base.py

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

import sys

import numpy as np

from scipy._lib.six import xrange
from scipy._lib._numpy_compat import broadcast_to
from .sputils import (isdense, isscalarlike, isintlike,
                      get_sum_dtype, validateaxis, check_reshape_kwargs,
                      check_shape)

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


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._shape = None
        if self.__class__.__name__ == 'spmatrix':
            raise ValueError("This class is not intended"
                             " to be instantiated directly.")
        self.maxprint = maxprint

    def set_shape(self, shape):
        """See `reshape`."""
        # Make sure copy is False since this is in place
        # Make sure format is unchanged because we are doing a __dict__ swap
        new_matrix = self.reshape(shape, copy=False).asformat(self.format)
        self.__dict__ = new_matrix.__dict__

    def get_shape(self):
        """Get shape of a matrix."""
        return self._shape

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

    def reshape(self, *args, **kwargs):
        """reshape(self, shape, order='C', copy=False)

        Gives a new shape to a sparse matrix without changing its data.

        Parameters
        ----------
        shape : length-2 tuple of ints
            The new shape should be compatible with the original shape.
        order : {'C', 'F'}, optional
            Read the elements using this index order. 'C' means to read and
            write the elements using C-like index order; e.g. read entire first
            row, then second row, etc. 'F' means to read and write the elements
            using Fortran-like index order; e.g. read entire first column, then
            second column, etc.
        copy : bool, optional
            Indicates whether or not attributes of self should be copied
            whenever possible. The degree to which attributes are copied varies
            depending on the type of sparse matrix being used.

        Returns
        -------
        reshaped_matrix : sparse matrix
            A sparse matrix with the given `shape`, not necessarily of the same
            format as the current object.

        See Also
        --------
        np.matrix.reshape : NumPy's implementation of 'reshape' for matrices
        """
        # If the shape already matches, don't bother doing an actual reshape
        # Otherwise, the default is to convert to COO and use its reshape
        shape = check_shape(args, self.shape)
        order, copy = check_reshape_kwargs(kwargs)
        if shape == self.shape:
            if copy:
                return self.copy()
            else:
                return self

        return self.tocoo(copy=copy).reshape(shape, order=order, copy=False)

    def resize(self, shape):
        """Resize the matrix in-place to dimensions given by ``shape``

        Any elements that lie within the new shape will remain at the same
        indices, while non-zero elements lying outside the new shape are
        removed.

        Parameters
        ----------
        shape : (int, int)
            number of rows and columns in the new matrix

        Notes
        -----
        The semantics are not identical to `numpy.ndarray.resize` or
        `numpy.resize`.  Here, the same data will be maintained at each index
        before and after reshape, if that index is within the new bounds.  In
        numpy, resizing maintains contiguity of the array, moving elements
        around in the logical matrix but not within a flattened representation.

        We give no guarantees about whether the underlying data attributes
        (arrays, etc.) will be modified in place or replaced with new objects.
        """
        # As an inplace operation, this requires implementation in each format.
        raise NotImplementedError(
            '{}.resize is not implemented'.format(type(self).__name__))

    def astype(self, dtype, casting='unsafe', copy=True):
        """Cast the matrix elements to a specified type.

        Parameters
        ----------
        dtype : string or numpy dtype
            Typecode or data-type to which to cast the data.
        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.
        copy : bool, optional
            If `copy` is `False`, the result might share some memory with this
            matrix. If `copy` is `True`, it is guaranteed that the result and
            this matrix do not share any memory.
        """

        dtype = np.dtype(dtype)
        if self.dtype != dtype:
            return self.tocsr().astype(
                dtype, casting=casting, copy=copy).asformat(self.format)
        elif copy:
            return self.copy()
        else:
            return self

    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):
        """Maximum number of elements to display when printed."""
        return self.maxprint

    def count_nonzero(self):
        """Number of non-zero entries, equivalent to

        np.count_nonzero(a.toarray())

        Unlike getnnz() and the nnz property, which return the number of stored
        entries (the length of the data attribute), this method counts the
        actual number of non-zero entries in data.
        """
        raise NotImplementedError("count_nonzero not implemented for %s." %
                                  self.__class__.__name__)

    def getnnz(self, axis=None):
        """Number of stored values, including explicit zeros.

        Parameters
        ----------
        axis : None, 0, or 1
            Select between the number of values across the whole matrix, in
            each column, or in each row.

        See also
        --------
        count_nonzero : Number of non-zero entries
        """
        raise NotImplementedError("getnnz not implemented for %s." %
                                  self.__class__.__name__)

    @property
    def nnz(self):
        """Number of stored values, including explicit zeros.

