base.py

"""Base class for sparse matrices"""
from __future__ import division, print_function, absolute_import

__all__ = ['spmatrix', 'isspmatrix', 'issparse',
        'SparseWarning','SparseEfficiencyWarning']

import sys

import numpy as np

from scipy._lib.six import xrange
from .sputils import isdense, isscalarlike, isintlike


class SparseWarning(Warning):
    pass


class SparseFormatWarning(SparseWarning):
    pass


class SparseEfficiencyWarning(SparseWarning):
    pass


# The formats that we might potentially understand.
_formats = {'csc':[0, "Compressed Sparse Column"],
            'csr':[1, "Compressed Sparse Row"],
            'dok':[2, "Dictionary Of Keys"],
            'lil':[3, "LInked List"],
            'dod':[4, "Dictionary of Dictionaries"],
            'sss':[5, "Symmetric Sparse Skyline"],
            'coo':[6, "COOrdinate"],
            'lba':[7, "Linpack BAnded"],
            'egd':[8, "Ellpack-itpack Generalized Diagonal"],
            'dia':[9, "DIAgonal"],
            'bsr':[10, "Block Sparse Row"],
            'msr':[11, "Modified compressed Sparse Row"],
            'bsc':[12, "Block Sparse Column"],
            'msc':[13, "Modified compressed Sparse Column"],
            'ssk':[14, "Symmetric SKyline"],
            'nsk':[15, "Nonsymmetric SKyline"],
            'jad':[16, "JAgged Diagonal"],
            'uss':[17, "Unsymmetric Sparse Skyline"],
            'vbr':[18, "Variable Block Row"],
            'und':[19, "Undefined"]
            }


# These univariate ufuncs preserve zeros.
_ufuncs_with_fixed_point_at_zero = frozenset([
        np.sin, np.tan, np.arcsin, np.arctan, np.sinh, np.tanh, np.arcsinh,
        np.arctanh, np.rint, np.sign, np.expm1, np.log1p, np.deg2rad,
        np.rad2deg, np.floor, np.ceil, np.trunc, np.sqrt])


MAXPRINT = 50


class spmatrix(object):
    """ This class provides a base class for all sparse matrices.  It
    cannot be instantiated.  Most of the work is provided by subclasses.
    """

    __array_priority__ = 10.1
    ndim = 2

    def __init__(self, maxprint=MAXPRINT):
        self.format = self.__class__.__name__[:3]
        self._shape = None
        if self.format == 'spm':
            raise ValueError("This class is not intended"
                            " to be instantiated directly.")
        self.maxprint = maxprint

    def set_shape(self,shape):
        shape = tuple(shape)

        if len(shape) != 2:
            raise ValueError("Only two-dimensional sparse arrays "
                                     "are supported.")
        try:
            shape = int(shape[0]),int(shape[1])  # floats, other weirdness
        except:
            raise TypeError('invalid shape')

        if not (shape[0] >= 0 and shape[1] >= 0):
            raise ValueError('invalid shape')

        if (self._shape != shape) and (self._shape is not None):
            try:
                self = self.reshape(shape)
            except NotImplementedError:
                raise NotImplementedError("Reshaping not implemented for %s." %
                                          self.__class__.__name__)
        self._shape = shape

    def get_shape(self):
        return self._shape

    shape = property(fget=get_shape, fset=set_shape)

    def reshape(self, shape):
        raise NotImplementedError("Reshaping not implemented for %s." %
                                  self.__class__.__name__)

    def astype(self, t):
        return self.tocsr().astype(t).asformat(self.format)

    def asfptype(self):
        """Upcast matrix to a floating point format (if necessary)"""

        fp_types = ['f','d','F','D']

        if self.dtype.char in fp_types:
            return self
        else:
            for fp_type in fp_types:
                if self.dtype <= np.dtype(fp_type):
                    return self.astype(fp_type)

            raise TypeError('cannot upcast [%s] to a floating '
                             'point format' % self.dtype.name)

    def __iter__(self):
        for r in xrange(self.shape[0]):
            yield self[r,:]

    def getmaxprint(self):
        try:
            maxprint = self.maxprint
        except AttributeError:
            maxprint = MAXPRINT
        return maxprint

