Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/sparse/__init__.py

@@ -0,0 +1,249 @@
+"""
+=====================================
+Sparse matrices (:mod:`scipy.sparse`)
+=====================================
+
+.. currentmodule:: scipy.sparse
+
+SciPy 2-D sparse matrix package for numeric data.
+
+Contents
+========
+
+Sparse matrix classes
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   bsr_matrix - Block Sparse Row matrix
+   coo_matrix - A sparse matrix in COOrdinate format
+   csc_matrix - Compressed Sparse Column matrix
+   csr_matrix - Compressed Sparse Row matrix
+   dia_matrix - Sparse matrix with DIAgonal storage
+   dok_matrix - Dictionary Of Keys based sparse matrix
+   lil_matrix - Row-based list of lists sparse matrix
+   spmatrix - Sparse matrix base class
+
+Functions
+---------
+
+Building sparse matrices:
+
+.. autosummary::
+   :toctree: generated/
+
+   eye - Sparse MxN matrix whose k-th diagonal is all ones
+   identity - Identity matrix in sparse format
+   kron - kronecker product of two sparse matrices
+   kronsum - kronecker sum of sparse matrices
+   diags - Return a sparse matrix from diagonals
+   spdiags - Return a sparse matrix from diagonals
+   block_diag - Build a block diagonal sparse matrix
+   tril - Lower triangular portion of a matrix in sparse format
+   triu - Upper triangular portion of a matrix in sparse format
+   bmat - Build a sparse matrix from sparse sub-blocks
+   hstack - Stack sparse matrices horizontally (column wise)
+   vstack - Stack sparse matrices vertically (row wise)
+   rand - Random values in a given shape
+   random - Random values in a given shape
+
+Save and load sparse matrices:
+
+.. autosummary::
+   :toctree: generated/
+
+   save_npz - Save a sparse matrix to a file using ``.npz`` format.
+   load_npz - Load a sparse matrix from a file using ``.npz`` format.
+
+Sparse matrix tools:
+
+.. autosummary::
+   :toctree: generated/
+
+   find
+
+Identifying sparse matrices:
+
+.. autosummary::
+   :toctree: generated/
+
+   issparse
+   isspmatrix
+   isspmatrix_csc
+   isspmatrix_csr
+   isspmatrix_bsr
+   isspmatrix_lil
+   isspmatrix_dok
+   isspmatrix_coo
+   isspmatrix_dia
+
+Submodules
+----------
+
+.. autosummary::
+
+   csgraph - Compressed sparse graph routines
+   linalg - sparse linear algebra routines
+
+Exceptions
+----------
+
+.. autosummary::
+   :toctree: generated/
+
+   SparseEfficiencyWarning
+   SparseWarning
+
+
+Usage information
+=================
+
+There are seven available sparse matrix types:
+
+    1. csc_matrix: Compressed Sparse Column format
+    2. csr_matrix: Compressed Sparse Row format
+    3. bsr_matrix: Block Sparse Row format
+    4. lil_matrix: List of Lists format
+    5. dok_matrix: Dictionary of Keys format
+    6. coo_matrix: COOrdinate format (aka IJV, triplet format)
+    7. dia_matrix: DIAgonal format
+
+To construct a matrix efficiently, use either dok_matrix or lil_matrix.
+The lil_matrix class supports basic slicing and fancy indexing with a
+similar syntax to NumPy arrays. As illustrated below, the COO format
+may also be used to efficiently construct matrices. Despite their
+similarity to NumPy arrays, it is **strongly discouraged** to use NumPy
+functions directly on these matrices because NumPy may not properly convert
+them for computations, leading to unexpected (and incorrect) results. If you
+do want to apply a NumPy function to these matrices, first check if SciPy has
+its own implementation for the given sparse matrix class, or **convert the
+sparse matrix to a NumPy array** (e.g., using the `toarray()` method of the
+class) first before applying the method.
+
+To perform manipulations such as multiplication or inversion, first
+convert the matrix to either CSC or CSR format. The lil_matrix format is
+row-based, so conversion to CSR is efficient, whereas conversion to CSC
+is less so.
+
+All conversions among the CSR, CSC, and COO formats are efficient,
+linear-time operations.
+
+Matrix vector product
+---------------------
+To do a vector product between a sparse matrix and a vector simply use
+the matrix `dot` method, as described in its docstring:
+
+>>> 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)
+
+.. warning:: As of NumPy 1.7, `np.dot` is not aware of sparse matrices,
+  therefore using it will result on unexpected results or errors.
+  The corresponding dense array should be obtained first instead:
+
+  >>> np.dot(A.toarray(), v)
+  array([ 1, -3, -1], dtype=int64)
+
+  but then all the performance advantages would be lost.
+
+The CSR format is specially suitable for fast matrix vector products.
+
+Example 1
+---------
+Construct a 1000x1000 lil_matrix and add some values to it:
+
+>>> from scipy.sparse import lil_matrix
+>>> from scipy.sparse.linalg import spsolve
+>>> from numpy.linalg import solve, norm
+>>> from numpy.random import rand
+
+>>> A = lil_matrix((1000, 1000))
+>>> A[0, :100] = rand(100)
+>>> A[1, 100:200] = A[0, :100]
+>>> A.setdiag(rand(1000))
+
+Now convert it to CSR format and solve A x = b for x:
+
+>>> A = A.tocsr()
+>>> b = rand(1000)
+>>> x = spsolve(A, b)
+
+Convert it to a dense matrix and solve, and check that the result
+is the same:
+
+>>> x_ = solve(A.toarray(), b)
+
+Now we can compute norm of the error with:
+
+>>> err = norm(x-x_)
+>>> err < 1e-10
+True
+
+It should be small :)
+
+
+Example 2
+---------
+
+Construct a matrix in COO format:
+
+>>> from scipy import sparse
+>>> from numpy import array
+>>> I = array([0,3,1,0])
+>>> J = array([0,3,1,2])
+>>> V = array([4,5,7,9])
+>>> A = sparse.coo_matrix((V,(I,J)),shape=(4,4))
+
+Notice that the indices do not need to be sorted.
+
+Duplicate (i,j) entries are summed when converting to CSR or CSC.
+
+>>> I = array([0,0,1,3,1,0,0])
+>>> J = array([0,2,1,3,1,0,0])
+>>> V = array([1,1,1,1,1,1,1])
+>>> B = sparse.coo_matrix((V,(I,J)),shape=(4,4)).tocsr()
+
+This is useful for constructing finite-element stiffness and mass matrices.
+
+Further details
+---------------
+
+CSR column indices are not necessarily sorted. Likewise for CSC row
+indices. Use the .sorted_indices() and .sort_indices() methods when
+sorted indices are required (e.g., when passing data to other libraries).
+
+"""
+
+# Original code by Travis Oliphant.
+# Modified and extended by Ed Schofield, Robert Cimrman,
+# Nathan Bell, and Jake Vanderplas.
+
+import warnings as _warnings
+
+from .base import *
+from .csr import *
+from .csc import *
+from .lil import *
+from .dok import *
+from .coo import *
+from .dia import *
+from .bsr import *
+from .construct import *
+from .extract import *
+from ._matrix_io import *
+
+# For backward compatibility with v0.19.
+from . import csgraph
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+# Filter PendingDeprecationWarning for np.matrix introduced with numpy 1.15
+_warnings.filterwarnings('ignore', message='the matrix subclass is not the recommended way')
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

venv/Lib/site-packages/scipy/sparse/_index.py

@@ -0,0 +1,367 @@
+"""Indexing mixin for sparse matrix classes.
+"""
+import numpy as np
+from .sputils import isintlike
+
+try:
+    INT_TYPES = (int, long, np.integer)
+except NameError:
+    # long is not defined in Python3
+    INT_TYPES = (int, np.integer)
+
+
+def _broadcast_arrays(a, b):
+    """
+    Same as np.broadcast_arrays(a, b) but old writeability rules.
+
+    NumPy >= 1.17.0 transitions broadcast_arrays to return
+    read-only arrays. Set writeability explicitly to avoid warnings.
+    Retain the old writeability rules, as our Cython code assumes
+    the old behavior.
+    """
+    x, y = np.broadcast_arrays(a, b)
+    x.flags.writeable = a.flags.writeable
+    y.flags.writeable = b.flags.writeable
+    return x, y
+
+
+class IndexMixin(object):
+    """
+    This class provides common dispatching and validation logic for indexing.
+    """
+    def __getitem__(self, key):
+        row, col = self._validate_indices(key)
+        # Dispatch to specialized methods.
+        if isinstance(row, INT_TYPES):
+            if isinstance(col, INT_TYPES):
+                return self._get_intXint(row, col)
+            elif isinstance(col, slice):
+                return self._get_intXslice(row, col)
+            elif col.ndim == 1:
+                return self._get_intXarray(row, col)
+            raise IndexError('index results in >2 dimensions')
+        elif isinstance(row, slice):
+            if isinstance(col, INT_TYPES):
+                return self._get_sliceXint(row, col)
+            elif isinstance(col, slice):
+                if row == slice(None) and row == col:
+                    return self.copy()
+                return self._get_sliceXslice(row, col)
+            elif col.ndim == 1:
+                return self._get_sliceXarray(row, col)
+            raise IndexError('index results in >2 dimensions')
+        elif row.ndim == 1:
+            if isinstance(col, INT_TYPES):
+                return self._get_arrayXint(row, col)
+            elif isinstance(col, slice):
+                return self._get_arrayXslice(row, col)
+        else:  # row.ndim == 2
+            if isinstance(col, INT_TYPES):
+                return self._get_arrayXint(row, col)
+            elif isinstance(col, slice):
+                raise IndexError('index results in >2 dimensions')
+            elif row.shape[1] == 1 and (col.ndim == 1 or col.shape[0] == 1):
+                # special case for outer indexing
+                return self._get_columnXarray(row[:,0], col.ravel())
+
+        # The only remaining case is inner (fancy) indexing
+        row, col = _broadcast_arrays(row, col)
+        if row.shape != col.shape:
+            raise IndexError('number of row and column indices differ')
+        if row.size == 0:
+            return self.__class__(np.atleast_2d(row).shape, dtype=self.dtype)
+        return self._get_arrayXarray(row, col)
+
+    def __setitem__(self, key, x):
+        row, col = self._validate_indices(key)
+
+        if isinstance(row, INT_TYPES) and isinstance(col, INT_TYPES):
+            x = np.asarray(x, dtype=self.dtype)
+            if x.size != 1:
+                raise ValueError('Trying to assign a sequence to an item')
+            self._set_intXint(row, col, x.flat[0])
+            return
+
+        if isinstance(row, slice):
+            row = np.arange(*row.indices(self.shape[0]))[:, None]
+        else:
+            row = np.atleast_1d(row)
+
+        if isinstance(col, slice):
+            col = np.arange(*col.indices(self.shape[1]))[None, :]
+            if row.ndim == 1:
+                row = row[:, None]
+        else:
+            col = np.atleast_1d(col)
+
+        i, j = _broadcast_arrays(row, col)
+        if i.shape != j.shape:
+            raise IndexError('number of row and column indices differ')
+
+        from .base import isspmatrix
+        if isspmatrix(x):
+            if i.ndim == 1:
+                # Inner indexing, so treat them like row vectors.
+                i = i[None]
+                j = j[None]
+            broadcast_row = x.shape[0] == 1 and i.shape[0] != 1
+            broadcast_col = x.shape[1] == 1 and i.shape[1] != 1
+            if not ((broadcast_row or x.shape[0] == i.shape[0]) and
+                    (broadcast_col or x.shape[1] == i.shape[1])):
+                raise ValueError('shape mismatch in assignment')
+            if x.size == 0:
+                return
+            x = x.tocoo(copy=True)
+            x.sum_duplicates()
+            self._set_arrayXarray_sparse(i, j, x)
+        else:
+            # Make x and i into the same shape
+            x = np.asarray(x, dtype=self.dtype)
+            x, _ = _broadcast_arrays(x, i)
+            if x.size == 0:
+                return
+            x = x.reshape(i.shape)
+            self._set_arrayXarray(i, j, x)
+
+    def _validate_indices(self, key):
+        M, N = self.shape
+        row, col = _unpack_index(key)
+
+        if isintlike(row):
+            row = int(row)
+            if row < -M or row >= M:
+                raise IndexError('row index (%d) out of range' % row)
+            if row < 0:
+                row += M
+        elif not isinstance(row, slice):
+            row = self._asindices(row, M)
+
+        if isintlike(col):
+            col = int(col)
+            if col < -N or col >= N:
+                raise IndexError('column index (%d) out of range' % col)
+            if col < 0:
+                col += N
+        elif not isinstance(col, slice):
+            col = self._asindices(col, N)
+
+        return row, col
+
+    def _asindices(self, idx, length):
+        """Convert `idx` to a valid index for an axis with a given length.
+
+        Subclasses that need special validation can override this method.
+        """
+        try:
+            x = np.asarray(idx)
+        except (ValueError, TypeError, MemoryError):
+            raise IndexError('invalid index')
+
+        if x.ndim not in (1, 2):
+            raise IndexError('Index dimension must be <= 2')
+
+        if x.size == 0:
+            return x
+
+        # Check bounds
+        max_indx = x.max()
+        if max_indx >= length:
+            raise IndexError('index (%d) out of range' % max_indx)
+
+        min_indx = x.min()
+        if min_indx < 0:
+            if min_indx < -length:
+                raise IndexError('index (%d) out of range' % min_indx)
+            if x is idx or not x.flags.owndata:
+                x = x.copy()
+            x[x < 0] += length
+        return x
+
+    def getrow(self, i):
+        """Return a copy of row i of the matrix, as a (1 x n) row vector.
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < -M or i >= M:
+            raise IndexError('index (%d) out of range' % i)
+        if i < 0:
+            i += M
+        return self._get_intXslice(i, slice(None))
+
+    def getcol(self, i):
+        """Return a copy of column i of the matrix, as a (m x 1) column vector.
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < -N or i >= N:
+            raise IndexError('index (%d) out of range' % i)
+        if i < 0:
+            i += N
+        return self._get_sliceXint(slice(None), i)
+
+    def _get_intXint(self, row, col):
+        raise NotImplementedError()
+
+    def _get_intXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _get_intXslice(self, row, col):
+        raise NotImplementedError()
+
+    def _get_sliceXint(self, row, col):
+        raise NotImplementedError()
+
+    def _get_sliceXslice(self, row, col):
+        raise NotImplementedError()
+
+    def _get_sliceXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _get_arrayXint(self, row, col):
+        raise NotImplementedError()
+
+    def _get_arrayXslice(self, row, col):
+        raise NotImplementedError()
+
+    def _get_columnXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _get_arrayXarray(self, row, col):
+        raise NotImplementedError()
+
+    def _set_intXint(self, row, col, x):
+        raise NotImplementedError()
+
+    def _set_arrayXarray(self, row, col, x):
+        raise NotImplementedError()
+
+    def _set_arrayXarray_sparse(self, row, col, x):
+        # Fall back to densifying x
+        x = np.asarray(x.toarray(), dtype=self.dtype)
+        x, _ = _broadcast_arrays(x, row)
+        self._set_arrayXarray(row, col, x)
+
+
+def _unpack_index(index):
+    """ Parse index. Always return a tuple of the form (row, col).
+    Valid type for row/col is integer, slice, or array of integers.
+    """
+    # First, check if indexing with single boolean matrix.
+    from .base import spmatrix, isspmatrix
+    if (isinstance(index, (spmatrix, np.ndarray)) and
+            index.ndim == 2 and index.dtype.kind == 'b'):
+        return index.nonzero()
+
+    # Parse any ellipses.
+    index = _check_ellipsis(index)
+
+    # Next, parse the tuple or object
+    if isinstance(index, tuple):
+        if len(index) == 2:
+            row, col = index
+        elif len(index) == 1:
+            row, col = index[0], slice(None)
+        else:
+            raise IndexError('invalid number of indices')
+    else:
+        idx = _compatible_boolean_index(index)
+        if idx is None:
+            row, col = index, slice(None)
+        elif idx.ndim < 2:
+            return _boolean_index_to_array(idx), slice(None)
+        elif idx.ndim == 2:
+            return idx.nonzero()
+    # Next, check for validity and transform the index as needed.
+    if isspmatrix(row) or isspmatrix(col):
+        # Supporting sparse boolean indexing with both row and col does
+        # not work because spmatrix.ndim is always 2.
+        raise IndexError(
+            'Indexing with sparse matrices is not supported '
+            'except boolean indexing where matrix and index '
+            'are equal shapes.')
+    bool_row = _compatible_boolean_index(row)
+    bool_col = _compatible_boolean_index(col)
+    if bool_row is not None:
+        row = _boolean_index_to_array(bool_row)
+    if bool_col is not None:
+        col = _boolean_index_to_array(bool_col)
+    return row, col
+
+
+def _check_ellipsis(index):
+    """Process indices with Ellipsis. Returns modified index."""
+    if index is Ellipsis:
+        return (slice(None), slice(None))
+
+    if not isinstance(index, tuple):
+        return index
+
+    # TODO: Deprecate this multiple-ellipsis handling,
+    #       as numpy no longer supports it.
+
+    # Find first ellipsis.
+    for j, v in enumerate(index):
+        if v is Ellipsis:
+            first_ellipsis = j
+            break
+    else:
+        return index
+
+    # Try to expand it using shortcuts for common cases
+    if len(index) == 1:
+        return (slice(None), slice(None))
+    if len(index) == 2:
+        if first_ellipsis == 0:
+            if index[1] is Ellipsis:
+                return (slice(None), slice(None))
+            return (slice(None), index[1])
+        return (index[0], slice(None))
+
+    # Expand it using a general-purpose algorithm
+    tail = []
+    for v in index[first_ellipsis+1:]:
+        if v is not Ellipsis:
+            tail.append(v)
+    nd = first_ellipsis + len(tail)
+    nslice = max(0, 2 - nd)
+    return index[:first_ellipsis] + (slice(None),)*nslice + tuple(tail)
+
+
+def _maybe_bool_ndarray(idx):
+    """Returns a compatible array if elements are boolean.
+    """
+    idx = np.asanyarray(idx)
+    if idx.dtype.kind == 'b':
+        return idx
+    return None
+
+
+def _first_element_bool(idx, max_dim=2):
+    """Returns True if first element of the incompatible
+    array type is boolean.
+    """
+    if max_dim < 1:
+        return None
+    try:
+        first = next(iter(idx), None)
+    except TypeError:
+        return None
+    if isinstance(first, bool):
+        return True
+    return _first_element_bool(first, max_dim-1)
+
+
+def _compatible_boolean_index(idx):
+    """Returns a boolean index array that can be converted to
+    integer array. Returns None if no such array exists.
+    """
+    # Presence of attribute `ndim` indicates a compatible array type.
+    if hasattr(idx, 'ndim') or _first_element_bool(idx):
+        return _maybe_bool_ndarray(idx)
+    return None
+
+
+def _boolean_index_to_array(idx):
+    if idx.ndim > 1:
+        raise IndexError('invalid index shape')
+    return np.where(idx)[0]

venv/Lib/site-packages/scipy/sparse/_matrix_io.py

@@ -0,0 +1,149 @@
+import numpy as np
+import scipy.sparse
+
+__all__ = ['save_npz', 'load_npz']
+
+
+# Make loading safe vs. malicious input
+PICKLE_KWARGS = dict(allow_pickle=False)
+
+
+def save_npz(file, matrix, compressed=True):
+    """ Save a sparse matrix to a file using ``.npz`` format.
+
+    Parameters
+    ----------
+    file : str or file-like object
+        Either the file name (string) or an open file (file-like object)
+        where the data will be saved. If file is a string, the ``.npz``
+        extension will be appended to the file name if it is not already
+        there.
+    matrix: spmatrix (format: ``csc``, ``csr``, ``bsr``, ``dia`` or coo``)
+        The sparse matrix to save.
+    compressed : bool, optional
+        Allow compressing the file. Default: True
+
+    See Also
+    --------
+    scipy.sparse.load_npz: Load a sparse matrix from a file using ``.npz`` format.
+    numpy.savez: Save several arrays into a ``.npz`` archive.
+    numpy.savez_compressed : Save several arrays into a compressed ``.npz`` archive.
+
+    Examples
+    --------
+    Store sparse matrix to disk, and load it again:
+
+    >>> import scipy.sparse
+    >>> sparse_matrix = scipy.sparse.csc_matrix(np.array([[0, 0, 3], [4, 0, 0]]))
+    >>> sparse_matrix
+    <2x3 sparse matrix of type '<class 'numpy.int64'>'
+       with 2 stored elements in Compressed Sparse Column format>
+    >>> sparse_matrix.todense()
+    matrix([[0, 0, 3],
+            [4, 0, 0]], dtype=int64)
+
+    >>> scipy.sparse.save_npz('/tmp/sparse_matrix.npz', sparse_matrix)
+    >>> sparse_matrix = scipy.sparse.load_npz('/tmp/sparse_matrix.npz')
+
+    >>> sparse_matrix
+    <2x3 sparse matrix of type '<class 'numpy.int64'>'
+       with 2 stored elements in Compressed Sparse Column format>
+    >>> sparse_matrix.todense()
+    matrix([[0, 0, 3],
+            [4, 0, 0]], dtype=int64)
+    """
+    arrays_dict = {}
+    if matrix.format in ('csc', 'csr', 'bsr'):
+        arrays_dict.update(indices=matrix.indices, indptr=matrix.indptr)
+    elif matrix.format == 'dia':
+        arrays_dict.update(offsets=matrix.offsets)
+    elif matrix.format == 'coo':
+        arrays_dict.update(row=matrix.row, col=matrix.col)
+    else:
+        raise NotImplementedError('Save is not implemented for sparse matrix of format {}.'.format(matrix.format))
+    arrays_dict.update(
+        format=matrix.format.encode('ascii'),
+        shape=matrix.shape,
+        data=matrix.data
+    )
+    if compressed:
+        np.savez_compressed(file, **arrays_dict)
+    else:
+        np.savez(file, **arrays_dict)
+
+
+def load_npz(file):
+    """ Load a sparse matrix from a file using ``.npz`` format.
+
+    Parameters
+    ----------
+    file : str or file-like object
+        Either the file name (string) or an open file (file-like object)
+        where the data will be loaded.
+
+    Returns
+    -------
+    result : csc_matrix, csr_matrix, bsr_matrix, dia_matrix or coo_matrix
+        A sparse matrix containing the loaded data.
+
+    Raises
+    ------
+    IOError
+        If the input file does not exist or cannot be read.
+
+    See Also
+    --------
+    scipy.sparse.save_npz: Save a sparse matrix to a file using ``.npz`` format.
+    numpy.load: Load several arrays from a ``.npz`` archive.
+
+    Examples
+    --------
+    Store sparse matrix to disk, and load it again:
+
+    >>> import scipy.sparse
+    >>> sparse_matrix = scipy.sparse.csc_matrix(np.array([[0, 0, 3], [4, 0, 0]]))
+    >>> sparse_matrix
+    <2x3 sparse matrix of type '<class 'numpy.int64'>'
+       with 2 stored elements in Compressed Sparse Column format>
+    >>> sparse_matrix.todense()
+    matrix([[0, 0, 3],
+            [4, 0, 0]], dtype=int64)
+
+    >>> scipy.sparse.save_npz('/tmp/sparse_matrix.npz', sparse_matrix)
+    >>> sparse_matrix = scipy.sparse.load_npz('/tmp/sparse_matrix.npz')
+
+    >>> sparse_matrix
+    <2x3 sparse matrix of type '<class 'numpy.int64'>'
+        with 2 stored elements in Compressed Sparse Column format>
+    >>> sparse_matrix.todense()
+    matrix([[0, 0, 3],
+            [4, 0, 0]], dtype=int64)
+    """
+
+    with np.load(file, **PICKLE_KWARGS) as loaded:
+        try:
+            matrix_format = loaded['format']
+        except KeyError:
+            raise ValueError('The file {} does not contain a sparse matrix.'.format(file))
+
+        matrix_format = matrix_format.item()
+
+        if not isinstance(matrix_format, str):
+            # Play safe with Python 2 vs 3 backward compatibility;
+            # files saved with SciPy < 1.0.0 may contain unicode or bytes.
+            matrix_format = matrix_format.decode('ascii')
+
+        try:
+            cls = getattr(scipy.sparse, '{}_matrix'.format(matrix_format))
+        except AttributeError:
+            raise ValueError('Unknown matrix format "{}"'.format(matrix_format))
+
+        if matrix_format in ('csc', 'csr', 'bsr'):
+            return cls((loaded['data'], loaded['indices'], loaded['indptr']), shape=loaded['shape'])
+        elif matrix_format == 'dia':
+            return cls((loaded['data'], loaded['offsets']), shape=loaded['shape'])
+        elif matrix_format == 'coo':
+            return cls((loaded['data'], (loaded['row'], loaded['col'])), shape=loaded['shape'])
+        else:
+            raise NotImplementedError('Load is not implemented for '
+                                      'sparse matrix of format {}.'.format(matrix_format))

