import copy as _copy import operator from collections.abc import Iterable, Iterator, Sized from collections import defaultdict, deque from functools import reduce import warnings import numpy as np import numba import scipy.sparse from numpy.lib.mixins import NDArrayOperatorsMixin from .._common import dot, matmul from .indexing import getitem from .._umath import elemwise, broadcast_to from .._sparse_array import SparseArray, _reduce_super_ufunc from .._utils import ( normalize_axis, equivalent, check_zero_fill_value, _zero_of_dtype, can_store, ) class COO(SparseArray, NDArrayOperatorsMixin): # lgtm [py/missing-equals] """ A sparse multidimensional array. This is stored in COO format. It depends on NumPy and Scipy.sparse for computation, but supports arrays of arbitrary dimension. Parameters ---------- coords : numpy.ndarray (COO.ndim, COO.nnz) An array holding the index locations of every value Should have shape (number of dimensions, number of non-zeros). data : numpy.ndarray (COO.nnz,) An array of Values. A scalar can also be supplied if the data is the same across all coordinates. If not given, defers to :obj:`as_coo`. shape : tuple[int] (COO.ndim,) The shape of the array. has_duplicates : bool, optional A value indicating whether the supplied value for :code:`coords` has duplicates. Note that setting this to `False` when :code:`coords` does have duplicates may result in undefined behaviour. See :obj:`COO.sum_duplicates` sorted : bool, optional A value indicating whether the values in `coords` are sorted. Note that setting this to `True` when :code:`coords` isn't sorted may result in undefined behaviour. See :obj:`COO.sort_indices`. prune : bool, optional A flag indicating whether or not we should prune any fill-values present in ``data``. cache : bool, optional Whether to enable cacheing for various operations. See :obj:`COO.enable_caching` fill_value: scalar, optional The fill value for this array. Attributes ---------- coords : numpy.ndarray (ndim, nnz) An array holding the coordinates of every nonzero element. data : numpy.ndarray (nnz,) An array holding the values corresponding to :obj:`COO.coords`. shape : tuple[int] (ndim,) The dimensions of this array. See Also -------- DOK : A mostly write-only sparse array. as_coo : Convert any given format to :obj:`COO`. Examples -------- You can create :obj:`COO` objects from Numpy arrays. >>> x = np.eye(4, dtype=np.uint8) >>> x[2, 3] = 5 >>> s = COO.from_numpy(x) >>> s >>> s.data # doctest: +NORMALIZE_WHITESPACE array([1, 1, 1, 5, 1], dtype=uint8) >>> s.coords # doctest: +NORMALIZE_WHITESPACE array([[0, 1, 2, 2, 3], [0, 1, 2, 3, 3]]) :obj:`COO` objects support basic arithmetic and binary operations. >>> x2 = np.eye(4, dtype=np.uint8) >>> x2[3, 2] = 5 >>> s2 = COO.from_numpy(x2) >>> (s + s2).todense() # doctest: +NORMALIZE_WHITESPACE array([[2, 0, 0, 0], [0, 2, 0, 0], [0, 0, 2, 5], [0, 0, 5, 2]], dtype=uint8) >>> (s * s2).todense() # doctest: +NORMALIZE_WHITESPACE array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], dtype=uint8) Binary operations support broadcasting. >>> x3 = np.zeros((4, 1), dtype=np.uint8) >>> x3[2, 0] = 1 >>> s3 = COO.from_numpy(x3) >>> (s * s3).todense() # doctest: +NORMALIZE_WHITESPACE array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 5], [0, 0, 0, 0]], dtype=uint8) :obj:`COO` objects also support dot products and reductions. >>> s.dot(s.T).sum(axis=0).todense() # doctest: +NORMALIZE_WHITESPACE array([ 1, 1, 31, 6], dtype=uint64) You can use Numpy :code:`ufunc` operations on :obj:`COO` arrays as well. >>> np.sum(s, axis=1).todense() # doctest: +NORMALIZE_WHITESPACE array([1, 1, 6, 1], dtype=uint64) >>> np.round(np.sqrt(s, dtype=np.float64), decimals=1).todense() # doctest: +SKIP array([[ 1. , 0. , 0. , 0. ], [ 0. , 1. , 0. , 0. ], [ 0. , 0. , 1. , 2.2], [ 0. , 0. , 0. , 1. ]]) Operations that will result in a dense array will usually result in a different fill value, such as the following. >>> np.exp(s) You can also create :obj:`COO` arrays from coordinates and data. >>> coords = [[0, 0, 0, 1, 1], ... [0, 1, 2, 0, 3], ... [0, 3, 2, 0, 1]] >>> data = [1, 2, 3, 4, 5] >>> s4 = COO(coords, data, shape=(3, 4, 5)) >>> s4 If the data is same across all coordinates, you can also specify a scalar. >>> coords = [[0, 0, 0, 1, 1], ... [0, 1, 2, 0, 3], ... [0, 3, 2, 0, 1]] >>> data = 1 >>> s5 = COO(coords, data, shape=(3, 4, 5)) >>> s5 Following scipy.sparse conventions you can also pass