arr = np.arange(10) >>> np.random.shuffle(arr) >>> arr [1 7 5 2 9 4 3 6 0 8] This function only shuffles the array along the first index of a multi-dimensional array: >>> arr = np.arange(9).reshape((3, 3)) >>> np.random.shuffle(arr) >>> arr array([[3, 4, 5], [6, 7, 8], [0, 1, 2]]) """ return None def standard_cauchy(self, size): """ standard_cauchy(size=None) Standard Cauchy distribution with mode = 0. Also known as the Lorentz distribution. Parameters ---------- size : int or tuple of ints Shape of the output. Returns ------- samples : ndarray or scalar The drawn samples. Notes ----- The probability density function for the full Cauchy distribution is .. math:: P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+ (\frac{x-x_0}{\gamma})^2 \bigr] } and the Standard Cauchy distribution just sets :math:`x_0=0` and :math:`\gamma=1` The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis. When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails. References ---------- .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "Cauchy Distribution", http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm .. [2] Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CauchyDistribution.html .. [3] Wikipedia, "Cauchy distribution" http://en.wikipedia.org/wiki/Cauchy_distribution Examples -------- Draw samples and plot the distribution: >>> s = np.random.standard_cauchy(1000000) >>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well >>> plt.hist(s, bins=100) >>> plt.show() """ return ndarray() if False else float() def standard_exponential(self, size): """ standard_exponential(size=None) Draw samples from the standard exponential distribution. `standard_exponential` is identical to the exponential distribution with a scale parameter of 1. Parameters ---------- size : int or tuple of ints Shape of the output. Returns ------- out : float or ndarray Drawn samples. Examples -------- Output a 3x8000 array: >>> n = np.random.standard_exponential((3, 8000)) """ return float() if False else ndarray() def standard_gamma(self, shape, size): """ standard_gamma(shape, size=None) Draw samples from a Standard Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated "k") and scale=1. Parameters ---------- shape : float Parameter, should be > 0. size : int or tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : ndarray or scalar The drawn samples. See Also -------- scipy.stats.distributions.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma-distribution", http://en.wikipedia.org/wiki/Gamma-distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 1. # mean and width >>> s = np.random.standard_gamma(shape, 1000000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ \ ... (sps.gamma(shape) * scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') >>> plt.show() """ return ndarray() if False else float() def standard_normal(self, size): """ standard_normal(size=None) Returns samples from a Standard Normal distribution (mean=0, stdev=1). Parameters ---------- size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- out : float or ndarray Drawn samples. Examples -------- >>> s = np.random.standard_normal(8000) >>> s array([ 0.6888893 , 0.78096262, -0.89086505, ..., 0.49876311, #random -0.38672696, -0.4685006 ]) #random >>> s.shape (8000,) >>> s = np.random.standard_normal(size=(3, 4, 2)) >>> s.shape (3, 4, 2) """ return float() if False else ndarray() def standard_t(self, df, size): """ standard_t(df, size=None) Standard Student's t distribution with df degrees of freedom. A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution (`standard_normal`). Parameters ---------- df : int Degrees of freedom, should be > 0. size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar Drawn samples. Notes ----- The probability density function for the t distribution is .. math:: P(x, df) = \frac{\Gamma(\frac{df+1}{2})}{\sqrt{\pi df} \Gamma(\frac{df}{2})}\Bigl( 1+\frac{x^2}{df} \Bigr)^{-(df+1)/2} The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean. The derivation of the t-distribution was forst published in 1908 by William Gisset while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics With R", Springer, 2002. .. [2] Wikipedia, "Student's t-distribution" http://en.wikipedia.org/wiki/Student's_t-distribution Examples -------- From Dalgaard page 83 [1]_, suppose the daily energy intake for 11 women in Kj is: >>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \ ... 7515, 8230, 8770]) Does their energy intake deviate systematically from the recommended value of 7725 kJ? We have 10 degrees of freedom, so is the sample mean within 95% of the recommended value? >>> s = np.random.standard_t(10, size=100000) >>> np.mean(intake) 6753.636363636364 >>> intake.std(ddof=1) 1142.1232221373727 Calculate the t statistic, setting the ddof parameter to the unbiased value so the divisor in the standard deviation will be degrees of freedom, N-1. >>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake))) >>> import matplotlib.pyplot as plt >>> h = plt.hist(s, bins=100, normed=True) For a one-sided t-test, how far out in the distribution does the t statistic appear? >>> >>> np.sum(s>> RS = np.random.mtrand.RandomState() # need a RandomState object >>> RS.tomaxint((2,2,2)) array([[[1170048599, 1600360186], [ 739731006, 1947757578]], [[1871712945, 752307660], [1601631370, 1479324245]]]) >>> import sys >>> sys.maxint 2147483647 >>> RS.tomaxint((2,2,2)) < sys.maxint array([[[ True, True], [ True, True]], [[ True, True], [ True, True]]], dtype=bool) """ return ndarray() def triangular(self, left, mode, right, size): """ triangular(left, mode, right, size=None) Draw samples from the triangular distribution. The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf. Parameters ---------- left : scalar Lower limit. mode : scalar The value where the peak of the distribution occurs. The value should fulfill the condition ``left <= mode <= right``. right : scalar Upper limit, should be larger than `left`. size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar The returned samples all lie in the interval [left, right]. Notes ----- The probability density function for the Triangular distribution is .. math:: P(x;l, m, r) = \begin{cases} \frac{2(x-l)}{(r-l)(m-l)}& \text{for $l \leq x \leq m$},\\ \frac{2(m-x)}{(r-l)(r-m)}& \text{for $m \leq x \leq r$},\\ 0& \text{otherwise}. \end{cases} The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations. References ---------- .. [1] Wikipedia, "Triangular distribution" http://en.wikipedia.org/wiki/Triangular_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.triangular(-3, 0, 8, 100000), bins=200, ... normed=True) >>> plt.show() """ return ndarray() if False else float() def uniform(self, low, high, size): """ uniform(low=0.0, high=1.0, size=1) Draw samples from a uniform distribution. Samples are uniformly distributed over the half-open interval ``[low, high)`` (includes low, but excludes high). In other words, any value within the given interval is equally likely to be drawn by `uniform`. Parameters ---------- low : float, optional Lower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0. high : float Upper boundary of the output interval. All values generated will be less than high. The default value is 1.0. size : int or tuple of ints, optional Shape of output. If the given size is, for example, (m,n,k), m*n*k samples are generated. If no shape is specified, a single sample is returned. Returns ------- out : ndarray Drawn samples, with shape `size`. See Also -------- randint : Discrete uniform distribution, yielding integers. random_integers : Discrete uniform distribution over the closed interval ``[low, high]``. random_sample : Floats uniformly distributed over ``[0, 1)``. random : Alias for `random_sample`. rand : Convenience function that accepts dimensions as input, e.g., ``rand(2,2)`` would generate a 2-by-2 array of floats, uniformly distributed over ``[0, 1)``. Notes ----- The probability density function of the uniform distribution is .. math:: p(x) = \frac{1}{b - a} anywhere within the interval ``[a, b)``, and zero elsewhere. Examples -------- Draw samples from the distribution: >>> s = np.random.uniform(-1,0,1000) All values are within the given interval: >>> np.all(s >= -1) True >>> np.all(s < 0) True Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 15, normed=True) >>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r') >>> plt.show() """ return ndarray() def vonmises(self, mu, kappa, size): """ vonmises(mu, kappa, size=None) Draw samples from a von Mises distribution. Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi]. The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution. Parameters ---------- mu : float Mode ("center") of the distribution. kappa : float Dispersion of the distribution, has to be >=0. size : int or tuple of int Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : scalar or ndarray The returned samples, which are in the interval [-pi, pi]. See Also -------- scipy.stats.distributions.vonmises : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the von Mises distribution is .. math:: p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)}, where :math:`\mu` is the mode and :math:`\kappa` the dispersion, and :math:`I_0(\kappa)` is the modified Bessel function of order 0. The von Mises is named for Richard Edler von Mises, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science. References ---------- Abramowitz, M. and Stegun, I. A. (ed.), *Handbook of Mathematical Functions*, New York: Dover, 1965. von Mises, R., *Mathematical Theory of Probability and Statistics*, New York: Academic Press, 1964. Examples -------- Draw samples from the distribution: >>> mu, kappa = 0.0, 4.0 # mean and dispersion >>> s = np.random.vonmises(mu, kappa, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> x = np.arange(-np.pi, np.pi, 2*np.pi/50.) >>> y = -np.exp(kappa*np.cos(x-mu))/(2*np.pi*sps.jn(0,kappa)) >>> plt.plot(x, y/max(y), linewidth=2, color='r') >>> plt.show() """ return float() if False else ndarray() def wald(self, mean, scale, size): """ wald(mean, scale, size=None) Draw samples from a Wald, or Inverse Gaussian, distribution. As the scale approaches infinity, the distribution becomes more like a Gaussian. Some references claim that the Wald is an Inverse Gaussian with mean=1, but this is by no means universal. The Inverse Gaussian distribution was first studied in relationship to Brownian motion. In 1956 M.C.K. Tweedie used the name Inverse Gaussian because there is an inverse relationship between the time to cover a unit distance and distance covered in unit time. Parameters ---------- mean : scalar Distribution mean, should be > 0. scale : scalar Scale parameter, should be >= 0. size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar Drawn sample, all greater than zero. Notes ----- The probability density function for the Wald distribution is .. math:: P(x;mean,scale) = \sqrt{\frac{scale}{2\pi x^3}}e^ \frac{-scale(x-mean)^2}{2\cdotp mean^2x} As noted above the Inverse Gaussian distribution first arise from attempts to model Brownian Motion. It is also a competitor to the Weibull for use in reliability modeling and modeling stock returns and interest rate processes. References ---------- .. [1] Brighton Webs Ltd., Wald Distribution, http://www.brighton-webs.co.uk/distributions/wald.asp .. [2] Chhikara, Raj S., and Folks, J. Leroy, "The Inverse Gaussian Distribution: Theory : Methodology, and Applications", CRC Press, 1988. .. [3] Wikipedia, "Wald distribution" http://en.wikipedia.org/wiki/Wald_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.wald(3, 2, 100000), bins=200, normed=True) >>> plt.show() """ return ndarray() if False else float() def weibull(self, a, size): """ weibull(a, size=None) Weibull distribution. Draw samples from a 1-parameter Weibull distribution with the given shape parameter `a`. .. math:: X = (-ln(U))^{1/a} Here, U is drawn from the uniform distribution over (0,1]. The more common 2-parameter Weibull, including a scale parameter :math:`\lambda` is just :math:`X = \lambda(-ln(U))^{1/a}`. Parameters ---------- a : float Shape of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. See Also -------- scipy.stats.distributions.weibull_max scipy.stats.distributions.weibull_min scipy.stats.distributions.genextreme gumbel Notes ----- The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions. The probability density for the Weibull distribution is .. math:: p(x) = \frac{a} {\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a}, where :math:`a` is the shape and :math:`\lambda` the scale. The function has its peak (the mode) at :math:`\lambda(\frac{a-1}{a})^{1/a}`. When ``a = 1``, the Weibull distribution reduces to the exponential distribution. References ---------- .. [1] Waloddi Weibull, Professor, Royal Technical University, Stockholm, 1939 "A Statistical Theory Of The Strength Of Materials", Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm. .. [2] Waloddi Weibull, 1951 "A Statistical Distribution Function of Wide Applicability", Journal Of Applied Mechanics ASME Paper. .. [3] Wikipedia, "Weibull distribution", http://en.wikipedia.org/wiki/Weibull_distribution Examples -------- Draw samples from the distribution: >>> a = 5. # shape >>> s = np.random.weibull(a, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> x = np.arange(1,100.)/50. >>> def weib(x,n,a): ... return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a) >>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000)) >>> x = np.arange(1,100.)/50. >>> scale = count.max()/weib(x, 1., 5.).max() >>> plt.plot(x, weib(x, 1., 5.)*scale) >>> plt.show() """ return None def zipf(self, a, size): """ zipf(a, size=None) Draw samples from a Zipf distribution. Samples are drawn from a Zipf distribution with specified parameter `a` > 1. The Zipf distribution (also known as the zeta distribution) is a continuous probability distribution that satisfies Zipf's law: the frequency of an item is inversely proportional to its rank in a frequency table. Parameters ---------- a : float > 1 Distribution parameter. size : int or tuple of int, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn; a single integer is equivalent in its result to providing a mono-tuple, i.e., a 1-D array of length *size* is returned. The default is None, in which case a single scalar is returned. Returns ------- samples : scalar or ndarray The returned samples are greater than or equal to one. See Also -------- scipy.stats.distributions.zipf : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the Zipf distribution is .. math:: p(x) = \frac{x^{-a}}{\zeta(a)}, where :math:`\zeta` is the Riemann Zeta function. It is named for the American linguist George Kingsley Zipf, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table. References ---------- Zipf, G. K., *Selected Studies of the Principle of Relative Frequency in Language*, Cambridge, MA: Harvard Univ. Press, 1932. Examples -------- Draw samples from the distribution: >>> a = 2. # parameter >>> s = np.random.zipf(a, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps Truncate s values at 50 so plot is interesting >>> count, bins, ignored = plt.hist(s[s<50], 50, normed=True) >>> x = np.arange(1., 50.) >>> y = x**(-a)/sps.zetac(a) >>> plt.plot(x, y/max(y), linewidth=2, color='r') >>> plt.show() """ return float() if False else ndarray() class NoseTester: __dict__ = dictproxy() __doc__ = str() __module__ = str() __weakref__ = getset_descriptor() def _get_custom_doctester(self, _): """ Return instantiated plugin for doctests Allows subclassing of this class to override doctester A return value of None means use the nose builtin doctest plugin """ return None def _show_system_info(self, _): """None""" return None def _test_argv(self, label, verbose, extra_argv): """ Generate argv for nosetest command Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional see ``test`` docstring verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- argv : list command line arguments that will be passed to nose """ return list() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() excludes = list() def prepare_test_args(self=False, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False): """ Run tests for module using nose. This method does the heavy lifting for the `test` method. It takes all the same arguments, for details see `test`. See Also -------- test """ return None def test(self=None, label="fast", verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None): """ Run tests for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the tests to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow tests as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for test outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. doctests : bool, optional If True, run doctests in module. Default is False. coverage : bool, optional If True, report coverage of NumPy code. Default is False. (This requires the `coverage module: `_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() __all__ = list() __builtins__ = dict() __doc__ = str() __file__ = str() __name__ = str() __package__ = str() __path__ = list() __warningregistry__ = dict() absolute_import = instance() def bench(self=None, label="fast", verbose=1, extra_argv=None): """ Run benchmarks for module using nose. Parameters ---------- label : {'fast', 'full', '', attribute identifier}, optional Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the '-A' option, or one of several special values. Special values are: * 'fast' - the default - which corresponds to the ``nosetests -A`` option of 'not slow'. * 'full' - fast (as above) and slow benchmarks as in the 'no -A' option to nosetests - this is the same as ''. * None or '' - run all tests. attribute_identifier - string passed directly to nosetests as '-A'. verbose : int, optional Verbosity value for benchmark outputs, in the range 1-10. Default is 1. extra_argv : list, optional List with any extra arguments to pass to nosetests. Returns ------- success : bool Returns True if running the benchmarks works, False if an error occurred. Notes ----- Benchmarks are like tests, but have names starting with "bench" instead of "test", and can be found under the "benchmarks" sub-directory of the module. Each NumPy module exposes `bench` in its namespace to run all benchmarks for it. Examples -------- >>> success = np.lib.bench() #doctest: +SKIP Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK >>> success #doctest: +SKIP True """ return bool() def beta(self, a, b, size): """ beta(a, b, size=None) The Beta distribution over ``[0, 1]``. The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function .. math:: f(x; a,b) = \frac{1}{B(\alpha, \beta)} x^{\alpha - 1} (1 - x)^{\beta - 1}, where the normalisation, B, is the beta function, .. math:: B(\alpha, \beta) = \int_0^1 t^{\alpha - 1} (1 - t)^{\beta - 1} dt. It is often seen in Bayesian inference and order statistics. Parameters ---------- a : float Alpha, non-negative. b : float Beta, non-negative. size : tuple of ints, optional The number of samples to draw. The output is packed according to the size given. Returns ------- out : ndarray Array of the given shape, containing values drawn from a Beta distribution. """ return ndarray() def binomial(self, n, p, size): """ binomial(n, p, size=None) Draw samples from a binomial distribution. Samples are drawn from a Binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. (n may be input as a float, but it is truncated to an integer in use) Parameters ---------- n : float (but truncated to an integer) parameter, >= 0. p : float parameter, >= 0 and <=1. size : {tuple, int} Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} where the values are all integers in [0, n]. See Also -------- scipy.stats.distributions.binom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Binomial distribution is .. math:: P(N) = \binom{n}{N}p^N(1-p)^{n-N}, where :math:`n` is the number of trials, :math:`p` is the probability of success, and :math:`N` is the number of successes. When estimating the standard error of a proportion in a population by using a random sample, the normal distribution works well unless the product p*n <=5, where p = population proportion estimate, and n = number of samples, in which case the binomial distribution is used instead. For example, a sample of 15 people shows 4 who are left handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4, so the binomial distribution should be used in this case. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics with R", Springer-Verlag, 2002. .. [2] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill, Fifth Edition, 2002. .. [3] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [4] Weisstein, Eric W. "Binomial Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/BinomialDistribution.html .. [5] Wikipedia, "Binomial-distribution", http://en.wikipedia.org/wiki/Binomial_distribution Examples -------- Draw samples from the distribution: >>> n, p = 10, .5 # number of trials, probability of each trial >>> s = np.random.binomial(n, p, 1000) # result of flipping a coin 10 times, tested 1000 times. A real world example. A company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of 0.1. All nine wells fail. What is the probability of that happening? Let's do 20,000 trials of the model, and count the number that generate zero positive results. >>> sum(np.random.binomial(9,0.1,20000)==0)/20000. answer = 0.38885, or 38%. """ return ndarray() def bytes(self, length): """ bytes(length) Return random bytes. Parameters ---------- length : int Number of random bytes. Returns ------- out : str String of length `length`. Examples -------- >>> np.random.bytes(10) ' eh\x85\x022SZ\xbf\xa4' #random """ return str() def chisquare(self, df, size): """ chisquare(df, size=None) Draw samples from a chi-square distribution. When `df` independent random variables, each with standard normal distributions (mean 0, variance 1), are squared and summed, the resulting distribution is chi-square (see Notes). This distribution is often used in hypothesis testing. Parameters ---------- df : int Number of degrees of freedom. size : tuple of ints, int, optional Size of the returned array. By default, a scalar is returned. Returns ------- output : ndarray Samples drawn from the distribution, packed in a `size`-shaped array. Raises ------ ValueError When `df` <= 0 or when an inappropriate `size` (e.g. ``size=-1``) is given. Notes ----- The variable obtained by summing the squares of `df` independent, standard normally distributed random variables: .. math:: Q = \sum_{i=0}^{\mathtt{df}} X^2_i is chi-square