venv/Lib/site-packages/scipy/sparse/bsr.py

@@ -0,0 +1,715 @@
+"""Compressed Block Sparse Row matrix format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['bsr_matrix', 'isspmatrix_bsr']
+
+from warnings import warn
+
+import numpy as np
+
+from .data import _data_matrix, _minmax_mixin
+from .compressed import _cs_matrix
+from .base import isspmatrix, _formats, spmatrix
+from .sputils import (isshape, getdtype, to_native, upcast, get_index_dtype,
+                      check_shape)
+from . import _sparsetools
+from ._sparsetools import (bsr_matvec, bsr_matvecs, csr_matmat_maxnnz,
+                           bsr_matmat, bsr_transpose, bsr_sort_indices,
+                           bsr_tocsr)
+
+
+class bsr_matrix(_cs_matrix, _minmax_mixin):
+    """Block Sparse Row matrix
+
+    This can be instantiated in several ways:
+        bsr_matrix(D, [blocksize=(R,C)])
+            where D is a dense matrix or 2-D ndarray.
+
+        bsr_matrix(S, [blocksize=(R,C)])
+            with another sparse matrix S (equivalent to S.tobsr())
+
+        bsr_matrix((M, N), [blocksize=(R,C), dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)])
+            where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]``
+
+        bsr_matrix((data, indices, indptr), [shape=(M, N)])
+            is the standard BSR representation where the block column
+            indices for row i are stored in ``indices[indptr[i]:indptr[i+1]]``
+            and their corresponding block values are stored in
+            ``data[ indptr[i]: indptr[i+1] ]``. If the shape parameter is not
+            supplied, the matrix dimensions are inferred from the index arrays.
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    nnz
+        Number of stored values, including explicit zeros
+    data
+        Data array of the matrix
+    indices
+        BSR format index array
+    indptr
+        BSR format index pointer array
+    blocksize
+        Block size of the matrix
+    has_sorted_indices
+        Whether indices are sorted
+
+    Notes
+    -----
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    **Summary of BSR format**
+
+    The Block Compressed Row (BSR) format is very similar to the Compressed
+    Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense
+    sub matrices like the last example below.  Block matrices often arise in
+    vector-valued finite element discretizations. In such cases, BSR is
+    considerably more efficient than CSR and CSC for many sparse arithmetic
+    operations.
+
+    **Blocksize**
+
+    The blocksize (R,C) must evenly divide the shape of the matrix (M,N).
+    That is, R and C must satisfy the relationship ``M % R = 0`` and
+    ``N % C = 0``.
+
+    If no blocksize is specified, a simple heuristic is applied to determine
+    an appropriate blocksize.
+
+    Examples
+    --------
+    >>> from scipy.sparse import bsr_matrix
+    >>> bsr_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 0, 1, 2, 2, 2])
+    >>> col = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3 ,4, 5, 6])
+    >>> bsr_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)
+    >>> bsr_matrix((data,indices,indptr), shape=(6, 6)).toarray()
+    array([[1, 1, 0, 0, 2, 2],
+           [1, 1, 0, 0, 2, 2],
+           [0, 0, 0, 0, 3, 3],
+           [0, 0, 0, 0, 3, 3],
+           [4, 4, 5, 5, 6, 6],
+           [4, 4, 5, 5, 6, 6]])
+
+    """
+    format = 'bsr'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False, blocksize=None):
+        _data_matrix.__init__(self)
+
+        if isspmatrix(arg1):
+            if isspmatrix_bsr(arg1) and copy:
+                arg1 = arg1.copy()
+            else:
+                arg1 = arg1.tobsr(blocksize=blocksize)
+            self._set_self(arg1)
+
+        elif isinstance(arg1,tuple):
+            if isshape(arg1):
+                # it's a tuple of matrix dimensions (M,N)
+                self._shape = check_shape(arg1)
+                M,N = self.shape
+                # process blocksize
+                if blocksize is None:
+                    blocksize = (1,1)
+                else:
+                    if not isshape(blocksize):
+                        raise ValueError('invalid blocksize=%s' % blocksize)
+                    blocksize = tuple(blocksize)
+                self.data = np.zeros((0,) + blocksize, getdtype(dtype, default=float))
+
+                R,C = blocksize
+                if (M % R) != 0 or (N % C) != 0:
+                    raise ValueError('shape must be multiple of blocksize')
+
+                # Select index dtype large enough to pass array and
+                # scalar parameters to sparsetools
+                idx_dtype = get_index_dtype(maxval=max(M//R, N//C, R, C))
+                self.indices = np.zeros(0, dtype=idx_dtype)
+                self.indptr = np.zeros(M//R + 1, dtype=idx_dtype)
+
+            elif len(arg1) == 2:
+                # (data,(row,col)) format
+                from .coo import coo_matrix
+                self._set_self(coo_matrix(arg1, dtype=dtype).tobsr(blocksize=blocksize))
+
+            elif len(arg1) == 3:
+                # (data,indices,indptr) format
+                (data, indices, indptr) = arg1
+
+                # Select index dtype large enough to pass array and
+                # scalar parameters to sparsetools
+                maxval = 1
+                if shape is not None:
+                    maxval = max(shape)
+                if blocksize is not None:
+                    maxval = max(maxval, max(blocksize))
+                idx_dtype = get_index_dtype((indices, indptr), maxval=maxval, check_contents=True)
+
+                self.indices = np.array(indices, copy=copy, dtype=idx_dtype)
+                self.indptr = np.array(indptr, copy=copy, dtype=idx_dtype)
+                self.data = np.array(data, copy=copy, dtype=getdtype(dtype, data))
+            else:
+                raise ValueError('unrecognized bsr_matrix constructor usage')
+        else:
+            # must be dense
+            try:
+                arg1 = np.asarray(arg1)
+            except Exception:
+                raise ValueError("unrecognized form for"
+                        " %s_matrix constructor" % self.format)
+            from .coo import coo_matrix
+            arg1 = coo_matrix(arg1, dtype=dtype).tobsr(blocksize=blocksize)
+            self._set_self(arg1)
+
+        if shape is not None:
+            self._shape = check_shape(shape)
+        else:
+            if self.shape is None:
+                # shape not already set, try to infer dimensions
+                try:
+                    M = len(self.indptr) - 1
+                    N = self.indices.max() + 1
+                except Exception:
+                    raise ValueError('unable to infer matrix dimensions')
+                else:
+                    R,C = self.blocksize
+                    self._shape = check_shape((M*R,N*C))
+
+        if self.shape is None:
+            if shape is None:
+                # TODO infer shape here
+                raise ValueError('need to infer shape')
+            else:
+                self._shape = check_shape(shape)
+
+        if dtype is not None:
+            self.data = self.data.astype(dtype, copy=False)
+
+        self.check_format(full_check=False)
+
+    def check_format(self, full_check=True):
+        """check whether the matrix format is valid
+
+            *Parameters*:
+                full_check:
+                    True  - rigorous check, O(N) operations : default
+                    False - basic check, O(1) operations
+
+        """
+        M,N = self.shape
+        R,C = self.blocksize
+
+        # index arrays should have integer data types
+        if self.indptr.dtype.kind != 'i':
+            warn("indptr array has non-integer dtype (%s)"
+                    % self.indptr.dtype.name)
+        if self.indices.dtype.kind != 'i':
+            warn("indices array has non-integer dtype (%s)"
+                    % self.indices.dtype.name)
+
+        idx_dtype = get_index_dtype((self.indices, self.indptr))
+        self.indptr = np.asarray(self.indptr, dtype=idx_dtype)
+        self.indices = np.asarray(self.indices, dtype=idx_dtype)
+        self.data = to_native(self.data)
+
+        # check array shapes
+        if self.indices.ndim != 1 or self.indptr.ndim != 1:
+            raise ValueError("indices, and indptr should be 1-D")
+        if self.data.ndim != 3:
+            raise ValueError("data should be 3-D")
+
+        # check index pointer
+        if (len(self.indptr) != M//R + 1):
+            raise ValueError("index pointer size (%d) should be (%d)" %
+                                (len(self.indptr), M//R + 1))
+        if (self.indptr[0] != 0):
+            raise ValueError("index pointer should start with 0")
+
+        # check index and data arrays
+        if (len(self.indices) != len(self.data)):
+            raise ValueError("indices and data should have the same size")
+        if (self.indptr[-1] > len(self.indices)):
+            raise ValueError("Last value of index pointer should be less than "
+                                "the size of index and data arrays")
+
+        self.prune()
+
+        if full_check:
+            # check format validity (more expensive)
+            if self.nnz > 0:
+                if self.indices.max() >= N//C:
+                    raise ValueError("column index values must be < %d (now max %d)" % (N//C, self.indices.max()))
+                if self.indices.min() < 0:
+                    raise ValueError("column index values must be >= 0")
+                if np.diff(self.indptr).min() < 0:
+                    raise ValueError("index pointer values must form a "
+                                        "non-decreasing sequence")
+
+        # if not self.has_sorted_indices():
+        #    warn('Indices were not in sorted order. Sorting indices.')
+        #    self.sort_indices(check_first=False)
+
+    def _get_blocksize(self):
+        return self.data.shape[1:]
+    blocksize = property(fget=_get_blocksize)
+
+    def getnnz(self, axis=None):
+        if axis is not None:
+            raise NotImplementedError("getnnz over an axis is not implemented "
+                                      "for BSR format")
+        R,C = self.blocksize
+        return int(self.indptr[-1] * R * C)
+
+    getnnz.__doc__ = spmatrix.getnnz.__doc__
+
+    def __repr__(self):
+        format = _formats[self.getformat()][1]
+        return ("<%dx%d sparse matrix of type '%s'\n"
+                "\twith %d stored elements (blocksize = %dx%d) in %s format>" %
+                (self.shape + (self.dtype.type, self.nnz) + self.blocksize +
+                 (format,)))
+
+    def diagonal(self, k=0):
+        rows, cols = self.shape
+        if k <= -rows or k >= cols:
+            return np.empty(0, dtype=self.data.dtype)
+        R, C = self.blocksize
+        y = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
+                     dtype=upcast(self.dtype))
+        _sparsetools.bsr_diagonal(k, rows // R, cols // C, R, C,
+                                  self.indptr, self.indices,
+                                  np.ravel(self.data), y)
+        return y
+
+    diagonal.__doc__ = spmatrix.diagonal.__doc__
+
+    ##########################
+    # NotImplemented methods #
+    ##########################
+
+    def __getitem__(self,key):
+        raise NotImplementedError
+
+    def __setitem__(self,key,val):
+        raise NotImplementedError
+
+    ######################
+    # Arithmetic methods #
+    ######################
+
+    @np.deprecate(message="BSR matvec is deprecated in SciPy 0.19.0. "
+                          "Use * operator instead.")
+    def matvec(self, other):
+        """Multiply matrix by vector."""
+        return self * other
+
+    @np.deprecate(message="BSR matmat is deprecated in SciPy 0.19.0. "
+                          "Use * operator instead.")
+    def matmat(self, other):
+        """Multiply this sparse matrix by other matrix."""
+        return self * other
+
+    def _add_dense(self, other):
+        return self.tocoo(copy=False)._add_dense(other)
+
+    def _mul_vector(self, other):
+        M,N = self.shape
+        R,C = self.blocksize
+
+        result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype))
+
+        bsr_matvec(M//R, N//C, R, C,
+            self.indptr, self.indices, self.data.ravel(),
+            other, result)
+
+        return result
+
+    def _mul_multivector(self,other):
+        R,C = self.blocksize
+        M,N = self.shape
+        n_vecs = other.shape[1]  # number of column vectors
+
+        result = np.zeros((M,n_vecs), dtype=upcast(self.dtype,other.dtype))
+
+        bsr_matvecs(M//R, N//C, n_vecs, R, C,
+                self.indptr, self.indices, self.data.ravel(),
+                other.ravel(), result.ravel())
+
+        return result
+
+    def _mul_sparse_matrix(self, other):
+        M, K1 = self.shape
+        K2, N = other.shape
+
+        R,n = self.blocksize
+
+        # convert to this format
+        if isspmatrix_bsr(other):
+            C = other.blocksize[1]
+        else:
+            C = 1
+
+        from .csr import isspmatrix_csr
+
+        if isspmatrix_csr(other) and n == 1:
+            other = other.tobsr(blocksize=(n,C), copy=False)  # lightweight conversion
+        else:
+            other = other.tobsr(blocksize=(n,C))
+
+        idx_dtype = get_index_dtype((self.indptr, self.indices,
+                                     other.indptr, other.indices))
+
+        bnnz = csr_matmat_maxnnz(M//R, N//C,
+                                 self.indptr.astype(idx_dtype),
+                                 self.indices.astype(idx_dtype),
+                                 other.indptr.astype(idx_dtype),
+                                 other.indices.astype(idx_dtype))
+
+        idx_dtype = get_index_dtype((self.indptr, self.indices,
+                                     other.indptr, other.indices),
+                                    maxval=bnnz)
+        indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
+        indices = np.empty(bnnz, dtype=idx_dtype)
+        data = np.empty(R*C*bnnz, dtype=upcast(self.dtype,other.dtype))
+
+        bsr_matmat(bnnz, M//R, N//C, R, C, n,
+                   self.indptr.astype(idx_dtype),
+                   self.indices.astype(idx_dtype),
+                   np.ravel(self.data),
+                   other.indptr.astype(idx_dtype),
+                   other.indices.astype(idx_dtype),
+                   np.ravel(other.data),
+                   indptr,
+                   indices,
+                   data)
+
+        data = data.reshape(-1,R,C)
+
+        # TODO eliminate zeros
+
+        return bsr_matrix((data,indices,indptr),shape=(M,N),blocksize=(R,C))
+
+    ######################
+    # Conversion methods #
+    ######################
+
+    def tobsr(self, blocksize=None, copy=False):
+        """Convert this matrix into Block Sparse Row Format.
+
+        With copy=False, the data/indices may be shared between this
+        matrix and the resultant bsr_matrix.
+
+        If blocksize=(R, C) is provided, it will be used for determining
+        block size of the bsr_matrix.
+        """
+        if blocksize not in [None, self.blocksize]:
+            return self.tocsr().tobsr(blocksize=blocksize)
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    def tocsr(self, copy=False):
+        M, N = self.shape
+        R, C = self.blocksize
+        nnz = self.nnz
+        idx_dtype = get_index_dtype((self.indptr, self.indices),
+                                    maxval=max(nnz, N))
+        indptr = np.empty(M + 1, dtype=idx_dtype)
+        indices = np.empty(nnz, dtype=idx_dtype)
+        data = np.empty(nnz, dtype=upcast(self.dtype))
+
+        bsr_tocsr(M // R,  # n_brow
+                  N // C,  # n_bcol
+                  R, C,
+                  self.indptr.astype(idx_dtype, copy=False),
+                  self.indices.astype(idx_dtype, copy=False),
+                  self.data,
+                  indptr,
+                  indices,
+                  data)
+        from .csr import csr_matrix
+        return csr_matrix((data, indices, indptr), shape=self.shape)
+
+    tocsr.__doc__ = spmatrix.tocsr.__doc__
+
+    def tocsc(self, copy=False):
+        return self.tocsr(copy=False).tocsc(copy=copy)
+
+    tocsc.__doc__ = spmatrix.tocsc.__doc__
+
+    def tocoo(self, copy=True):
+        """Convert this matrix to COOrdinate format.
+
+        When copy=False the data array will be shared between
+        this matrix and the resultant coo_matrix.
+        """
+
+        M,N = self.shape
+        R,C = self.blocksize
+
+        indptr_diff = np.diff(self.indptr)
+        if indptr_diff.dtype.itemsize > np.dtype(np.intp).itemsize:
+            # Check for potential overflow
+            indptr_diff_limited = indptr_diff.astype(np.intp)
+            if np.any(indptr_diff_limited != indptr_diff):
+                raise ValueError("Matrix too big to convert")
+            indptr_diff = indptr_diff_limited
+
+        row = (R * np.arange(M//R)).repeat(indptr_diff)
+        row = row.repeat(R*C).reshape(-1,R,C)
+        row += np.tile(np.arange(R).reshape(-1,1), (1,C))
+        row = row.reshape(-1)
+
+        col = (C * self.indices).repeat(R*C).reshape(-1,R,C)
+        col += np.tile(np.arange(C), (R,1))
+        col = col.reshape(-1)
+
+        data = self.data.reshape(-1)
+
+        if copy:
+            data = data.copy()
+
+        from .coo import coo_matrix
+        return coo_matrix((data,(row,col)), shape=self.shape)
+
+    def toarray(self, order=None, out=None):
+        return self.tocoo(copy=False).toarray(order=order, out=out)
+
+    toarray.__doc__ = spmatrix.toarray.__doc__
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None:
+            raise ValueError(("Sparse matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation."))
+
+        R, C = self.blocksize
+        M, N = self.shape
+        NBLK = self.nnz//(R*C)
+
+        if self.nnz == 0:
+            return bsr_matrix((N, M), blocksize=(C, R),
+                              dtype=self.dtype, copy=copy)
+
+        indptr = np.empty(N//C + 1, dtype=self.indptr.dtype)
+        indices = np.empty(NBLK, dtype=self.indices.dtype)
+        data = np.empty((NBLK, C, R), dtype=self.data.dtype)
+
+        bsr_transpose(M//R, N//C, R, C,
+                      self.indptr, self.indices, self.data.ravel(),
+                      indptr, indices, data.ravel())
+
+        return bsr_matrix((data, indices, indptr),
+                          shape=(N, M), copy=copy)
+
+    transpose.__doc__ = spmatrix.transpose.__doc__
+
+    ##############################################################
+    # methods that examine or modify the internal data structure #
+    ##############################################################
+
+    def eliminate_zeros(self):
+        """Remove zero elements in-place."""
+
+        if not self.nnz:
+            return  # nothing to do
+
+        R,C = self.blocksize
+        M,N = self.shape
+
+        mask = (self.data != 0).reshape(-1,R*C).sum(axis=1)  # nonzero blocks
+
+        nonzero_blocks = mask.nonzero()[0]
+
+        self.data[:len(nonzero_blocks)] = self.data[nonzero_blocks]
+
+        # modifies self.indptr and self.indices *in place*
+        _sparsetools.csr_eliminate_zeros(M//R, N//C, self.indptr,
+                                         self.indices, mask)
+        self.prune()
+
+    def sum_duplicates(self):
+        """Eliminate duplicate matrix entries by adding them together
+
+        The is an *in place* operation
+        """
+        if self.has_canonical_format:
+            return
+        self.sort_indices()
+        R, C = self.blocksize
+        M, N = self.shape
+
+        # port of _sparsetools.csr_sum_duplicates
+        n_row = M // R
+        nnz = 0
+        row_end = 0
+        for i in range(n_row):
+            jj = row_end
+            row_end = self.indptr[i+1]
+            while jj < row_end:
+                j = self.indices[jj]
+                x = self.data[jj]
+                jj += 1
+                while jj < row_end and self.indices[jj] == j:
+                    x += self.data[jj]
+                    jj += 1
+                self.indices[nnz] = j
+                self.data[nnz] = x
+                nnz += 1
+            self.indptr[i+1] = nnz
+
+        self.prune()  # nnz may have changed
+        self.has_canonical_format = True
+
+    def sort_indices(self):
+        """Sort the indices of this matrix *in place*
+        """
+        if self.has_sorted_indices:
+            return
+
+        R,C = self.blocksize
+        M,N = self.shape
+
+        bsr_sort_indices(M//R, N//C, R, C, self.indptr, self.indices, self.data.ravel())
+
+        self.has_sorted_indices = True
+
+    def prune(self):
+        """ Remove empty space after all non-zero elements.
+        """
+
+        R,C = self.blocksize
+        M,N = self.shape
+
+        if len(self.indptr) != M//R + 1:
+            raise ValueError("index pointer has invalid length")
+
+        bnnz = self.indptr[-1]
+
+        if len(self.indices) < bnnz:
+            raise ValueError("indices array has too few elements")
+        if len(self.data) < bnnz:
+            raise ValueError("data array has too few elements")
+
+        self.data = self.data[:bnnz]
+        self.indices = self.indices[:bnnz]
+
+    # utility functions
+    def _binopt(self, other, op, in_shape=None, out_shape=None):
+        """Apply the binary operation fn to two sparse matrices."""
+
+        # Ideally we'd take the GCDs of the blocksize dimensions
+        # and explode self and other to match.
+        other = self.__class__(other, blocksize=self.blocksize)
+
+        # e.g. bsr_plus_bsr, etc.
+        fn = getattr(_sparsetools, self.format + op + self.format)
+
+        R,C = self.blocksize
+
+        max_bnnz = len(self.data) + len(other.data)
+        idx_dtype = get_index_dtype((self.indptr, self.indices,
+                                     other.indptr, other.indices),
+                                    maxval=max_bnnz)
+        indptr = np.empty(self.indptr.shape, dtype=idx_dtype)
+        indices = np.empty(max_bnnz, dtype=idx_dtype)
+
+        bool_ops = ['_ne_', '_lt_', '_gt_', '_le_', '_ge_']
+        if op in bool_ops:
+            data = np.empty(R*C*max_bnnz, dtype=np.bool_)
+        else:
+            data = np.empty(R*C*max_bnnz, dtype=upcast(self.dtype,other.dtype))
+
+        fn(self.shape[0]//R, self.shape[1]//C, R, C,
+           self.indptr.astype(idx_dtype),
+           self.indices.astype(idx_dtype),
+           self.data,
+           other.indptr.astype(idx_dtype),
+           other.indices.astype(idx_dtype),
+           np.ravel(other.data),
+           indptr,
+           indices,
+           data)
+
+        actual_bnnz = indptr[-1]
+        indices = indices[:actual_bnnz]
+        data = data[:R*C*actual_bnnz]
+
+        if actual_bnnz < max_bnnz/2:
+            indices = indices.copy()
+            data = data.copy()
+
+        data = data.reshape(-1,R,C)
+
+        return self.__class__((data, indices, indptr), shape=self.shape)
+
+    # needed by _data_matrix
+    def _with_data(self,data,copy=True):
+        """Returns a matrix with the same sparsity structure as self,
+        but with different data.  By default the structure arrays
+        (i.e. .indptr and .indices) are copied.
+        """
+        if copy:
+            return self.__class__((data,self.indices.copy(),self.indptr.copy()),
+                                   shape=self.shape,dtype=data.dtype)
+        else:
+            return self.__class__((data,self.indices,self.indptr),
+                                   shape=self.shape,dtype=data.dtype)
+
+#    # these functions are used by the parent class
+#    # to remove redudancy between bsc_matrix and bsr_matrix
+#    def _swap(self,x):
+#        """swap the members of x if this is a column-oriented matrix
+#        """
+#        return (x[0],x[1])
+
+
+def isspmatrix_bsr(x):
+    """Is x of a bsr_matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a bsr matrix
+
+    Returns
+    -------
+    bool
+        True if x is a bsr matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import bsr_matrix, isspmatrix_bsr
+    >>> isspmatrix_bsr(bsr_matrix([[5]]))
+    True
+
+    >>> from scipy.sparse import bsr_matrix, csr_matrix, isspmatrix_bsr
+    >>> isspmatrix_bsr(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, bsr_matrix)