these as a tuple with rows and columns >>> rows = [0, 1, 2, 3, 4] >>> cols = [0, 0, 0, 1, 1] >>> data = [10, 20, 30, 40, 50] >>> z = COO((data, (rows, cols))) >>> z.todense() # doctest: +NORMALIZE_WHITESPACE array([[10, 0], [20, 0], [30, 0], [ 0, 40], [ 0, 50]]) You can also pass a dictionary or iterable of index/value pairs. Repeated indices imply summation: >>> d = {(0, 0, 0): 1, (1, 2, 3): 2, (1, 1, 0): 3} >>> COO(d) >>> L = [((0, 0), 1), ... ((1, 1), 2), ... ((0, 0), 3)] >>> COO(L).todense() # doctest: +NORMALIZE_WHITESPACE array([[4, 0], [0, 2]]) You can convert :obj:`DOK` arrays to :obj:`COO` arrays. >>> from sparse import DOK >>> s6 = DOK((5, 5), dtype=np.int64) >>> s6[1:3, 1:3] = [[4, 5], [6, 7]] >>> s6 >>> s7 = s6.asformat('coo') >>> s7 >>> s7.todense() # doctest: +NORMALIZE_WHITESPACE array([[0, 0, 0, 0, 0], [0, 4, 5, 0, 0], [0, 6, 7, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) """ __array_priority__ = 12 def __init__( self, coords, data=None, shape=None, has_duplicates=True, sorted=False, prune=False, cache=False, fill_value=None, idx_dtype=None, ): self._cache = None if cache: self.enable_caching() if data is None: arr = as_coo( coords, shape=shape, fill_value=fill_value, idx_dtype=idx_dtype ) self._make_shallow_copy_of(arr) if cache: self.enable_caching() return self.data = np.asarray(data) self.coords = np.asarray(coords) if self.coords.ndim == 1: if self.coords.size == 0 and shape is not None: self.coords = self.coords.reshape((len(shape), len(data))) else: self.coords = self.coords[None, :] if self.data.ndim == 0: self.data = np.broadcast_to(self.data, self.coords.shape[1]) if self.data.ndim != 1: raise ValueError("data must be a scalar or 1-dimensional.") if shape and not self.coords.size: self.coords = np.zeros( (len(shape) if isinstance(shape, Iterable) else 1, 0), dtype=np.intp ) if shape is None: if self.coords.nbytes: shape = tuple((self.coords.max(axis=1) + 1)) else: shape = () if not isinstance(shape, Iterable): shape = (shape,) super().__init__(shape, fill_value=fill_value) if idx_dtype: if not can_store(idx_dtype, max(shape)): raise ValueError( "cannot cast array with shape {} to dtype {}.".format( shape, idx_dtype ) ) self.coords = self.coords.astype(idx_dtype) if self.shape: if len(self.data) != self.coords.shape[1]: msg = ( "The data length does not match the coordinates " "given.\nlen(data) = {}, but {} coords specified." ) raise ValueError(msg.format(len(data), self.coords.shape[1])) if len(self.shape) != self.coords.shape[0]: msg = ( "Shape specified by `shape` doesn't match the " "shape of `coords`; len(shape)={} != coords.shape[0]={}" "(and coords.shape={})" ) raise ValueError( msg.format(len(shape), self.coords.shape[0], self.coords.shape) ) from .._settings import WARN_ON_TOO_DENSE if WARN_ON_TOO_DENSE and self.nbytes >= self.size * self.data.itemsize: warnings.warn( "Attempting to create a sparse array that takes no less " "memory than than an equivalent dense array. You may want to " "use a dense array here instead.", RuntimeWarning, ) if not sorted: self._sort_indices() if has_duplicates: self._sum_duplicates() if prune: self._prune() def __getstate__(self): return (self.coords, self.data, self.shape, self.fill_value) def __setstate__(self, state): self.coords, self.data, self.shape, self.fill_value = state self._cache = None def __dask_tokenize__(self): "Produce a deterministic, content-based hash for dask." from dask.base import normalize_token return normalize_token( (type(self), self.coords, self.data, self.shape, self.fill_value) ) def copy(self, deep=True): """Return a copy of the array. Parameters ---------- deep : boolean, optional If True (default), the internal coords and data arrays are also copied. Set to ``False`` to only make a shallow copy. """ return _copy.deepcopy(self) if deep else _copy.copy(self) def enable_caching(self): """Enable caching of reshape, transpose, and tocsr/csc operations This enables efficient iterative workflows that make heavy use of csr/csc operations, such as tensordot. This maintains a cache of recent results of reshape and transpose so that operations like tensordot (which uses both internally) store efficiently stored representations for repeated use. This can significantly cut down on computational costs in common numeric algorithms. However, this also assumes that neither this object, nor the downstream objects will have their data mutated. Examples -------- >>> s.enable_caching() # doctest: +SKIP >>> csr1 = s.transpose((2, 0, 1)).reshape((100, 120)).tocsr() # doctest: +SKIP >>> csr2 = s.transpose((2, 0, 1)).reshape((100, 120)).tocsr() # doctest: +SKIP >>> csr1 is csr2 # doctest: +SKIP True """ self._cache = defaultdict(lambda: deque(maxlen=3)) @classmethod def from_numpy(cls, x, fill_value=None, idx_dtype=None): """ Convert the given :obj:`numpy.ndarray` to a :obj:`COO` object. Parameters ---------- x : np.ndarray The dense array to convert. fill_value : scalar The fill value of the constructed :obj:`COO` array. Zero if unspecified. Returns ------- COO The converted COO array. Examples -------- >>> x = np.eye(5) >>> s = COO.from_numpy(x) >>> s >>> x[x == 0] = np.nan >>> COO.from_numpy(x, fill_value=np.nan) """ x = np.asanyarray(x).view(type=np.ndarray) if fill_value is None: fill_value = _zero_of_dtype(x.dtype) if x.shape else x coords = np.atleast_2d(np.flatnonzero(~equivalent(x, fill_value))) data = x.ravel()[tuple(coords)] return cls( coords, data, shape=x.size, has_duplicates=False, sorted=True, fill_value=fill_value, idx_dtype=idx_dtype, ).reshape(x.shape) def todense(self): """ Convert this :obj:`COO` array to a dense :obj:`numpy.ndarray`. Note that this may take a large amount of memory if the :obj:`COO` object's :code:`shape` is large. Returns ------- numpy.ndarray The converted dense array. See Also -------- DOK.todense : Equivalent :obj:`DOK` array method. scipy.sparse.coo_matrix.todense : Equivalent Scipy method. Examples -------- >>> x = np.random.randint(100, size=(7, 3)) >>> s = COO.from_numpy(x) >>> x2 = s.todense() >>> np.array_equal(x, x2) True """ x = np.full(self.shape, self.fill_value, self.dtype) coords = tuple([self.coords[i, :] for i in range(self.ndim)]) data = self.data if coords != (): x[coords] = data else: if len(data) != 0: x[coords] = data return x @classmethod def from_scipy_sparse(cls, x): """ Construct a :obj:`COO` array from a :obj:`scipy.sparse.spmatrix` Parameters ---------- x : scipy.sparse.spmatrix The sparse matrix to construct the array from. Returns ------- COO The converted :obj:`COO` object. Examples -------- >>> x = scipy.sparse.rand(6, 3, density=0.2) >>> s = COO.from_scipy_sparse(x) >>> np.array_equal(x.todense(), s.todense()) True """ x = x.asformat("coo") coords = np.empty((2, x.nnz), dtype=x.row.dtype) coords[0, :] = x.row coords[1, :] = x.col return COO( coords, x.data, shape=x.shape, has_duplicates=not x.has_canonical_format, sorted=x.has_canonical_format, ) @classmethod def from_iter(cls, x, shape=None, fill_value=None, dtype=None): """ Converts an iterable in certain formats to a :obj:`COO` array. See examples for details. Parameters ---------- x : Iterable or Iterator The iterable to convert to :obj:`COO`. shape : tuple[int], optional The shape of the array. fill_value : scalar The fill value for this array. dtype : numpy.dtype The dtype of the input array. Inferred from the input if not given. Returns ------- out : COO The output :obj:`COO` array. Examples -------- You can convert items of the format ``[((i, j, k), value), ((i, j, k), value)]`` to :obj:`COO`. Here, the first part represents the coordinate and the second part represents the value. >>> x = [((0, 0), 1), ((1, 1), 1)] >>> s = COO.from_iter(x) >>> s.todense() array([[1, 0], [0, 1]]) You can also have a similar format with a dictionary. >>> x = {(0, 0): 1, (1, 1): 1} >>> s = COO.from_iter(x) >>> s.todense() array([[1, 0], [0, 1]]) The third supported format is ``(data, (..., row, col))``. >>> x = ([1, 1], ([0, 1], [0, 1])) >>> s = COO.from_iter(x) >>> s.todense() array([[1, 0], [0, 1]]) You can also pass in a :obj:`collections.Iterator` object. >>> x = [((0, 0), 1), ((1, 1), 1)].__iter__() >>> s = COO.from_iter(x) >>> s.todense() array([[1, 0], [0, 1]]) """ if isinstance(x, dict): x = list(x.items()) if not isinstance(x, Sized): x = list(x) if len(x) != 2 and not all(len(item) == 2 for item in x): raise ValueError("Invalid iterable to convert to COO.") if not x: ndim = 0 if shape is None else len(shape) coords = np.empty((ndim, 0), dtype=np.uint8) data = np.empty((0,), dtype=dtype) shape = () if shape is None else shape elif not isinstance(x[0][0], Iterable): coords = np.stack(x[1], axis=0) data = np.asarray(x[0], dtype=dtype) else: coords = np.array([item[0] for item in x]).T data = np.array([item[1] for item in x], dtype=dtype) if not ( coords.ndim == 2 and data.ndim == 1 and np.issubdtype(coords.dtype, np.integer) and