distributed, denoted .. math:: Q \sim \chi^2_k. The probability density function of the chi-squared distribution is .. math:: p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}, where :math:`\Gamma` is the gamma function, .. math:: \Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt. References ---------- `NIST/SEMATECH e-Handbook of Statistical Methods `_ Examples -------- >>> np.random.chisquare(2,4) array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) """ return ndarray() def choice(self, a, size, replace, p): """ choice(a, size=None, replace=True, p=None) Generates a random sample from a given 1-D array .. versionadded:: 1.7.0 Parameters ----------- a : 1-D array-like or int If an ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if a was np.arange(n) size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. replace : boolean, optional Whether the sample is with or without replacement p : 1-D array-like, optional The probabilities associated with each entry in a. If not given the sample assumes a uniform distribtion over all entries in a. Returns -------- samples : 1-D ndarray, shape (size,) The generated random samples Raises ------- ValueError If a is an int and less than zero, if a or p are not 1-dimensional, if a is an array-like of size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size See Also --------- randint, shuffle, permutation Examples --------- Generate a uniform random sample from np.arange(5) of size 3: >>> np.random.choice(5, 3) array([0, 3, 4]) >>> #This is equivalent to np.random.randint(0,5,3) Generate a non-uniform random sample from np.arange(5) of size 3: >>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0]) array([3, 3, 0]) Generate a uniform random sample from np.arange(5) of size 3 without replacement: >>> np.random.choice(5, 3, replace=False) array([3,1,0]) >>> #This is equivalent to np.random.shuffle(np.arange(5))[:3] Generate a non-uniform random sample from np.arange(5) of size 3 without replacement: >>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0]) array([2, 3, 0]) Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance: >>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher'] >>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3]) array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], dtype='|S11') """ return _1_D() def dirichlet(self, alpha, size): """ dirichlet(alpha, size=None) Draw samples from the Dirichlet distribution. Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. Dirichlet pdf is the conjugate prior of a multinomial in Bayesian inference. Parameters ---------- alpha : array Parameter of the distribution (k dimension for sample of dimension k). size : array Number of samples to draw. Returns ------- samples : ndarray, The drawn samples, of shape (alpha.ndim, size). Notes ----- .. math:: X \approx \prod_{i=1}^{k}{x^{\alpha_i-1}_i} Uses the following property for computation: for each dimension, draw a random sample y_i from a standard gamma generator of shape `alpha_i`, then :math:`X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, \ldots, y_n)` is Dirichlet distributed. References ---------- .. [1] David McKay, "Information Theory, Inference and Learning Algorithms," chapter 23, http://www.inference.phy.cam.ac.uk/mackay/ .. [2] Wikipedia, "Dirichlet distribution", http://en.wikipedia.org/wiki/Dirichlet_distribution Examples -------- Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces. >>> s = np.random.dirichlet((10, 5, 3), 20).transpose() >>> plt.barh(range(20), s[0]) >>> plt.barh(range(20), s[1], left=s[0], color='g') >>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r') >>> plt.title("Lengths of Strings") """ return ndarray() division = instance() def exponential(self, scale, size): """ exponential(scale=1.0, size=None) Exponential distribution. Its probability density function is .. math:: f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}), for ``x > 0`` and 0 elsewhere. :math:`\beta` is the scale parameter, which is the inverse of the rate parameter :math:`\lambda = 1/\beta`. The rate parameter is an alternative, widely used parameterization of the exponential distribution [3]_. The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [1]_, or the time between page requests to Wikipedia [2]_. Parameters ---------- scale : float The scale parameter, :math:`\beta = 1/\lambda`. size : tuple of ints Number of samples to draw. The output is shaped according to `size`. References ---------- .. [1] Peyton Z. Peebles Jr., "Probability, Random Variables and Random Signal Principles", 4th ed, 2001, p. 57. .. [2] "Poisson Process", Wikipedia, http://en.wikipedia.org/wiki/Poisson_process .. [3] "Exponential Distribution, Wikipedia, http://en.wikipedia.org/wiki/Exponential_distribution """ return None def f(self, dfnum, dfden, size): """ f(dfnum, dfden, size=None) Draw samples from a F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters should be greater than zero. The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates. Parameters ---------- dfnum : float Degrees of freedom in numerator. Should be greater than zero. dfden : float Degrees of freedom in denominator. Should be greater than zero. size : {tuple, int}, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. By default only one sample is returned. Returns ------- samples : {ndarray, scalar} Samples from the Fisher distribution. See Also -------- scipy.stats.distributions.f : probability density function, distribution or cumulative density function, etc. Notes ----- The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable `dfnum` is the number of samples minus one, the between-groups degrees of freedom, while `dfden` is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups. References ---------- .. [1] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill, Fifth Edition, 2002. .. [2] Wikipedia, "F-distribution", http://en.wikipedia.org/wiki/F-distribution Examples -------- An example from Glantz[1], pp 47-40. Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children's blood glucose levels? Calculating the F statistic from the data gives a value of 36.01. Draw samples from the distribution: >>> dfnum = 1. # between group degrees of freedom >>> dfden = 48. # within groups degrees of freedom >>> s = np.random.f(dfnum, dfden, 1000) The lower bound for the top 1% of the samples is : >>> sort(s)[-10] 7.61988120985 So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level. """ return ndarray() def gamma(self, shape, scale, size): """ gamma(shape, scale=1.0, size=None) Draw samples from a Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, `shape` (sometimes designated "k") and `scale` (sometimes designated "theta"), where both parameters are > 0. Parameters ---------- shape : scalar > 0 The shape of the gamma distribution. scale : scalar > 0, optional The scale of the gamma distribution. Default is equal to 1. size : shape_tuple, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- out : ndarray, float Returns one sample unless `size` parameter is specified. See Also -------- scipy.stats.distributions.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma-distribution", http://en.wikipedia.org/wiki/Gamma-distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 2. # mean and dispersion >>> s = np.random.gamma(shape, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> y = bins**(shape-1)*(np.exp(-bins/scale) / ... (sps.gamma(shape)*scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') >>> plt.show() """ return ndarray() def geometric(self, p, size): """ geometric(p, size=None) Draw samples from the geometric distribution. Bernoulli trials are experiments with one of two outcomes: success or failure (an example of such an experiment is flipping a coin). The geometric distribution models the number of trials that must be run in order to achieve success. It is therefore supported on the positive integers, ``k = 1, 2, ...``. The probability mass function of the geometric distribution is .. math:: f(k) = (1 - p)^{k - 1} p where `p` is the probability of success of an individual trial. Parameters ---------- p : float The probability of success of an individual trial. size : tuple of ints Number of values to draw from the distribution. The output is shaped according to `size`. Returns ------- out : ndarray Samples from the geometric distribution, shaped according to `size`. Examples -------- Draw ten thousand values from the geometric distribution, with the probability of an individual success equal to 0.35: >>> z = np.random.geometric(p=0.35, size=10000) How many trials succeeded after a single run? >>> (z == 1).sum() / 10000. 0.34889999999999999 #random """ return ndarray() def get_state(self, _): """ get_state() Return a tuple representing the internal state of the generator. For more details, see `set_state`. Returns ------- out : tuple(str, ndarray of 624 uints, int, int, float) The returned tuple has the following items: 1. the string 'MT19937'. 2. a 1-D array of 624 unsigned integer keys. 3. an integer ``pos``. 4. an integer ``has_gauss``. 5. a float ``cached_gaussian``. See Also -------- set_state Notes ----- `set_state` and `get_state` are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing. """ return None def gumbel(self, loc, scale, size): """ gumbel(loc=0.0, scale=1.0, size=None) Gumbel distribution. Draw samples from a Gumbel distribution with specified location and scale. For more information on the Gumbel distribution, see Notes and References below. Parameters ---------- loc : float The location of the mode of the distribution. scale : float The scale parameter of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- out : ndarray The samples See Also -------- scipy.stats.gumbel_l scipy.stats.gumbel_r scipy.stats.genextreme probability density function, distribution, or cumulative density function, etc. for each of the above weibull Notes ----- The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value Type I) distribution is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The Gumbel is a special case of the Extreme Value Type I distribution for maximums from distributions with "exponential-like" tails. The probability density for the Gumbel distribution is .. math:: p(x) = \frac{e^{-(x - \mu)/ \beta}}{\beta} e^{ -e^{-(x - \mu)/ \beta}}, where :math:`\mu` is the mode, a location parameter, and :math:`\beta` is the scale parameter. The Gumbel (named for German mathematician Emil Julius Gumbel) was used very early in the hydrology literature, for modeling the occurrence of flood events. It is also used for modeling maximum wind speed and rainfall rates. It is a "fat-tailed" distribution - the probability of an event in the tail of the distribution is larger than if one used a Gaussian, hence the surprisingly frequent occurrence of 100-year floods. Floods were initially modeled as a Gaussian process, which underestimated the frequency of extreme events. It is one of a class of extreme value distributions, the Generalized Extreme Value (GEV) distributions, which also includes the Weibull and Frechet. The function has a mean of :math:`\mu + 0.57721\beta` and a variance of :math:`\frac{\pi^2}{6}\beta^2`. References ---------- Gumbel, E. J., *Statistics of Extremes*, New York: Columbia University Press, 1958. Reiss, R.