venv/Lib/site-packages/scipy/sparse/construct.py

@@ -0,0 +1,843 @@
+"""Functions to construct sparse matrices
+"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['spdiags', 'eye', 'identity', 'kron', 'kronsum',
+           'hstack', 'vstack', 'bmat', 'rand', 'random', 'diags', 'block_diag']
+
+
+from functools import partial
+import numpy as np
+
+from scipy._lib._util import check_random_state, rng_integers
+from .sputils import upcast, get_index_dtype, isscalarlike
+
+from .csr import csr_matrix
+from .csc import csc_matrix
+from .bsr import bsr_matrix
+from .coo import coo_matrix
+from .dia import dia_matrix
+
+from .base import issparse
+
+
+def spdiags(data, diags, m, n, format=None):
+    """
+    Return a sparse matrix from diagonals.
+
+    Parameters
+    ----------
+    data : array_like
+        matrix diagonals stored row-wise
+    diags : diagonals to set
+        - k = 0  the main diagonal
+        - k > 0  the k-th upper diagonal
+        - k < 0  the k-th lower diagonal
+    m, n : int
+        shape of the result
+    format : str, optional
+        Format of the result. By default (format=None) an appropriate sparse
+        matrix format is returned. This choice is subject to change.
+
+    See Also
+    --------
+    diags : more convenient form of this function
+    dia_matrix : the sparse DIAgonal format.
+
+    Examples
+    --------
+    >>> from scipy.sparse import spdiags
+    >>> data = np.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])
+    >>> diags = np.array([0, -1, 2])
+    >>> spdiags(data, diags, 4, 4).toarray()
+    array([[1, 0, 3, 0],
+           [1, 2, 0, 4],
+           [0, 2, 3, 0],
+           [0, 0, 3, 4]])
+
+    """
+    return dia_matrix((data, diags), shape=(m,n)).asformat(format)
+
+
+def diags(diagonals, offsets=0, shape=None, format=None, dtype=None):
+    """
+    Construct a sparse matrix from diagonals.
+
+    Parameters
+    ----------
+    diagonals : sequence of array_like
+        Sequence of arrays containing the matrix diagonals,
+        corresponding to `offsets`.
+    offsets : sequence of int or an int, optional
+        Diagonals to set:
+          - k = 0  the main diagonal (default)
+          - k > 0  the kth upper diagonal
+          - k < 0  the kth lower diagonal
+    shape : tuple of int, optional
+        Shape of the result. If omitted, a square matrix large enough
+        to contain the diagonals is returned.
+    format : {"dia", "csr", "csc", "lil", ...}, optional
+        Matrix format of the result. By default (format=None) an
+        appropriate sparse matrix format is returned. This choice is
+        subject to change.
+    dtype : dtype, optional
+        Data type of the matrix.
+
+    See Also
+    --------
+    spdiags : construct matrix from diagonals
+
+    Notes
+    -----
+    This function differs from `spdiags` in the way it handles
+    off-diagonals.
+
+    The result from `diags` is the sparse equivalent of::
+
+        np.diag(diagonals[0], offsets[0])
+        + ...
+        + np.diag(diagonals[k], offsets[k])
+
+    Repeated diagonal offsets are disallowed.
+
+    .. versionadded:: 0.11
+
+    Examples
+    --------
+    >>> from scipy.sparse import diags
+    >>> diagonals = [[1, 2, 3, 4], [1, 2, 3], [1, 2]]
+    >>> diags(diagonals, [0, -1, 2]).toarray()
+    array([[1, 0, 1, 0],
+           [1, 2, 0, 2],
+           [0, 2, 3, 0],
+           [0, 0, 3, 4]])
+
+    Broadcasting of scalars is supported (but shape needs to be
+    specified):
+
+    >>> diags([1, -2, 1], [-1, 0, 1], shape=(4, 4)).toarray()
+    array([[-2.,  1.,  0.,  0.],
+           [ 1., -2.,  1.,  0.],
+           [ 0.,  1., -2.,  1.],
+           [ 0.,  0.,  1., -2.]])
+
+
+    If only one diagonal is wanted (as in `numpy.diag`), the following
+    works as well:
+
+    >>> diags([1, 2, 3], 1).toarray()
+    array([[ 0.,  1.,  0.,  0.],
+           [ 0.,  0.,  2.,  0.],
+           [ 0.,  0.,  0.,  3.],
+           [ 0.,  0.,  0.,  0.]])
+    """
+    # if offsets is not a sequence, assume that there's only one diagonal
+    if isscalarlike(offsets):
+        # now check that there's actually only one diagonal
+        if len(diagonals) == 0 or isscalarlike(diagonals[0]):
+            diagonals = [np.atleast_1d(diagonals)]
+        else:
+            raise ValueError("Different number of diagonals and offsets.")
+    else:
+        diagonals = list(map(np.atleast_1d, diagonals))
+
+    offsets = np.atleast_1d(offsets)
+
+    # Basic check
+    if len(diagonals) != len(offsets):
+        raise ValueError("Different number of diagonals and offsets.")
+
+    # Determine shape, if omitted
+    if shape is None:
+        m = len(diagonals[0]) + abs(int(offsets[0]))
+        shape = (m, m)
+
+    # Determine data type, if omitted
+    if dtype is None:
+        dtype = np.common_type(*diagonals)
+
+    # Construct data array
+    m, n = shape
+
+    M = max([min(m + offset, n - offset) + max(0, offset)
+             for offset in offsets])
+    M = max(0, M)
+    data_arr = np.zeros((len(offsets), M), dtype=dtype)
+
+    K = min(m, n)
+
+    for j, diagonal in enumerate(diagonals):
+        offset = offsets[j]
+        k = max(0, offset)
+        length = min(m + offset, n - offset, K)
+        if length < 0:
+            raise ValueError("Offset %d (index %d) out of bounds" % (offset, j))
+        try:
+            data_arr[j, k:k+length] = diagonal[...,:length]
+        except ValueError:
+            if len(diagonal) != length and len(diagonal) != 1:
+                raise ValueError(
+                    "Diagonal length (index %d: %d at offset %d) does not "
+                    "agree with matrix size (%d, %d)." % (
+                    j, len(diagonal), offset, m, n))
+            raise
+
+    return dia_matrix((data_arr, offsets), shape=(m, n)).asformat(format)
+
+
+def identity(n, dtype='d', format=None):
+    """Identity matrix in sparse format
+
+    Returns an identity matrix with shape (n,n) using a given
+    sparse format and dtype.
+
+    Parameters
+    ----------
+    n : int
+        Shape of the identity matrix.
+    dtype : dtype, optional
+        Data type of the matrix
+    format : str, optional
+        Sparse format of the result, e.g., format="csr", etc.
+
+    Examples
+    --------
+    >>> from scipy.sparse import identity
+    >>> identity(3).toarray()
+    array([[ 1.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  1.]])
+    >>> identity(3, dtype='int8', format='dia')
+    <3x3 sparse matrix of type '<class 'numpy.int8'>'
+            with 3 stored elements (1 diagonals) in DIAgonal format>
+
+    """
+    return eye(n, n, dtype=dtype, format=format)
+
+
+def eye(m, n=None, k=0, dtype=float, format=None):
+    """Sparse matrix with ones on diagonal
+
+    Returns a sparse (m x n) matrix where the kth diagonal
+    is all ones and everything else is zeros.
+
+    Parameters
+    ----------
+    m : int
+        Number of rows in the matrix.
+    n : int, optional
+        Number of columns. Default: `m`.
+    k : int, optional
+        Diagonal to place ones on. Default: 0 (main diagonal).
+    dtype : dtype, optional
+        Data type of the matrix.
+    format : str, optional
+        Sparse format of the result, e.g., format="csr", etc.
+
+    Examples
+    --------
+    >>> from scipy import sparse
+    >>> sparse.eye(3).toarray()
+    array([[ 1.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  1.]])
+    >>> sparse.eye(3, dtype=np.int8)
+    <3x3 sparse matrix of type '<class 'numpy.int8'>'
+        with 3 stored elements (1 diagonals) in DIAgonal format>
+
+    """
+    if n is None:
+        n = m
+    m,n = int(m),int(n)
+
+    if m == n and k == 0:
+        # fast branch for special formats
+        if format in ['csr', 'csc']:
+            idx_dtype = get_index_dtype(maxval=n)
+            indptr = np.arange(n+1, dtype=idx_dtype)
+            indices = np.arange(n, dtype=idx_dtype)
+            data = np.ones(n, dtype=dtype)
+            cls = {'csr': csr_matrix, 'csc': csc_matrix}[format]
+            return cls((data,indices,indptr),(n,n))
+        elif format == 'coo':
+            idx_dtype = get_index_dtype(maxval=n)
+            row = np.arange(n, dtype=idx_dtype)
+            col = np.arange(n, dtype=idx_dtype)
+            data = np.ones(n, dtype=dtype)
+            return coo_matrix((data,(row,col)),(n,n))
+
+    diags = np.ones((1, max(0, min(m + k, n))), dtype=dtype)
+    return spdiags(diags, k, m, n).asformat(format)
+
+
+def kron(A, B, format=None):
+    """kronecker product of sparse matrices A and B
+
+    Parameters
+    ----------
+    A : sparse or dense matrix
+        first matrix of the product
+    B : sparse or dense matrix
+        second matrix of the product
+    format : str, optional
+        format of the result (e.g. "csr")
+
+    Returns
+    -------
+    kronecker product in a sparse matrix format
+
+
+    Examples
+    --------
+    >>> from scipy import sparse
+    >>> A = sparse.csr_matrix(np.array([[0, 2], [5, 0]]))
+    >>> B = sparse.csr_matrix(np.array([[1, 2], [3, 4]]))
+    >>> sparse.kron(A, B).toarray()
+    array([[ 0,  0,  2,  4],
+           [ 0,  0,  6,  8],
+           [ 5, 10,  0,  0],
+           [15, 20,  0,  0]])
+
+    >>> sparse.kron(A, [[1, 2], [3, 4]]).toarray()
+    array([[ 0,  0,  2,  4],
+           [ 0,  0,  6,  8],
+           [ 5, 10,  0,  0],
+           [15, 20,  0,  0]])
+
+    """
+    B = coo_matrix(B)
+
+    if (format is None or format == "bsr") and 2*B.nnz >= B.shape[0] * B.shape[1]:
+        # B is fairly dense, use BSR
+        A = csr_matrix(A,copy=True)
+
+        output_shape = (A.shape[0]*B.shape[0], A.shape[1]*B.shape[1])
+
+        if A.nnz == 0 or B.nnz == 0:
+            # kronecker product is the zero matrix
+            return coo_matrix(output_shape)
+
+        B = B.toarray()
+        data = A.data.repeat(B.size).reshape(-1,B.shape[0],B.shape[1])
+        data = data * B
+
+        return bsr_matrix((data,A.indices,A.indptr), shape=output_shape)
+    else:
+        # use COO
+        A = coo_matrix(A)
+        output_shape = (A.shape[0]*B.shape[0], A.shape[1]*B.shape[1])
+
+        if A.nnz == 0 or B.nnz == 0:
+            # kronecker product is the zero matrix
+            return coo_matrix(output_shape)
+
+        # expand entries of a into blocks
+        row = A.row.repeat(B.nnz)
+        col = A.col.repeat(B.nnz)
+        data = A.data.repeat(B.nnz)
+
+        if max(A.shape[0]*B.shape[0], A.shape[1]*B.shape[1]) > np.iinfo('int32').max:
+            row = row.astype(np.int64)
+            col = col.astype(np.int64)
+
+        row *= B.shape[0]
+        col *= B.shape[1]
+
+        # increment block indices
+        row,col = row.reshape(-1,B.nnz),col.reshape(-1,B.nnz)
+        row += B.row
+        col += B.col
+        row,col = row.reshape(-1),col.reshape(-1)
+
+        # compute block entries
+        data = data.reshape(-1,B.nnz) * B.data
+        data = data.reshape(-1)
+
+        return coo_matrix((data,(row,col)), shape=output_shape).asformat(format)
+
+
+def kronsum(A, B, format=None):
+    """kronecker sum of sparse matrices A and B
+
+    Kronecker sum of two sparse matrices is a sum of two Kronecker
+    products kron(I_n,A) + kron(B,I_m) where A has shape (m,m)
+    and B has shape (n,n) and I_m and I_n are identity matrices
+    of shape (m,m) and (n,n), respectively.
+
+    Parameters
+    ----------
+    A
+        square matrix
+    B
+        square matrix
+    format : str
+        format of the result (e.g. "csr")
+
+    Returns
+    -------
+    kronecker sum in a sparse matrix format
+
+    Examples
+    --------
+
+
+    """
+    A = coo_matrix(A)
+    B = coo_matrix(B)
+
+    if A.shape[0] != A.shape[1]:
+        raise ValueError('A is not square')
+
+    if B.shape[0] != B.shape[1]:
+        raise ValueError('B is not square')
+
+    dtype = upcast(A.dtype, B.dtype)
+
+    L = kron(eye(B.shape[0],dtype=dtype), A, format=format)
+    R = kron(B, eye(A.shape[0],dtype=dtype), format=format)
+
+    return (L+R).asformat(format)  # since L + R is not always same format
+
+
+def _compressed_sparse_stack(blocks, axis):
+    """
+    Stacking fast path for CSR/CSC matrices
+    (i) vstack for CSR, (ii) hstack for CSC.
+    """
+    other_axis = 1 if axis == 0 else 0
+    data = np.concatenate([b.data for b in blocks])
+    constant_dim = blocks[0].shape[other_axis]
+    idx_dtype = get_index_dtype(arrays=[b.indptr for b in blocks],
+                                maxval=max(data.size, constant_dim))
+    indices = np.empty(data.size, dtype=idx_dtype)
+    indptr = np.empty(sum(b.shape[axis] for b in blocks) + 1, dtype=idx_dtype)
+    last_indptr = idx_dtype(0)
+    sum_dim = 0
+    sum_indices = 0
+    for b in blocks:
+        if b.shape[other_axis] != constant_dim:
+            raise ValueError('incompatible dimensions for axis %d' % other_axis)
+        indices[sum_indices:sum_indices+b.indices.size] = b.indices
+        sum_indices += b.indices.size
+        idxs = slice(sum_dim, sum_dim + b.shape[axis])
+        indptr[idxs] = b.indptr[:-1]
+        indptr[idxs] += last_indptr
+        sum_dim += b.shape[axis]
+        last_indptr += b.indptr[-1]
+    indptr[-1] = last_indptr
+    if axis == 0:
+        return csr_matrix((data, indices, indptr),
+                          shape=(sum_dim, constant_dim))
+    else:
+        return csc_matrix((data, indices, indptr),
+                          shape=(constant_dim, sum_dim))
+
+
+def hstack(blocks, format=None, dtype=None):
+    """
+    Stack sparse matrices horizontally (column wise)
+
+    Parameters
+    ----------
+    blocks
+        sequence of sparse matrices with compatible shapes
+    format : str
+        sparse format of the result (e.g., "csr")
+        by default an appropriate sparse matrix format is returned.
+        This choice is subject to change.
+    dtype : dtype, optional
+        The data-type of the output matrix. If not given, the dtype is
+        determined from that of `blocks`.
+
+    See Also
+    --------
+    vstack : stack sparse matrices vertically (row wise)
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_matrix, hstack
+    >>> A = coo_matrix([[1, 2], [3, 4]])
+    >>> B = coo_matrix([[5], [6]])
+    >>> hstack([A,B]).toarray()
+    array([[1, 2, 5],
+           [3, 4, 6]])
+
+    """
+    return bmat([blocks], format=format, dtype=dtype)
+
+
+def vstack(blocks, format=None, dtype=None):
+    """
+    Stack sparse matrices vertically (row wise)
+
+    Parameters
+    ----------
+    blocks
+        sequence of sparse matrices with compatible shapes
+    format : str, optional
+        sparse format of the result (e.g., "csr")
+        by default an appropriate sparse matrix format is returned.
+        This choice is subject to change.
+    dtype : dtype, optional
+        The data-type of the output matrix. If not given, the dtype is
+        determined from that of `blocks`.
+
+    See Also
+    --------
+    hstack : stack sparse matrices horizontally (column wise)
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_matrix, vstack
+    >>> A = coo_matrix([[1, 2], [3, 4]])
+    >>> B = coo_matrix([[5, 6]])
+    >>> vstack([A, B]).toarray()
+    array([[1, 2],
+           [3, 4],
+           [5, 6]])
+
+    """
+    return bmat([[b] for b in blocks], format=format, dtype=dtype)
+
+
+def bmat(blocks, format=None, dtype=None):
+    """
+    Build a sparse matrix from sparse sub-blocks
+
+    Parameters
+    ----------
+    blocks : array_like
+        Grid of sparse matrices with compatible shapes.
+        An entry of None implies an all-zero matrix.
+    format : {'bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil'}, optional
+        The sparse format of the result (e.g. "csr"). By default an
+        appropriate sparse matrix format is returned.
+        This choice is subject to change.
+    dtype : dtype, optional
+        The data-type of the output matrix. If not given, the dtype is
+        determined from that of `blocks`.
+
+    Returns
+    -------
+    bmat : sparse matrix
+
+    See Also
+    --------
+    block_diag, diags
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_matrix, bmat
+    >>> A = coo_matrix([[1, 2], [3, 4]])
+    >>> B = coo_matrix([[5], [6]])
+    >>> C = coo_matrix([[7]])
+    >>> bmat([[A, B], [None, C]]).toarray()
+    array([[1, 2, 5],
+           [3, 4, 6],
+           [0, 0, 7]])
+
+    >>> bmat([[A, None], [None, C]]).toarray()
+    array([[1, 2, 0],
+           [3, 4, 0],
+           [0, 0, 7]])
+
+    """
+
+    blocks = np.asarray(blocks, dtype='object')
+
+    if blocks.ndim != 2:
+        raise ValueError('blocks must be 2-D')
+
+    M,N = blocks.shape
+
+    # check for fast path cases
+    if (N == 1 and format in (None, 'csr') and all(isinstance(b, csr_matrix)
+                                                   for b in blocks.flat)):
+        A = _compressed_sparse_stack(blocks[:,0], 0)
+        if dtype is not None:
+            A = A.astype(dtype)
+        return A
+    elif (M == 1 and format in (None, 'csc')
+          and all(isinstance(b, csc_matrix) for b in blocks.flat)):
+        A = _compressed_sparse_stack(blocks[0,:], 1)
+        if dtype is not None:
+            A = A.astype(dtype)
+        return A
+
+    block_mask = np.zeros(blocks.shape, dtype=bool)
+    brow_lengths = np.zeros(M, dtype=np.int64)
+    bcol_lengths = np.zeros(N, dtype=np.int64)
+
+    # convert everything to COO format
+    for i in range(M):
+        for j in range(N):
+            if blocks[i,j] is not None:
+                A = coo_matrix(blocks[i,j])
+                blocks[i,j] = A
+                block_mask[i,j] = True
+
+                if brow_lengths[i] == 0:
+                    brow_lengths[i] = A.shape[0]
+                elif brow_lengths[i] != A.shape[0]:
+                    msg = ('blocks[{i},:] has incompatible row dimensions. '
+                           'Got blocks[{i},{j}].shape[0] == {got}, '
+                           'expected {exp}.'.format(i=i, j=j,
+                                                    exp=brow_lengths[i],
+                                                    got=A.shape[0]))
+                    raise ValueError(msg)
+
+                if bcol_lengths[j] == 0:
+                    bcol_lengths[j] = A.shape[1]
+                elif bcol_lengths[j] != A.shape[1]:
+                    msg = ('blocks[:,{j}] has incompatible row dimensions. '
+                           'Got blocks[{i},{j}].shape[1] == {got}, '
+                           'expected {exp}.'.format(i=i, j=j,
+                                                    exp=bcol_lengths[j],
+                                                    got=A.shape[1]))
+                    raise ValueError(msg)
+
+    nnz = sum(block.nnz for block in blocks[block_mask])
+    if dtype is None:
+        all_dtypes = [blk.dtype for blk in blocks[block_mask]]
+        dtype = upcast(*all_dtypes) if all_dtypes else None
+
+    row_offsets = np.append(0, np.cumsum(brow_lengths))
+    col_offsets = np.append(0, np.cumsum(bcol_lengths))
+
+    shape = (row_offsets[-1], col_offsets[-1])
+
+    data = np.empty(nnz, dtype=dtype)
+    idx_dtype = get_index_dtype(maxval=max(shape))
+    row = np.empty(nnz, dtype=idx_dtype)
+    col = np.empty(nnz, dtype=idx_dtype)
+
+    nnz = 0
+    ii, jj = np.nonzero(block_mask)
+    for i, j in zip(ii, jj):
+        B = blocks[i, j]
+        idx = slice(nnz, nnz + B.nnz)
+        data[idx] = B.data
+        row[idx] = B.row + row_offsets[i]
+        col[idx] = B.col + col_offsets[j]
+        nnz += B.nnz
+
+    return coo_matrix((data, (row, col)), shape=shape).asformat(format)
+
+
+def block_diag(mats, format=None, dtype=None):
+    """
+    Build a block diagonal sparse matrix from provided matrices.
+
+    Parameters
+    ----------
+    mats : sequence of matrices
+        Input matrices.
+    format : str, optional
+        The sparse format of the result (e.g., "csr"). If not given, the matrix
+        is returned in "coo" format.
+    dtype : dtype specifier, optional
+        The data-type of the output matrix. If not given, the dtype is
+        determined from that of `blocks`.
+
+    Returns
+    -------
+    res : sparse matrix
+
+    Notes
+    -----
+
+    .. versionadded:: 0.11.0
+
+    See Also
+    --------
+    bmat, diags
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_matrix, block_diag
+    >>> A = coo_matrix([[1, 2], [3, 4]])
+    >>> B = coo_matrix([[5], [6]])
+    >>> C = coo_matrix([[7]])
+    >>> block_diag((A, B, C)).toarray()
+    array([[1, 2, 0, 0],
+           [3, 4, 0, 0],
+           [0, 0, 5, 0],
+           [0, 0, 6, 0],
+           [0, 0, 0, 7]])
+
+    """
+    nmat = len(mats)
+    rows = []
+    for ia, a in enumerate(mats):
+        row = [None]*nmat
+        if issparse(a):
+            row[ia] = a
+        else:
+            row[ia] = coo_matrix(a)
+        rows.append(row)
+    return bmat(rows, format=format, dtype=dtype)
+
+
+def random(m, n, density=0.01, format='coo', dtype=None,
+           random_state=None, data_rvs=None):
+    """Generate a sparse matrix of the given shape and density with randomly
+    distributed values.
+
+    Parameters
+    ----------
+    m, n : int
+        shape of the matrix
+    density : real, optional
+        density of the generated matrix: density equal to one means a full
+        matrix, density of 0 means a matrix with no non-zero items.
+    format : str, optional
+        sparse matrix format.
+    dtype : dtype, optional
+        type of the returned matrix values.
+    random_state : {numpy.random.RandomState, int}, optional
+        Random number generator or random seed. If not given, the singleton
+        numpy.random will be used. This random state will be used
+        for sampling the sparsity structure, but not necessarily for sampling
+        the values of the structurally nonzero entries of the matrix.
+    data_rvs : callable, optional
+        Samples a requested number of random values.
+        This function should take a single argument specifying the length
+        of the ndarray that it will return. The structurally nonzero entries
+        of the sparse random matrix will be taken from the array sampled
+        by this function. By default, uniform [0, 1) random values will be
+        sampled using the same random state as is used for sampling
+        the sparsity structure.
+
+    Returns
+    -------
+    res : sparse matrix
+
+    Notes
+    -----
+    Only float types are supported for now.
+
+    Examples
+    --------
+    >>> from scipy.sparse import random
+    >>> from scipy import stats
+
+    >>> class CustomRandomState(np.random.RandomState):
+    ...     def randint(self, k):
+    ...         i = np.random.randint(k)
+    ...         return i - i % 2
+    >>> np.random.seed(12345)
+    >>> rs = CustomRandomState()
+    >>> rvs = stats.poisson(25, loc=10).rvs
+    >>> S = random(3, 4, density=0.25, random_state=rs, data_rvs=rvs)
+    >>> S.A
+    array([[ 36.,   0.,  33.,   0.],   # random
+           [  0.,   0.,   0.,   0.],
+           [  0.,   0.,  36.,   0.]])
+
+    >>> from scipy.sparse import random
+    >>> from scipy.stats import rv_continuous
+    >>> class CustomDistribution(rv_continuous):
+    ...     def _rvs(self,  size=None, random_state=None):
+    ...         return random_state.randn(*size)
+    >>> X = CustomDistribution(seed=2906)
+    >>> Y = X()  # get a frozen version of the distribution
+    >>> S = random(3, 4, density=0.25, random_state=2906, data_rvs=Y.rvs)
+    >>> S.A
+    array([[ 0.        ,  0.        ,  0.        ,  0.        ],
+           [ 0.13569738,  1.9467163 , -0.81205367,  0.        ],
+           [ 0.        ,  0.        ,  0.        ,  0.        ]])
+
+    """
+    if density < 0 or density > 1:
+        raise ValueError("density expected to be 0 <= density <= 1")
+    dtype = np.dtype(dtype)
+
+    mn = m * n
+
+    tp = np.intc
+    if mn > np.iinfo(tp).max:
+        tp = np.int64
+
+    if mn > np.iinfo(tp).max:
+        msg = """\
+Trying to generate a random sparse matrix such as the product of dimensions is
+greater than %d - this is not supported on this machine
+"""
+        raise ValueError(msg % np.iinfo(tp).max)
+
+    # Number of non zero values
+    k = int(round(density * m * n))
+
+    random_state = check_random_state(random_state)
+
+    if data_rvs is None:
+        if np.issubdtype(dtype, np.integer):
+            def data_rvs(n):
+                return rng_integers(random_state,
+                                    np.iinfo(dtype).min,
+                                    np.iinfo(dtype).max,
+                                    n,
+                                    dtype=dtype)
+        elif np.issubdtype(dtype, np.complexfloating):
+            def data_rvs(n):
+                return (random_state.uniform(size=n) +
+                        random_state.uniform(size=n) * 1j)
+        else:
+            data_rvs = partial(random_state.uniform, 0., 1.)
+
+    ind = random_state.choice(mn, size=k, replace=False)
+
+    j = np.floor(ind * 1. / m).astype(tp, copy=False)
+    i = (ind - j * m).astype(tp, copy=False)
+    vals = data_rvs(k).astype(dtype, copy=False)
+    return coo_matrix((vals, (i, j)), shape=(m, n)).asformat(format,
+                                                             copy=False)
+
+
+def rand(m, n, density=0.01, format="coo", dtype=None, random_state=None):
+    """Generate a sparse matrix of the given shape and density with uniformly
+    distributed values.
+
+    Parameters
+    ----------
+    m, n : int
+        shape of the matrix
+    density : real, optional
+        density of the generated matrix: density equal to one means a full
+        matrix, density of 0 means a matrix with no non-zero items.
+    format : str, optional
+        sparse matrix format.
+    dtype : dtype, optional
+        type of the returned matrix values.
+    random_state : {numpy.random.RandomState, int, np.random.Generator}, optional
+        Random number generator or random seed. If not given, the singleton
+        numpy.random will be used.
+
+    Returns
+    -------
+    res : sparse matrix
+
+    Notes
+    -----
+    Only float types are supported for now.
+
+    See Also
+    --------
+    scipy.sparse.random : Similar function that allows a user-specified random
+        data source.
+
+    Examples
+    --------
+    >>> from scipy.sparse import rand
+    >>> matrix = rand(3, 4, density=0.25, format="csr", random_state=42)
+    >>> matrix
+    <3x4 sparse matrix of type '<class 'numpy.float64'>'
+       with 3 stored elements in Compressed Sparse Row format>
+    >>> matrix.todense()
+    matrix([[0.05641158, 0.        , 0.        , 0.65088847],
+            [0.        , 0.        , 0.        , 0.14286682],
+            [0.        , 0.        , 0.        , 0.        ]])
+
+    """
+    return random(m, n, density, format, dtype, random_state)