    # def typecode(self):
    #    try:
    #        typ = self.dtype.char
    #    except AttributeError:
    #        typ = None
    #    return typ

    def getnnz(self):
        try:
            return self.nnz
        except AttributeError:
            raise AttributeError("nnz not defined")

    def getformat(self):
        try:
            format = self.format
        except AttributeError:
            format = 'und'
        return format

    def __repr__(self):
        nnz = self.getnnz()
        format = self.getformat()
        return "<%dx%d sparse matrix of type '%s'\n" \
               "\twith %d stored elements in %s format>" % \
               (self.shape + (self.dtype.type, nnz, _formats[format][1]))

    def __str__(self):
        maxprint = self.getmaxprint()

        A = self.tocoo()
        nnz = self.getnnz()

        # helper function, outputs "(i,j)  v"
        def tostr(row,col,data):
            triples = zip(list(zip(row,col)),data)
            return '\n'.join([('  %s\t%s' % t) for t in triples])

        if nnz > maxprint:
            half = maxprint // 2
            out = tostr(A.row[:half], A.col[:half], A.data[:half])
            out += "\n  :\t:\n"
            half = maxprint - maxprint//2
            out += tostr(A.row[-half:], A.col[-half:], A.data[-half:])
        else:
            out = tostr(A.row, A.col, A.data)

        return out

    def __bool__(self):  # Simple -- other ideas?
        if self.shape == (1, 1):
            return True if self.nnz == 1 else False
        else:
            raise ValueError("The truth value of an array with more than one "
                             "element is ambiguous. Use a.any() or a.all().")
    __nonzero__ = __bool__

    # What should len(sparse) return? For consistency with dense matrices,
    # perhaps it should be the number of rows?  But for some uses the number of
    # non-zeros is more important.  For now, raise an exception!
    def __len__(self):
        # return self.getnnz()
        raise TypeError("sparse matrix length is ambiguous; use getnnz()"
                         " or shape[0]")

    def asformat(self, format):
        """Return this matrix in a given sparse format

        Parameters
        ----------
        format : {string, None}
            desired sparse matrix format
                - None for no format conversion
                - "csr" for csr_matrix format
                - "csc" for csc_matrix format
                - "lil" for lil_matrix format
                - "dok" for dok_matrix format and so on

        """

        if format is None or format == self.format:
            return self
        else:
            return getattr(self,'to' + format)()

    ###################################################################
    #  NOTE: All arithmetic operations use csr_matrix by default.
    # Therefore a new sparse matrix format just needs to define a
    # .tocsr() method to provide arithmetic support.  Any of these
    # methods can be overridden for efficiency.
    ####################################################################

    def multiply(self, other):
        """Point-wise multiplication by another matrix
        """
        return self.tocsr().multiply(other)

    def maximum(self, other):
        return self.tocsr().maximum(other)

    def minimum(self, other):
        return self.tocsr().minimum(other)

    def dot(self, other):
        """Ordinary dot product

        Examples
        --------
        >>> import numpy as np
        >>> from scipy.sparse import csr_matrix
        >>> A = csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
        >>> v = np.array([1, 0, -1])
        >>> A.dot(v)
        array([ 1, -3, -1], dtype=int64)

        """
        return self * other

    def power(self, n, dtype=None):            
        return self.tocsr().power(n, dtype=dtype)

    def __eq__(self, other):
        return self.tocsr().__eq__(other)

    def __ne__(self, other):
        return self.tocsr().__ne__(other)

    def __lt__(self,other):
        return self.tocsr().__lt__(other)

    def __gt__(self,other):
        return self.tocsr().__gt__(other)

    def __le__(self,other):
        return self.tocsr().__le__(other)

    def __ge__(self,other):
        return self.tocsr().__ge__(other)

    def __abs__(self):
        return abs(self.tocsr())

    def __add__(self, other):   # self + other
        return self.tocsr().__add__(other)

    def __radd__(self, other):  # other + self
        return self.tocsr().__radd__(other)

    def __sub__(self, other):   # self - other
        # note: this can't be replaced by self + (-other) for unsigned types
        return self.tocsr().__sub__(other)

    def __rsub__(self, other):  # other - self
        return self.tocsr().__rsub__(other)

    def __mul__(self, other):
        """interpret other and call one of the following

        self._mul_scalar()
        self._mul_vector()
        self._mul_multivector()
        self._mul_sparse_matrix()
        """