-D. and Thomas, M., *Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields*, Basel: Birkhauser Verlag, 2001. Examples -------- Draw samples from the distribution: >>> mu, beta = 0, 0.1 # location and scale >>> s = np.random.gumbel(mu, beta, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, normed=True) >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp( -np.exp( -(bins - mu) /beta) ), ... linewidth=2, color='r') >>> plt.show() Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian: >>> means = [] >>> maxima = [] >>> for i in range(0,1000) : ... a = np.random.normal(mu, beta, 1000) ... means.append(a.mean()) ... maxima.append(a.max()) >>> count, bins, ignored = plt.hist(maxima, 30, normed=True) >>> beta = np.std(maxima)*np.pi/np.sqrt(6) >>> mu = np.mean(maxima) - 0.57721*beta >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp(-np.exp(-(bins - mu)/beta)), ... linewidth=2, color='r') >>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi)) ... * np.exp(-(bins - mu)**2 / (2 * beta**2)), ... linewidth=2, color='g') >>> plt.show() """ return ndarray() def hypergeometric(self, ngood, nbad, nsample, size): """ hypergeometric(ngood, nbad, nsample, size=None) Draw samples from a Hypergeometric distribution. Samples are drawn from a Hypergeometric distribution with specified parameters, ngood (ways to make a good selection), nbad (ways to make a bad selection), and nsample = number of items sampled, which is less than or equal to the sum ngood + nbad. Parameters ---------- ngood : int or array_like Number of ways to make a good selection. Must be nonnegative. nbad : int or array_like Number of ways to make a bad selection. Must be nonnegative. nsample : int or array_like Number of items sampled. Must be at least 1 and at most ``ngood + nbad``. size : int or tuple of int Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : ndarray or scalar The values are all integers in [0, n]. See Also -------- scipy.stats.distributions.hypergeom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Hypergeometric distribution is .. math:: P(x) = \frac{\binom{m}{n}\binom{N-m}{n-x}}{\binom{N}{n}}, where :math:`0 \le x \le m` and :math:`n+m-N \le x \le n` for P(x) the probability of x successes, n = ngood, m = nbad, and N = number of samples. Consider an urn with black and white marbles in it, ngood of them black and nbad are white. If you draw nsample balls without replacement, then the Hypergeometric distribution describes the distribution of black balls in the drawn sample. Note that this distribution is very similar to the Binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the Binomial. References ---------- .. [1] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [2] Weisstein, Eric W. "Hypergeometric Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HypergeometricDistribution.html .. [3] Wikipedia, "Hypergeometric-distribution", http://en.wikipedia.org/wiki/Hypergeometric-distribution Examples -------- Draw samples from the distribution: >>> ngood, nbad, nsamp = 100, 2, 10 # number of good, number of bad, and number of samples >>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000) >>> hist(s) # note that it is very unlikely to grab both bad items Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color? >>> s = np.random.hypergeometric(15, 15, 15, 100000) >>> sum(s>=12)/100000. + sum(s<=3)/100000. # answer = 0.003 ... pretty unlikely! """ return ndarray() if False else float() def laplace(self, loc, scale): """ laplace(loc=0.0, scale=1.0, size=None) Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables. Parameters ---------- loc : float The position, :math:`\mu`, of the distribution peak. scale : float :math:`\lambda`, the exponential decay. Notes ----- It has the probability density function .. math:: f(x; \mu, \lambda) = \frac{1}{2\lambda} \exp\left(-\frac{|x - \mu|}{\lambda}\right). The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in Economics and Health sciences, this distribution seems to model the data better than the standard Gaussian distribution References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972. .. [2] The Laplace distribution and generalizations By Samuel Kotz, Tomasz J. Kozubowski, Krzysztof Podgorski, Birkhauser, 2001. .. [3] Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LaplaceDistribution.html .. [4] Wikipedia, "Laplace distribution", http://en.wikipedia.org/wiki/Laplace_distribution Examples -------- Draw samples from the distribution >>> loc, scale = 0., 1. >>> s = np.random.laplace(loc, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, normed=True) >>> x = np.arange(-8., 8., .01) >>> pdf = np.exp(-abs(x-loc/scale))/(2.*scale) >>> plt.plot(x, pdf) Plot Gaussian for comparison: >>> g = (1/(scale * np.sqrt(2 * np.pi)) * ... np.exp( - (x - loc)**2 / (2 * scale**2) )) >>> plt.plot(x,g) """ return None def logistic(self, loc, scale, size): """ logistic(loc=0.0, scale=1.0, size=None) Draw samples from a Logistic distribution. Samples are drawn from a Logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0). Parameters ---------- loc : float scale : float > 0. size : {tuple, int} Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} where the values are all integers in [0, n]. See Also -------- scipy.stats.distributions.logistic : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Logistic distribution is .. math:: P(x) = P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2}, where :math:`\mu` = location and :math:`s` = scale. The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable. References ---------- .. [1] Reiss, R.-D. and Thomas M. (2001), Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields, Birkhauser Verlag, Basel, pp 132-133. .. [2] Weisstein, Eric W. "Logistic Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LogisticDistribution.html .. [3] Wikipedia, "Logistic-distribution", http://en.wikipedia.org/wiki/Logistic-distribution Examples -------- Draw samples from the distribution: >>> loc, scale = 10, 1 >>> s = np.random.logistic(loc, scale, 10000) >>> count, bins, ignored = plt.hist(s, bins=50) # plot against distribution >>> def logist(x, loc, scale): ... return exp((loc-x)/scale)/(scale*(1+exp((loc-x)/scale))**2) >>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\ ... logist(bins, loc, scale).max()) >>> plt.show() """ return ndarray() def lognormal(self, mean, sigma, size): """ lognormal(mean=0.0, sigma=1.0, size=None) Return samples drawn from a log-normal distribution. Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from. Parameters ---------- mean : float Mean value of the underlying normal distribution sigma : float, > 0. Standard deviation of the underlying normal distribution size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : ndarray or float The desired samples. An array of the same shape as `size` if given, if `size` is None a float is returned. See Also -------- scipy.stats.lognorm : probability density function, distribution, cumulative density function, etc. Notes ----- A variable `x` has a log-normal distribution if `log(x)` is normally distributed. The probability density function for the log-normal distribution is: .. math:: p(x) = \frac{1}{\sigma x \sqrt{2\pi}} e^{(-\frac{(ln(x)-\mu)^2}{2\sigma^2})} where :math:`\mu` is the mean and :math:`\sigma` is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the *product* of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the *sum* of a large number of independent, identically-distributed variables. References ---------- Limpert, E., Stahel, W. A., and Abbt, M., "Log-normal Distributions across the Sciences: Keys and Clues," *BioScience*, Vol. 51, No. 5, May, 2001. http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf Reiss, R.D. and Thomas, M., *Statistical Analysis of Extreme Values*, Basel: Birkhauser Verlag, 2001, pp. 31-32. Examples -------- Draw samples from the distribution: >>> mu, sigma = 3., 1. # mean and standard deviation >>> s = np.random.lognormal(mu, sigma, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='mid') >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, linewidth=2, color='r') >>> plt.axis('tight') >>> plt.show() Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function. >>> # Generate a thousand samples: each is the product of 100 random >>> # values, drawn from a normal distribution. >>> b = [] >>> for i in range(1000): ... a = 10. + np.random.random(100) ... b.append(np.product(a)) >>> b = np.array(b) / np.min(b) # scale values to be positive >>> count, bins, ignored = plt.hist(b, 100, normed=True, align='center') >>> sigma = np.std(np.log(b)) >>> mu = np.mean(np.log(b)) >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, color='r', linewidth=2) >>> plt.show() """ return ndarray() if False else float() def logseries(self, loc, scale, size): """ logseries(p, size=None) Draw samples from a Logarithmic Series distribution. Samples are drawn from a Log Series distribution with specified parameter, p (probability, 0 < p < 1). Parameters ---------- loc : float scale : float > 0. size : {tuple, int} Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} where the values are all integers in [0, n]. See Also -------- scipy.stats.distributions.logser : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Log Series distribution is .. math:: P(k) = \frac{-p^k}{k \ln(1-p)}, where p = probability. The Log Series distribution is frequently used to represent species richness and occurrence, first proposed by Fisher, Corbet, and Williams in 1943 [2]. It may also be used to model the numbers of occupants seen in cars [3]. References ---------- .. [1] Buzas, Martin A.; Culver, Stephen J., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9). .. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58. .. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small Data Sets, CRC Press, 1994. .. [4] Wikipedia, "Logarithmic-distribution", http://en.wikipedia.org/wiki/Logarithmic-distribution Examples -------- Draw samples from the distribution: >>> a = .6 >>> s = np.random.logseries(a, 10000) >>> count, bins, ignored = plt.hist(s) # plot against distribution >>> def logseries(k, p): ... return -p**k/(k*log(1-p)) >>> plt.plot(bins, logseries(bins, a)*count.max()/ logseries(bins, a).max(), 'r') >>> plt.show() """ return ndarray() def multinomial(self, n, pvals, size): """ multinomial(n, pvals, size=None) Draw samples from a multinomial distribution. The multinomial distribution is a multivariate generalisation of the binomial distribution. Take an experiment with one of ``p`` possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents `n` such experiments. Its values, ``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the outcome was ``i``. Parameters ---------- n : int Number of experiments. pvals : sequence of floats, length p Probabilities of each of the ``p`` different outcomes. These should sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as ``sum(pvals[:-1]) <= 1)``. size : tuple of ints Given a `size` of ``(M, N, K)``, then ``M*N*K`` samples are drawn, and the output shape becomes ``(M, N, K, p)``, since each sample has shape ``(p,)``. Examples -------- Throw a dice 20 times: >>> np.random.multinomial(20, [1/6.]*6, size=1) array([[4, 1, 7, 5, 2, 1]]) It landed 4 times on 1, once on 2, etc. Now, throw the dice 20 times, and 20 times again: >>> np.random.multinomial(20, [1/6.]