venv/Lib/site-packages/scipy/sparse/coo.py

@@ -0,0 +1,617 @@
+""" A sparse matrix in COOrdinate or 'triplet' format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['coo_matrix', 'isspmatrix_coo']
+
+from warnings import warn
+
+import numpy as np
+
+
+from ._sparsetools import coo_tocsr, coo_todense, coo_matvec
+from .base import isspmatrix, SparseEfficiencyWarning, spmatrix
+from .data import _data_matrix, _minmax_mixin
+from .sputils import (upcast, upcast_char, to_native, isshape, getdtype,
+                      get_index_dtype, downcast_intp_index, check_shape,
+                      check_reshape_kwargs, matrix)
+
+import operator
+
+
+class coo_matrix(_data_matrix, _minmax_mixin):
+    """
+    A sparse matrix in COOrdinate format.
+
+    Also known as the 'ijv' or 'triplet' format.
+
+    This can be instantiated in several ways:
+        coo_matrix(D)
+            with a dense matrix D
+
+        coo_matrix(S)
+            with another sparse matrix S (equivalent to S.tocoo())
+
+        coo_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        coo_matrix((data, (i, j)), [shape=(M, N)])
+            to construct from three arrays:
+                1. data[:]   the entries of the matrix, in any order
+                2. i[:]      the row indices of the matrix entries
+                3. j[:]      the column indices of the matrix entries
+
+            Where ``A[i[k], j[k]] = data[k]``.  When shape is not
+            specified, it is inferred from the index arrays
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    nnz
+        Number of stored values, including explicit zeros
+    data
+        COO format data array of the matrix
+    row
+        COO format row index array of the matrix
+    col
+        COO format column index array of the matrix
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the COO format
+        - facilitates fast conversion among sparse formats
+        - permits duplicate entries (see example)
+        - very fast conversion to and from CSR/CSC formats
+
+    Disadvantages of the COO format
+        - does not directly support:
+            + arithmetic operations
+            + slicing
+
+    Intended Usage
+        - COO is a fast format for constructing sparse matrices
+        - Once a matrix has been constructed, convert to CSR or
+          CSC format for fast arithmetic and matrix vector operations
+        - By default when converting to CSR or CSC format, duplicate (i,j)
+          entries will be summed together.  This facilitates efficient
+          construction of finite element matrices and the like. (see example)
+
+    Examples
+    --------
+
+    >>> # Constructing an empty matrix
+    >>> from scipy.sparse import coo_matrix
+    >>> coo_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> # Constructing a matrix using ijv format
+    >>> row  = np.array([0, 3, 1, 0])
+    >>> col  = np.array([0, 3, 1, 2])
+    >>> data = np.array([4, 5, 7, 9])
+    >>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray()
+    array([[4, 0, 9, 0],
+           [0, 7, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 5]])
+
+    >>> # Constructing a matrix with duplicate indices
+    >>> row  = np.array([0, 0, 1, 3, 1, 0, 0])
+    >>> col  = np.array([0, 2, 1, 3, 1, 0, 0])
+    >>> data = np.array([1, 1, 1, 1, 1, 1, 1])
+    >>> coo = coo_matrix((data, (row, col)), shape=(4, 4))
+    >>> # Duplicate indices are maintained until implicitly or explicitly summed
+    >>> np.max(coo.data)
+    1
+    >>> coo.toarray()
+    array([[3, 0, 1, 0],
+           [0, 2, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 1]])
+
+    """
+    format = 'coo'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False):
+        _data_matrix.__init__(self)
+
+        if isinstance(arg1, tuple):
+            if isshape(arg1):
+                M, N = arg1
+                self._shape = check_shape((M, N))
+                idx_dtype = get_index_dtype(maxval=max(M, N))
+                self.row = np.array([], dtype=idx_dtype)
+                self.col = np.array([], dtype=idx_dtype)
+                self.data = np.array([], getdtype(dtype, default=float))
+                self.has_canonical_format = True
+            else:
+                try:
+                    obj, (row, col) = arg1
+                except (TypeError, ValueError):
+                    raise TypeError('invalid input format')
+
+                if shape is None:
+                    if len(row) == 0 or len(col) == 0:
+                        raise ValueError('cannot infer dimensions from zero '
+                                         'sized index arrays')
+                    M = operator.index(np.max(row)) + 1
+                    N = operator.index(np.max(col)) + 1
+                    self._shape = check_shape((M, N))
+                else:
+                    # Use 2 steps to ensure shape has length 2.
+                    M, N = shape
+                    self._shape = check_shape((M, N))
+
+                idx_dtype = get_index_dtype(maxval=max(self.shape))
+                self.row = np.array(row, copy=copy, dtype=idx_dtype)
+                self.col = np.array(col, copy=copy, dtype=idx_dtype)
+                self.data = np.array(obj, copy=copy)
+                self.has_canonical_format = False
+
+        else:
+            if isspmatrix(arg1):
+                if isspmatrix_coo(arg1) and copy:
+                    self.row = arg1.row.copy()
+                    self.col = arg1.col.copy()
+                    self.data = arg1.data.copy()
+                    self._shape = check_shape(arg1.shape)
+                else:
+                    coo = arg1.tocoo()
+                    self.row = coo.row
+                    self.col = coo.col
+                    self.data = coo.data
+                    self._shape = check_shape(coo.shape)
+                self.has_canonical_format = False
+            else:
+                #dense argument
+                M = np.atleast_2d(np.asarray(arg1))
+
+                if M.ndim != 2:
+                    raise TypeError('expected dimension <= 2 array or matrix')
+
+                self._shape = check_shape(M.shape)
+                if shape is not None:
+                    if check_shape(shape) != self._shape:
+                        raise ValueError('inconsistent shapes: %s != %s' %
+                                         (shape, self._shape))
+
+                self.row, self.col = M.nonzero()
+                self.data = M[self.row, self.col]
+                self.has_canonical_format = True
+
+        if dtype is not None:
+            self.data = self.data.astype(dtype, copy=False)
+
+        self._check()
+
+    def reshape(self, *args, **kwargs):
+        shape = check_shape(args, self.shape)
+        order, copy = check_reshape_kwargs(kwargs)
+
+        # Return early if reshape is not required
+        if shape == self.shape:
+            if copy:
+                return self.copy()
+            else:
+                return self
+
+        nrows, ncols = self.shape
+
+        if order == 'C':
+            # Upcast to avoid overflows: the coo_matrix constructor
+            # below will downcast the results to a smaller dtype, if
+            # possible.
+            dtype = get_index_dtype(maxval=(ncols * max(0, nrows - 1) + max(0, ncols - 1)))
+
+            flat_indices = np.multiply(ncols, self.row, dtype=dtype) + self.col
+            new_row, new_col = divmod(flat_indices, shape[1])
+        elif order == 'F':
+            dtype = get_index_dtype(maxval=(nrows * max(0, ncols - 1) + max(0, nrows - 1)))
+
+            flat_indices = np.multiply(nrows, self.col, dtype=dtype) + self.row
+            new_col, new_row = divmod(flat_indices, shape[0])
+        else:
+            raise ValueError("'order' must be 'C' or 'F'")
+
+        # Handle copy here rather than passing on to the constructor so that no
+        # copy will be made of new_row and new_col regardless
+        if copy:
+            new_data = self.data.copy()
+        else:
+            new_data = self.data
+
+        return coo_matrix((new_data, (new_row, new_col)),
+                          shape=shape, copy=False)
+
+    reshape.__doc__ = spmatrix.reshape.__doc__
+
+    def getnnz(self, axis=None):
+        if axis is None:
+            nnz = len(self.data)
+            if nnz != len(self.row) or nnz != len(self.col):
+                raise ValueError('row, column, and data array must all be the '
+                                 'same length')
+
+            if self.data.ndim != 1 or self.row.ndim != 1 or \
+                    self.col.ndim != 1:
+                raise ValueError('row, column, and data arrays must be 1-D')
+
+            return int(nnz)
+
+        if axis < 0:
+            axis += 2
+        if axis == 0:
+            return np.bincount(downcast_intp_index(self.col),
+                               minlength=self.shape[1])
+        elif axis == 1:
+            return np.bincount(downcast_intp_index(self.row),
+                               minlength=self.shape[0])
+        else:
+            raise ValueError('axis out of bounds')
+
+    getnnz.__doc__ = spmatrix.getnnz.__doc__
+
+    def _check(self):
+        """ Checks data structure for consistency """
+
+        # index arrays should have integer data types
+        if self.row.dtype.kind != 'i':
+            warn("row index array has non-integer dtype (%s)  "
+                    % self.row.dtype.name)
+        if self.col.dtype.kind != 'i':
+            warn("col index array has non-integer dtype (%s) "
+                    % self.col.dtype.name)
+
+        idx_dtype = get_index_dtype(maxval=max(self.shape))
+        self.row = np.asarray(self.row, dtype=idx_dtype)
+        self.col = np.asarray(self.col, dtype=idx_dtype)
+        self.data = to_native(self.data)
+
+        if self.nnz > 0:
+            if self.row.max() >= self.shape[0]:
+                raise ValueError('row index exceeds matrix dimensions')
+            if self.col.max() >= self.shape[1]:
+                raise ValueError('column index exceeds matrix dimensions')
+            if self.row.min() < 0:
+                raise ValueError('negative row index found')
+            if self.col.min() < 0:
+                raise ValueError('negative column index found')
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None:
+            raise ValueError(("Sparse matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation."))
+
+        M, N = self.shape
+        return coo_matrix((self.data, (self.col, self.row)),
+                          shape=(N, M), copy=copy)
+
+    transpose.__doc__ = spmatrix.transpose.__doc__
+
+    def resize(self, *shape):
+        shape = check_shape(shape)
+        new_M, new_N = shape
+        M, N = self.shape
+
+        if new_M < M or new_N < N:
+            mask = np.logical_and(self.row < new_M, self.col < new_N)
+            if not mask.all():
+                self.row = self.row[mask]
+                self.col = self.col[mask]
+                self.data = self.data[mask]
+
+        self._shape = shape
+
+    resize.__doc__ = spmatrix.resize.__doc__
+
+    def toarray(self, order=None, out=None):
+        """See the docstring for `spmatrix.toarray`."""
+        B = self._process_toarray_args(order, out)
+        fortran = int(B.flags.f_contiguous)
+        if not fortran and not B.flags.c_contiguous:
+            raise ValueError("Output array must be C or F contiguous")
+        M,N = self.shape
+        coo_todense(M, N, self.nnz, self.row, self.col, self.data,
+                    B.ravel('A'), fortran)
+        return B
+
+    def tocsc(self, copy=False):
+        """Convert this matrix to Compressed Sparse Column format
+
+        Duplicate entries will be summed together.
+
+        Examples
+        --------
+        >>> from numpy import array
+        >>> from scipy.sparse import coo_matrix
+        >>> row  = array([0, 0, 1, 3, 1, 0, 0])
+        >>> col  = array([0, 2, 1, 3, 1, 0, 0])
+        >>> data = array([1, 1, 1, 1, 1, 1, 1])
+        >>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsc()
+        >>> A.toarray()
+        array([[3, 0, 1, 0],
+               [0, 2, 0, 0],
+               [0, 0, 0, 0],
+               [0, 0, 0, 1]])
+
+        """
+        from .csc import csc_matrix
+        if self.nnz == 0:
+            return csc_matrix(self.shape, dtype=self.dtype)
+        else:
+            M,N = self.shape
+            idx_dtype = get_index_dtype((self.col, self.row),
+                                        maxval=max(self.nnz, M))
+            row = self.row.astype(idx_dtype, copy=False)
+            col = self.col.astype(idx_dtype, copy=False)
+
+            indptr = np.empty(N + 1, dtype=idx_dtype)
+            indices = np.empty_like(row, dtype=idx_dtype)
+            data = np.empty_like(self.data, dtype=upcast(self.dtype))
+
+            coo_tocsr(N, M, self.nnz, col, row, self.data,
+                      indptr, indices, data)
+
+            x = csc_matrix((data, indices, indptr), shape=self.shape)
+            if not self.has_canonical_format:
+                x.sum_duplicates()
+            return x
+
+    def tocsr(self, copy=False):
+        """Convert this matrix to Compressed Sparse Row format
+
+        Duplicate entries will be summed together.
+
+        Examples
+        --------
+        >>> from numpy import array
+        >>> from scipy.sparse import coo_matrix
+        >>> row  = array([0, 0, 1, 3, 1, 0, 0])
+        >>> col  = array([0, 2, 1, 3, 1, 0, 0])
+        >>> data = array([1, 1, 1, 1, 1, 1, 1])
+        >>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsr()
+        >>> A.toarray()
+        array([[3, 0, 1, 0],
+               [0, 2, 0, 0],
+               [0, 0, 0, 0],
+               [0, 0, 0, 1]])
+
+        """
+        from .csr import csr_matrix
+        if self.nnz == 0:
+            return csr_matrix(self.shape, dtype=self.dtype)
+        else:
+            M,N = self.shape
+            idx_dtype = get_index_dtype((self.row, self.col),
+                                        maxval=max(self.nnz, N))
+            row = self.row.astype(idx_dtype, copy=False)
+            col = self.col.astype(idx_dtype, copy=False)
+
+            indptr = np.empty(M + 1, dtype=idx_dtype)
+            indices = np.empty_like(col, dtype=idx_dtype)
+            data = np.empty_like(self.data, dtype=upcast(self.dtype))
+
+            coo_tocsr(M, N, self.nnz, row, col, self.data,
+                      indptr, indices, data)
+
+            x = csr_matrix((data, indices, indptr), shape=self.shape)
+            if not self.has_canonical_format:
+                x.sum_duplicates()
+            return x
+
+    def tocoo(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tocoo.__doc__ = spmatrix.tocoo.__doc__
+
+    def todia(self, copy=False):
+        from .dia import dia_matrix
+
+        self.sum_duplicates()
+        ks = self.col - self.row  # the diagonal for each nonzero
+        diags, diag_idx = np.unique(ks, return_inverse=True)
+
+        if len(diags) > 100:
+            # probably undesired, should todia() have a maxdiags parameter?
+            warn("Constructing a DIA matrix with %d diagonals "
+                 "is inefficient" % len(diags), SparseEfficiencyWarning)
+
+        #initialize and fill in data array
+        if self.data.size == 0:
+            data = np.zeros((0, 0), dtype=self.dtype)
+        else:
+            data = np.zeros((len(diags), self.col.max()+1), dtype=self.dtype)
+            data[diag_idx, self.col] = self.data
+
+        return dia_matrix((data,diags), shape=self.shape)
+
+    todia.__doc__ = spmatrix.todia.__doc__
+
+    def todok(self, copy=False):
+        from .dok import dok_matrix
+
+        self.sum_duplicates()
+        dok = dok_matrix((self.shape), dtype=self.dtype)
+        dok._update(zip(zip(self.row,self.col),self.data))
+
+        return dok
+
+    todok.__doc__ = spmatrix.todok.__doc__
+
+    def diagonal(self, k=0):
+        rows, cols = self.shape
+        if k <= -rows or k >= cols:
+            return np.empty(0, dtype=self.data.dtype)
+        diag = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
+                        dtype=self.dtype)
+        diag_mask = (self.row + k) == self.col
+
+        if self.has_canonical_format:
+            row = self.row[diag_mask]
+            data = self.data[diag_mask]
+        else:
+            row, _, data = self._sum_duplicates(self.row[diag_mask],
+                                                self.col[diag_mask],
+                                                self.data[diag_mask])
+        diag[row + min(k, 0)] = data
+
+        return diag
+
+    diagonal.__doc__ = _data_matrix.diagonal.__doc__
+
+    def _setdiag(self, values, k):
+        M, N = self.shape
+        if values.ndim and not len(values):
+            return
+        idx_dtype = self.row.dtype
+
+        # Determine which triples to keep and where to put the new ones.
+        full_keep = self.col - self.row != k
+        if k < 0:
+            max_index = min(M+k, N)
+            if values.ndim:
+                max_index = min(max_index, len(values))
+            keep = np.logical_or(full_keep, self.col >= max_index)
+            new_row = np.arange(-k, -k + max_index, dtype=idx_dtype)
+            new_col = np.arange(max_index, dtype=idx_dtype)
+        else:
+            max_index = min(M, N-k)
+            if values.ndim:
+                max_index = min(max_index, len(values))
+            keep = np.logical_or(full_keep, self.row >= max_index)
+            new_row = np.arange(max_index, dtype=idx_dtype)
+            new_col = np.arange(k, k + max_index, dtype=idx_dtype)
+
+        # Define the array of data consisting of the entries to be added.
+        if values.ndim:
+            new_data = values[:max_index]
+        else:
+            new_data = np.empty(max_index, dtype=self.dtype)
+            new_data[:] = values
+
+        # Update the internal structure.
+        self.row = np.concatenate((self.row[keep], new_row))
+        self.col = np.concatenate((self.col[keep], new_col))
+        self.data = np.concatenate((self.data[keep], new_data))
+        self.has_canonical_format = False
+
+    # needed by _data_matrix
+    def _with_data(self,data,copy=True):
+        """Returns a matrix with the same sparsity structure as self,
+        but with different data.  By default the index arrays
+        (i.e. .row and .col) are copied.
+        """
+        if copy:
+            return coo_matrix((data, (self.row.copy(), self.col.copy())),
+                                   shape=self.shape, dtype=data.dtype)
+        else:
+            return coo_matrix((data, (self.row, self.col)),
+                                   shape=self.shape, dtype=data.dtype)
+
+    def sum_duplicates(self):
+        """Eliminate duplicate matrix entries by adding them together
+
+        This is an *in place* operation
+        """
+        if self.has_canonical_format:
+            return
+        summed = self._sum_duplicates(self.row, self.col, self.data)
+        self.row, self.col, self.data = summed
+        self.has_canonical_format = True
+
+    def _sum_duplicates(self, row, col, data):
+        # Assumes (data, row, col) not in canonical format.
+        if len(data) == 0:
+            return row, col, data
+        order = np.lexsort((row, col))
+        row = row[order]
+        col = col[order]
+        data = data[order]
+        unique_mask = ((row[1:] != row[:-1]) |
+                       (col[1:] != col[:-1]))
+        unique_mask = np.append(True, unique_mask)
+        row = row[unique_mask]
+        col = col[unique_mask]
+        unique_inds, = np.nonzero(unique_mask)
+        data = np.add.reduceat(data, unique_inds, dtype=self.dtype)
+        return row, col, data
+
+    def eliminate_zeros(self):
+        """Remove zero entries from the matrix
+
+        This is an *in place* operation
+        """
+        mask = self.data != 0
+        self.data = self.data[mask]
+        self.row = self.row[mask]
+        self.col = self.col[mask]
+
+    #######################
+    # Arithmetic handlers #
+    #######################
+
+    def _add_dense(self, other):
+        if other.shape != self.shape:
+            raise ValueError('Incompatible shapes.')
+        dtype = upcast_char(self.dtype.char, other.dtype.char)
+        result = np.array(other, dtype=dtype, copy=True)
+        fortran = int(result.flags.f_contiguous)
+        M, N = self.shape
+        coo_todense(M, N, self.nnz, self.row, self.col, self.data,
+                    result.ravel('A'), fortran)
+        return matrix(result, copy=False)
+
+    def _mul_vector(self, other):
+        #output array
+        result = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
+                                                            other.dtype.char))
+        coo_matvec(self.nnz, self.row, self.col, self.data, other, result)
+        return result
+
+    def _mul_multivector(self, other):
+        result = np.zeros((other.shape[1], self.shape[0]),
+                          dtype=upcast_char(self.dtype.char, other.dtype.char))
+        for i, col in enumerate(other.T):
+            coo_matvec(self.nnz, self.row, self.col, self.data, col, result[i])
+        return result.T.view(type=type(other))
+
+
+def isspmatrix_coo(x):
+    """Is x of coo_matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a coo matrix
+
+    Returns
+    -------
+    bool
+        True if x is a coo matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import coo_matrix, isspmatrix_coo
+    >>> isspmatrix_coo(coo_matrix([[5]]))
+    True
+
+    >>> from scipy.sparse import coo_matrix, csr_matrix, isspmatrix_coo
+    >>> isspmatrix_coo(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, coo_matrix)

