from functools import reduce import operator import warnings from collections.abc import Iterable import numpy as np import scipy.sparse import numba from .._sparse_array import SparseArray from .._utils import ( isscalar, is_unsigned_dtype, normalize_axis, check_zero_fill_value, check_consistent_fill_value, can_store, ) def asCOO(x, name="asCOO", check=True): """ Convert the input to :obj:`COO`. Passes through :obj:`COO` objects as-is. Parameters ---------- x : Union[SparseArray, scipy.sparse.spmatrix, numpy.ndarray] The input array to convert. name : str, optional The name of the operation to use in the exception. check : bool, optional Whether to check for a dense input. Returns ------- COO The converted :obj:`COO` array. Raises ------ ValueError If ``check`` is true and a dense input is supplied. """ from .core import COO if check and not isinstance(x, (SparseArray, scipy.sparse.spmatrix)): raise ValueError( "Performing this operation would produce a dense result: %s" % name ) if not isinstance(x, COO): x = COO(x) return x def linear_loc(coords, shape): if shape == () and len(coords) == 0: # `np.ravel_multi_index` is not aware of arrays, so cannot produce a # sensible result here (https://github.com/numpy/numpy/issues/15690). # Since `coords` is an array and not a sequence, we know the correct # dimensions. return np.zeros(coords.shape[1:], dtype=np.intp) else: return np.ravel_multi_index(coords, shape) def kron(a, b): """Kronecker product of 2 sparse arrays. Parameters ---------- a, b : SparseArray, scipy.sparse.spmatrix, or np.ndarray The arrays over which to compute the Kronecker product. Returns ------- res : COO The kronecker product Raises ------ ValueError If all arguments are dense or arguments have nonzero fill-values. Examples -------- >>> from sparse import eye >>> a = eye(3, dtype='i8') >>> b = np.array([1, 2, 3], dtype='i8') >>> res = kron(a, b) >>> res.todense() # doctest: +SKIP array([[1, 2, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 2, 3]], dtype=int64) """ from .core import COO from .._umath import _cartesian_product check_zero_fill_value(a, b) a_sparse = isinstance(a, (SparseArray, scipy.sparse.spmatrix)) b_sparse = isinstance(b, (SparseArray, scipy.sparse.spmatrix)) a_ndim = np.ndim(a) b_ndim = np.ndim(b) if not (a_sparse or b_sparse): raise ValueError( "Performing this operation would produce a dense " "result: kron" ) if a_ndim == 0 or b_ndim == 0: return a * b a = asCOO(a, check=False) b = asCOO(b, check=False) # Match dimensions max_dim = max(a.ndim, b.ndim) a = a.reshape((1,) * (max_dim - a.ndim) + a.shape) b = b.reshape((1,) * (max_dim - b.ndim) + b.shape) a_idx, b_idx = _cartesian_product(np.arange(a.nnz), np.arange(b.nnz)) a_expanded_coords = a.coords[:, a_idx] b_expanded_coords = b.coords[:, b_idx] o_coords = a_expanded_coords * np.asarray(b.shape)[:, None] + b_expanded_coords o_data = a.data[a_idx] * b.data[b_idx] o_shape = tuple(i * j for i, j in zip(a.shape, b.shape)) return COO(o_coords, o_data, shape=o_shape, has_duplicates=False) def concatenate(arrays, axis=0): """ Concatenate the input arrays along the given dimension. Parameters ---------- arrays : Iterable[SparseArray] The input arrays to concatenate. axis : int, optional The axis along which to concatenate the input arrays. The default is zero. Returns ------- COO The output concatenated array. Raises ------ ValueError If all elements of :code:`arrays` don't have the same fill-value. See Also -------- numpy.concatenate : NumPy equivalent function """ from .core import COO check_consistent_fill_value(arrays) arrays = [x if isinstance(x, COO) else COO(x) for x in arrays] axis = normalize_axis(axis, arrays[0].ndim) assert all( x.shape[ax] == arrays[0].shape[ax] for x in arrays for ax in set(range(arrays[0].ndim)) - {axis} ) nnz = 0 dim = sum(x.shape[axis] for x in arrays) shape = list(arrays[0].shape) shape[axis] = dim data = np.concatenate([x.data for x in arrays]) coords = np.concatenate([x.coords for x in arrays], axis=1) if not can_store(coords.dtype, max(shape)): coords = coords.astype(np.min_scalar_type(max(shape))) dim = 0 for x in arrays: if dim: coords[axis, nnz : x.nnz + nnz] += dim dim += x.shape[axis] nnz += x.nnz return COO( coords, data, shape=shape, has_duplicates=False, sorted=(axis == 0), fill_value=arrays[0].fill_value, ) def stack(arrays, axis=0): """ Stack the input arrays along the given dimension. Parameters ---------- arrays : Iterable[SparseArray] The input arrays to stack. axis : int, optional The axis along which to stack the input arrays. Returns ------- COO The output stacked array. Raises ------ ValueError If all elements of :code:`arrays` don't have the same fill-value. See Also -------- numpy.stack : NumPy equivalent function """ from .core import COO check_consistent_fill_value(arrays) assert len({x.shape for x in arrays}) == 1 arrays = [x if isinstance(x, COO) else COO(x) for x in arrays] axis = normalize_axis(axis, arrays[0].ndim + 1) data = np.concatenate([x.data for x in arrays]) coords = np.concatenate([x.coords for x in arrays], axis=1) shape = list(arrays[0].shape) shape.insert(axis, len(arrays)) nnz = 0 dim = 0 new = np.empty(shape=(coords.shape[1],), dtype=np.intp) for x in arrays: new[nnz : x.nnz + nnz] = dim dim += 1 nnz += x.nnz coords = [coords[i] for i in range(coords.shape[0])] coords.insert(axis, new) coords = np.stack(coords, axis=0) return COO( coords, data, shape=shape, has_duplicates=False, sorted=(axis == 0), fill_value=arrays[0].fill_value, ) def triu(x, k=0): """ Returns an array with all elements below the k-th diagonal set to zero. Parameters ---------- x : COO The input array. k : int, optional The diagonal below which elements are set to zero. The default is zero, which corresponds to the main diagonal. Returns ------- COO The output upper-triangular matrix. Raises ------ ValueError If :code:`x` doesn't have zero fill-values. See Also -------- numpy.triu : NumPy equivalent function """ from .core import COO check_zero_fill_value(x) if not x.ndim >= 2: raise NotImplementedError( "sparse.triu is not implemented for scalars or 1-D arrays." ) mask = x.coords[-2] + k <= x.coords[-1] coords = x.coords[:, mask] data = x.data[mask] return COO(coords, data, shape=x.shape, has_duplicates=False, sorted=True) def tril(x, k=0): """ Returns an array with all elements above the k-th diagonal set to zero. Parameters ---------- x : COO The input array. k : int, optional The diagonal above which elements are set to zero. The default is zero, which corresponds to the main diagonal. Returns ------- COO The output lower-triangular matrix. Raises ------ ValueError If :code:`x` doesn't have zero fill-values. See Also -------- numpy.tril : NumPy equivalent function """ from .core import COO check_zero_fill_value(x) if not x.ndim >= 2: raise NotImplementedError( "sparse.tril is not implemented for scalars or 1-D arrays." ) mask = x.coords[-2] + k >= x.coords[-1] coords = x.coords[:, mask] data = x.data[mask] return COO(coords, data, shape=x.shape, has_duplicates=False, sorted=True) def nansum(x, axis=None, keepdims=False, dtype=None, out=None): """ Performs a ``NaN`` skipping sum operation along the given axes. Uses all axes by default. Parameters ---------- x : SparseArray The array to perform the reduction on. axis : Union[int, Iterable[int]], optional The axes along which to sum. Uses all axes by default. keepdims : bool, optional Whether or not to keep the dimensions of the original array. dtype : numpy.dtype The data type of the output array. Returns ------- COO The reduced