*6, size=2) array([[3, 4, 3, 3, 4, 3], [2, 4, 3, 4, 0, 7]]) For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc. A loaded dice is more likely to land on number 6: >>> np.random.multinomial(100, [1/7.]*5) array([13, 16, 13, 16, 42]) """ return None def multivariate_normal(self, mean, cov, size): """ multivariate_normal(mean, cov[, size]) Draw random samples from a multivariate normal distribution. The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Such a distribution is specified by its mean and covariance matrix. These parameters are analogous to the mean (average or "center") and variance (standard deviation, or "width," squared) of the one-dimensional normal distribution. Parameters ---------- mean : 1-D array_like, of length N Mean of the N-dimensional distribution. cov : 2-D array_like, of shape (N, N) Covariance matrix of the distribution. Must be symmetric and positive semi-definite for "physically meaningful" results. size : int or tuple of ints, optional Given a shape of, for example, ``(m,n,k)``, ``m*n*k`` samples are generated, and packed in an `m`-by-`n`-by-`k` arrangement. Because each sample is `N`-dimensional, the output shape is ``(m,n,k,N)``. If no shape is specified, a single (`N`-D) sample is returned. Returns ------- out : ndarray The drawn samples, of shape *size*, if that was provided. If not, the shape is ``(N,)``. In other words, each entry ``out[i,j,...,:]`` is an N-dimensional value drawn from the distribution. Notes ----- The mean is a coordinate in N-dimensional space, which represents the location where samples are most likely to be generated. This is analogous to the peak of the bell curve for the one-dimensional or univariate normal distribution. Covariance indicates the level to which two variables vary together. From the multivariate normal distribution, we draw N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]`. The covariance matrix element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance of :math:`x_i` (i.e. its "spread"). Instead of specifying the full covariance matrix, popular approximations include: - Spherical covariance (*cov* is a multiple of the identity matrix) - Diagonal covariance (*cov* has non-negative elements, and only on the diagonal) This geometrical property can be seen in two dimensions by plotting generated data-points: >>> mean = [0,0] >>> cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis >>> import matplotlib.pyplot as plt >>> x,y = np.random.multivariate_normal(mean,cov,5000).T >>> plt.plot(x,y,'x'); plt.axis('equal'); plt.show() Note that the covariance matrix must be non-negative definite. References ---------- Papoulis, A., *Probability, Random Variables, and Stochastic Processes*, 3rd ed., New York: McGraw-Hill, 1991. Duda, R. O., Hart, P. E., and Stork, D. G., *Pattern Classification*, 2nd ed., New York: Wiley, 2001. Examples -------- >>> mean = (1,2) >>> cov = [[1,0],[1,0]] >>> x = np.random.multivariate_normal(mean,cov,(3,3)) >>> x.shape (3, 3, 2) The following is probably true, given that 0.6 is roughly twice the standard deviation: >>> print list( (x[0,0,:] - mean) < 0.6 ) [True, True] """ return ndarray() def negative_binomial(self, n, p, size): """ negative_binomial(n, p, size=None) Draw samples from a negative_binomial distribution. Samples are drawn from a negative_Binomial distribution with specified parameters, `n` trials and `p` probability of success where `n` is an integer > 0 and `p` is in the interval [0, 1]. Parameters ---------- n : int Parameter, > 0. p : float Parameter, >= 0 and <=1. size : int or tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : int or ndarray of ints Drawn samples. Notes ----- The probability density for the Negative Binomial distribution is .. math:: P(N;n,p) = \binom{N+n-1}{n-1}p^{n}(1-p)^{N}, where :math:`n-1` is the number of successes, :math:`p` is the probability of success, and :math:`N+n-1` is the number of trials. The negative binomial distribution gives the probability of n-1 successes and N failures in N+n-1 trials, and success on the (N+n)th trial. If one throws a die repeatedly until the third time a "1" appears, then the probability distribution of the number of non-"1"s that appear before the third "1" is a negative binomial distribution. References ---------- .. [1] Weisstein, Eric W. "Negative Binomial Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NegativeBinomialDistribution.html .. [2] Wikipedia, "Negative binomial distribution", http://en.wikipedia.org/wiki/Negative_binomial_distribution Examples -------- Draw samples from the distribution: A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.? >>> s = np.random.negative_binomial(1, 0.1, 100000) >>> for i in range(1, 11): ... probability = sum(s= 1. nonc : float Non-centrality, should be > 0. size : int or tuple of ints Shape of the output. Notes ----- The probability density function for the noncentral Chi-square distribution is .. math:: P(x;df,nonc) = \sum^{\infty}_{i=0} \frac{e^{-nonc/2}(nonc/2)^{i}}{i!}P_{Y_{df+2i}}(x), where :math:`Y_{q}` is the Chi-square with q degrees of freedom. In Delhi (2007), it is noted that the noncentral chi-square is useful in bombing and coverage problems, the probability of killing the point target given by the noncentral chi-squared distribution. References ---------- .. [1] Delhi, M.S. Holla, "On a noncentral chi-square distribution in the analysis of weapon systems effectiveness", Metrika, Volume 15, Number 1 / December, 1970. .. [2] Wikipedia, "Noncentral chi-square distribution" http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution Examples -------- Draw values from the distribution and plot the histogram >>> import matplotlib.pyplot as plt >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000), ... bins=200, normed=True) >>> plt.show() Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare. >>> plt.figure() >>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000), ... bins=np.arange(0., 25, .1), normed=True) >>> values2 = plt.hist(np.random.chisquare(3, 100000), ... bins=np.arange(0., 25, .1), normed=True) >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob') >>> plt.show() Demonstrate how large values of non-centrality lead to a more symmetric distribution. >>> plt.figure() >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000), ... bins=200, normed=True) >>> plt.show() """ return None def noncentral_f(self, dfnum, dfden, nonc, size): """ noncentral_f(dfnum, dfden, nonc, size=None) Draw samples from the noncentral F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters > 1. `nonc` is the non-centrality parameter. Parameters ---------- dfnum : int Parameter, should be > 1. dfden : int Parameter, should be > 1. nonc : float Parameter, should be >= 0. size : int or tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : scalar or ndarray Drawn samples. Notes ----- When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic. References ---------- Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html Wikipedia, "Noncentral F distribution", http://en.wikipedia.org/wiki/Noncentral_F-distribution Examples -------- In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We'll plot the two probability distributions for comparison. >>> dfnum = 3 # between group deg of freedom >>> dfden = 20 # within groups degrees of freedom >>> nonc = 3.0 >>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000) >>> NF = np.histogram(nc_vals, bins=50, normed=True) >>> c_vals = np.random.f(dfnum, dfden, 1000000) >>> F = np.histogram(c_vals, bins=50, normed=True) >>> plt.plot(F[1][1:], F[0]) >>> plt.plot(NF[1][1:], NF[0]) >>> plt.show() """ return float() if False else ndarray() def normal(self, loc, scale, size): """ normal(loc=0.0, scale=1.0, size=None) Draw random samples from a normal (Gaussian) distribution. The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [2]_, is often called the bell curve because of its characteristic shape (see the example below). The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [2]_. Parameters ---------- loc : float Mean ("centre") of the distribution. scale : float Standard deviation (spread or "width") of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. See Also -------- scipy.stats.distributions.norm : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gaussian distribution is .. math:: p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }} e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} }, where :math:`\mu` is the mean and :math:`\sigma` the standard deviation. The square of the standard deviation, :math:`\sigma^2`, is called the variance. The function has its peak at the mean, and its "spread" increases with the standard deviation (the function reaches 0.607 times its maximum at :math:`x + \sigma` and :math:`x - \sigma` [2]_). This implies that `numpy.random.normal` is more likely to return samples lying close to the mean, rather than those far away. References ---------- .. [1] Wikipedia, "Normal distribution", http://en.wikipedia.org/wiki/Normal_distribution .. [2] P. R. Peebles Jr., "Central Limit Theorem" in "Probability, Random Variables and Random Signal Principles", 4th ed., 2001, pp. 51, 51, 125. Examples -------- Draw samples from the distribution: >>> mu, sigma = 0, 0.1 # mean and standard deviation >>> s = np.random.normal(mu, sigma, 1000) Verify the mean and the variance: >>> abs(mu - np.mean(s)) < 0.01 True >>> abs(sigma - np.std(s, ddof=1)) < 0.01 True Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, normed=True) >>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * ... np.exp( - (bins - mu)**2 / (2 * sigma**2) ), ... linewidth=2, color='r') >>> plt.show() """ return None def pareto(self, shape, size): """ pareto(a, size=None) Draw samples from a Pareto II or Lomax distribution with specified shape. The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding the location parameter m, see below. The smallest value of the Lomax distribution is zero while for the classical Pareto distribution it is m, where the standard Pareto distribution has location m=1. Lomax can also be considered as a simplified version of the Generalized Pareto distribution (available in SciPy), with the scale set to one and the location set to zero. The Pareto distribution must be greater than zero, and is unbounded above. It is also known as the "80-20 rule". In this distribution, 80 percent of the weights are in the lowest 20 percent of the range, while the other 20 percent fill the remaining 80 percent of the range. Parameters ---------- shape : float, > 0. Shape of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. See Also -------- scipy.stats.distributions.lomax.pdf : probability density function, distribution or cumulative density function, etc. scipy.stats.distributions.genpareto.pdf : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Pareto distribution is .. math:: p(x) = \frac{am^a}{x^{a+1}} where :math:`a` is the shape and :math:`m` the location The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution useful in many real world problems. Outside the field of economics it is generally referred to as the Bradford distribution. Pareto developed the distribution to describe the distribution of wealth in an economy. It has also found use in insurance, web page access statistics, oil field sizes, and many other problems, including the download frequency for projects in Sourceforge [1]. It is one of the so-called "fat-tailed" distributions. References ---------- .. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of Sourceforge projects. .. [2] Pareto, V. (1896). Course of Political Economy. Lausanne. .. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme Values, Birkhauser Verlag, Basel, pp 23-30. .. [4] Wikipedia, "Pareto distribution", http://en.wikipedia.org/wiki/Pareto_distribution Examples -------- Draw samples from the distribution: >>> a, m = 3., 1. # shape and mode >>> s = np.random.pareto(a, 1000) + m Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 100, normed=True, align='center') >>> fit = a*m**a/bins**(a+1) >>> plt.plot(bins, max(count)*fit/max(fit),linewidth=2, color='r') >>> plt.show() """ return None def permutation(self, x): """ permutation(x) Randomly permute a sequence, or return a permuted range. If `x` is a multi-dimensional array, it is only shuffled along its first index. Parameters ---------- x : int or array_like If `x` is an integer, randomly permute ``np.arange(x)``. If `x` is an array, make a copy and shuffle the elements randomly. Returns ------- out : ndarray Permuted sequence or array range. Examples -------- >>> np.random.permutation(10) array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6]) >>> np.random.permutation([1, 4, 9, 12, 15]) array([15, 1, 9, 4, 12]) >>> arr = np.arange(9).reshape((3, 3)) >>> np.random.permutation(arr) array([[6, 7, 8], [0, 1, 2], [3, 4, 5]]) """ return ndarray() def poisson(self, lam, size): """ poisson(lam=1.0, size=None) Draw samples from a Poisson distribution. The Poisson distribution is the limit of the Binomial distribution for large N. Parameters ---------- lam : float Expectation of interval, should be >= 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Notes ----- The Poisson distribution .. math:: f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!} For events with an expected separation :math:`\lambda` the Poisson distribution :math:`f(k; \lambda)` describes the probability of :math:`k` events occurring within the observed interval :math:`\lambda`. Because the output is limited to the range of the C long type, a ValueError is raised when `lam` is within 10 sigma of the maximum representable value. References ---------- .. [1] Weisstein, Eric W. "Poisson Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html .. [2] Wikipedia, "Poisson distribution", http://en.wikipedia.org/wiki/Poisson_distribution Examples -------- Draw samples from the distribution: >>> import numpy as np >>> s = np.random.poisson(5, 10000) Display histogram of the sample: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 14, normed=True) >>> plt.show() """ return None def power(self, a, size): """ power(a, size=None) Draws samples in [0, 1] from a power distribution with positive exponent a - 1. Also known as the power function distribution. Parameters ---------- a : float parameter, > 0 size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : {ndarray, scalar} The returned samples lie in [0, 1]. Raises ------ ValueError If a<1. Notes ----- The probability density function is .. math:: P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0. The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution. It is used, for example, in modeling the over-reporting of insurance claims. References ---------- .. [1] Christian Kleiber, Samuel Kotz, "Statistical size distributions in economics and actuarial sciences", Wiley, 2003. .. [2] Heckert, N. A. and Filliben, James J. (2003). NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions", National Institute of Standards and Technology Handbook Series, June 2003. http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf Examples -------- Draw samples from the distribution: >>> a = 5. # shape >>> samples = 1000 >>> s = np.random.power(a, samples) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, bins=30) >>> x = np.linspace(0, 1, 100) >>> y = a*x**(a-1.) >>> normed_y = samples*np.diff(bins)[0]*y >>> plt.plot(x, normed_y) >>> plt.show() Compare the power function distribution to the inverse of the Pareto. >>> from scipy import stats >>> rvs = np.random.power(5, 1000000) >>> rvsp = np.random.pareto(5, 1000000) >>> xx = np.linspace(0,1,100) >>> powpdf = stats.powerlaw.pdf(xx,5) >>> plt.figure() >>> plt.hist(rvs, bins=50, normed=True) >>> plt.plot(xx,powpdf,'r-') >>> plt.title('np.random.power(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, normed=True) >>> plt.plot(xx,powpdf,'r-') >>> plt.title('inverse of 1 + np.random.pareto(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, normed=True) >>> plt.plot(xx,powpdf,'r-') >>> plt.title('inverse of stats.pareto(5)') """ return ndarray() print_function = instance() def rand(self, d0d1more_argsdn): """ rand(d0, d1, ..., dn) Random values in a given shape. Create an array of the given shape and propagate it with random samples from a uniform distribution over ``[0, 1)``. Parameters ---------- d0, d1, ..., dn : int, optional The dimensions of the returned array, should all be positive. If no argument is given a single Python float is returned. Returns ------- out : ndarray, shape ``(d0, d1, ..., dn)`` Random values. See Also -------- random Notes ----- This is a convenience function. If you want an interface that takes a shape-tuple as the first argument, refer to np.random.random_sample . Examples -------- >>> np.random.rand(3,2) array([[ 0.14022471, 0.96360618], #random [ 0.37601032, 0.25528411], #random [ 0.49313049, 0.94909878]]) #random """ return None def randint(self, low, high, size): """ randint(low, high=None, size=None) Return random integers from `low` (inclusive) to `high` (exclusive). Return random integers from the "discrete uniform" distribution in the "half-open" interval [`low`, `high`). If `high` is None (the default), then results are from [0, `low`). Parameters ---------- low : int Lowest (signed) integer to be drawn from the distribution (unless ``high=None``, in which case this parameter is the *highest* such integer). high : int, optional If provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if ``high=None``). size : int or tuple of ints, optional Output shape. Default is None, in which case a single int is returned. Returns ------- out : int or ndarray of ints `size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided. See Also -------- random.random_integers : similar to `randint`, only for the closed interval [`low`, `high`], and 1 is the lowest value if `high` is omitted. In particular, this other one is the one to use to generate uniformly distributed discrete non-integers. Examples -------- >>> np.random.randint(2, size=10) array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) >>> np.random.randint(1, size=10) array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) Generate a 2 x 4 array of ints between 0 and 4, inclusive: >>> np.random.randint(5, size=(2, 4)) array([[4, 0, 2, 1], [3, 2, 2, 0]]) """ return int() if False else ndarray() def randn(self, d0d1more_argsdn): """ randn(d0, d1, ..., dn) Return a sample (or samples) from the "standard normal" distribution. If positive, int_like or int-convertible arguments are provided, `randn` generates an array of shape ``(d0, d1, ..., dn)``, filled with random floats sampled from a univariate "normal" (Gaussian) distribution of mean 0 and variance 1 (if any of the :math:`d_i` are floats, they are first converted to integers by truncation). A single float randomly sampled from the distribution is returned if no argument is provided. This is a convenience function. If you want an interface that takes a tuple as the first argument, use `numpy.random.standard_normal` instead. Parameters ---------- d0, d1, ..., dn : int, optional The dimensions of the returned array, should be all positive. If no argument is given a single Python float is returned. Returns ------- Z : ndarray or float A ``(d0, d1, ..., dn)``-shaped array of floating-point samples from the standard normal distribution, or a single such float if no parameters were supplied. See Also -------- random.standard_normal : Similar, but takes a tuple as its argument. Notes ----- For random samples from :math:`N(\mu, \sigma^2)`, use: ``sigma * np.random.randn(...) + mu`` Examples -------- >>> np.random.randn() 2.1923875335537315 #random Two-by-four array of samples from N(3, 6.25): >>> 2.5 * np.random.randn(2, 4) + 3 array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], #random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) #random """ return ndarray() if False else float() def random_sample(self, size): """ random_sample(size=None) Return random floats in the half-open interval [0.0, 1.0). Results are from the "continuous uniform" distribution over the stated interval. To sample :math:`Unif[a, b), b > a` multiply the output of `random_sample` by `(b-a)` and add `a`:: (b - a) * random_sample() + a Parameters ---------- size : int or tuple of ints, optional Defines the shape of the returned array of random floats. If None (the default), returns a single float. Returns ------- out : float or ndarray of floats Array of random floats of shape `size` (unless ``size=None``, in which case a single float is returned). Examples -------- >>> np.random.random_sample() 0.47108547995356098 >>> type(np.random.random_sample()) >>> np.random.random_sample((5,)) array([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) Three-by-two array of random numbers from [-5, 0): >>> 5 * np.random.random_sample((3, 2)) - 5 array([[-3.99149989, -0.52338984], [-2.99091858, -0.79479508], [-1.23204345, -1.75224494]]) """ return float() if False else ndarray() def random_integers(self, low, high, size): """ random_integers(low, high=None, size=None) Return random integers between `low` and `high`, inclusive. Return random integers from the "discrete uniform" distribution in the closed interval [`low`, `high`]. If `high` is None (the default), then results are from [1, `low`]. Parameters ---------- low : int Lowest (signed) integer to be drawn from the distribution (unless ``high=None``, in which case this parameter is the *highest* such integer). high : int, optional If provided, the largest (signed) integer to be drawn from the distribution (see above for behavior if ``high=None``). size : int or tuple of ints, optional Output shape. Default is None, in which case a single int is returned. Returns ------- out : int or ndarray of ints `size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided. See Also -------- random.randint : Similar to `random_integers`, only for the half-open interval [`low`, `high`), and 0 is the lowest value if `high` is omitted. Notes ----- To sample from N evenly spaced floating-point numbers between a and b, use:: a + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.) Examples -------- >>> np.random.random_integers(5) 4 >>> type(np.random.random_integers(5)) >>> np.random.random_integers(5, size=(3.,2.)) array([[5, 4], [3, 3], [4, 5]]) Choose five random numbers from the set of five evenly-spaced numbers between 0 and 2.5, inclusive (*i.e.