venv/Lib/site-packages/scipy/sparse/csc.py

@@ -0,0 +1,259 @@
+"""Compressed Sparse Column matrix format"""
+__docformat__ = "restructuredtext en"
+
+__all__ = ['csc_matrix', 'isspmatrix_csc']
+
+
+import numpy as np
+
+from .base import spmatrix
+from ._sparsetools import csc_tocsr, expandptr
+from .sputils import upcast, get_index_dtype
+
+from .compressed import _cs_matrix
+
+
+class csc_matrix(_cs_matrix):
+    """
+    Compressed Sparse Column matrix
+
+    This can be instantiated in several ways:
+
+        csc_matrix(D)
+            with a dense matrix or rank-2 ndarray D
+
+        csc_matrix(S)
+            with another sparse matrix S (equivalent to S.tocsc())
+
+        csc_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        csc_matrix((data, (row_ind, col_ind)), [shape=(M, N)])
+            where ``data``, ``row_ind`` and ``col_ind`` satisfy the
+            relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
+
+        csc_matrix((data, indices, indptr), [shape=(M, N)])
+            is the standard CSC representation where the row indices for
+            column i are stored in ``indices[indptr[i]:indptr[i+1]]``
+            and their corresponding values are stored in
+            ``data[indptr[i]:indptr[i+1]]``.  If the shape parameter is
+            not supplied, the matrix dimensions are inferred from
+            the index arrays.
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    nnz
+        Number of stored values, including explicit zeros
+    data
+        Data array of the matrix
+    indices
+        CSC format index array
+    indptr
+        CSC format index pointer array
+    has_sorted_indices
+        Whether indices are sorted
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the CSC format
+        - efficient arithmetic operations CSC + CSC, CSC * CSC, etc.
+        - efficient column slicing
+        - fast matrix vector products (CSR, BSR may be faster)
+
+    Disadvantages of the CSC format
+      - slow row slicing operations (consider CSR)
+      - changes to the sparsity structure are expensive (consider LIL or DOK)
+
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_matrix
+    >>> csc_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 2, 2, 0, 1, 2])
+    >>> col = np.array([0, 0, 1, 2, 2, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csc_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 4],
+           [0, 0, 5],
+           [2, 3, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csc_matrix((data, indices, indptr), shape=(3, 3)).toarray()
+    array([[1, 0, 4],
+           [0, 0, 5],
+           [2, 3, 6]])
+
+    """
+    format = 'csc'
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None:
+            raise ValueError(("Sparse matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation."))
+
+        M, N = self.shape
+
+        from .csr import csr_matrix
+        return csr_matrix((self.data, self.indices,
+                           self.indptr), (N, M), copy=copy)
+
+    transpose.__doc__ = spmatrix.transpose.__doc__
+
+    def __iter__(self):
+        for r in self.tocsr():
+            yield r
+
+    def tocsc(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tocsc.__doc__ = spmatrix.tocsc.__doc__
+
+    def tocsr(self, copy=False):
+        M,N = self.shape
+        idx_dtype = get_index_dtype((self.indptr, self.indices),
+                                    maxval=max(self.nnz, N))
+        indptr = np.empty(M + 1, dtype=idx_dtype)
+        indices = np.empty(self.nnz, dtype=idx_dtype)
+        data = np.empty(self.nnz, dtype=upcast(self.dtype))
+
+        csc_tocsr(M, N,
+                  self.indptr.astype(idx_dtype),
+                  self.indices.astype(idx_dtype),
+                  self.data,
+                  indptr,
+                  indices,
+                  data)
+
+        from .csr import csr_matrix
+        A = csr_matrix((data, indices, indptr), shape=self.shape, copy=False)
+        A.has_sorted_indices = True
+        return A
+
+    tocsr.__doc__ = spmatrix.tocsr.__doc__
+
+    def nonzero(self):
+        # CSC can't use _cs_matrix's .nonzero method because it
+        # returns the indices sorted for self transposed.
+
+        # Get row and col indices, from _cs_matrix.tocoo
+        major_dim, minor_dim = self._swap(self.shape)
+        minor_indices = self.indices
+        major_indices = np.empty(len(minor_indices), dtype=self.indices.dtype)
+        expandptr(major_dim, self.indptr, major_indices)
+        row, col = self._swap((major_indices, minor_indices))
+
+        # Remove explicit zeros
+        nz_mask = self.data != 0
+        row = row[nz_mask]
+        col = col[nz_mask]
+
+        # Sort them to be in C-style order
+        ind = np.argsort(row, kind='mergesort')
+        row = row[ind]
+        col = col[ind]
+
+        return row, col
+
+    nonzero.__doc__ = _cs_matrix.nonzero.__doc__
+
+    def getrow(self, i):
+        """Returns a copy of row i of the matrix, as a (1 x n)
+        CSR matrix (row vector).
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += M
+        if i < 0 or i >= M:
+            raise IndexError('index (%d) out of range' % i)
+        return self._get_submatrix(minor=i).tocsr()
+
+    def getcol(self, i):
+        """Returns a copy of column i of the matrix, as a (m x 1)
+        CSC matrix (column vector).
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += N
+        if i < 0 or i >= N:
+            raise IndexError('index (%d) out of range' % i)
+        return self._get_submatrix(major=i, copy=True)
+
+    def _get_intXarray(self, row, col):
+        return self._major_index_fancy(col)._get_submatrix(minor=row)
+
+    def _get_intXslice(self, row, col):
+        if col.step in (1, None):
+            return self._get_submatrix(major=col, minor=row, copy=True)
+        return self._major_slice(col)._get_submatrix(minor=row)
+
+    def _get_sliceXint(self, row, col):
+        if row.step in (1, None):
+            return self._get_submatrix(major=col, minor=row, copy=True)
+        return self._get_submatrix(major=col)._minor_slice(row)
+
+    def _get_sliceXarray(self, row, col):
+        return self._major_index_fancy(col)._minor_slice(row)
+
+    def _get_arrayXint(self, row, col):
+        return self._get_submatrix(major=col)._minor_index_fancy(row)
+
+    def _get_arrayXslice(self, row, col):
+        return self._major_slice(col)._minor_index_fancy(row)
+
+    # these functions are used by the parent class (_cs_matrix)
+    # to remove redudancy between csc_matrix and csr_matrix
+    def _swap(self, x):
+        """swap the members of x if this is a column-oriented matrix
+        """
+        return x[1], x[0]
+
+
+def isspmatrix_csc(x):
+    """Is x of csc_matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a csc matrix
+
+    Returns
+    -------
+    bool
+        True if x is a csc matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_matrix, isspmatrix_csc
+    >>> isspmatrix_csc(csc_matrix([[5]]))
+    True
+
+    >>> from scipy.sparse import csc_matrix, csr_matrix, isspmatrix_csc
+    >>> isspmatrix_csc(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, csc_matrix)

venv/Lib/site-packages/scipy/sparse/csgraph/__init__.py

@@ -0,0 +1,195 @@
+r"""
+Compressed sparse graph routines (:mod:`scipy.sparse.csgraph`)
+==============================================================
+
+.. currentmodule:: scipy.sparse.csgraph
+
+Fast graph algorithms based on sparse matrix representations.
+
+Contents
+--------
+
+.. autosummary::
+   :toctree: generated/
+
+   connected_components -- determine connected components of a graph
+   laplacian -- compute the laplacian of a graph
+   shortest_path -- compute the shortest path between points on a positive graph
+   dijkstra -- use Dijkstra's algorithm for shortest path
+   floyd_warshall -- use the Floyd-Warshall algorithm for shortest path
+   bellman_ford -- use the Bellman-Ford algorithm for shortest path
+   johnson -- use Johnson's algorithm for shortest path
+   breadth_first_order -- compute a breadth-first order of nodes
+   depth_first_order -- compute a depth-first order of nodes
+   breadth_first_tree -- construct the breadth-first tree from a given node
+   depth_first_tree -- construct a depth-first tree from a given node
+   minimum_spanning_tree -- construct the minimum spanning tree of a graph
+   reverse_cuthill_mckee -- compute permutation for reverse Cuthill-McKee ordering
+   maximum_flow -- solve the maximum flow problem for a graph
+   maximum_bipartite_matching -- compute a maximum matching of a bipartite graph
+   structural_rank -- compute the structural rank of a graph
+   NegativeCycleError
+
+.. autosummary::
+   :toctree: generated/
+
+   construct_dist_matrix
+   csgraph_from_dense
+   csgraph_from_masked
+   csgraph_masked_from_dense
+   csgraph_to_dense
+   csgraph_to_masked
+   reconstruct_path
+
+Graph Representations
+---------------------
+This module uses graphs which are stored in a matrix format. A
+graph with N nodes can be represented by an (N x N) adjacency matrix G.
+If there is a connection from node i to node j, then G[i, j] = w, where
+w is the weight of the connection. For nodes i and j which are
+not connected, the value depends on the representation:
+
+- for dense array representations, non-edges are represented by
+  G[i, j] = 0, infinity, or NaN.
+
+- for dense masked representations (of type np.ma.MaskedArray), non-edges
+  are represented by masked values. This can be useful when graphs with
+  zero-weight edges are desired.
+
+- for sparse array representations, non-edges are represented by
+  non-entries in the matrix. This sort of sparse representation also
+  allows for edges with zero weights.
+
+As a concrete example, imagine that you would like to represent the following
+undirected graph::
+
+              G
+
+             (0)
+            /   \
+           1     2
+          /       \
+        (2)       (1)
+
+This graph has three nodes, where node 0 and 1 are connected by an edge of
+weight 2, and nodes 0 and 2 are connected by an edge of weight 1.
+We can construct the dense, masked, and sparse representations as follows,
+keeping in mind that an undirected graph is represented by a symmetric matrix::
+
+    >>> G_dense = np.array([[0, 2, 1],
+    ...                     [2, 0, 0],
+    ...                     [1, 0, 0]])
+    >>> G_masked = np.ma.masked_values(G_dense, 0)
+    >>> from scipy.sparse import csr_matrix
+    >>> G_sparse = csr_matrix(G_dense)
+
+This becomes more difficult when zero edges are significant. For example,
+consider the situation when we slightly modify the above graph::
+
+             G2
+
+             (0)
+            /   \
+           0     2
+          /       \
+        (2)       (1)
+
+This is identical to the previous graph, except nodes 0 and 2 are connected
+by an edge of zero weight. In this case, the dense representation above
+leads to ambiguities: how can non-edges be represented if zero is a meaningful
+value? In this case, either a masked or sparse representation must be used
+to eliminate the ambiguity::
+
+    >>> G2_data = np.array([[np.inf, 2,      0     ],
+    ...                     [2,      np.inf, np.inf],
+    ...                     [0,      np.inf, np.inf]])
+    >>> G2_masked = np.ma.masked_invalid(G2_data)
+    >>> from scipy.sparse.csgraph import csgraph_from_dense
+    >>> # G2_sparse = csr_matrix(G2_data) would give the wrong result
+    >>> G2_sparse = csgraph_from_dense(G2_data, null_value=np.inf)
+    >>> G2_sparse.data
+    array([ 2.,  0.,  2.,  0.])
+
+Here we have used a utility routine from the csgraph submodule in order to
+convert the dense representation to a sparse representation which can be
+understood by the algorithms in submodule. By viewing the data array, we
+can see that the zero values are explicitly encoded in the graph.
+
+Directed vs. undirected
+^^^^^^^^^^^^^^^^^^^^^^^
+Matrices may represent either directed or undirected graphs. This is
+specified throughout the csgraph module by a boolean keyword. Graphs are
+assumed to be directed by default. In a directed graph, traversal from node
+i to node j can be accomplished over the edge G[i, j], but not the edge
+G[j, i].  Consider the following dense graph::
+
+    >>> G_dense = np.array([[0, 1, 0],
+    ...                     [2, 0, 3],
+    ...                     [0, 4, 0]])
+
+When ``directed=True`` we get the graph::
+
+      ---1--> ---3-->
+    (0)     (1)     (2)
+      <--2--- <--4---
+
+In a non-directed graph, traversal from node i to node j can be
+accomplished over either G[i, j] or G[j, i].  If both edges are not null,
+and the two have unequal weights, then the smaller of the two is used.
+
+So for the same graph, when ``directed=False`` we get the graph::
+
+    (0)--1--(1)--2--(2)
+
+Note that a symmetric matrix will represent an undirected graph, regardless
+of whether the 'directed' keyword is set to True or False. In this case,
+using ``directed=True`` generally leads to more efficient computation.
+
+The routines in this module accept as input either scipy.sparse representations
+(csr, csc, or lil format), masked representations, or dense representations
+with non-edges indicated by zeros, infinities, and NaN entries.
+"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['connected_components',
+           'laplacian',
+           'shortest_path',
+           'floyd_warshall',
+           'dijkstra',
+           'bellman_ford',
+           'johnson',
+           'breadth_first_order',
+           'depth_first_order',
+           'breadth_first_tree',
+           'depth_first_tree',
+           'minimum_spanning_tree',
+           'reverse_cuthill_mckee',
+           'maximum_flow',
+           'maximum_bipartite_matching',
+           'structural_rank',
+           'construct_dist_matrix',
+           'reconstruct_path',
+           'csgraph_masked_from_dense',
+           'csgraph_from_dense',
+           'csgraph_from_masked',
+           'csgraph_to_dense',
+           'csgraph_to_masked',
+           'NegativeCycleError']
+
+from ._laplacian import laplacian
+from ._shortest_path import shortest_path, floyd_warshall, dijkstra,\
+    bellman_ford, johnson, NegativeCycleError
+from ._traversal import breadth_first_order, depth_first_order, \
+    breadth_first_tree, depth_first_tree, connected_components
+from ._min_spanning_tree import minimum_spanning_tree
+from ._flow import maximum_flow
+from ._matching import maximum_bipartite_matching
+from ._reordering import reverse_cuthill_mckee, structural_rank
+from ._tools import construct_dist_matrix, reconstruct_path,\
+    csgraph_from_dense, csgraph_to_dense, csgraph_masked_from_dense,\
+    csgraph_from_masked, csgraph_to_masked
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