        M,N = self.shape

        if other.__class__ is np.ndarray:
            # Fast path for the most common case
            if other.shape == (N,):
                return self._mul_vector(other)
            elif other.shape == (N, 1):
                return self._mul_vector(other.ravel()).reshape(M, 1)
            elif other.ndim == 2 and other.shape[0] == N:
                return self._mul_multivector(other)

        if isscalarlike(other):
            # scalar value
            return self._mul_scalar(other)

        if issparse(other):
            if self.shape[1] != other.shape[0]:
                raise ValueError('dimension mismatch')
            return self._mul_sparse_matrix(other)

        try:
            other.shape
        except AttributeError:
            # If it's a list or whatever, treat it like a matrix
            other_a = np.asanyarray(other)

            if other_a.ndim == 0 and other_a.dtype == np.object_:
                # Not interpretable as an array; return NotImplemented so that
                # other's __rmul__ can kick in if that's implemented.
                return NotImplemented

            other = other_a

        if other.ndim == 1 or other.ndim == 2 and other.shape[1] == 1:
            # dense row or column vector
            if other.shape != (N,) and other.shape != (N,1):
                raise ValueError('dimension mismatch')

            result = self._mul_vector(np.ravel(other))

            if isinstance(other, np.matrix):
                result = np.asmatrix(result)

            if other.ndim == 2 and other.shape[1] == 1:
                # If 'other' was an (nx1) column vector, reshape the result
                result = result.reshape(-1,1)

            return result

        elif other.ndim == 2:
            ##
            # dense 2D array or matrix ("multivector")

            if other.shape[0] != self.shape[1]:
                raise ValueError('dimension mismatch')

            result = self._mul_multivector(np.asarray(other))

            if isinstance(other, np.matrix):
                result = np.asmatrix(result)

            return result
        else:
            raise ValueError('could not interpret dimensions')

    # by default, use CSR for __mul__ handlers
    def _mul_scalar(self, other):
        return self.tocsr()._mul_scalar(other)

    def _mul_vector(self, other):
        return self.tocsr()._mul_vector(other)

    def _mul_multivector(self, other):
        return self.tocsr()._mul_multivector(other)

    def _mul_sparse_matrix(self, other):
        return self.tocsr()._mul_sparse_matrix(other)

    def __rmul__(self, other):  # other * self
        if isscalarlike(other):
            return self.__mul__(other)
        else:
            # Don't use asarray unless we have to
            try:
                tr = other.transpose()
            except AttributeError:
                tr = np.asarray(other).transpose()
            return (self.transpose() * tr).transpose()

    #####################################
    # matmul (@) operator (Python 3.5+) #
    #####################################

    def __matmul__(self, other):
        if isscalarlike(other):
            raise ValueError("Scalar operands are not allowed, "
                             "use '*' instead")
        return self.__mul__(other)

    def __rmatmul__(self, other):
        if isscalarlike(other):
            raise ValueError("Scalar operands are not allowed, "
                             "use '*' instead")
        return self.__rmul__(other)

    ####################
    # Other Arithmetic #
    ####################

    def _divide(self, other, true_divide=False, rdivide=False):
        if isscalarlike(other):
            if rdivide:
                if true_divide:
                    return np.true_divide(other, self.todense())
                else:
                    return np.divide(other, self.todense())

            if true_divide and np.can_cast(self.dtype, np.float_):
                return self.astype(np.float_)._mul_scalar(1./other)
            else:
                r = self._mul_scalar(1./other)

                scalar_dtype = np.asarray(other).dtype
                if (np.issubdtype(self.dtype, np.integer)
                        and np.issubdtype(scalar_dtype, np.integer)):
                    return r.astype(self.dtype)
                else:
                    return r

        elif isdense(other):
            if not rdivide:
                if true_divide:
                    return np.true_divide(self.todense(), other)
                else:
                    return np.divide(self.todense(), other)
            else:
                if true_divide:
                    return np.true_divide(other, self.todense())
                else:
                    return np.divide(other, self.todense())
        elif isspmatrix(other):
            if rdivide:
                return other._divide(self, true_divide, rdivide=False)

            self_csr = self.tocsr()
            if true_divide and np.can_cast(self.dtype, np.float_):
                return self_csr.astype(np.float_)._divide_sparse(other)
            else:
                return self_csr._divide_sparse(other)
        else:
            return NotImplemented