np.all(coords >= 0) ): raise ValueError("Invalid iterable to convert to COO.") return COO(coords, data, shape=shape, fill_value=fill_value) @property def dtype(self): """ The datatype of this array. Returns ------- numpy.dtype The datatype of this array. See Also -------- numpy.ndarray.dtype : Numpy equivalent property. scipy.sparse.coo_matrix.dtype : Scipy equivalent property. Examples -------- >>> x = (200 * np.random.rand(5, 4)).astype(np.int32) >>> s = COO.from_numpy(x) >>> s.dtype dtype('int32') >>> x.dtype == s.dtype True """ return self.data.dtype @property def nnz(self): """ The number of nonzero elements in this array. Note that any duplicates in :code:`coords` are counted multiple times. To avoid this, call :obj:`COO.sum_duplicates`. Returns ------- int The number of nonzero elements in this array. See Also -------- DOK.nnz : Equivalent :obj:`DOK` array property. numpy.count_nonzero : A similar Numpy function. scipy.sparse.coo_matrix.nnz : The Scipy equivalent property. Examples -------- >>> x = np.array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0]) >>> np.count_nonzero(x) 6 >>> s = COO.from_numpy(x) >>> s.nnz 6 >>> np.count_nonzero(x) == s.nnz True """ return self.coords.shape[1] @property def nbytes(self): """ The number of bytes taken up by this object. Note that for small arrays, this may undercount the number of bytes due to the large constant overhead. Returns ------- int The approximate bytes of memory taken by this object. See Also -------- numpy.ndarray.nbytes : The equivalent Numpy property. Examples -------- >>> data = np.arange(6, dtype=np.uint8) >>> coords = np.random.randint(1000, size=(3, 6), dtype=np.uint16) >>> s = COO(coords, data, shape=(1000, 1000, 1000)) >>> s.nbytes 42 """ return self.data.nbytes + self.coords.nbytes def __len__(self): """ Get "length" of array, which is by definition the size of the first dimension. Returns ------- int The size of the first dimension. See Also -------- numpy.ndarray.__len__ : Numpy equivalent property. Examples -------- >>> x = np.zeros((10, 10)) >>> s = COO.from_numpy(x) >>> len(s) 10 """ return self.shape[0] def __sizeof__(self): return self.nbytes __getitem__ = getitem def __str__(self): return "".format( self.shape, self.dtype, self.nnz, self.fill_value ) __repr__ = __str__ def _reduce_calc(self, method, axis, keepdims=False, **kwargs): if axis[0] is None: axis = tuple(range(self.ndim)) axis = tuple(a if a >= 0 else a + self.ndim for a in axis) neg_axis = tuple(ax for ax in range(self.ndim) if ax not in set(axis)) a = self.transpose(neg_axis + axis) a = a.reshape( ( np.prod([self.shape[d] for d in neg_axis], dtype=np.intp), np.prod([self.shape[d] for d in axis], dtype=np.intp), ) ) data, inv_idx, counts = _grouped_reduce(a.data, a.coords[0], method, **kwargs) n_cols = a.shape[1] arr_attrs = (a, neg_axis, inv_idx) return (data, counts, axis, n_cols, arr_attrs) def _reduce_return(self, data, arr_attrs, result_fill_value): a, neg_axis, inv_idx = arr_attrs coords = a.coords[0:1, inv_idx] out = COO( coords, data, shape=(a.shape[0],), has_duplicates=False, sorted=True, prune=True, fill_value=result_fill_value, ) return out.reshape(tuple(self.shape[d] for d in neg_axis)) def transpose(self, axes=None): """ Returns a new array which has the order of the axes switched. Parameters ---------- axes : Iterable[int], optional The new order of the axes compared to the previous one. Reverses the axes by default. Returns ------- COO The new array with the axes in the desired order. See Also -------- :obj:`COO.T` : A quick property to reverse the order of the axes. numpy.ndarray.transpose : Numpy equivalent function. Examples -------- We can change the order of the dimensions of any :obj:`COO` array with this function. >>> x = np.add.outer(np.arange(5), np.arange(5)[::-1]) >>> x # doctest: +NORMALIZE_WHITESPACE array([[4, 3, 2, 1, 0], [5, 4, 3, 2, 1], [6, 5, 4, 3, 2], [7, 6, 5, 4, 3], [8, 7, 6, 5, 4]]) >>> s = COO.from_numpy(x) >>> s.transpose((1, 0)).todense() # doctest: +NORMALIZE_WHITESPACE array([[4, 5, 6, 7, 8], [3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [1, 2, 3, 4, 5], [0, 1, 2, 3, 4]]) Note that by default, this reverses the order of the axes rather than switching the last and second-to-last axes as required by some linear algebra operations. >>> x = np.random.rand(2, 3, 4) >>> s = COO.from_numpy(x) >>> s.transpose().shape (4, 3, 2) """ if axes is None: axes = list(reversed(range(self.ndim))) # Normalize