venv/Lib/site-packages/scipy/sparse/csgraph/_laplacian.py

@@ -0,0 +1,126 @@
+"""
+Laplacian of a compressed-sparse graph
+"""
+
+# Authors: Aric Hagberg <hagberg@lanl.gov>
+#          Gael Varoquaux <gael.varoquaux@normalesup.org>
+#          Jake Vanderplas <vanderplas@astro.washington.edu>
+# License: BSD
+
+import numpy as np
+from scipy.sparse import isspmatrix
+
+
+###############################################################################
+# Graph laplacian
+def laplacian(csgraph, normed=False, return_diag=False, use_out_degree=False):
+    """
+    Return the Laplacian matrix of a directed graph.
+
+    Parameters
+    ----------
+    csgraph : array_like or sparse matrix, 2 dimensions
+        compressed-sparse graph, with shape (N, N).
+    normed : bool, optional
+        If True, then compute symmetric normalized Laplacian.
+    return_diag : bool, optional
+        If True, then also return an array related to vertex degrees.
+    use_out_degree : bool, optional
+        If True, then use out-degree instead of in-degree.
+        This distinction matters only if the graph is asymmetric.
+        Default: False.
+
+    Returns
+    -------
+    lap : ndarray or sparse matrix
+        The N x N laplacian matrix of csgraph. It will be a NumPy array (dense)
+        if the input was dense, or a sparse matrix otherwise.
+    diag : ndarray, optional
+        The length-N diagonal of the Laplacian matrix.
+        For the normalized Laplacian, this is the array of square roots
+        of vertex degrees or 1 if the degree is zero.
+
+    Notes
+    -----
+    The Laplacian matrix of a graph is sometimes referred to as the
+    "Kirchoff matrix" or the "admittance matrix", and is useful in many
+    parts of spectral graph theory. In particular, the eigen-decomposition
+    of the laplacian matrix can give insight into many properties of the graph.
+
+    Examples
+    --------
+    >>> from scipy.sparse import csgraph
+    >>> G = np.arange(5) * np.arange(5)[:, np.newaxis]
+    >>> G
+    array([[ 0,  0,  0,  0,  0],
+           [ 0,  1,  2,  3,  4],
+           [ 0,  2,  4,  6,  8],
+           [ 0,  3,  6,  9, 12],
+           [ 0,  4,  8, 12, 16]])
+    >>> csgraph.laplacian(G, normed=False)
+    array([[  0,   0,   0,   0,   0],
+           [  0,   9,  -2,  -3,  -4],
+           [  0,  -2,  16,  -6,  -8],
+           [  0,  -3,  -6,  21, -12],
+           [  0,  -4,  -8, -12,  24]])
+    """
+    if csgraph.ndim != 2 or csgraph.shape[0] != csgraph.shape[1]:
+        raise ValueError('csgraph must be a square matrix or array')
+
+    if normed and (np.issubdtype(csgraph.dtype, np.signedinteger)
+                   or np.issubdtype(csgraph.dtype, np.uint)):
+        csgraph = csgraph.astype(float)
+
+    create_lap = _laplacian_sparse if isspmatrix(csgraph) else _laplacian_dense
+    degree_axis = 1 if use_out_degree else 0
+    lap, d = create_lap(csgraph, normed=normed, axis=degree_axis)
+    if return_diag:
+        return lap, d
+    return lap
+
+
+def _setdiag_dense(A, d):
+    A.flat[::len(d)+1] = d
+
+
+def _laplacian_sparse(graph, normed=False, axis=0):
+    if graph.format in ('lil', 'dok'):
+        m = graph.tocoo()
+        needs_copy = False
+    else:
+        m = graph
+        needs_copy = True
+    w = m.sum(axis=axis).getA1() - m.diagonal()
+    if normed:
+        m = m.tocoo(copy=needs_copy)
+        isolated_node_mask = (w == 0)
+        w = np.where(isolated_node_mask, 1, np.sqrt(w))
+        m.data /= w[m.row]
+        m.data /= w[m.col]
+        m.data *= -1
+        m.setdiag(1 - isolated_node_mask)
+    else:
+        if m.format == 'dia':
+            m = m.copy()
+        else:
+            m = m.tocoo(copy=needs_copy)
+        m.data *= -1
+        m.setdiag(w)
+    return m, w
+
+
+def _laplacian_dense(graph, normed=False, axis=0):
+    m = np.array(graph)
+    np.fill_diagonal(m, 0)
+    w = m.sum(axis=axis)
+    if normed:
+        isolated_node_mask = (w == 0)
+        w = np.where(isolated_node_mask, 1, np.sqrt(w))
+        m /= w
+        m /= w[:, np.newaxis]
+        m *= -1
+        _setdiag_dense(m, 1 - isolated_node_mask)
+    else:
+        m *= -1
+        _setdiag_dense(m, w)
+    return m, w

venv/Lib/site-packages/scipy/sparse/csgraph/_validation.py

@@ -0,0 +1,56 @@
+import numpy as np
+from scipy.sparse import csr_matrix, isspmatrix, isspmatrix_csc
+from ._tools import csgraph_to_dense, csgraph_from_dense,\
+    csgraph_masked_from_dense, csgraph_from_masked
+
+DTYPE = np.float64
+
+
+def validate_graph(csgraph, directed, dtype=DTYPE,
+                   csr_output=True, dense_output=True,
+                   copy_if_dense=False, copy_if_sparse=False,
+                   null_value_in=0, null_value_out=np.inf,
+                   infinity_null=True, nan_null=True):
+    """Routine for validation and conversion of csgraph inputs"""
+    if not (csr_output or dense_output):
+        raise ValueError("Internal: dense or csr output must be true")
+
+    # if undirected and csc storage, then transposing in-place
+    # is quicker than later converting to csr.
+    if (not directed) and isspmatrix_csc(csgraph):
+        csgraph = csgraph.T
+
+    if isspmatrix(csgraph):
+        if csr_output:
+            csgraph = csr_matrix(csgraph, dtype=DTYPE, copy=copy_if_sparse)
+        else:
+            csgraph = csgraph_to_dense(csgraph, null_value=null_value_out)
+    elif np.ma.isMaskedArray(csgraph):
+        if dense_output:
+            mask = csgraph.mask
+            csgraph = np.array(csgraph.data, dtype=DTYPE, copy=copy_if_dense)
+            csgraph[mask] = null_value_out
+        else:
+            csgraph = csgraph_from_masked(csgraph)
+    else:
+        if dense_output:
+            csgraph = csgraph_masked_from_dense(csgraph,
+                                                copy=copy_if_dense,
+                                                null_value=null_value_in,
+                                                nan_null=nan_null,
+                                                infinity_null=infinity_null)
+            mask = csgraph.mask
+            csgraph = np.asarray(csgraph.data, dtype=DTYPE)
+            csgraph[mask] = null_value_out
+        else:
+            csgraph = csgraph_from_dense(csgraph, null_value=null_value_in,
+                                         infinity_null=infinity_null,
+                                         nan_null=nan_null)
+
+    if csgraph.ndim != 2:
+        raise ValueError("compressed-sparse graph must be 2-D")
+
+    if csgraph.shape[0] != csgraph.shape[1]:
+        raise ValueError("compressed-sparse graph must be shape (N, N)")
+
+    return csgraph

venv/Lib/site-packages/scipy/sparse/csgraph/setup.py

@@ -0,0 +1,38 @@
+
+def configuration(parent_package='', top_path=None):
+    import numpy
+    from numpy.distutils.misc_util import Configuration
+
+    config = Configuration('csgraph', parent_package, top_path)
+
+    config.add_data_dir('tests')
+
+    config.add_extension('_shortest_path',
+         sources=['_shortest_path.c'],
+         include_dirs=[numpy.get_include()])
+
+    config.add_extension('_traversal',
+         sources=['_traversal.c'],
+         include_dirs=[numpy.get_include()])
+
+    config.add_extension('_min_spanning_tree',
+         sources=['_min_spanning_tree.c'],
+         include_dirs=[numpy.get_include()])
+
+    config.add_extension('_matching',
+         sources=['_matching.c'],
+         include_dirs=[numpy.get_include()])
+    
+    config.add_extension('_flow',
+         sources=['_flow.c'],
+         include_dirs=[numpy.get_include()])
+    
+    config.add_extension('_reordering',
+         sources=['_reordering.c'],
+         include_dirs=[numpy.get_include()])
+
+    config.add_extension('_tools',
+         sources=['_tools.c'],
+         include_dirs=[numpy.get_include()])
+
+    return config

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_connected_components.py

@@ -0,0 +1,99 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_array_almost_equal
+from scipy.sparse import csgraph
+
+
+def test_weak_connections():
+    Xde = np.array([[0, 1, 0],
+                    [0, 0, 0],
+                    [0, 0, 0]])
+
+    Xsp = csgraph.csgraph_from_dense(Xde, null_value=0)
+
+    for X in Xsp, Xde:
+        n_components, labels =\
+            csgraph.connected_components(X, directed=True,
+                                         connection='weak')
+
+        assert_equal(n_components, 2)
+        assert_array_almost_equal(labels, [0, 0, 1])
+
+
+def test_strong_connections():
+    X1de = np.array([[0, 1, 0],
+                     [0, 0, 0],
+                     [0, 0, 0]])
+    X2de = X1de + X1de.T
+
+    X1sp = csgraph.csgraph_from_dense(X1de, null_value=0)
+    X2sp = csgraph.csgraph_from_dense(X2de, null_value=0)
+
+    for X in X1sp, X1de:
+        n_components, labels =\
+            csgraph.connected_components(X, directed=True,
+                                         connection='strong')
+
+        assert_equal(n_components, 3)
+        labels.sort()
+        assert_array_almost_equal(labels, [0, 1, 2])
+
+    for X in X2sp, X2de:
+        n_components, labels =\
+            csgraph.connected_components(X, directed=True,
+                                         connection='strong')
+
+        assert_equal(n_components, 2)
+        labels.sort()
+        assert_array_almost_equal(labels, [0, 0, 1])
+
+
+def test_strong_connections2():
+    X = np.array([[0, 0, 0, 0, 0, 0],
+                  [1, 0, 1, 0, 0, 0],
+                  [0, 0, 0, 1, 0, 0],
+                  [0, 0, 1, 0, 1, 0],
+                  [0, 0, 0, 0, 0, 0],
+                  [0, 0, 0, 0, 1, 0]])
+    n_components, labels =\
+        csgraph.connected_components(X, directed=True,
+                                     connection='strong')
+    assert_equal(n_components, 5)
+    labels.sort()
+    assert_array_almost_equal(labels, [0, 1, 2, 2, 3, 4])
+
+
+def test_weak_connections2():
+    X = np.array([[0, 0, 0, 0, 0, 0],
+                  [1, 0, 0, 0, 0, 0],
+                  [0, 0, 0, 1, 0, 0],
+                  [0, 0, 1, 0, 1, 0],
+                  [0, 0, 0, 0, 0, 0],
+                  [0, 0, 0, 0, 1, 0]])
+    n_components, labels =\
+        csgraph.connected_components(X, directed=True,
+                                     connection='weak')
+    assert_equal(n_components, 2)
+    labels.sort()
+    assert_array_almost_equal(labels, [0, 0, 1, 1, 1, 1])
+
+
+def test_ticket1876():
+    # Regression test: this failed in the original implementation
+    # There should be two strongly-connected components; previously gave one
+    g = np.array([[0, 1, 1, 0],
+                  [1, 0, 0, 1],
+                  [0, 0, 0, 1],
+                  [0, 0, 1, 0]])
+    n_components, labels = csgraph.connected_components(g, connection='strong')
+
+    assert_equal(n_components, 2)
+    assert_equal(labels[0], labels[1])
+    assert_equal(labels[2], labels[3])
+
+
+def test_fully_connected_graph():
+    # Fully connected dense matrices raised an exception.
+    # https://github.com/scipy/scipy/issues/3818
+    g = np.ones((4, 4))
+    n_components, labels = csgraph.connected_components(g)
+    assert_equal(n_components, 1)

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_conversions.py

@@ -0,0 +1,61 @@
+import numpy as np
+from numpy.testing import assert_array_almost_equal
+from scipy.sparse import csr_matrix
+from scipy.sparse.csgraph import csgraph_from_dense, csgraph_to_dense
+
+
+def test_csgraph_from_dense():
+    np.random.seed(1234)
+    G = np.random.random((10, 10))
+    some_nulls = (G < 0.4)
+    all_nulls = (G < 0.8)
+
+    for null_value in [0, np.nan, np.inf]:
+        G[all_nulls] = null_value
+        with np.errstate(invalid="ignore"):
+            G_csr = csgraph_from_dense(G, null_value=0)
+
+        G[all_nulls] = 0
+        assert_array_almost_equal(G, G_csr.toarray())
+
+    for null_value in [np.nan, np.inf]:
+        G[all_nulls] = 0
+        G[some_nulls] = null_value
+        with np.errstate(invalid="ignore"):
+            G_csr = csgraph_from_dense(G, null_value=0)
+
+        G[all_nulls] = 0
+        assert_array_almost_equal(G, G_csr.toarray())
+
+
+def test_csgraph_to_dense():
+    np.random.seed(1234)
+    G = np.random.random((10, 10))
+    nulls = (G < 0.8)
+    G[nulls] = np.inf
+
+    G_csr = csgraph_from_dense(G)
+
+    for null_value in [0, 10, -np.inf, np.inf]:
+        G[nulls] = null_value
+        assert_array_almost_equal(G, csgraph_to_dense(G_csr, null_value))
+
+
+def test_multiple_edges():
+    # create a random sqare matrix with an even number of elements
+    np.random.seed(1234)
+    X = np.random.random((10, 10))
+    Xcsr = csr_matrix(X)
+
+    # now double-up every other column
+    Xcsr.indices[::2] = Xcsr.indices[1::2]
+
+    # normal sparse toarray() will sum the duplicated edges
+    Xdense = Xcsr.toarray()
+    assert_array_almost_equal(Xdense[:, 1::2],
+                              X[:, ::2] + X[:, 1::2])
+
+    # csgraph_to_dense chooses the minimum of each duplicated edge
+    Xdense = csgraph_to_dense(Xcsr)
+    assert_array_almost_equal(Xdense[:, 1::2],
+                              np.minimum(X[:, ::2], X[:, 1::2]))

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_flow.py

@@ -0,0 +1,124 @@
+import numpy as np
+from numpy.testing import assert_array_equal
+import pytest
+
+from scipy.sparse import csr_matrix, csc_matrix
+from scipy.sparse.csgraph import maximum_flow
+
+
+def test_raises_on_dense_input():
+    with pytest.raises(TypeError):
+        graph = np.array([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, 1)
+
+
+def test_raises_on_csc_input():
+    with pytest.raises(TypeError):
+        graph = csc_matrix([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, 1)
+
+
+def test_raises_on_floating_point_input():
+    with pytest.raises(ValueError):
+        graph = csr_matrix([[0, 1.5], [0, 0]], dtype=np.float64)
+        maximum_flow(graph, 0, 1)
+
+
+def test_raises_when_source_is_sink():
+    with pytest.raises(ValueError):
+        graph = csr_matrix([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, 0)
+
+
+@pytest.mark.parametrize('source', [-1, 2, 3])
+def test_raises_when_source_is_out_of_bounds(source):
+    with pytest.raises(ValueError):
+        graph = csr_matrix([[0, 1], [0, 0]])
+        maximum_flow(graph, source, 1)
+
+
+@pytest.mark.parametrize('sink', [-1, 2, 3])
+def test_raises_when_sink_is_out_of_bounds(sink):
+    with pytest.raises(ValueError):
+        graph = csr_matrix([[0, 1], [0, 0]])
+        maximum_flow(graph, 0, sink)
+
+
+def test_simple_graph():
+    # This graph looks as follows:
+    #     (0) --5--> (1)
+    graph = csr_matrix([[0, 5], [0, 0]])
+    res = maximum_flow(graph, 0, 1)
+    assert res.flow_value == 5
+    expected_residual = np.array([[0, 5], [-5, 0]])
+    assert_array_equal(res.residual.toarray(), expected_residual)
+
+
+def test_bottle_neck_graph():
+    # This graph cannot use the full capacity between 0 and 1:
+    #     (0) --5--> (1) --3--> (2)
+    graph = csr_matrix([[0, 5, 0], [0, 0, 3], [0, 0, 0]])
+    res = maximum_flow(graph, 0, 2)
+    assert res.flow_value == 3
+    expected_residual = np.array([[0, 3, 0], [-3, 0, 3], [0, -3, 0]])
+    assert_array_equal(res.residual.toarray(), expected_residual)
+
+
+def test_backwards_flow():
+    # This example causes backwards flow between vertices 3 and 4,
+    # and so this test ensures that we handle that accordingly. See
+    #     https://stackoverflow.com/q/38843963/5085211
+    # for more information.
+    graph = csr_matrix([[0, 10, 0, 0, 10, 0, 0, 0],
+                        [0, 0, 10, 0, 0, 0, 0, 0],
+                        [0, 0, 0, 10, 0, 0, 0, 0],
+                        [0, 0, 0, 0, 0, 0, 0, 10],
+                        [0, 0, 0, 10, 0, 10, 0, 0],
+                        [0, 0, 0, 0, 0, 0, 10, 0],
+                        [0, 0, 0, 0, 0, 0, 0, 10],
+                        [0, 0, 0, 0, 0, 0, 0, 0]])
+    res = maximum_flow(graph, 0, 7)
+    assert res.flow_value == 20
+    expected_residual = np.array([[0, 10, 0, 0, 10, 0, 0, 0],
+                                  [-10, 0, 10, 0, 0, 0, 0, 0],
+                                  [0, -10, 0, 10, 0, 0, 0, 0],
+                                  [0, 0, -10, 0, 0, 0, 0, 10],
+                                  [-10, 0, 0, 0, 0, 10, 0, 0],
+                                  [0, 0, 0, 0, -10, 0, 10, 0],
+                                  [0, 0, 0, 0, 0, -10, 0, 10],
+                                  [0, 0, 0, -10, 0, 0, -10, 0]])
+    assert_array_equal(res.residual.toarray(), expected_residual)
+
+
+def test_example_from_clrs_chapter_26_1():
+    # See page 659 in CLRS second edition, but note that the maximum flow
+    # we find is slightly different than the one in CLRS; we push a flow of
+    # 12 to v_1 instead of v_2.
+    graph = csr_matrix([[0, 16, 13, 0, 0, 0],
+                        [0, 0, 10, 12, 0, 0],
+                        [0, 4, 0, 0, 14, 0],
+                        [0, 0, 9, 0, 0, 20],
+                        [0, 0, 0, 7, 0, 4],
+                        [0, 0, 0, 0, 0, 0]])
+    res = maximum_flow(graph, 0, 5)
+    assert res.flow_value == 23
+    expected_residual = np.array([[0, 12, 11, 0, 0, 0],
+                                  [-12, 0, 0, 12, 0, 0],
+                                  [-11, 0, 0, 0, 11, 0],
+                                  [0, -12, 0, 0, -7, 19],
+                                  [0, 0, -11, 7, 0, 4],
+                                  [0, 0, 0, -19, -4, 0]])
+    assert_array_equal(res.residual.toarray(), expected_residual)
+
+
+def test_disconnected_graph():
+    # This tests the following disconnected graph:
+    #     (0) --5--> (1)    (2) --3--> (3)
+    graph = csr_matrix([[0, 5, 0, 0],
+                        [0, 0, 0, 0],
+                        [0, 0, 9, 3],
+                        [0, 0, 0, 0]])
+    res = maximum_flow(graph, 0, 3)
+    assert res.flow_value == 0
+    expected_residual = np.zeros((4, 4), dtype=np.int32)
+    assert_array_equal(res.residual.toarray(), expected_residual)

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_graph_laplacian.py

@@ -0,0 +1,134 @@
+# Author: Gael Varoquaux <gael.varoquaux@normalesup.org>
+#         Jake Vanderplas <vanderplas@astro.washington.edu>
+# License: BSD
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_almost_equal
+from pytest import raises as assert_raises
+from scipy import sparse
+
+from scipy.sparse import csgraph
+
+
+def _explicit_laplacian(x, normed=False):
+    if sparse.issparse(x):
+        x = x.todense()
+    x = np.asarray(x)
+    y = -1.0 * x
+    for j in range(y.shape[0]):
+        y[j,j] = x[j,j+1:].sum() + x[j,:j].sum()
+    if normed:
+        d = np.diag(y).copy()
+        d[d == 0] = 1.0
+        y /= d[:,None]**.5
+        y /= d[None,:]**.5
+    return y
+
+
+def _check_symmetric_graph_laplacian(mat, normed):
+    if not hasattr(mat, 'shape'):
+        mat = eval(mat, dict(np=np, sparse=sparse))
+
+    if sparse.issparse(mat):
+        sp_mat = mat
+        mat = sp_mat.todense()
+    else:
+        sp_mat = sparse.csr_matrix(mat)
+
+    laplacian = csgraph.laplacian(mat, normed=normed)
+    n_nodes = mat.shape[0]
+    if not normed:
+        assert_array_almost_equal(laplacian.sum(axis=0), np.zeros(n_nodes))
+    assert_array_almost_equal(laplacian.T, laplacian)
+    assert_array_almost_equal(laplacian,
+            csgraph.laplacian(sp_mat, normed=normed).todense())
+
+    assert_array_almost_equal(laplacian,
+            _explicit_laplacian(mat, normed=normed))
+
+
+def test_laplacian_value_error():
+    for t in int, float, complex:
+        for m in ([1, 1],
+                  [[[1]]],
+                  [[1, 2, 3], [4, 5, 6]],
+                  [[1, 2], [3, 4], [5, 5]]):
+            A = np.array(m, dtype=t)
+            assert_raises(ValueError, csgraph.laplacian, A)
+
+
+def test_symmetric_graph_laplacian():
+    symmetric_mats = ('np.arange(10) * np.arange(10)[:, np.newaxis]',
+            'np.ones((7, 7))',
+            'np.eye(19)',
+            'sparse.diags([1, 1], [-1, 1], shape=(4,4))',
+            'sparse.diags([1, 1], [-1, 1], shape=(4,4)).todense()',
+            'np.asarray(sparse.diags([1, 1], [-1, 1], shape=(4,4)).todense())',
+            'np.vander(np.arange(4)) + np.vander(np.arange(4)).T')
+    for mat_str in symmetric_mats:
+        for normed in True, False:
+            _check_symmetric_graph_laplacian(mat_str, normed)
+
+
+def _assert_allclose_sparse(a, b, **kwargs):
+    # helper function that can deal with sparse matrices
+    if sparse.issparse(a):
+        a = a.toarray()
+    if sparse.issparse(b):
+        b = a.toarray()
+    assert_allclose(a, b, **kwargs)
+
+
+def _check_laplacian(A, desired_L, desired_d, normed, use_out_degree):
+    for arr_type in np.array, sparse.csr_matrix, sparse.coo_matrix:
+        for t in int, float, complex:
+            adj = arr_type(A, dtype=t)
+            L = csgraph.laplacian(adj, normed=normed, return_diag=False,
+                                  use_out_degree=use_out_degree)
+            _assert_allclose_sparse(L, desired_L, atol=1e-12)
+            L, d = csgraph.laplacian(adj, normed=normed, return_diag=True,
+                                  use_out_degree=use_out_degree)
+            _assert_allclose_sparse(L, desired_L, atol=1e-12)
+            _assert_allclose_sparse(d, desired_d, atol=1e-12)
+
+
+def test_asymmetric_laplacian():
+    # adjacency matrix
+    A = [[0, 1, 0],
+         [4, 2, 0],
+         [0, 0, 0]]
+
+    # Laplacian matrix using out-degree
+    L = [[1, -1, 0],
+         [-4, 4, 0],
+         [0, 0, 0]]
+    d = [1, 4, 0]
+    _check_laplacian(A, L, d, normed=False, use_out_degree=True)
+
+    # normalized Laplacian matrix using out-degree
+    L = [[1, -0.5, 0],
+         [-2, 1, 0],
+         [0, 0, 0]]
+    d = [1, 2, 1]
+    _check_laplacian(A, L, d, normed=True, use_out_degree=True)
+
+    # Laplacian matrix using in-degree
+    L = [[4, -1, 0],
+         [-4, 1, 0],
+         [0, 0, 0]]
+    d = [4, 1, 0]
+    _check_laplacian(A, L, d, normed=False, use_out_degree=False)
+
+    # normalized Laplacian matrix using in-degree
+    L = [[1, -0.5, 0],
+         [-2, 1, 0],
+         [0, 0, 0]]
+    d = [2, 1, 1]
+    _check_laplacian(A, L, d, normed=True, use_out_degree=False)
+
+
+def test_sparse_formats():
+    for fmt in ('csr', 'csc', 'coo', 'lil', 'dok', 'dia', 'bsr'):
+        mat = sparse.diags([1, 1], [-1, 1], shape=(4,4), format=fmt)
+        for normed in True, False:
+            _check_symmetric_graph_laplacian(mat, normed)
+