    def __truediv__(self, other):
        return self._divide(other, true_divide=True)

    def __div__(self, other):
        # Always do true division
        return self._divide(other, true_divide=True)

    def __rtruediv__(self, other):
        # Implementing this as the inverse would be too magical -- bail out
        return NotImplemented

    def __rdiv__(self, other):
        # Implementing this as the inverse would be too magical -- bail out
        return NotImplemented

    def __neg__(self):
        return -self.tocsr()

    def __iadd__(self, other):
        return NotImplemented

    def __isub__(self, other):
        return NotImplemented

    def __imul__(self, other):
        return NotImplemented

    def __idiv__(self, other):
        return self.__itruediv__(other)

    def __itruediv__(self, other):
        return NotImplemented

    def __pow__(self, other):
        if self.shape[0] != self.shape[1]:
            raise TypeError('matrix is not square')

        if isintlike(other):
            other = int(other)
            if other < 0:
                raise ValueError('exponent must be >= 0')

            if other == 0:
                from .construct import eye
                return eye(self.shape[0], dtype=self.dtype)
            elif other == 1:
                return self.copy()
            else:
                tmp = self.__pow__(other//2)
                if (other % 2):
                    return self * tmp * tmp
                else:
                    return tmp * tmp
        elif isscalarlike(other):
            raise ValueError('exponent must be an integer')
        else:
            return NotImplemented

    def __getattr__(self, attr):
        if attr == 'A':
            return self.toarray()
        elif attr == 'T':
            return self.transpose()
        elif attr == 'H':
            return self.getH()
        elif attr == 'real':
            return self._real()
        elif attr == 'imag':
            return self._imag()
        elif attr == 'size':
            return self.getnnz()
        else:
            raise AttributeError(attr + " not found")

    def transpose(self):
        return self.tocsr().transpose()

    def conj(self):
        return self.tocsr().conj()

    def conjugate(self):
        return self.conj()

    # Renamed conjtranspose() -> getH() for compatibility with dense matrices
    def getH(self):
        return self.transpose().conj()

    def _real(self):
        return self.tocsr()._real()

    def _imag(self):
        return self.tocsr()._imag()

    def nonzero(self):
        """nonzero indices

        Returns a tuple of arrays (row,col) containing the indices
        of the non-zero elements of the matrix.

        Examples
        --------
        >>> from scipy.sparse import csr_matrix
        >>> A = csr_matrix([[1,2,0],[0,0,3],[4,0,5]])
        >>> A.nonzero()
        (array([0, 0, 1, 2, 2]), array([0, 1, 2, 0, 2]))

        """

        # convert to COOrdinate format
        A = self.tocoo()
        nz_mask = A.data != 0
        return (A.row[nz_mask],A.col[nz_mask])

    def getcol(self, j):
        """Returns a copy of column j of the matrix, as an (m x 1) sparse
        matrix (column vector).
        """
        # Spmatrix subclasses should override this method for efficiency.
        # Post-multiply by a (n x 1) column vector 'a' containing all zeros
        # except for a_j = 1
        from .csc import csc_matrix
        n = self.shape[1]
        if j < 0:
            j += n
        if j < 0 or j >= n:
            raise IndexError("index out of bounds")
        col_selector = csc_matrix(([1], [[j], [0]]), shape=(n,1), dtype=self.dtype)
        return self * col_selector

    def getrow(self, i):
        """Returns a copy of row i of the matrix, as a (1 x n) sparse
        matrix (row vector).
        """
        # Spmatrix subclasses should override this method for efficiency.
        # Pre-multiply by a (1 x m) row vector 'a' containing all zeros
        # except for a_i = 1
        from .csr import csr_matrix
        m = self.shape[0]
        if i < 0:
            i += m
        if i < 0 or i >= m:
            raise IndexError("index out of bounds")
        row_selector = csr_matrix(([1], [[0], [i]]), shape=(1,m), dtype=self.dtype)
        return row_selector * self

    # def __array__(self):
    #    return self.toarray()

    def todense(self, order=None, out=None):
        """
        Return a dense matrix representation of this matrix.