*, from the set :math:`{0, 5/8, 10/8, 15/8, 20/8}`): >>> 2.5 * (np.random.random_integers(5, size=(5,)) - 1) / 4. array([ 0.625, 1.25 , 0.625, 0.625, 2.5 ]) Roll two six sided dice 1000 times and sum the results: >>> d1 = np.random.random_integers(1, 6, 1000) >>> d2 = np.random.random_integers(1, 6, 1000) >>> dsums = d1 + d2 Display results as a histogram: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(dsums, 11, normed=True) >>> plt.show() """ return int() if False else ndarray() def random_sample(self, size): """ random_sample(size=None) Return random floats in the half-open interval [0.0, 1.0). Results are from the "continuous uniform" distribution over the stated interval. To sample :math:`Unif[a, b), b > a` multiply the output of `random_sample` by `(b-a)` and add `a`:: (b - a) * random_sample() + a Parameters ---------- size : int or tuple of ints, optional Defines the shape of the returned array of random floats. If None (the default), returns a single float. Returns ------- out : float or ndarray of floats Array of random floats of shape `size` (unless ``size=None``, in which case a single float is returned). Examples -------- >>> np.random.random_sample() 0.47108547995356098 >>> type(np.random.random_sample()) >>> np.random.random_sample((5,)) array([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) Three-by-two array of random numbers from [-5, 0): >>> 5 * np.random.random_sample((3, 2)) - 5 array([[-3.99149989, -0.52338984], [-2.99091858, -0.79479508], [-1.23204345, -1.75224494]]) """ return float() if False else ndarray() def random_sample(self, size): """ random_sample(size=None) Return random floats in the half-open interval [0.0, 1.0). Results are from the "continuous uniform" distribution over the stated interval. To sample :math:`Unif[a, b), b > a` multiply the output of `random_sample` by `(b-a)` and add `a`:: (b - a) * random_sample() + a Parameters ---------- size : int or tuple of ints, optional Defines the shape of the returned array of random floats. If None (the default), returns a single float. Returns ------- out : float or ndarray of floats Array of random floats of shape `size` (unless ``size=None``, in which case a single float is returned). Examples -------- >>> np.random.random_sample() 0.47108547995356098 >>> type(np.random.random_sample()) >>> np.random.random_sample((5,)) array([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) Three-by-two array of random numbers from [-5, 0): >>> 5 * np.random.random_sample((3, 2)) - 5 array([[-3.99149989, -0.52338984], [-2.99091858, -0.79479508], [-1.23204345, -1.75224494]]) """ return float() if False else ndarray() def rayleigh(self, scale, size): """ rayleigh(scale=1.0, size=None) Draw samples from a Rayleigh distribution. The :math:`\chi` and Weibull distributions are generalizations of the Rayleigh. Parameters ---------- scale : scalar Scale, also equals the mode. Should be >= 0. size : int or tuple of ints, optional Shape of the output. Default is None, in which case a single value is returned. Notes ----- The probability density function for the Rayleigh distribution is .. math:: P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}} The Rayleigh distribution arises if the wind speed and wind direction are both gaussian variables, then the vector wind velocity forms a Rayleigh distribution. The Rayleigh distribution is used to model the expected output from wind turbines. References ---------- .. [1] Brighton Webs Ltd., Rayleigh Distribution, http://www.brighton-webs.co.uk/distributions/rayleigh.asp .. [2] Wikipedia, "Rayleigh distribution" http://en.wikipedia.org/wiki/Rayleigh_distribution Examples -------- Draw values from the distribution and plot the histogram >>> values = hist(np.random.rayleigh(3, 100000), bins=200, normed=True) Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters? >>> meanvalue = 1 >>> modevalue = np.sqrt(2 / np.pi) * meanvalue >>> s = np.random.rayleigh(modevalue, 1000000) The percentage of waves larger than 3 meters is: >>> 100.*sum(s>3)/1000000. 0.087300000000000003 """ return None def random_sample(self, size): """ random_sample(size=None) Return random floats in the half-open interval [0.0, 1.0). Results are from the "continuous uniform" distribution over the stated interval. To sample :math:`Unif[a, b), b > a` multiply the output of `random_sample` by `(b-a)` and add `a`:: (b - a) * random_sample() + a Parameters ---------- size : int or tuple of ints, optional Defines the shape of the returned array of random floats. If None (the default), returns a single float. Returns ------- out : float or ndarray of floats Array of random floats of shape `size` (unless ``size=None``, in which case a single float is returned). Examples -------- >>> np.random.random_sample() 0.47108547995356098 >>> type(np.random.random_sample()) >>> np.random.random_sample((5,)) array([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) Three-by-two array of random numbers from [-5, 0): >>> 5 * np.random.random_sample((3, 2)) - 5 array([[-3.99149989, -0.52338984], [-2.99091858, -0.79479508], [-1.23204345, -1.75224494]]) """ return float() if False else ndarray() def seed(self, seed): """ seed(seed=None) Seed the generator. This method is called when `RandomState` is initialized. It can be called again to re-seed the generator. For details, see `RandomState`. Parameters ---------- seed : int or array_like, optional Seed for `RandomState`. See Also -------- RandomState """ return None def set_state(self, state): """ set_state(state) Set the internal state of the generator from a tuple. For use if one has reason to manually (re-)set the internal state of the "Mersenne Twister"[1]_ pseudo-random number generating algorithm. Parameters ---------- state : tuple(str, ndarray of 624 uints, int, int, float) The `state` tuple has the following items: 1. the string 'MT19937', specifying the Mersenne Twister algorithm. 2. a 1-D array of 624 unsigned integers ``keys``. 3. an integer ``pos``. 4. an integer ``has_gauss``. 5. a float ``cached_gaussian``. Returns ------- out : None Returns 'None' on success. See Also -------- get_state Notes ----- `set_state` and `get_state` are not needed to work with any of the random distributions in NumPy. If the internal state is manually altered, the user should know exactly what he/she is doing. For backwards compatibility, the form (str, array of 624 uints, int) is also accepted although it is missing some information about the cached Gaussian value: ``state = ('MT19937', keys, pos)``. References ---------- .. [1] M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator," *ACM Trans. on Modeling and Computer Simulation*, Vol. 8, No. 1, pp. 3-30, Jan. 1998. """ return None def shuffle(self, x): """ shuffle(x) Modify a sequence in-place by shuffling its contents. Parameters ---------- x : array_like The array or list to be shuffled. Returns ------- None Examples -------- >>> arr = np.arange(10) >>> np.random.shuffle(arr) >>> arr [1 7 5 2 9 4 3 6 0 8] This function only shuffles the array along the first index of a multi-dimensional array: >>> arr = np.arange(9).reshape((3, 3)) >>> np.random.shuffle(arr) >>> arr array([[3, 4, 5], [6, 7, 8], [0, 1, 2]]) """ return None def standard_cauchy(self, size): """ standard_cauchy(size=None) Standard Cauchy distribution with mode = 0. Also known as the Lorentz distribution. Parameters ---------- size : int or tuple of ints Shape of the output. Returns ------- samples : ndarray or scalar The drawn samples. Notes ----- The probability density function for the full Cauchy distribution is .. math:: P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+ (\frac{x-x_0}{\gamma})^2 \bigr] } and the Standard Cauchy distribution just sets :math:`x_0=0` and :math:`\gamma=1` The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis. When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails. References ---------- .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "Cauchy Distribution", http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm .. [2] Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CauchyDistribution.html .. [3] Wikipedia, "Cauchy distribution" http://en.wikipedia.org/wiki/Cauchy_distribution Examples -------- Draw samples and plot the distribution: >>> s = np.random.standard_cauchy(1000000) >>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well >>> plt.hist(s, bins=100) >>> plt.show() """ return ndarray() if False else float() def standard_exponential(self, size): """ standard_exponential(size=None) Draw samples from the standard exponential distribution. `standard_exponential` is identical to the exponential distribution with a scale parameter of 1. Parameters ---------- size : int or tuple of ints Shape of the output. Returns ------- out : float or ndarray Drawn samples. Examples -------- Output a 3x8000 array: >>> n = np.random.standard_exponential((3, 8000)) """ return float() if False else ndarray() def standard_gamma(self, shape, size): """ standard_gamma(shape, size=None) Draw samples from a Standard Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated "k") and scale=1. Parameters ---------- shape : float Parameter, should be > 0. size : int or tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : ndarray or scalar The drawn samples. See Also -------- scipy.stats.distributions.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma-distribution", http://en.wikipedia.org/wiki/Gamma-distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 1. # mean and width >>> s = np.random.standard_gamma(shape, 1000000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ \ ... (sps.gamma(shape) * scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') >>> plt.show() """ return ndarray() if False else float() def standard_normal(self, size): """ standard_normal(size=None) Returns samples from a Standard Normal distribution (mean=0, stdev=1). Parameters ---------- size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- out : float or ndarray Drawn samples. Examples -------- >>> s = np.random.standard_normal(8000) >>> s array([ 0.6888893 , 0.78096262, -0.89086505, ..., 0.49876311, #random -0.38672696, -0.4685006 ]) #random >>> s.shape (8000,) >>> s = np.random.standard_normal(size=(3, 4, 2)) >>> s.shape (3, 4, 2) """ return float() if False else ndarray() def standard_t(self, df, size): """ standard_t(df, size=None) Standard Student's t distribution with df degrees of freedom. A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution (`standard_normal`). Parameters ---------- df : int Degrees of freedom, should be > 0. size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar Drawn samples. Notes ----- The probability density function for the t distribution is .. math:: P(x, df) = \frac{\Gamma(\frac{df+1}{2})}{\sqrt{\pi df} \Gamma(\frac{df}{2})}\Bigl( 1+\frac{x^2}{df} \Bigr)^{-(df+1)/2} The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean. The derivation of the t-distribution was forst published in 1908 by William Gisset while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics With R", Springer, 2002. .. [2] Wikipedia, "Student's t-distribution" http://en.wikipedia.org/wiki/Student's_t-distribution Examples -------- From Dalgaard page 83 [1]_, suppose the daily energy intake for 11 women in Kj is: >>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \ ... 