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_matching.py

@@ -0,0 +1,145 @@
+import numpy as np
+from numpy.testing import assert_array_equal, assert_equal
+import pytest
+
+from scipy.sparse import csr_matrix, coo_matrix, diags
+from scipy.sparse.csgraph import maximum_bipartite_matching
+
+
+def test_raises_on_dense_input():
+    with pytest.raises(TypeError):
+        graph = np.array([[0, 1], [0, 0]])
+        maximum_bipartite_matching(graph)
+
+
+def test_empty_graph():
+    graph = csr_matrix((0, 0))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    expected_matching = np.array([])
+    assert_array_equal(expected_matching, x)
+    assert_array_equal(expected_matching, y)
+
+
+def test_empty_left_partition():
+    graph = csr_matrix((2, 0))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert_array_equal(np.array([]), x)
+    assert_array_equal(np.array([-1, -1]), y)
+
+
+def test_empty_right_partition():
+    graph = csr_matrix((0, 3))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert_array_equal(np.array([-1, -1, -1]), x)
+    assert_array_equal(np.array([]), y)
+
+
+def test_graph_with_no_edges():
+    graph = csr_matrix((2, 2))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert_array_equal(np.array([-1, -1]), x)
+    assert_array_equal(np.array([-1, -1]), y)
+
+
+def test_graph_that_causes_augmentation():
+    # In this graph, column 1 is initially assigned to row 1, but it should be
+    # reassigned to make room for row 2.
+    graph = csr_matrix([[1, 1], [1, 0]])
+    x = maximum_bipartite_matching(graph, perm_type='column')
+    y = maximum_bipartite_matching(graph, perm_type='row')
+    expected_matching = np.array([1, 0])
+    assert_array_equal(expected_matching, x)
+    assert_array_equal(expected_matching, y)
+
+
+def test_graph_with_more_rows_than_columns():
+    graph = csr_matrix([[1, 1], [1, 0], [0, 1]])
+    x = maximum_bipartite_matching(graph, perm_type='column')
+    y = maximum_bipartite_matching(graph, perm_type='row')
+    assert_array_equal(np.array([0, -1, 1]), x)
+    assert_array_equal(np.array([0, 2]), y)
+
+
+def test_graph_with_more_columns_than_rows():
+    graph = csr_matrix([[1, 1, 0], [0, 0, 1]])
+    x = maximum_bipartite_matching(graph, perm_type='column')
+    y = maximum_bipartite_matching(graph, perm_type='row')
+    assert_array_equal(np.array([0, 2]), x)
+    assert_array_equal(np.array([0, -1, 1]), y)
+
+
+def test_explicit_zeros_count_as_edges():
+    data = [0, 0]
+    indices = [1, 0]
+    indptr = [0, 1, 2]
+    graph = csr_matrix((data, indices, indptr), shape=(2, 2))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    expected_matching = np.array([1, 0])
+    assert_array_equal(expected_matching, x)
+    assert_array_equal(expected_matching, y)
+
+
+def test_feasibility_of_result():
+    # This is a regression test for GitHub issue #11458
+    data = np.ones(50, dtype=int)
+    indices = [11, 12, 19, 22, 23, 5, 22, 3, 8, 10, 5, 6, 11, 12, 13, 5, 13,
+               14, 20, 22, 3, 15, 3, 13, 14, 11, 12, 19, 22, 23, 5, 22, 3, 8,
+               10, 5, 6, 11, 12, 13, 5, 13, 14, 20, 22, 3, 15, 3, 13, 14]
+    indptr = [0, 5, 7, 10, 10, 15, 20, 22, 22, 23, 25, 30, 32, 35, 35, 40, 45,
+              47, 47, 48, 50]
+    graph = csr_matrix((data, indices, indptr), shape=(20, 25))
+    x = maximum_bipartite_matching(graph, perm_type='row')
+    y = maximum_bipartite_matching(graph, perm_type='column')
+    assert (x != -1).sum() == 13
+    assert (y != -1).sum() == 13
+    # Ensure that each element of the matching is in fact an edge in the graph.
+    for u, v in zip(range(graph.shape[0]), y):
+        if v != -1:
+            assert graph[u, v]
+    for u, v in zip(x, range(graph.shape[1])):
+        if u != -1:
+            assert graph[u, v]
+
+
+def test_large_random_graph_with_one_edge_incident_to_each_vertex():
+    np.random.seed(42)
+    A = diags(np.ones(25), offsets=0, format='csr')
+    rand_perm = np.random.permutation(25)
+    rand_perm2 = np.random.permutation(25)
+
+    Rrow = np.arange(25)
+    Rcol = rand_perm
+    Rdata = np.ones(25, dtype=int)
+    Rmat = coo_matrix((Rdata, (Rrow, Rcol))).tocsr()
+
+    Crow = rand_perm2
+    Ccol = np.arange(25)
+    Cdata = np.ones(25, dtype=int)
+    Cmat = coo_matrix((Cdata, (Crow, Ccol))).tocsr()
+    # Randomly permute identity matrix
+    B = Rmat * A * Cmat
+
+    # Row permute
+    perm = maximum_bipartite_matching(B, perm_type='row')
+    Rrow = np.arange(25)
+    Rcol = perm
+    Rdata = np.ones(25, dtype=int)
+    Rmat = coo_matrix((Rdata, (Rrow, Rcol))).tocsr()
+    C1 = Rmat * B
+
+    # Column permute
+    perm2 = maximum_bipartite_matching(B, perm_type='column')
+    Crow = perm2
+    Ccol = np.arange(25)
+    Cdata = np.ones(25, dtype=int)
+    Cmat = coo_matrix((Cdata, (Crow, Ccol))).tocsr()
+    C2 = B * Cmat
+
+    # Should get identity matrix back
+    assert_equal(any(C1.diagonal() == 0), False)
+    assert_equal(any(C2.diagonal() == 0), False)

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_reordering.py

@@ -0,0 +1,70 @@
+import numpy as np
+from numpy.testing import assert_equal
+from scipy.sparse.csgraph import reverse_cuthill_mckee, structural_rank
+from scipy.sparse import csc_matrix, csr_matrix, coo_matrix
+
+
+def test_graph_reverse_cuthill_mckee():
+    A = np.array([[1, 0, 0, 0, 1, 0, 0, 0],
+                [0, 1, 1, 0, 0, 1, 0, 1],
+                [0, 1, 1, 0, 1, 0, 0, 0],
+                [0, 0, 0, 1, 0, 0, 1, 0],
+                [1, 0, 1, 0, 1, 0, 0, 0],
+                [0, 1, 0, 0, 0, 1, 0, 1],
+                [0, 0, 0, 1, 0, 0, 1, 0],
+                [0, 1, 0, 0, 0, 1, 0, 1]], dtype=int)
+    
+    graph = csr_matrix(A)
+    perm = reverse_cuthill_mckee(graph)
+    correct_perm = np.array([6, 3, 7, 5, 1, 2, 4, 0])
+    assert_equal(perm, correct_perm)
+    
+    # Test int64 indices input
+    graph.indices = graph.indices.astype('int64')
+    graph.indptr = graph.indptr.astype('int64')
+    perm = reverse_cuthill_mckee(graph, True)
+    assert_equal(perm, correct_perm)
+
+
+def test_graph_reverse_cuthill_mckee_ordering():
+    data = np.ones(63,dtype=int)
+    rows = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 
+                2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5,
+                6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9,
+                9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 
+                12, 12, 12, 13, 13, 13, 13, 14, 14, 14,
+                14, 15, 15, 15, 15, 15])
+    cols = np.array([0, 2, 5, 8, 10, 1, 3, 9, 11, 0, 2,
+                7, 10, 1, 3, 11, 4, 6, 12, 14, 0, 7, 13, 
+                15, 4, 6, 14, 2, 5, 7, 15, 0, 8, 10, 13,
+                1, 9, 11, 0, 2, 8, 10, 15, 1, 3, 9, 11,
+                4, 12, 14, 5, 8, 13, 15, 4, 6, 12, 14,
+                5, 7, 10, 13, 15])
+    graph = coo_matrix((data, (rows,cols))).tocsr()
+    perm = reverse_cuthill_mckee(graph)
+    correct_perm = np.array([12, 14, 4, 6, 10, 8, 2, 15,
+                0, 13, 7, 5, 9, 11, 1, 3])
+    assert_equal(perm, correct_perm)
+
+
+def test_graph_structural_rank():
+    # Test square matrix #1
+    A = csc_matrix([[1, 1, 0], 
+                    [1, 0, 1],
+                    [0, 1, 0]])
+    assert_equal(structural_rank(A), 3)
+    
+    # Test square matrix #2
+    rows = np.array([0,0,0,0,0,1,1,2,2,3,3,3,3,3,3,4,4,5,5,6,6,7,7])
+    cols = np.array([0,1,2,3,4,2,5,2,6,0,1,3,5,6,7,4,5,5,6,2,6,2,4])
+    data = np.ones_like(rows)
+    B = coo_matrix((data,(rows,cols)), shape=(8,8))
+    assert_equal(structural_rank(B), 6)
+    
+    #Test non-square matrix
+    C = csc_matrix([[1, 0, 2, 0], 
+                    [2, 0, 4, 0]])
+    assert_equal(structural_rank(C), 2)
+    
+    #Test tall matrix
+    assert_equal(structural_rank(C.T), 2)

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_shortest_path.py

@@ -0,0 +1,334 @@
+import numpy as np
+from numpy.testing import assert_array_almost_equal, assert_array_equal
+from pytest import raises as assert_raises
+from scipy.sparse.csgraph import (shortest_path, dijkstra, johnson,
+                                  bellman_ford, construct_dist_matrix,
+                                  NegativeCycleError)
+import scipy.sparse
+import pytest
+
+directed_G = np.array([[0, 3, 3, 0, 0],
+                       [0, 0, 0, 2, 4],
+                       [0, 0, 0, 0, 0],
+                       [1, 0, 0, 0, 0],
+                       [2, 0, 0, 2, 0]], dtype=float)
+
+undirected_G = np.array([[0, 3, 3, 1, 2],
+                         [3, 0, 0, 2, 4],
+                         [3, 0, 0, 0, 0],
+                         [1, 2, 0, 0, 2],
+                         [2, 4, 0, 2, 0]], dtype=float)
+
+unweighted_G = (directed_G > 0).astype(float)
+
+directed_SP = [[0, 3, 3, 5, 7],
+               [3, 0, 6, 2, 4],
+               [np.inf, np.inf, 0, np.inf, np.inf],
+               [1, 4, 4, 0, 8],
+               [2, 5, 5, 2, 0]]
+
+directed_sparse_zero_G = scipy.sparse.csr_matrix(([0, 1, 2, 3, 1], 
+                                            ([0, 1, 2, 3, 4], 
+                                             [1, 2, 0, 4, 3])), 
+                                            shape = (5, 5))
+
+directed_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
+                      [3, 0, 1, np.inf, np.inf],
+                      [2, 2, 0, np.inf, np.inf],
+                      [np.inf, np.inf, np.inf, 0, 3],
+                      [np.inf, np.inf, np.inf, 1, 0]]
+
+undirected_sparse_zero_G = scipy.sparse.csr_matrix(([0, 0, 1, 1, 2, 2, 1, 1], 
+                                              ([0, 1, 1, 2, 2, 0, 3, 4], 
+                                               [1, 0, 2, 1, 0, 2, 4, 3])), 
+                                              shape = (5, 5))
+
+undirected_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
+                        [0, 0, 1, np.inf, np.inf],
+                        [1, 1, 0, np.inf, np.inf],
+                        [np.inf, np.inf, np.inf, 0, 1],
+                        [np.inf, np.inf, np.inf, 1, 0]]
+
+directed_pred = np.array([[-9999, 0, 0, 1, 1],
+                          [3, -9999, 0, 1, 1],
+                          [-9999, -9999, -9999, -9999, -9999],
+                          [3, 0, 0, -9999, 1],
+                          [4, 0, 0, 4, -9999]], dtype=float)
+
+undirected_SP = np.array([[0, 3, 3, 1, 2],
+                          [3, 0, 6, 2, 4],
+                          [3, 6, 0, 4, 5],
+                          [1, 2, 4, 0, 2],
+                          [2, 4, 5, 2, 0]], dtype=float)
+
+undirected_SP_limit_2 = np.array([[0, np.inf, np.inf, 1, 2],
+                                  [np.inf, 0, np.inf, 2, np.inf],
+                                  [np.inf, np.inf, 0, np.inf, np.inf],
+                                  [1, 2, np.inf, 0, 2],
+                                  [2, np.inf, np.inf, 2, 0]], dtype=float)
+
+undirected_SP_limit_0 = np.ones((5, 5), dtype=float) - np.eye(5)
+undirected_SP_limit_0[undirected_SP_limit_0 > 0] = np.inf
+
+undirected_pred = np.array([[-9999, 0, 0, 0, 0],
+                            [1, -9999, 0, 1, 1],
+                            [2, 0, -9999, 0, 0],
+                            [3, 3, 0, -9999, 3],
+                            [4, 4, 0, 4, -9999]], dtype=float)
+
+methods = ['auto', 'FW', 'D', 'BF', 'J']
+
+
+def test_dijkstra_limit():
+    limits = [0, 2, np.inf]
+    results = [undirected_SP_limit_0,
+               undirected_SP_limit_2,
+               undirected_SP]
+
+    def check(limit, result):
+        SP = dijkstra(undirected_G, directed=False, limit=limit)
+        assert_array_almost_equal(SP, result)
+
+    for limit, result in zip(limits, results):
+        check(limit, result)
+
+
+def test_directed():
+    def check(method):
+        SP = shortest_path(directed_G, method=method, directed=True,
+                           overwrite=False)
+        assert_array_almost_equal(SP, directed_SP)
+
+    for method in methods:
+        check(method)
+
+
+def test_undirected():
+    def check(method, directed_in):
+        if directed_in:
+            SP1 = shortest_path(directed_G, method=method, directed=False,
+                                overwrite=False)
+            assert_array_almost_equal(SP1, undirected_SP)
+        else:
+            SP2 = shortest_path(undirected_G, method=method, directed=True,
+                                overwrite=False)
+            assert_array_almost_equal(SP2, undirected_SP)
+
+    for method in methods:
+        for directed_in in (True, False):
+            check(method, directed_in)
+
+def test_directed_sparse_zero():
+    # test directed sparse graph with zero-weight edge and two connected components
+    def check(method):
+        SP = shortest_path(directed_sparse_zero_G, method=method, directed=True,
+                           overwrite=False)
+        assert_array_almost_equal(SP, directed_sparse_zero_SP)
+
+    for method in methods:
+        check(method)
+
+def test_undirected_sparse_zero():
+    def check(method, directed_in):
+        if directed_in:
+            SP1 = shortest_path(directed_sparse_zero_G, method=method, directed=False,
+                                overwrite=False)
+            assert_array_almost_equal(SP1, undirected_sparse_zero_SP)
+        else:
+            SP2 = shortest_path(undirected_sparse_zero_G, method=method, directed=True,
+                                overwrite=False)
+            assert_array_almost_equal(SP2, undirected_sparse_zero_SP)
+
+    for method in methods:
+        for directed_in in (True, False):
+            check(method, directed_in)
+
+
+@pytest.mark.parametrize('directed, SP_ans',
+                         ((True, directed_SP),
+                          (False, undirected_SP)))
+@pytest.mark.parametrize('indices', ([0, 2, 4], [0, 4], [3, 4], [0, 0]))
+def test_dijkstra_indices_min_only(directed, SP_ans, indices):
+    SP_ans = np.array(SP_ans)
+    indices = np.array(indices, dtype=np.int64)
+    min_ind_ans = indices[np.argmin(SP_ans[indices, :], axis=0)]
+    min_d_ans = np.zeros(SP_ans.shape[0], SP_ans.dtype)
+    for k in range(SP_ans.shape[0]):
+        min_d_ans[k] = SP_ans[min_ind_ans[k], k]
+    min_ind_ans[np.isinf(min_d_ans)] = -9999
+
+    SP, pred, sources = dijkstra(directed_G,
+                                 directed=directed,
+                                 indices=indices,
+                                 min_only=True,
+                                 return_predecessors=True)
+    assert_array_almost_equal(SP, min_d_ans)
+    assert_array_equal(min_ind_ans, sources)
+    SP = dijkstra(directed_G,
+                  directed=directed,
+                  indices=indices,
+                  min_only=True,
+                  return_predecessors=False)
+    assert_array_almost_equal(SP, min_d_ans)
+
+
+@pytest.mark.parametrize('n', (10, 100, 1000))
+def test_shortest_path_min_only_random(n):
+    np.random.seed(1234)
+    data = scipy.sparse.rand(n, n, density=0.5, format='lil',
+                             random_state=42, dtype=np.float64)
+    data.setdiag(np.zeros(n, dtype=np.bool_))
+    # choose some random vertices
+    v = np.arange(n)
+    np.random.shuffle(v)
+    indices = v[:int(n*.1)]
+    ds, pred, sources = dijkstra(data,
+                                 directed=False,
+                                 indices=indices,
+                                 min_only=True,
+                                 return_predecessors=True)
+    for k in range(n):
+        p = pred[k]
+        s = sources[k]
+        while(p != -9999):
+            assert(sources[p] == s)
+            p = pred[p]
+
+
+def test_shortest_path_indices():
+    indices = np.arange(4)
+
+    def check(func, indshape):
+        outshape = indshape + (5,)
+        SP = func(directed_G, directed=False,
+                  indices=indices.reshape(indshape))
+        assert_array_almost_equal(SP, undirected_SP[indices].reshape(outshape))
+
+    for indshape in [(4,), (4, 1), (2, 2)]:
+        for func in (dijkstra, bellman_ford, johnson, shortest_path):
+            check(func, indshape)
+
+    assert_raises(ValueError, shortest_path, directed_G, method='FW',
+                  indices=indices)
+
+
+def test_predecessors():
+    SP_res = {True: directed_SP,
+              False: undirected_SP}
+    pred_res = {True: directed_pred,
+                False: undirected_pred}
+
+    def check(method, directed):
+        SP, pred = shortest_path(directed_G, method, directed=directed,
+                                 overwrite=False,
+                                 return_predecessors=True)
+        assert_array_almost_equal(SP, SP_res[directed])
+        assert_array_almost_equal(pred, pred_res[directed])
+
+    for method in methods:
+        for directed in (True, False):
+            check(method, directed)
+
+
+def test_construct_shortest_path():
+    def check(method, directed):
+        SP1, pred = shortest_path(directed_G,
+                                  directed=directed,
+                                  overwrite=False,
+                                  return_predecessors=True)
+        SP2 = construct_dist_matrix(directed_G, pred, directed=directed)
+        assert_array_almost_equal(SP1, SP2)
+
+    for method in methods:
+        for directed in (True, False):
+            check(method, directed)
+
+
+def test_unweighted_path():
+    def check(method, directed):
+        SP1 = shortest_path(directed_G,
+                            directed=directed,
+                            overwrite=False,
+                            unweighted=True)
+        SP2 = shortest_path(unweighted_G,
+                            directed=directed,
+                            overwrite=False,
+                            unweighted=False)
+        assert_array_almost_equal(SP1, SP2)
+
+    for method in methods:
+        for directed in (True, False):
+            check(method, directed)
+
+
+def test_negative_cycles():
+    # create a small graph with a negative cycle
+    graph = np.ones([5, 5])
+    graph.flat[::6] = 0
+    graph[1, 2] = -2
+
+    def check(method, directed):
+        assert_raises(NegativeCycleError, shortest_path, graph, method,
+                      directed)
+
+    for method in ['FW', 'J', 'BF']:
+        for directed in (True, False):
+            check(method, directed)
+
+
+def test_masked_input():
+    np.ma.masked_equal(directed_G, 0)
+
+    def check(method):
+        SP = shortest_path(directed_G, method=method, directed=True,
+                           overwrite=False)
+        assert_array_almost_equal(SP, directed_SP)
+
+    for method in methods:
+        check(method)
+
+
+def test_overwrite():
+    G = np.array([[0, 3, 3, 1, 2],
+                  [3, 0, 0, 2, 4],
+                  [3, 0, 0, 0, 0],
+                  [1, 2, 0, 0, 2],
+                  [2, 4, 0, 2, 0]], dtype=float)
+    foo = G.copy()
+    shortest_path(foo, overwrite=False)
+    assert_array_equal(foo, G)
+
+
+@pytest.mark.parametrize('method', methods)
+def test_buffer(method):
+    # Smoke test that sparse matrices with read-only buffers (e.g., those from
+    # joblib workers) do not cause::
+    #
+    #     ValueError: buffer source array is read-only
+    #
+    G = scipy.sparse.csr_matrix([[1.]])
+    G.data.flags['WRITEABLE'] = False
+    shortest_path(G, method=method)
+
+
+def test_NaN_warnings():
+    with pytest.warns(None) as record:
+        shortest_path(np.array([[0, 1], [np.nan, 0]]))
+    for r in record:
+        assert r.category is not RuntimeWarning
+
+
+def test_sparse_matrices():
+    # Test that using lil,csr and csc sparse matrix do not cause error
+    G_dense = np.array([[0, 3, 0, 0, 0],
+                        [0, 0, -1, 0, 0],
+                        [0, 0, 0, 2, 0],
+                        [0, 0, 0, 0, 4],
+                        [0, 0, 0, 0, 0]], dtype=float)
+    SP = shortest_path(G_dense)
+    G_csr = scipy.sparse.csr_matrix(G_dense)
+    G_csc = scipy.sparse.csc_matrix(G_dense)
+    G_lil = scipy.sparse.lil_matrix(G_dense)
+    assert_array_almost_equal(SP, shortest_path(G_csr))
+    assert_array_almost_equal(SP, shortest_path(G_csc))
+    assert_array_almost_equal(SP, shortest_path(G_lil))