        Parameters
        ----------
        order : {'C', 'F'}, optional
            Whether to store multi-dimensional data in C (row-major)
            or Fortran (column-major) order in memory. The default
            is 'None', indicating the NumPy default of C-ordered.
            Cannot be specified in conjunction with the `out`
            argument.

        out : ndarray, 2-dimensional, optional
            If specified, uses this array (or `numpy.matrix`) as the
            output buffer instead of allocating a new array to
            return. The provided array must have the same shape and
            dtype as the sparse matrix on which you are calling the
            method.

        Returns
        -------
        arr : numpy.matrix, 2-dimensional
            A NumPy matrix object with the same shape and containing
            the same data represented by the sparse matrix, with the
            requested memory order. If `out` was passed and was an
            array (rather than a `numpy.matrix`), it will be filled
            with the appropriate values and returned wrapped in a
            `numpy.matrix` object that shares the same memory.
        """
        return np.asmatrix(self.toarray(order=order, out=out))

    def toarray(self, order=None, out=None):
        """
        Return a dense ndarray representation of this matrix.

        Parameters
        ----------
        order : {'C', 'F'}, optional
            Whether to store multi-dimensional data in C (row-major)
            or Fortran (column-major) order in memory. The default
            is 'None', indicating the NumPy default of C-ordered.
            Cannot be specified in conjunction with the `out`
            argument.

        out : ndarray, 2-dimensional, optional
            If specified, uses this array as the output buffer
            instead of allocating a new array to return. The provided
            array must have the same shape and dtype as the sparse
            matrix on which you are calling the method. For most
            sparse types, `out` is required to be memory contiguous
            (either C or Fortran ordered).

        Returns
        -------
        arr : ndarray, 2-dimensional
            An array with the same shape and containing the same
            data represented by the sparse matrix, with the requested
            memory order. If `out` was passed, the same object is
            returned after being modified in-place to contain the
            appropriate values.
        """
        return self.tocoo().toarray(order=order, out=out)

    def todok(self):
        return self.tocoo().todok()

    def tocoo(self):
        return self.tocsr().tocoo()

    def tolil(self):
        return self.tocsr().tolil()

    def todia(self):
        return self.tocoo().todia()

    def tobsr(self, blocksize=None):
        return self.tocsr().tobsr(blocksize=blocksize)

    def copy(self):
        return self.__class__(self,copy=True)

    def sum(self, axis=None):
        """Sum the matrix over the given axis.  If the axis is None, sum
        over both rows and columns, returning a scalar.
        """
        # We use multiplication by an array of ones to achieve this.
        # For some sparse matrix formats more efficient methods are
        # possible -- these should override this function.
        m, n = self.shape

        # Mimic numpy's casting.
        if np.issubdtype(self.dtype, np.float_):
            res_dtype = np.float_
        elif (np.issubdtype(self.dtype, np.int_) or
              np.issubdtype(self.dtype, np.bool_)):
                res_dtype = np.int_
        elif np.issubdtype(self.dtype, np.complex_):
            res_dtype = np.complex_
        else:
            res_dtype = self.dtype

        if axis is None:
            # sum over rows and columns
            return (self * np.asmatrix(np.ones((n, 1), dtype=res_dtype))).sum()

        if axis < 0:
            axis += 2
        if axis == 0:
            # sum over columns
            return np.asmatrix(np.ones((1, m), dtype=res_dtype)) * self
        elif axis == 1:
            # sum over rows
            return self * np.asmatrix(np.ones((n, 1), dtype=res_dtype))
        else:
            raise ValueError("axis out of bounds")

    def mean(self, axis=None):
        """Average the matrix over the given axis.  If the axis is None,
        average over both rows and columns, returning a scalar.
        """
        # Mimic numpy's casting.
        if (np.issubdtype(self.dtype, np.float_) or
                np.issubdtype(self.dtype, np.integer) or
                np.issubdtype(self.dtype, np.bool_)):
            res_dtype = np.float_
        elif np.issubdtype(self.dtype, np.complex_):
            res_dtype = np.complex_
        else:
            res_dtype = self.dtype

        if axis is None:
            return self.sum(None) * 1.0 / (self.shape[0]*self.shape[1])

        if axis < 0:
            axis += 2
        if axis == 0:
            mean = self.astype(res_dtype).sum(0)
            mean *= 1.0 / self.shape[0]
            return mean
        elif axis == 1:
            mean = self.astype(res_dtype).sum(1)
            mean *= 1.0 / self.shape[1]
            return mean
        else:
            raise ValueError("axis out of bounds")

    def diagonal(self):
        """Returns the main diagonal of the matrix
        """
        # TODO support k != 0
        return self.tocsr().diagonal()

    def setdiag(self, values, k=0):
        """
        Set diagonal or off-diagonal elements of the array.