output sparse array. See Also -------- :obj:`COO.sum` : Function without ``NaN`` skipping. numpy.nansum : Equivalent Numpy function. """ assert out is None x = asCOO(x, name="nansum") return nanreduce(x, np.add, axis=axis, keepdims=keepdims, dtype=dtype) def nanmean(x, axis=None, keepdims=False, dtype=None, out=None): """ Performs a ``NaN`` skipping mean operation along the given axes. Uses all axes by default. Parameters ---------- x : SparseArray The array to perform the reduction on. axis : Union[int, Iterable[int]], optional The axes along which to compute the mean. Uses all axes by default. keepdims : bool, optional Whether or not to keep the dimensions of the original array. dtype : numpy.dtype The data type of the output array. Returns ------- COO The reduced output sparse array. See Also -------- :obj:`COO.mean` : Function without ``NaN`` skipping. numpy.nanmean : Equivalent Numpy function. """ assert out is None x = asCOO(x, name="nanmean") if not np.issubdtype(x.dtype, np.floating): return x.mean(axis=axis, keepdims=keepdims, dtype=dtype) mask = np.isnan(x) x2 = where(mask, 0, x) # Count the number non-nan elements along axis nancount = mask.sum(axis=axis, dtype="i8", keepdims=keepdims) if axis is None: axis = tuple(range(x.ndim)) elif not isinstance(axis, tuple): axis = (axis,) den = reduce(operator.mul, (x.shape[i] for i in axis), 1) den -= nancount if (den == 0).any(): warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=2) num = np.sum(x2, axis=axis, dtype=dtype, keepdims=keepdims) with np.errstate(invalid="ignore", divide="ignore"): if num.ndim: return np.true_divide(num, den, casting="unsafe") return (num / den).astype(dtype) def nanmax(x, axis=None, keepdims=False, dtype=None, out=None): """ Maximize along the given axes, skipping ``NaN`` values. Uses all axes by default. Parameters ---------- x : SparseArray The array to perform the reduction on. axis : Union[int, Iterable[int]], optional The axes along which to maximize. Uses all axes by default. keepdims : bool, optional Whether or not to keep the dimensions of the original array. dtype : numpy.dtype The data type of the output array. Returns ------- COO The reduced output sparse array. See Also -------- :obj:`COO.max` : Function without ``NaN`` skipping. numpy.nanmax : Equivalent Numpy function. """ assert out is None x = asCOO(x, name="nanmax") ar = x.reduce(np.fmax, axis=axis, keepdims=keepdims, dtype=dtype) if (isscalar(ar) and np.isnan(ar)) or np.isnan(ar.data).any(): warnings.warn("All-NaN slice encountered", RuntimeWarning, stacklevel=2) return ar def nanmin(x, axis=None, keepdims=False, dtype=None, out=None): """ Minimize along the given axes, skipping ``NaN`` values. Uses all axes by default. Parameters ---------- x : SparseArray The array to perform the reduction on. axis : Union[int, Iterable[int]], optional The axes along which to minimize. Uses all axes by default. keepdims : bool, optional Whether or not to keep the dimensions of the original array. dtype : numpy.dtype The data type of the output array. Returns ------- COO The reduced output sparse array. See Also -------- :obj:`COO.min` : Function without ``NaN`` skipping. numpy.nanmin : Equivalent Numpy function. """ assert out is None x = asCOO(x, name="nanmin") ar = x.reduce(np.fmin, axis=axis, keepdims=keepdims, dtype=dtype) if (isscalar(ar) and np.isnan(ar)) or np.isnan(ar.data).any(): warnings.warn("All-NaN slice encountered", RuntimeWarning, stacklevel=2) return ar def nanprod(x, axis=None, keepdims=False, dtype=None, out=None): """ Performs a product operation along the given axes, skipping ``NaN`` values. Uses all axes by default. Parameters ---------- x : SparseArray The array to perform the reduction on. axis : Union[int, Iterable[int]], optional The axes