all axes indices to positive values axes = normalize_axis(axes, self.ndim) if len(np.unique(axes)) < len(axes): raise ValueError("repeated axis in transpose") if not len(axes) == self.ndim: raise ValueError("axes don't match array") axes = tuple(axes) if axes == tuple(range(self.ndim)): return self if self._cache is not None: for ax, value in self._cache["transpose"]: if ax == axes: return value shape = tuple(self.shape[ax] for ax in axes) result = COO( self.coords[axes, :], self.data, shape, has_duplicates=False, cache=self._cache is not None, fill_value=self.fill_value, ) if self._cache is not None: self._cache["transpose"].append((axes, result)) return result @property def T(self): """ Returns a new array which has the order of the axes reversed. Returns ------- COO The new array with the axes in the desired order. See Also -------- :obj:`COO.transpose` : A method where you can specify the order of the axes. numpy.ndarray.T : Numpy equivalent property. Examples -------- We can change the order of the dimensions of any :obj:`COO` array with this function. >>> x = np.add.outer(np.arange(5), np.arange(5)[::-1]) >>> x # doctest: +NORMALIZE_WHITESPACE array([[4, 3, 2, 1, 0], [5, 4, 3, 2, 1], [6, 5, 4, 3, 2], [7, 6, 5, 4, 3], [8, 7, 6, 5, 4]]) >>> s = COO.from_numpy(x) >>> s.T.todense() # doctest: +NORMALIZE_WHITESPACE array([[4, 5, 6, 7, 8], [3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [1, 2, 3, 4, 5], [0, 1, 2, 3, 4]]) Note that by default, this reverses the order of the axes rather than switching the last and second-to-last axes as required by some linear algebra operations. >>> x = np.random.rand(2, 3, 4) >>> s = COO.from_numpy(x) >>> s.T.shape (4, 3, 2) """ return self.transpose(tuple(range(self.ndim))[::-1]) def swapaxes(self, axis1, axis2): """Returns array that has axes axis1 and axis2 swapped. Parameters ---------- axis1 : int first axis to swap axis2 : int second axis to swap Returns ------- COO The new array with the axes axis1 and axis2 swapped. Examples -------- >>> x = COO.from_numpy(np.ones((2, 3, 4))) >>> x.swapaxes(0, 2) """ # Normalize all axis1, axis2 to positive values axis1, axis2 = normalize_axis( (axis1, axis2), self.ndim ) # checks if axis1,2 are in range + raises ValueError axes = list(range(self.ndim)) axes[axis1], axes[axis2] = axes[axis2], axes[axis1] return self.transpose(axes) def dot(self, other): """ Performs the equivalent of :code:`x.dot(y)` for :obj:`COO`. Parameters ---------- other : Union[COO, numpy.ndarray, scipy.sparse.spmatrix] The second operand of the dot product operation. Returns ------- {COO, numpy.ndarray} The result of the dot product. If the result turns out to be dense, then a dense array is returned, otherwise, a sparse array. Raises ------ ValueError If all arguments don't have zero fill-values. See Also -------- dot : Equivalent function for two arguments. :obj:`numpy.dot` : Numpy equivalent function. scipy.sparse.coo_matrix.dot : Scipy equivalent function. Examples -------- >>> x = np.arange(4).reshape((2, 2)) >>> s = COO.from_numpy(x) >>> s.dot(s) # doctest: +SKIP array([[ 2, 3], [ 6, 11]], dtype=int64) """ return dot(self, other) def __matmul__(self, other): try: return matmul(self, other) except NotImplementedError: return NotImplemented def __rmatmul__(self, other): try: return matmul(other, self) except NotImplementedError: return NotImplemented def linear_loc(self): """ The nonzero coordinates of a flattened version of this array. Note that the coordinates may be out of order. Returns ------- numpy.ndarray The flattened coordinates. See Also -------- :obj:`numpy.flatnonzero` : Equivalent Numpy function. Examples -------- >>> x = np.eye(5) >>> s = COO.from_numpy(x) >>> s.linear_loc() # doctest: +NORMALIZE_WHITESPACE array([ 0, 6, 12, 18, 24]) >>> np.array_equal(np.flatnonzero(x), s.linear_loc()) True """ from .common import linear_loc return linear_loc(self.coords, self.shape) def flatten(self, order="C"): """ Returns a new :obj:`COO` array that is a flattened version of this array. Returns ------- COO The flattened output array. Notes ----- The :code:`order` parameter is provided just for compatibility with Numpy and isn't actually supported. Examples -------- >>> s = COO.from_numpy(np.arange(10)) >>> s2 = s.reshape((2, 5)).flatten() >>> s2.todense() array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) """ if order not in {"C", None}: raise NotImplementedError("The `order` parameter