        Parameters
        ----------
        values : array_like
            New values of the diagonal elements.

            Values may have any length.  If the diagonal is longer than values,
            then the remaining diagonal entries will not be set.  If values if
            longer than the diagonal, then the remaining values are ignored.

            If a scalar value is given, all of the diagonal is set to it.

        k : int, optional
            Which off-diagonal to set, corresponding to elements a[i,i+k].
            Default: 0 (the main diagonal).

        """
        M, N = self.shape
        if (k > 0 and k >= N) or (k < 0 and -k >= M):
            raise ValueError("k exceeds matrix dimensions")
        self._setdiag(np.asarray(values), k)

    def _setdiag(self, values, k):
        M, N = self.shape
        if k < 0:
            if values.ndim == 0:
                # broadcast
                max_index = min(M+k, N)
                for i in xrange(max_index):
                    self[i - k, i] = values
            else:
                max_index = min(M+k, N, len(values))
                if max_index <= 0:
                    return
                for i,v in enumerate(values[:max_index]):
                    self[i - k, i] = v
        else:
            if values.ndim == 0:
                # broadcast
                max_index = min(M, N-k)
                for i in xrange(max_index):
                    self[i, i + k] = values
            else:
                max_index = min(M, N-k, len(values))
                if max_index <= 0:
                    return
                for i,v in enumerate(values[:max_index]):
                    self[i, i + k] = v

    def _process_toarray_args(self, order, out):
        if out is not None:
            if order is not None:
                raise ValueError('order cannot be specified if out '
                                 'is not None')
            if out.shape != self.shape or out.dtype != self.dtype:
                raise ValueError('out array must be same dtype and shape as '
                                 'sparse matrix')
            out[...] = 0.
            return out
        else:
            return np.zeros(self.shape, dtype=self.dtype, order=order)

    def __numpy_ufunc__(self, func, method, pos, inputs, **kwargs):
        """Method for compatibility with NumPy's ufuncs and dot
        functions.
        """

        if any(not isinstance(x, spmatrix) and np.asarray(x).dtype == object
               for x in inputs):
            # preserve previous behavior with object arrays
            with_self = list(inputs)
            with_self[pos] = np.asarray(self, dtype=object)
            return getattr(func, method)(*with_self, **kwargs)

        out = kwargs.pop('out', None)
        if method != '__call__' or kwargs:
            return NotImplemented

        without_self = list(inputs)
        del without_self[pos]
        without_self = tuple(without_self)

        if func is np.multiply:
            result = self.multiply(*without_self)
        elif func is np.add:
            result = self.__add__(*without_self)
        elif func is np.dot:
            if pos == 0:
                result = self.__mul__(inputs[1])
            else:
                result = self.__rmul__(inputs[0])
        elif func is np.subtract:
            if pos == 0:
                result = self.__sub__(inputs[1])
            else:
                result = self.__rsub__(inputs[0])
        elif func is np.divide:
            true_divide = (sys.version_info[0] >= 3)
            rdivide = (pos == 1)
            result = self._divide(*without_self,
                                  true_divide=true_divide,
                                  rdivide=rdivide)
        elif func is np.true_divide:
            rdivide = (pos == 1)
            result = self._divide(*without_self, true_divide=True, rdivide=rdivide)
        elif func is np.maximum:
            result = self.maximum(*without_self)
        elif func is np.minimum:
            result = self.minimum(*without_self)
        elif func is np.absolute:
            result = abs(self)
        elif func in _ufuncs_with_fixed_point_at_zero:
            func_name = func.__name__
            if hasattr(self, func_name):
                result = getattr(self, func_name)()
            else:
                result = getattr(self.tocsr(), func_name)()
        else:
            return NotImplemented

        if out is not None:
            if not isinstance(out, spmatrix) and isinstance(result, spmatrix):
                out[...] = result.todense()
            else:
                out[...] = result
            result = out

        return result


def isspmatrix(x):
    return isinstance(x, spmatrix)

issparse = isspmatrix