along which to multiply. Uses all axes by default. keepdims : bool, optional Whether or not to keep the dimensions of the original array. dtype : numpy.dtype The data type of the output array. Returns ------- COO The reduced output sparse array. See Also -------- :obj:`COO.prod` : Function without ``NaN`` skipping. numpy.nanprod : Equivalent Numpy function. """ assert out is None x = asCOO(x) return nanreduce(x, np.multiply, axis=axis, keepdims=keepdims, dtype=dtype) def where(condition, x=None, y=None): """ Select values from either ``x`` or ``y`` depending on ``condition``. If ``x`` and ``y`` are not given, returns indices where ``condition`` is nonzero. Performs the equivalent of :obj:`numpy.where`. Parameters ---------- condition : SparseArray The condition based on which to select values from either ``x`` or ``y``. x : SparseArray, optional The array to select values from if ``condition`` is nonzero. y : SparseArray, optional The array to select values from if ``condition`` is zero. Returns ------- COO The output array with selected values if ``x`` and ``y`` are given; else where the array is nonzero. Raises ------ ValueError If the operation would produce a dense result; or exactly one of ``x`` and ``y`` are given. See Also -------- numpy.where : Equivalent Numpy function. """ from .._umath import elemwise x_given = x is not None y_given = y is not None if not (x_given or y_given): condition = asCOO(condition, name=str(np.where)) return tuple(condition.coords) if x_given != y_given: raise ValueError("either both or neither of x and y should be given") return elemwise(np.where, condition, x, y) 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: numpy.ndarray See Also -------- :obj:`where`, :obj:`COO.nonzero` Examples -------- >>> import sparse >>> x = sparse.COO(np.arange(6).reshape((2, 3))) >>> sparse.argwhere(x > 1) array([[0, 2], [1, 0], [1, 1], [1, 2]]) """ return np.transpose(a.nonzero()) def _replace_nan(array, value): """ Replaces ``NaN``s in ``array`` with ``value``. Parameters ---------- array : COO The input array. value : numpy.number The values to replace ``NaN`` with. Returns ------- COO A copy of ``array`` with the ``NaN``s replaced. """ if not np.issubdtype(array.dtype, np.floating): return array return where(np.isnan(array), value, array) def nanreduce(x, method, identity=None, axis=None, keepdims=False, **kwargs): """ Performs an ``NaN`` skipping reduction on this array. See the documentation on :obj:`COO.reduce` for examples. Parameters ---------- x : COO The array to reduce. method : numpy.ufunc The method to use for performing the reduction. identity : numpy.number The identity value for this reduction. Inferred from ``method`` if not given. Note that some ``ufunc`` objects don't have this, so it may be necessary to give it. axis : Union[int, Iterable[int]], optional The axes along which to perform the reduction. Uses all axes by default. keepdims : bool, optional Whether or not to keep the dimensions of the original array. **kwargs : dict Any extra arguments to pass to the reduction operation. Returns ------- COO The result of the reduction operation. Raises ------ ValueError If reducing an all-zero axis would produce a nonzero result. See Also -------- COO.reduce : Similar method without ``NaN`` skipping functionality. """ arr = _replace_nan(x, method.identity if identity is None else identity) return arr.reduce(method, axis, keepdims, **kwargs) def roll(a, shift, axis=None): """ Shifts elements of an array along specified axis. Elements that roll beyond the last position are circulated and re-introduced at the first. Parameters ---------- a : COO Input array shift : int or tuple of ints Number of index positions that elements are shifted. If a tuple is provided, then axis must be a tuple of the same size, and each of the given axes is shifted by the corresponding number. If an int while axis is a tuple of ints, then broadcasting is used so the same shift is applied to all axes. axis : int or tuple of ints, optional Axis or tuple specifying multiple axes. 