is not" "supported.") return self.reshape(-1) def reshape(self, shape, order="C"): """ Returns a new :obj:`COO` array that is a reshaped version of this array. Parameters ---------- shape : tuple[int] The desired shape of the output array. Returns ------- COO The reshaped output array. See Also -------- numpy.ndarray.reshape : The equivalent Numpy function. Notes ----- The :code:`order` parameter is provided just for compatibility with Numpy and isn't actually supported. Examples -------- >>> s = COO.from_numpy(np.arange(25)) >>> s2 = s.reshape((5, 5)) >>> s2.todense() # doctest: +NORMALIZE_WHITESPACE 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, 24]]) """ if isinstance(shape, Iterable): shape = tuple(shape) else: shape = (shape,) if order not in {"C", None}: raise NotImplementedError("The `order` parameter is not supported") if self.shape == shape: return self if any(d == -1 for d in shape): extra = int(self.size / np.prod([d for d in shape if d != -1])) shape = tuple([d if d != -1 else extra for d in shape]) if self.size != reduce(operator.mul, shape, 1): raise ValueError( "cannot reshape array of size {} into shape {}".format(self.size, shape) ) if self._cache is not None: for sh, value in self._cache["reshape"]: if sh == shape: return value # TODO: this self.size enforces a 2**64 limit to array size linear_loc = self.linear_loc() idx_dtype = self.coords.dtype if shape != () and not can_store(idx_dtype, max(shape)): idx_dtype = np.min_scalar_type(max(shape)) coords = np.empty((len(shape), self.nnz), dtype=idx_dtype) strides = 1 for i, d in enumerate(shape[::-1]): coords[-(i + 1), :] = (linear_loc // strides) % d strides *= d result = COO( coords, self.data, shape, has_duplicates=False, sorted=True, cache=self._cache is not None, fill_value=self.fill_value, ) if self._cache is not None: self._cache["reshape"].append((shape, result)) return result def resize(self, *args, refcheck=True, coords_dtype=np.intp): """ This method changes the shape and size of an array in-place. Parameters ---------- args : tuple, or series of integers The desired shape of the output array. See Also -------- numpy.ndarray.resize : The equivalent Numpy function. """ warnings.warn( "resize is deprecated on all SpraseArray objects.", DeprecationWarning ) if len(args) == 1 and isinstance(args[0], tuple): shape = args[0] elif all(isinstance(arg, int) for arg in args): shape = tuple(args) else: raise ValueError("Invalid input") if any(d < 0 for d in shape): raise ValueError("negative dimensions not allowed") new_size = reduce(operator.mul, shape, 1) # TODO: this self.size enforces a 2**64 limit to array size linear_loc = self.linear_loc() end_idx = np.searchsorted(linear_loc, new_size, side="left") linear_loc = linear_loc[:end_idx] idx_dtype = self.coords.dtype if shape != () and not can_store(idx_dtype, max(shape)): idx_dtype = np.min_scalar_type(max(shape)) coords = np.empty((len(shape), len(linear_loc)), dtype=idx_dtype) strides = 1 for i, d in enumerate(shape[::-1]): coords[-(i + 1), :] = (linear_loc // strides) % d strides *= d self.shape = shape self.coords = coords if len(self.data) != len(linear_loc): self.data = self.data[:end_idx].copy() def to_scipy_sparse(self): """ Converts this :obj:`COO` object into a :obj:`scipy.sparse.coo_matrix`. Returns ------- :obj:`scipy.sparse.coo_matrix` The converted Scipy sparse matrix. Raises ------ ValueError If the array is not two-dimensional. ValueError If all the array doesn't zero fill-values. See Also -------- COO.tocsr : Convert to a :obj:`scipy.sparse.csr_matrix`. COO.tocsc : Convert to a :obj:`scipy.sparse.csc_matrix`. """ check_zero_fill_value(self) if self.ndim != 2: raise ValueError( "Can only convert a 2-dimensional array to a Scipy sparse matrix." ) result = scipy.sparse.coo_matrix( (self.data, (self.coords[0], self.coords[1])), shape=self.shape ) result.has_canonical_format = True return result def _tocsr(self): if self.ndim != 2: raise ValueError( "This array must be two-dimensional for this conversion " "to work." ) row, col = self.coords # Pass 3: count nonzeros in each row indptr = np.zeros(self.shape[0] + 1, dtype=np.int64) np.cumsum(np.bincount(row, minlength=self.shape[0]), out=indptr[1:]) return scipy.sparse.csr_matrix((self.data, col, indptr), shape=self.shape) def tocsr(self): """ Converts this array to a :obj:`scipy.sparse.csr_matrix`. Returns ------- scipy.sparse.csr_matrix The result of the conversion. Raises ------ ValueError If the array is not two-dimensional. ValueError If all the array doesn't have zero fill-values. See Also -------- COO.tocsc : Convert to a :obj:`scipy.sparse.csc_matrix`. COO.to_scipy_sparse : Convert to a :obj:`scipy.sparse.coo_matrix`. scipy.sparse.coo_matrix.tocsr : Equivalent Scipy function. """ check_zero_fill_value(self) if self._cache is not None: try: return self._csr except AttributeError: pass try: self._csr = self._csc.tocsr() return self._csr except AttributeError: pass self._csr = csr = self._tocsr() else: csr = self._tocsr() return csr def tocsc(self): """ Converts this array to a :obj:`scipy.sparse.csc_matrix`. Returns ------- scipy.sparse.csc_matrix The result of the conversion. Raises ------ ValueError If the array is not two-dimensional. ValueError If the array doesn't have zero fill-values. See Also -------- COO.tocsr : Convert to a :obj:`scipy.sparse.csr_matrix`. COO.to_scipy_sparse : Convert to a :obj:`scipy.sparse.coo_matrix`. scipy.sparse.coo_matrix.tocsc : Equivalent Scipy function. """ check_zero_fill_value(self) if self._cache is not None: try: return self._csc except AttributeError: pass try: self._csc = self._csr.tocsc() return self._csc except AttributeError: pass self._csc = csc = self.tocsr().tocsc() else: csc = self.tocsr().tocsc() return csc def _sort_indices(self): """ Sorts the :obj:`COO.coords` attribute. Also sorts the data in :obj:`COO.data` to match. Examples -------- >>> coords = np.array([[1, 2, 0]], dtype=np.uint8) >>> data = np.array([4, 1, 3], dtype=np.uint8) >>> s = COO(coords, data) >>> s._sort_indices() >>> s.coords # doctest: +NORMALIZE_WHITESPACE array([[0, 1, 2]], dtype=uint8) >>> s.data # doctest: +NORMALIZE_WHITESPACE array([3, 4, 1], dtype=uint8) """ linear = self.linear_loc() if (np.diff(linear) >= 0).all(): # already sorted return order = np.argsort(linear, kind="mergesort") self.coords = self.coords[:, order] self.data = self.data[order] def _sum_duplicates(self): """ Sums data corresponding to duplicates in :obj:`COO.coords`. See Also -------- scipy.sparse.coo_matrix.sum_duplicates : Equivalent Scipy function. Examples -------- >>> coords = np.array([[0, 1, 1, 2]], dtype=np.uint8) >>> data = np.array([6, 5, 2, 2], dtype=np.uint8) >>> s = COO(coords, data) >>> s._sum_duplicates() >>> s.coords # doctest: +NORMALIZE_WHITESPACE array([[0, 1, 2]], dtype=uint8) >>> s.data # doctest: +NORMALIZE_WHITESPACE array([6, 7, 2], dtype=uint8) """ # Inspired by scipy/sparse/coo.py::sum_duplicates # See https://github.com/scipy/scipy/blob/master/LICENSE.txt linear = self.linear_loc() unique_mask = np.diff(linear) != 0 if unique_mask.sum() == len(unique_mask): # already unique return unique_mask = np.append(True, unique_mask) coords = self.coords[:, unique_mask] (unique_inds,) = np.nonzero(unique_mask) data = np.add.reduceat(self.data, unique_inds, dtype=self.data.dtype) self.data = data self.coords = coords def _prune(self): """ Prunes data so that if any fill-values are present, they are removed from both coordinates and data. Examples -------- >>> coords = np.array([[0, 1, 2, 3]]) >>> data = np.array([1, 0, 1, 2]) >>> s = COO(coords, data) >>> s._prune() >>> s.nnz 3 """ mask = ~equivalent(self.data, self.fill_value) self.coords = self.coords[:, mask] self.data = self.data[mask] def broadcast_to(self, shape): """ Performs the equivalent of :obj:`numpy.broadcast_to` for :obj:`COO`. Note that this function returns a new array instead of a view. Parameters ---------- shape : tuple[int] The shape to broadcast the data to. Returns ------- COO The broadcasted sparse array. Raises ------ ValueError If the operand cannot be broadcast to the given shape. See Also -------- :obj:`numpy.broadcast_to` : NumPy equivalent function """ return broadcast_to(self, shape) def maybe_densify(self, max_size=1000, min_density=0.25): """ Converts this :obj:`COO` array to a :obj:`numpy.ndarray` if not too costly. Parameters ---------- max_size : int Maximum number of elements in output min_density : float Minimum density of output Returns ------- numpy.ndarray The dense array. Raises ------ ValueError If the returned array would be too large. Examples -------- Convert a small sparse array to a dense array. >>> s = COO.from_numpy(np.random.rand(2, 3, 4)) >>> x = s.maybe_densify() >>> np.allclose(x, s.todense()) True You can also specify the minimum allowed density or the maximum number of output elements. If both conditions are unmet, this