        See also
        --------
        count_nonzero : Number of non-zero entries
        """
        return self.getnnz()

    def getformat(self):
        """Format of a matrix representation as a string."""
        return getattr(self, 'format', 'und')

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

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

        A = self.tocoo()

        # 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 self.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 self.nnz != 0
        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):
        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):
        """Element-wise maximum between this and another matrix."""
        return self.tocsr().maximum(other)

    def minimum(self, other):
        """Element-wise minimum between this and another matrix."""
        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):
        """Element-wise power."""
        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_sparse(self, other):
        return self.tocsr()._add_sparse(other)

    def _add_dense(self, other):
        return self.tocoo()._add_dense(other)

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

    def _sub_dense(self, other):
        return self.todense() - other

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

    def __add__(self, other):  # self + other
        if isscalarlike(other):
            if other == 0:
                return self.copy()
            # Now we would add this scalar to every element.
            raise NotImplementedError('adding a nonzero scalar to a '
                                      'sparse matrix is not supported')
        elif isspmatrix(other):
            if other.shape != self.shape:
                raise ValueError("inconsistent shapes")
            return self._add_sparse(other)
        elif isdense(other):
            other = broadcast_to(other, self.shape)
            return self._add_dense(other)
        else:
            return NotImplemented

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

    def __sub__(self, other):  # self - other
        if isscalarlike(other):
            if other == 0:
                return self.copy()
            raise NotImplementedError('subtracting a nonzero scalar from a '
                                      'sparse matrix is not supported')
        elif isspmatrix(other):
            if other.shape != self.shape:
                raise ValueError("inconsistent shapes")
            return self._sub_sparse(other)
        elif isdense(other):
            other = broadcast_to(other, self.shape)
            return self._sub_dense(other)
        else:
            return NotImplemented

    def __rsub__(self,other):  # other - self
        if isscalarlike(other):
            if other == 0:
                return -self.copy()
            raise NotImplementedError('subtracting a sparse matrix from a '
                                      'nonzero scalar is not supported')
        elif isdense(other):
            other = broadcast_to(other, self.shape)
            return self._rsub_dense(other)
        else:
            return NotImplemented

    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)

        # 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

        try:
            other.shape
        except AttributeError:
            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, axes=None, copy=False):
        """
        Reverses the dimensions of the sparse matrix.

        Parameters
        ----------
        axes : None, optional
            This argument is in the signature *solely* for NumPy
            compatibility reasons. Do not pass in anything except
            for the default value.
        copy : bool, optional
            Indicates whether or not attributes of `self` should be
            copied whenever possible. The degree to which attributes
            are copied varies depending on the type of sparse matrix
            being used.

        Returns
        -------
        p : `self` with the dimensions reversed.

        See Also
        --------
        np.matrix.transpose : NumPy's implementation of 'transpose'
                              for matrices
        """
        return self.tocsr().transpose(axes=axes, copy=copy)

    def conj(self):
        """Element-wise complex conjugation.

        If the matrix is of non-complex data type, then this method does
        nothing and the data is not copied.
        """
        return self.tocsr().conj()

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

    conjugate.__doc__ = conj.__doc__

    # Renamed conjtranspose() -> getH() for compatibility with dense matrices
    def getH(self):
        """Return the Hermitian transpose of this matrix.

        See Also
        --------
        np.matrix.getH : NumPy's implementation of `getH` for matrices
        """
        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(copy=False).toarray(order=order, out=out)

    # Any sparse matrix format deriving from spmatrix must define one of
    # tocsr or tocoo. The other conversion methods may be implemented for
    # efficiency, but are not required.
    def tocsr(self, copy=False):
        """Convert this matrix to Compressed Sparse Row format.

        With copy=False, the data/indices may be shared between this matrix and
        the resultant csr_matrix.
        """
        return self.tocoo(copy=copy).tocsr(copy=False)

    def todok(self, copy=False):
        """Convert this matrix to Dictionary Of Keys format.

        With copy=False, the data/indices may be shared between this matrix and
        the resultant dok_matrix.
        """
        return self.tocoo(copy=copy).todok(copy=False)

    def tocoo(self, copy=False):
        """Convert this matrix to COOrdinate format.

        With copy=False, the data/indices may be shared between this matrix and
        the resultant coo_matrix.
        """
        return self.tocsr(copy=False).tocoo(copy=copy)

    def tolil(self, copy=False):
        """Convert this matrix to LInked List format.

        With copy=False, the data/indices may be shared between this matrix and
        the resultant lil_matrix.
        """
        return self.tocsr(copy=False).tolil(copy=copy)

    def todia(self, copy=False):
        """Convert this matrix to sparse DIAgonal format.

        With copy=False, the data/indices may be shared between this matrix and
        the resultant dia_matrix.
        """
        return self.tocoo(copy=copy).todia(copy=False)

    def tobsr(self, blocksize=None, copy=False):
        """Convert this matrix to Block Sparse Row format.

        With copy=False, the data/indices may be shared between this matrix and
        the resultant bsr_matrix.

        When blocksize=(R, C) is provided, it will be used for construction of
        the bsr_matrix.
        """
        return self.tocsr(copy=False).tobsr(blocksize=blocksize, copy=copy)

    def tocsc(self, copy=False):
        """Convert this matrix to Compressed Sparse Column format.