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. """ from .core import COO, as_coo from numpy.core._exceptions import UFuncTypeError a = as_coo(a) # roll flattened array if axis is None: return roll(a.reshape((-1,)), shift, 0).reshape(a.shape) # roll across specified axis else: # parse axis input, wrap in tuple axis = normalize_axis(axis, a.ndim) if not isinstance(axis, tuple): axis = (axis,) # make shift iterable if not isinstance(shift, Iterable): shift = (shift,) elif np.ndim(shift) > 1: raise ValueError("'shift' and 'axis' must be integers or 1D sequences.") # handle broadcasting if len(shift) == 1: shift = np.full(len(axis), shift) # check if dimensions are consistent if len(axis) != len(shift): raise ValueError( "If 'shift' is a 1D sequence, " "'axis' must have equal length." ) if not can_store(a.coords.dtype, max(a.shape + shift)): raise ValueError( "cannot roll with coords.dtype {} and shift {}. Try casting coords to a larger dtype.".format( a.coords.dtype, shift, ) ) # shift elements coords, data = np.copy(a.coords), np.copy(a.data) try: for sh, ax in zip(shift, axis): coords[ax] += sh coords[ax] %= a.shape[ax] except UFuncTypeError: if is_unsigned_dtype(coords.dtype): raise ValueError( "rolling with coords.dtype as {} is not safe. Try using a signed dtype.".format( coords.dtype ) ) return COO( coords, data=data, shape=a.shape, has_duplicates=False, fill_value=a.fill_value, ) def diagonal(a, offset=0, axis1=0, axis2=1): """ Extract diagonal from a COO array. The equivalent of :obj:`numpy.diagonal`. Parameters ---------- a : COO The array to perform the operation on. offset : int, optional Offset of the diagonal from the main diagonal. Defaults to main diagonal (0). axis1 : int, optional First axis from which the diagonals should be taken. Defaults to first axis (0). axis2 : int, optional Second axis from which the diagonals should be taken. Defaults to second axis (1). Examples -------- >>> import sparse >>> x = sparse.as_coo(np.arange(9).reshape(3,3)) >>> sparse.diagonal(x).todense() array([0, 4, 8]) >>> sparse.diagonal(x,offset=1).todense() array([1, 5]) >>> x = sparse.as_coo(np.arange(12).reshape((2,3,2))) >>> x_diag = sparse.diagonal(x, axis1=0, axis2=2) >>> x_diag.shape (3, 2) >>> x_diag.todense() array([[ 0, 7], [ 2, 9], [ 4, 11]]) Returns ------- out: COO The result of the operation. Raises ------ ValueError If a.shape[axis1] != a.shape[axis2] See Also -------- :obj:`numpy.diagonal` : NumPy equivalent function """ from .core import COO if a.shape[axis1] != a.shape[axis2]: raise ValueError("a.shape[axis1] != a.shape[axis2]") diag_axes = [ axis for axis in range(len(a.shape)) if axis != axis1 and axis != axis2 ] + [axis1] diag_shape = [a.shape[axis] for axis in diag_axes] diag_shape[-1] -= abs(offset) diag_idx = _diagonal_idx(a.coords, axis1, axis2, offset) diag_coords = [a.coords[axis][diag_idx] for axis in diag_axes] diag_data = a.data[diag_idx] return COO(diag_coords, diag_data, diag_shape) def diagonalize(a, axis=0): """ Diagonalize a COO array. The new dimension is appended at the end. .. WARNING:: :obj:`diagonalize` is not :obj:`numpy` compatible as there is no direct :obj:`numpy` equivalent. The API may change in the future. Parameters ---------- a : Union[COO, np.ndarray, scipy.sparse.spmatrix] The array to diagonalize. axis : int, optional The axis to diagonalize. Defaults to first axis (0). Examples -------- >>> import sparse >>> x = sparse.as_coo(np.arange(1,4)) >>> sparse.diagonalize(x).todense() array([[1, 