method will throw an error. >>> x = np.zeros((5, 5), dtype=np.uint8) >>> x[2, 2] = 1 >>> s = COO.from_numpy(x) >>> s.maybe_densify(max_size=5, min_density=0.25) Traceback (most recent call last): ... ValueError: Operation would require converting large sparse array to dense """ if self.size <= max_size or self.density >= min_density: return self.todense() else: raise ValueError( "Operation would require converting " "large sparse array to dense" ) def nonzero(self): """ Get the indices where this array is nonzero. Returns ------- idx : tuple[numpy.ndarray] The indices where this array is nonzero. See Also -------- :obj:`numpy.ndarray.nonzero` : NumPy equivalent function Raises ------ ValueError If the array doesn't have zero fill-values. Examples -------- >>> s = COO.from_numpy(np.eye(5)) >>> s.nonzero() (array([0, 1, 2, 3, 4]), array([0, 1, 2, 3, 4])) """ check_zero_fill_value(self) return tuple(self.coords) def asformat(self, format, **kwargs): """ Convert this sparse array to a given format. Parameters ---------- format : str A format string. Returns ------- out : SparseArray The converted array. Raises ------ NotImplementedError If the format isn't supported. """ from sparse._utils import convert_format format = convert_format(format) if format == "gcxs": from .._compressed import GCXS return GCXS.from_coo(self, **kwargs) elif len(kwargs) != 0: raise TypeError(f"Invalid keyword arguments provided: {kwargs}") if format == "coo": return self if format == "dok": from .._dok import DOK return DOK.from_coo(self, **kwargs) return self.asformat("gcxs", **kwargs).asformat(format, **kwargs) def as_coo(x, shape=None, fill_value=None, idx_dtype=None): """ Converts any given format to :obj:`COO`. See the "See Also" section for details. Parameters ---------- x : SparseArray or numpy.ndarray or scipy.sparse.spmatrix or Iterable. The item to convert. shape : tuple[int], optional The shape of the output array. Can only be used in case of Iterable. Returns ------- out : COO The converted :obj:`COO` array. See Also -------- SparseArray.asformat : A utility function to convert between formats in this library. COO.from_numpy : Convert a Numpy array to :obj:`COO`. COO.from_scipy_sparse : Convert a SciPy sparse matrix to :obj:`COO`. COO.from_iter : Convert an iterable to :obj:`COO`. """ if hasattr(x, "shape") and shape is not None: raise ValueError( "Cannot provide a shape in combination with something " "that already has a shape." ) if hasattr(x, "fill_value") and fill_value is not None: raise ValueError( "Cannot provide a fill-value in combination with something " "that already has a fill-value." ) if isinstance(x, SparseArray): return x.asformat("coo") if isinstance(x, np.ndarray): return COO.from_numpy(x, fill_value=fill_value, idx_dtype=idx_dtype) if isinstance(x, scipy.sparse.spmatrix): return COO.from_scipy_sparse(x) if isinstance(x, (Iterable, Iterator)): return COO.from_iter(x, shape=shape, fill_value=fill_value) raise NotImplementedError( "Format not supported for conversion. Supplied type is " "%s, see help(sparse.as_coo) for supported formats." % type(x) ) @numba.jit(nopython=True, nogil=True) # pragma: no cover def _calc_counts_invidx(groups): inv_idx = [] counts = [] if len(groups) == 0: return ( np.array(inv_idx, dtype=groups.dtype), np.array(counts, dtype=groups.dtype), ) inv_idx.append(0) last_group = groups[0] for i in range(1, len(groups)): if groups[i] != last_group: counts.append(i - inv_idx[-1]) inv_idx.append(i) last_group = groups[i] counts.append(len(groups) - inv_idx[-1]) return (np.array(inv_idx, dtype=groups.dtype), np.array(counts, dtype=groups.dtype)) def _grouped_reduce(x, groups, method, **kwargs): """ Performs a :code:`ufunc` grouped reduce. Parameters ---------- x : np.ndarray The data to reduce. groups : np.ndarray The groups the data belongs to. The groups must be contiguous. method : np.ufunc The :code:`ufunc` to use to perform the reduction. **kwargs : dict The kwargs to pass to the :code:`ufunc`'s :code:`reduceat` function. Returns ------- result : np.ndarray The result of the grouped reduce operation. inv_idx : np.ndarray The index of the first element where each group is found. counts : np.ndarray The number of elements in each group. """ # Partial credit to @shoyer # Ref: https://gist.github.com/shoyer/f538ac78ae904c936844 inv_idx, counts = _calc_counts_invidx(groups) result = method.reduceat(x, inv_idx, **kwargs) return result, inv_idx, counts