        With copy=False, the data/indices may be shared between this matrix and
        the resultant csc_matrix.
        """
        return self.tocsr(copy=copy).tocsc(copy=False)

    def copy(self):
        """Returns a copy of this matrix.

        No data/indices will be shared between the returned value and current
        matrix.
        """
        return self.__class__(self, copy=True)

    def sum(self, axis=None, dtype=None, out=None):
        """
        Sum the matrix elements over a given axis.

        Parameters
        ----------
        axis : {-2, -1, 0, 1, None} optional
            Axis along which the sum is computed. The default is to
            compute the sum of all the matrix elements, returning a scalar
            (i.e. `axis` = `None`).
        dtype : dtype, optional
            The type of the returned matrix and of the accumulator in which
            the elements are summed.  The dtype of `a` is used by default
            unless `a` has an integer dtype of less precision than the default
            platform integer.  In that case, if `a` is signed then the platform
            integer is used while if `a` is unsigned then an unsigned integer
            of the same precision as the platform integer is used.

            .. versionadded:: 0.18.0

        out : np.matrix, optional
            Alternative output matrix 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.

            .. versionadded:: 0.18.0

        Returns
        -------
        sum_along_axis : np.matrix
            A matrix with the same shape as `self`, with the specified
            axis removed.

        See Also
        --------
        np.matrix.sum : NumPy's implementation of 'sum' for matrices

        """
        validateaxis(axis)

        # We use multiplication by a matrix 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.
        res_dtype = get_sum_dtype(self.dtype)

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

        if axis < 0:
            axis += 2

        # axis = 0 or 1 now
        if axis == 0:
            # sum over columns
            ret = np.asmatrix(np.ones(
                (1, m), dtype=res_dtype)) * self
        else:
            # sum over rows
            ret = self * np.asmatrix(
                np.ones((n, 1), dtype=res_dtype))

        if out is not None and out.shape != ret.shape:
            raise ValueError("dimensions do not match")

        return ret.sum(axis=(), dtype=dtype, out=out)

    def mean(self, axis=None, dtype=None, out=None):
        """
        Compute the arithmetic mean along the specified axis.

        Returns the average of the matrix elements. The average is taken
        over all elements in the matrix by default, otherwise over the
        specified axis. `float64` intermediate and return values are used
        for integer inputs.

        Parameters
        ----------
        axis : {-2, -1, 0, 1, None} optional
            Axis along which the mean is computed. The default is to compute
            the mean of all elements in the matrix (i.e. `axis` = `None`).
        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.

            .. versionadded:: 0.18.0

        out : np.matrix, optional
            Alternative output matrix 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.

            .. versionadded:: 0.18.0

        Returns
        -------
        m : np.matrix

        See Also
        --------
        np.matrix.mean : NumPy's implementation of 'mean' for matrices

        """
        def _is_integral(dtype):
            return (np.issubdtype(dtype, np.integer) or
                    np.issubdtype(dtype, np.bool_))

        validateaxis(axis)

        res_dtype = self.dtype.type
        integral = _is_integral(self.dtype)

        # output dtype
        if dtype is None:
            if integral:
                res_dtype = np.float64
        else:
            res_dtype = np.dtype(dtype).type

        # intermediate dtype for summation
        inter_dtype = np.float64 if integral else res_dtype
        inter_self = self.astype(inter_dtype)

        if axis is None:
            return (inter_self / np.array(
                self.shape[0] * self.shape[1]))\
                .sum(dtype=res_dtype, out=out)

        if axis < 0:
            axis += 2

        # axis = 0 or 1 now
        if axis == 0:
            return (inter_self * (1.0 / self.shape[0])).sum(
                axis=0, dtype=res_dtype, out=out)
        else:
            return (inter_self * (1.0 / self.shape[1])).sum(
                axis=1, dtype=res_dtype, out=out)

    def diagonal(self, k=0):
        """Returns the k-th diagonal of the matrix.

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

            .. versionadded:: 1.0

        See also
        --------
        numpy.diagonal : Equivalent numpy function.

        Examples
        --------
        >>> from scipy.sparse import csr_matrix
        >>> A = csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
        >>> A.diagonal()
        array([1, 0, 5])
        >>> A.diagonal(k=1)
        array([2, 3])
        """
        return self.tocsr().diagonal(k=k)

    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):
    """Is x of a sparse matrix type?

    Parameters
    ----------
    x
        object to check for being a sparse matrix

    Returns
    -------
    bool
        True if x is a sparse matrix, False otherwise

    Notes
    -----
    issparse and isspmatrix are aliases for the same function.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix, isspmatrix
    >>> isspmatrix(csr_matrix([[5]]))
    True

    >>> from scipy.sparse import isspmatrix
    >>> isspmatrix(5)
    False
    """
    return isinstance(x, spmatrix)

issparse = isspmatrix