0, 0], [0, 2, 0], [0, 0, 3]]) >>> x = sparse.as_coo(np.arange(24).reshape((2,3,4))) >>> x_diag = sparse.diagonalize(x, axis=1) >>> x_diag.shape (2, 3, 4, 3) :obj:`diagonalize` is the inverse of :obj:`diagonal` >>> a = sparse.random((3,3,3,3,3), density=0.3) >>> a_diag = sparse.diagonalize(a, axis=2) >>> (sparse.diagonal(a_diag, axis1=2, axis2=5) == a.transpose([0,1,3,4,2])).all() True Returns ------- out: COO The result of the operation. See Also -------- :obj:`numpy.diag` : NumPy equivalent for 1D array """ from .core import COO, as_coo a = as_coo(a) diag_shape = a.shape + (a.shape[axis],) diag_coords = np.vstack([a.coords, a.coords[axis]]) return COO(diag_coords, a.data, diag_shape) def isposinf(x, out=None): """ Test element-wise for positive infinity, return result as sparse ``bool`` array. Parameters ---------- x Input out, optional Output array Examples -------- >>> import sparse >>> x = sparse.as_coo(np.array([np.inf])) >>> sparse.isposinf(x).todense() array([ True]) See Also -------- numpy.isposinf : The NumPy equivalent """ from .core import elemwise return elemwise(lambda x, out=None, dtype=None: np.isposinf(x, out=out), x, out=out) def isneginf(x, out=None): """ Test element-wise for negative infinity, return result as sparse ``bool`` array. Parameters ---------- x Input out, optional Output array Examples -------- >>> import sparse >>> x = sparse.as_coo(np.array([-np.inf])) >>> sparse.isneginf(x).todense() array([ True]) See Also -------- numpy.isneginf : The NumPy equivalent """ from .core import elemwise return elemwise(lambda x, out=None, dtype=None: np.isneginf(x, out=out), x, out=out) def result_type(*arrays_and_dtypes): """Returns the type that results from applying the NumPy type promotion rules to the arguments. See Also -------- numpy.result_type : The NumPy equivalent """ return np.result_type(*(_as_result_type_arg(x) for x in arrays_and_dtypes)) def _as_result_type_arg(x): if not isinstance(x, SparseArray): return x if x.ndim > 0: return x.dtype # 0-dimensional arrays give different result_type outputs than their dtypes return x.todense() @numba.jit(nopython=True, nogil=True) def _diagonal_idx(coordlist, axis1, axis2, offset): """ Utility function that returns all indices that correspond to a diagonal element. Parameters ---------- coordlist : list of lists Coordinate indices. axis1, axis2 : int The axes of the diagonal. offset : int Offset of the diagonal from the main diagonal. Defaults to main diagonal (0). """ return np.array( [ i for i in range(len(coordlist[axis1])) if coordlist[axis1][i] + offset == coordlist[axis2][i] ] ) def clip(a, a_min=None, a_max=None, out=None): """ Clip (limit) the values in the array. Return an array whose values are limited to ``[min, max]``. One of min or max must be given. Parameters ---------- a a_min : scalar or `SparseArray` or `None` Minimum value. If `None`, clipping is not performed on lower interval edge. a_max : scalar or `SparseArray` or `None` Maximum value. If `None`, clipping is not performed on upper interval edge. out : SparseArray, optional If provided, 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 : SparseArray An array with the elements of `self`, but where values < `min` are replaced with `min`, and those > `max` with `max`. Examples -------- >>> import sparse >>> x = sparse.COO.from_numpy([0, 0, 0, 1, 2, 3]) >>> sparse.clip(x, a_min=1).todense() # doctest: +NORMALIZE_WHITESPACE array([1, 1, 1, 1, 2, 3]) >>> sparse.clip(x, a_max=1).todense() # doctest: +NORMALIZE_WHITESPACE array([0, 0, 0, 1, 1, 1]) >>> sparse.clip(x, a_min=1, a_max=2).todense() # doctest: +NORMALIZE_WHITESPACE array([1, 1, 1, 1, 2, 2]) See Also -------- numpy.clip : Equivalent NumPy function """ a = asCOO(a, name="clip") return a.clip(a_min, a_max)