7515, 8230, 8770]) Does their energy intake deviate systematically from the recommended value of 7725 kJ? We have 10 degrees of freedom, so is the sample mean within 95% of the recommended value? >>> s = np.random.standard_t(10, size=100000) >>> np.mean(intake) 6753.636363636364 >>> intake.std(ddof=1) 1142.1232221373727 Calculate the t statistic, setting the ddof parameter to the unbiased value so the divisor in the standard deviation will be degrees of freedom, N-1. >>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake))) >>> import matplotlib.pyplot as plt >>> h = plt.hist(s, bins=100, normed=True) For a one-sided t-test, how far out in the distribution does the t statistic appear? >>> >>> np.sum(s`_). raise_warnings : str or sequence of warnings, optional This specifies which warnings to configure as 'raise' instead of 'warn' during the test execution. Valid strings are: - "develop" : equals ``(DeprecationWarning, RuntimeWarning)`` - "release" : equals ``()``, don't raise on any warnings. Returns ------- result : object Returns the result of running the tests as a ``nose.result.TextTestResult`` object. Notes ----- Each NumPy module exposes `test` in its namespace to run all tests for it. For example, to run all tests for numpy.lib: >>> np.lib.test() #doctest: +SKIP Examples -------- >>> result = np.lib.test() #doctest: +SKIP Running unit tests for numpy.lib ... Ran 976 tests in 3.933s OK >>> result.errors #doctest: +SKIP [] >>> result.knownfail #doctest: +SKIP [] """ return object() def triangular(self, left, mode, right, size): """ triangular(left, mode, right, size=None) Draw samples from the triangular distribution. The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf. Parameters ---------- left : scalar Lower limit. mode : scalar The value where the peak of the distribution occurs. The value should fulfill the condition ``left <= mode <= right``. right : scalar Upper limit, should be larger than `left`. size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar The returned samples all lie in the interval [left, right]. Notes ----- The probability density function for the Triangular distribution is .. math:: P(x;l, m, r) = \begin{cases} \frac{2(x-l)}{(r-l)(m-l)}& \text{for $l \leq x \leq m$},\\ \frac{2(m-x)}{(r-l)(r-m)}& \text{for $m \leq x \leq r$},\\ 0& \text{otherwise}. \end{cases} The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations. References ---------- .. [1] Wikipedia, "Triangular distribution" http://en.wikipedia.org/wiki/Triangular_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.triangular(-3, 0, 8, 100000), bins=200, ... normed=True) >>> plt.show() """ return ndarray() if False else float() def uniform(self, low, high, size): """ uniform(low=0.0, high=1.0, size=1) Draw samples from a uniform distribution. Samples are uniformly distributed over the half-open interval ``[low, high)`` (includes low, but excludes high). In other words, any value within the given interval is equally likely to be drawn by `uniform`. Parameters ---------- low : float, optional Lower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0. high : float Upper boundary of the output interval. All values generated will be less than high. The default value is 1.0. size : int or tuple of ints, optional Shape of output. If the given size is, for example, (m,n,k), m*n*k samples are generated. If no shape is specified, a single sample is returned. Returns ------- out : ndarray Drawn samples, with shape `size`. See Also -------- randint : Discrete uniform distribution, yielding integers. random_integers : Discrete uniform distribution over the closed interval ``[low, high]``. random_sample : Floats uniformly distributed over ``[0, 1)``. random : Alias for `random_sample`. rand : Convenience function that accepts dimensions as input, e.g., ``rand(2,2)`` would generate a 2-by-2 array of floats, uniformly distributed over ``[0, 1)``. Notes ----- The probability density function of the uniform distribution is .. math:: p(x) = \frac{1}{b - a} anywhere within the interval ``[a, b)``, and zero elsewhere. Examples -------- Draw samples from the distribution: >>> s = np.random.uniform(-1,0,1000) All values are within the given interval: >>> np.all(s >= -1) True >>> np.all(s < 0) True Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 15, normed=True) >>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r') >>> plt.show() """ return ndarray() def vonmises(self, mu, kappa, size): """ vonmises(mu, kappa, size=None) Draw samples from a von Mises distribution. Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi]. The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution. Parameters ---------- mu : float Mode ("center") of the distribution. kappa : float Dispersion of the distribution, has to be >=0. size : int or tuple of int Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Returns ------- samples : scalar or ndarray The returned samples, which are in the interval [-pi, pi]. See Also -------- scipy.stats.distributions.vonmises : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the von Mises distribution is .. math:: p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)}, where :math:`\mu` is the mode and :math:`\kappa` the dispersion, and :math:`I_0(\kappa)` is the modified Bessel function of order 0. The von Mises is named for Richard Edler von Mises, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science. References ---------- Abramowitz, M. and Stegun, I. A. (ed.), *Handbook of Mathematical Functions*, New York: Dover, 1965. von Mises, R., *Mathematical Theory of Probability and Statistics*, New York: Academic Press, 1964. Examples -------- Draw samples from the distribution: >>> mu, kappa = 0.0, 4.0 # mean and dispersion >>> s = np.random.vonmises(mu, kappa, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> x = np.arange(-np.pi, np.pi, 2*np.pi/50.) >>> y = -np.exp(kappa*np.cos(x-mu))/(2*np.pi*sps.jn(0,kappa)) >>> plt.plot(x, y/max(y), linewidth=2, color='r') >>> plt.show() """ return float() if False else ndarray() def wald(self, mean, scale, size): """ wald(mean, scale, size=None) Draw samples from a Wald, or Inverse Gaussian, distribution. As the scale approaches infinity, the distribution becomes more like a Gaussian. Some references claim that the Wald is an Inverse Gaussian with mean=1, but this is by no means universal. The Inverse Gaussian distribution was first studied in relationship to Brownian motion. In 1956 M.C.K. Tweedie used the name Inverse Gaussian because there is an inverse relationship between the time to cover a unit distance and distance covered in unit time. Parameters ---------- mean : scalar Distribution mean, should be > 0. scale : scalar Scale parameter, should be >= 0. size : int or tuple of ints, optional Output shape. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar Drawn sample, all greater than zero. Notes ----- The probability density function for the Wald distribution is .. math:: P(x;mean,scale) = \sqrt{\frac{scale}{2\pi x^3}}e^ \frac{-scale(x-mean)^2}{2\cdotp mean^2x} As noted above the Inverse Gaussian distribution first arise from attempts to model Brownian Motion. It is also a competitor to the Weibull for use in reliability modeling and modeling stock returns and interest rate processes. References ---------- .. [1] Brighton Webs Ltd., Wald Distribution, http://www.brighton-webs.co.uk/distributions/wald.asp .. [2] Chhikara, Raj S., and Folks, J. Leroy, "The Inverse Gaussian Distribution: Theory : Methodology, and Applications", CRC Press, 1988. .. [3] Wikipedia, "Wald distribution" http://en.wikipedia.org/wiki/Wald_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.wald(3, 2, 100000), bins=200, normed=True) >>> plt.show() """ return ndarray() if False else float() def weibull(self, a, size): """ weibull(a, size=None) Weibull distribution. Draw samples from a 1-parameter Weibull distribution with the given shape parameter `a`. .. math:: X = (-ln(U))^{1/a} Here, U is drawn from the uniform distribution over (0,1]. The more common 2-parameter Weibull, including a scale parameter :math:`\lambda` is just :math:`X = \lambda(-ln(U))^{1/a}`. Parameters ---------- a : float Shape of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. See Also -------- scipy.stats.distributions.weibull_max scipy.stats.distributions.weibull_min scipy.stats.distributions.genextreme gumbel Notes ----- The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions. The probability density for the Weibull distribution is .. math:: p(x) = \frac{a} {\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a}, where :math:`a` is the shape and :math:`\lambda` the scale. The function has its peak (the mode) at :math:`\lambda(\frac{a-1}{a})^{1/a}`. When ``a = 1``, the Weibull distribution reduces to the exponential distribution. References ---------- .. [1] Waloddi Weibull, Professor, Royal Technical University, Stockholm, 1939 "A Statistical Theory Of The Strength Of Materials", Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm. .. [2] Waloddi Weibull, 1951 "A Statistical Distribution Function of Wide Applicability", Journal Of Applied Mechanics ASME Paper. .. [3] Wikipedia, "Weibull distribution", http://en.wikipedia.org/wiki/Weibull_distribution Examples -------- Draw samples from the distribution: >>> a = 5. # shape >>> s = np.random.weibull(a, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> x = np.arange(1,100.)/50. >>> def weib(x,n,a): ... return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a) >>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000)) >>> x = np.arange(1,100.)/50. >>> scale = count.max()/weib(x, 1., 5.).max() >>> plt.plot(x, weib(x, 1., 5.)*scale) >>> plt.show() """ return None def zipf(self, a, size): """ zipf(a, size=None) Draw samples from a Zipf distribution. Samples are drawn from a Zipf distribution with specified parameter `a` > 1. The Zipf distribution (also known as the zeta distribution) is a continuous probability distribution that satisfies Zipf's law: the frequency of an item is inversely proportional to its rank in a frequency table. Parameters ---------- a : float > 1 Distribution parameter. size : int or tuple of int, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn; a single integer is equivalent in its result to providing a mono-tuple, i.e., a 1-D array of length *size* is returned. The default is None, in which case a single scalar is returned. Returns ------- samples : scalar or ndarray The returned samples are greater than or equal to one. See Also -------- scipy.stats.distributions.zipf : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the Zipf distribution is .. math:: p(x) = \frac{x^{-a}}{\zeta(a)}, where :math:`\zeta` is the Riemann Zeta function. It is named for the American linguist George Kingsley Zipf, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table. References ---------- Zipf, G. K., *Selected Studies of the Principle of Relative Frequency in Language*, Cambridge, MA: Harvard Univ. Press, 1932. Examples -------- Draw samples from the distribution: >>> a = 2. # parameter >>> s = np.random.zipf(a, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps Truncate s values at 50 so plot is interesting >>> count, bins, ignored = plt.hist(s[s<50], 50, normed=True) >>> x = np.arange(1., 50.) >>> y = x**(-a)/sps.zetac(a) >>> plt.plot(x, y/max(y), linewidth=2, color='r') >>> plt.show() """ return float() if False else ndarray() fromfile = _fromfile frombuffer = _frombuffer fromstring = _fromstring