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_spanning_tree.py

@@ -0,0 +1,65 @@
+"""Test the minimum spanning tree function"""
+import numpy as np
+from numpy.testing import assert_
+import numpy.testing as npt
+from scipy.sparse import csr_matrix
+from scipy.sparse.csgraph import minimum_spanning_tree
+
+
+def test_minimum_spanning_tree():
+
+    # Create a graph with two connected components.
+    graph = [[0,1,0,0,0],
+             [1,0,0,0,0],
+             [0,0,0,8,5],
+             [0,0,8,0,1],
+             [0,0,5,1,0]]
+    graph = np.asarray(graph)
+
+    # Create the expected spanning tree.
+    expected = [[0,1,0,0,0],
+                [0,0,0,0,0],
+                [0,0,0,0,5],
+                [0,0,0,0,1],
+                [0,0,0,0,0]]
+    expected = np.asarray(expected)
+
+    # Ensure minimum spanning tree code gives this expected output.
+    csgraph = csr_matrix(graph)
+    mintree = minimum_spanning_tree(csgraph)
+    npt.assert_array_equal(mintree.todense(), expected,
+        'Incorrect spanning tree found.')
+
+    # Ensure that the original graph was not modified.
+    npt.assert_array_equal(csgraph.todense(), graph,
+        'Original graph was modified.')
+
+    # Now let the algorithm modify the csgraph in place.
+    mintree = minimum_spanning_tree(csgraph, overwrite=True)
+    npt.assert_array_equal(mintree.todense(), expected,
+        'Graph was not properly modified to contain MST.')
+
+    np.random.seed(1234)
+    for N in (5, 10, 15, 20):
+
+        # Create a random graph.
+        graph = 3 + np.random.random((N, N))
+        csgraph = csr_matrix(graph)
+
+        # The spanning tree has at most N - 1 edges.
+        mintree = minimum_spanning_tree(csgraph)
+        assert_(mintree.nnz < N)
+
+        # Set the sub diagonal to 1 to create a known spanning tree.
+        idx = np.arange(N-1)
+        graph[idx,idx+1] = 1
+        csgraph = csr_matrix(graph)
+        mintree = minimum_spanning_tree(csgraph)
+
+        # We expect to see this pattern in the spanning tree and otherwise
+        # have this zero.
+        expected = np.zeros((N, N))
+        expected[idx, idx+1] = 1
+
+        npt.assert_array_equal(mintree.todense(), expected,
+            'Incorrect spanning tree found.')

venv/Lib/site-packages/scipy/sparse/csgraph/tests/test_traversal.py

@@ -0,0 +1,68 @@
+import numpy as np
+from numpy.testing import assert_array_almost_equal
+from scipy.sparse.csgraph import (breadth_first_tree, depth_first_tree,
+    csgraph_to_dense, csgraph_from_dense)
+
+
+def test_graph_breadth_first():
+    csgraph = np.array([[0, 1, 2, 0, 0],
+                        [1, 0, 0, 0, 3],
+                        [2, 0, 0, 7, 0],
+                        [0, 0, 7, 0, 1],
+                        [0, 3, 0, 1, 0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    bfirst = np.array([[0, 1, 2, 0, 0],
+                       [0, 0, 0, 0, 3],
+                       [0, 0, 0, 7, 0],
+                       [0, 0, 0, 0, 0],
+                       [0, 0, 0, 0, 0]])
+
+    for directed in [True, False]:
+        bfirst_test = breadth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(bfirst_test),
+                                  bfirst)
+
+
+def test_graph_depth_first():
+    csgraph = np.array([[0, 1, 2, 0, 0],
+                        [1, 0, 0, 0, 3],
+                        [2, 0, 0, 7, 0],
+                        [0, 0, 7, 0, 1],
+                        [0, 3, 0, 1, 0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    dfirst = np.array([[0, 1, 0, 0, 0],
+                       [0, 0, 0, 0, 3],
+                       [0, 0, 0, 0, 0],
+                       [0, 0, 7, 0, 0],
+                       [0, 0, 0, 1, 0]])
+
+    for directed in [True, False]:
+        dfirst_test = depth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(dfirst_test),
+                                  dfirst)
+
+
+def test_graph_breadth_first_trivial_graph():
+    csgraph = np.array([[0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    bfirst = np.array([[0]])
+
+    for directed in [True, False]:
+        bfirst_test = breadth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(bfirst_test),
+                                  bfirst)
+
+
+def test_graph_depth_first_trivial_graph():
+    csgraph = np.array([[0]])
+    csgraph = csgraph_from_dense(csgraph, null_value=0)
+
+    bfirst = np.array([[0]])
+
+    for directed in [True, False]:
+        bfirst_test = depth_first_tree(csgraph, 0, directed)
+        assert_array_almost_equal(csgraph_to_dense(bfirst_test),
+                                  bfirst)

venv/Lib/site-packages/scipy/sparse/csr.py

@@ -0,0 +1,358 @@
+"""Compressed Sparse Row matrix format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['csr_matrix', 'isspmatrix_csr']
+
+import numpy as np
+
+from .base import spmatrix
+from ._sparsetools import (csr_tocsc, csr_tobsr, csr_count_blocks,
+                           get_csr_submatrix)
+from .sputils import upcast, get_index_dtype
+
+from .compressed import _cs_matrix
+
+
+class csr_matrix(_cs_matrix):
+    """
+    Compressed Sparse Row matrix
+
+    This can be instantiated in several ways:
+        csr_matrix(D)
+            with a dense matrix or rank-2 ndarray D
+
+        csr_matrix(S)
+            with another sparse matrix S (equivalent to S.tocsr())
+
+        csr_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+        csr_matrix((data, (row_ind, col_ind)), [shape=(M, N)])
+            where ``data``, ``row_ind`` and ``col_ind`` satisfy the
+            relationship ``a[row_ind[k], col_ind[k]] = data[k]``.
+
+        csr_matrix((data, indices, indptr), [shape=(M, N)])
+            is the standard CSR representation where the column indices for
+            row i are stored in ``indices[indptr[i]:indptr[i+1]]`` and their
+            corresponding values are stored in ``data[indptr[i]:indptr[i+1]]``.
+            If the shape parameter is not supplied, the matrix dimensions
+            are inferred from the index arrays.
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    nnz
+        Number of stored values, including explicit zeros
+    data
+        CSR format data array of the matrix
+    indices
+        CSR format index array of the matrix
+    indptr
+        CSR format index pointer array of the matrix
+    has_sorted_indices
+        Whether indices are sorted
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the CSR format
+      - efficient arithmetic operations CSR + CSR, CSR * CSR, etc.
+      - efficient row slicing
+      - fast matrix vector products
+
+    Disadvantages of the CSR format
+      - slow column slicing operations (consider CSC)
+      - changes to the sparsity structure are expensive (consider LIL or DOK)
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csr_matrix
+    >>> csr_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> row = np.array([0, 0, 1, 2, 2, 2])
+    >>> col = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    >>> indptr = np.array([0, 2, 3, 6])
+    >>> indices = np.array([0, 2, 2, 0, 1, 2])
+    >>> data = np.array([1, 2, 3, 4, 5, 6])
+    >>> csr_matrix((data, indices, indptr), shape=(3, 3)).toarray()
+    array([[1, 0, 2],
+           [0, 0, 3],
+           [4, 5, 6]])
+
+    Duplicate entries are summed together:
+
+    >>> row = np.array([0, 1, 2, 0])
+    >>> col = np.array([0, 1, 1, 0])
+    >>> data = np.array([1, 2, 4, 8])
+    >>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
+    array([[9, 0, 0],
+           [0, 2, 0],
+           [0, 4, 0]])
+
+    As an example of how to construct a CSR matrix incrementally,
+    the following snippet builds a term-document matrix from texts:
+
+    >>> docs = [["hello", "world", "hello"], ["goodbye", "cruel", "world"]]
+    >>> indptr = [0]
+    >>> indices = []
+    >>> data = []
+    >>> vocabulary = {}
+    >>> for d in docs:
+    ...     for term in d:
+    ...         index = vocabulary.setdefault(term, len(vocabulary))
+    ...         indices.append(index)
+    ...         data.append(1)
+    ...     indptr.append(len(indices))
+    ...
+    >>> csr_matrix((data, indices, indptr), dtype=int).toarray()
+    array([[2, 1, 0, 0],
+           [0, 1, 1, 1]])
+
+    """
+    format = 'csr'
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None:
+            raise ValueError(("Sparse matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation."))
+
+        M, N = self.shape
+
+        from .csc import csc_matrix
+        return csc_matrix((self.data, self.indices,
+                           self.indptr), shape=(N, M), copy=copy)
+
+    transpose.__doc__ = spmatrix.transpose.__doc__
+
+    def tolil(self, copy=False):
+        from .lil import lil_matrix
+        lil = lil_matrix(self.shape,dtype=self.dtype)
+
+        self.sum_duplicates()
+        ptr,ind,dat = self.indptr,self.indices,self.data
+        rows, data = lil.rows, lil.data
+
+        for n in range(self.shape[0]):
+            start = ptr[n]
+            end = ptr[n+1]
+            rows[n] = ind[start:end].tolist()
+            data[n] = dat[start:end].tolist()
+
+        return lil
+
+    tolil.__doc__ = spmatrix.tolil.__doc__
+
+    def tocsr(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tocsr.__doc__ = spmatrix.tocsr.__doc__
+
+    def tocsc(self, copy=False):
+        idx_dtype = get_index_dtype((self.indptr, self.indices),
+                                    maxval=max(self.nnz, self.shape[0]))
+        indptr = np.empty(self.shape[1] + 1, dtype=idx_dtype)
+        indices = np.empty(self.nnz, dtype=idx_dtype)
+        data = np.empty(self.nnz, dtype=upcast(self.dtype))
+
+        csr_tocsc(self.shape[0], self.shape[1],
+                  self.indptr.astype(idx_dtype),
+                  self.indices.astype(idx_dtype),
+                  self.data,
+                  indptr,
+                  indices,
+                  data)
+
+        from .csc import csc_matrix
+        A = csc_matrix((data, indices, indptr), shape=self.shape)
+        A.has_sorted_indices = True
+        return A
+
+    tocsc.__doc__ = spmatrix.tocsc.__doc__
+
+    def tobsr(self, blocksize=None, copy=True):
+        from .bsr import bsr_matrix
+
+        if blocksize is None:
+            from .spfuncs import estimate_blocksize
+            return self.tobsr(blocksize=estimate_blocksize(self))
+
+        elif blocksize == (1,1):
+            arg1 = (self.data.reshape(-1,1,1),self.indices,self.indptr)
+            return bsr_matrix(arg1, shape=self.shape, copy=copy)
+
+        else:
+            R,C = blocksize
+            M,N = self.shape
+
+            if R < 1 or C < 1 or M % R != 0 or N % C != 0:
+                raise ValueError('invalid blocksize %s' % blocksize)
+
+            blks = csr_count_blocks(M,N,R,C,self.indptr,self.indices)
+
+            idx_dtype = get_index_dtype((self.indptr, self.indices),
+                                        maxval=max(N//C, blks))
+            indptr = np.empty(M//R+1, dtype=idx_dtype)
+            indices = np.empty(blks, dtype=idx_dtype)
+            data = np.zeros((blks,R,C), dtype=self.dtype)
+
+            csr_tobsr(M, N, R, C,
+                      self.indptr.astype(idx_dtype),
+                      self.indices.astype(idx_dtype),
+                      self.data,
+                      indptr, indices, data.ravel())
+
+            return bsr_matrix((data,indices,indptr), shape=self.shape)
+
+    tobsr.__doc__ = spmatrix.tobsr.__doc__
+
+    # these functions are used by the parent class (_cs_matrix)
+    # to remove redudancy between csc_matrix and csr_matrix
+    def _swap(self, x):
+        """swap the members of x if this is a column-oriented matrix
+        """
+        return x
+
+    def __iter__(self):
+        indptr = np.zeros(2, dtype=self.indptr.dtype)
+        shape = (1, self.shape[1])
+        i0 = 0
+        for i1 in self.indptr[1:]:
+            indptr[1] = i1 - i0
+            indices = self.indices[i0:i1]
+            data = self.data[i0:i1]
+            yield csr_matrix((data, indices, indptr), shape=shape, copy=True)
+            i0 = i1
+
+    def getrow(self, i):
+        """Returns a copy of row i of the matrix, as a (1 x n)
+        CSR matrix (row vector).
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += M
+        if i < 0 or i >= M:
+            raise IndexError('index (%d) out of range' % i)
+        indptr, indices, data = get_csr_submatrix(
+            M, N, self.indptr, self.indices, self.data, i, i + 1, 0, N)
+        return csr_matrix((data, indices, indptr), shape=(1, N),
+                          dtype=self.dtype, copy=False)
+
+    def getcol(self, i):
+        """Returns a copy of column i of the matrix, as a (m x 1)
+        CSR matrix (column vector).
+        """
+        M, N = self.shape
+        i = int(i)
+        if i < 0:
+            i += N
+        if i < 0 or i >= N:
+            raise IndexError('index (%d) out of range' % i)
+        indptr, indices, data = get_csr_submatrix(
+            M, N, self.indptr, self.indices, self.data, 0, M, i, i + 1)
+        return csr_matrix((data, indices, indptr), shape=(M, 1),
+                          dtype=self.dtype, copy=False)
+
+    def _get_intXarray(self, row, col):
+        return self.getrow(row)._minor_index_fancy(col)
+
+    def _get_intXslice(self, row, col):
+        if col.step in (1, None):
+            return self._get_submatrix(row, col, copy=True)
+        # TODO: uncomment this once it's faster:
+        # return self.getrow(row)._minor_slice(col)
+
+        M, N = self.shape
+        start, stop, stride = col.indices(N)
+
+        ii, jj = self.indptr[row:row+2]
+        row_indices = self.indices[ii:jj]
+        row_data = self.data[ii:jj]
+
+        if stride > 0:
+            ind = (row_indices >= start) & (row_indices < stop)
+        else:
+            ind = (row_indices <= start) & (row_indices > stop)
+
+        if abs(stride) > 1:
+            ind &= (row_indices - start) % stride == 0
+
+        row_indices = (row_indices[ind] - start) // stride
+        row_data = row_data[ind]
+        row_indptr = np.array([0, len(row_indices)])
+
+        if stride < 0:
+            row_data = row_data[::-1]
+            row_indices = abs(row_indices[::-1])
+
+        shape = (1, int(np.ceil(float(stop - start) / stride)))
+        return csr_matrix((row_data, row_indices, row_indptr), shape=shape,
+                          dtype=self.dtype, copy=False)
+
+    def _get_sliceXint(self, row, col):
+        if row.step in (1, None):
+            return self._get_submatrix(row, col, copy=True)
+        return self._major_slice(row)._get_submatrix(minor=col)
+
+    def _get_sliceXarray(self, row, col):
+        return self._major_slice(row)._minor_index_fancy(col)
+
+    def _get_arrayXint(self, row, col):
+        return self._major_index_fancy(row)._get_submatrix(minor=col)
+
+    def _get_arrayXslice(self, row, col):
+        if col.step not in (1, None):
+            col = np.arange(*col.indices(self.shape[1]))
+            return self._get_arrayXarray(row, col)
+        return self._major_index_fancy(row)._get_submatrix(minor=col)
+
+
+def isspmatrix_csr(x):
+    """Is x of csr_matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a csr matrix
+
+    Returns
+    -------
+    bool
+        True if x is a csr matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_matrix, isspmatrix_csr
+    >>> isspmatrix_csr(csr_matrix([[5]]))
+    True
+
+    >>> from scipy.sparse import csc_matrix, csr_matrix, isspmatrix_csc
+    >>> isspmatrix_csr(csc_matrix([[5]]))
+    False
+    """
+    return isinstance(x, csr_matrix)

venv/Lib/site-packages/scipy/sparse/data.py

@@ -0,0 +1,397 @@
+"""Base class for sparse matrice with a .data attribute
+
+    subclasses must provide a _with_data() method that
+    creates a new matrix with the same sparsity pattern
+    as self but with a different data array
+
+"""
+
+import numpy as np
+
+from .base import spmatrix, _ufuncs_with_fixed_point_at_zero
+from .sputils import isscalarlike, validateaxis, matrix
+
+__all__ = []
+
+
+# TODO implement all relevant operations
+# use .data.__methods__() instead of /=, *=, etc.
+class _data_matrix(spmatrix):
+    def __init__(self):
+        spmatrix.__init__(self)
+
+    def _get_dtype(self):
+        return self.data.dtype
+
+    def _set_dtype(self, newtype):
+        self.data.dtype = newtype
+    dtype = property(fget=_get_dtype, fset=_set_dtype)
+
+    def _deduped_data(self):
+        if hasattr(self, 'sum_duplicates'):
+            self.sum_duplicates()
+        return self.data
+
+    def __abs__(self):
+        return self._with_data(abs(self._deduped_data()))
+
+    def __round__(self, ndigits=0):
+        return self._with_data(np.around(self._deduped_data(), decimals=ndigits))
+
+    def _real(self):
+        return self._with_data(self.data.real)
+
+    def _imag(self):
+        return self._with_data(self.data.imag)
+
+    def __neg__(self):
+        if self.dtype.kind == 'b':
+            raise NotImplementedError('negating a sparse boolean '
+                                      'matrix is not supported')
+        return self._with_data(-self.data)
+
+    def __imul__(self, other):  # self *= other
+        if isscalarlike(other):
+            self.data *= other
+            return self
+        else:
+            return NotImplemented
+
+    def __itruediv__(self, other):  # self /= other
+        if isscalarlike(other):
+            recip = 1.0 / other
+            self.data *= recip
+            return self
+        else:
+            return NotImplemented
+
+    def astype(self, dtype, casting='unsafe', copy=True):
+        dtype = np.dtype(dtype)
+        if self.dtype != dtype:
+            return self._with_data(
+                self._deduped_data().astype(dtype, casting=casting, copy=copy),
+                copy=copy)
+        elif copy:
+            return self.copy()
+        else:
+            return self
+
+    astype.__doc__ = spmatrix.astype.__doc__
+
+    def conj(self, copy=True):
+        if np.issubdtype(self.dtype, np.complexfloating):
+            return self._with_data(self.data.conj(), copy=copy)
+        elif copy:
+            return self.copy()
+        else:
+            return self
+
+    conj.__doc__ = spmatrix.conj.__doc__
+
+    def copy(self):
+        return self._with_data(self.data.copy(), copy=True)
+
+    copy.__doc__ = spmatrix.copy.__doc__
+
+    def count_nonzero(self):
+        return np.count_nonzero(self._deduped_data())
+
+    count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
+
+    def power(self, n, dtype=None):
+        """
+        This function performs element-wise power.
+
+        Parameters
+        ----------
+        n : n is a scalar
+
+        dtype : If dtype is not specified, the current dtype will be preserved.
+        """
+        if not isscalarlike(n):
+            raise NotImplementedError("input is not scalar")
+
+        data = self._deduped_data()
+        if dtype is not None:
+            data = data.astype(dtype)
+        return self._with_data(data ** n)
+
+    ###########################
+    # Multiplication handlers #
+    ###########################
+
+    def _mul_scalar(self, other):
+        return self._with_data(self.data * other)
+
+
+# Add the numpy unary ufuncs for which func(0) = 0 to _data_matrix.
+for npfunc in _ufuncs_with_fixed_point_at_zero:
+    name = npfunc.__name__
+
+    def _create_method(op):
+        def method(self):
+            result = op(self._deduped_data())
+            return self._with_data(result, copy=True)
+
+        method.__doc__ = ("Element-wise %s.\n\n"
+                          "See `numpy.%s` for more information." % (name, name))
+        method.__name__ = name
+
+        return method
+
+    setattr(_data_matrix, name, _create_method(npfunc))
+
+
+def _find_missing_index(ind, n):
+    for k, a in enumerate(ind):
+        if k != a:
+            return k
+
+    k += 1
+    if k < n:
+        return k
+    else:
+        return -1
+
+
+class _minmax_mixin(object):
+    """Mixin for min and max methods.
+
+    These are not implemented for dia_matrix, hence the separate class.
+    """
+
+    def _min_or_max_axis(self, axis, min_or_max):
+        N = self.shape[axis]
+        if N == 0:
+            raise ValueError("zero-size array to reduction operation")
+        M = self.shape[1 - axis]
+
+        mat = self.tocsc() if axis == 0 else self.tocsr()
+        mat.sum_duplicates()
+
+        major_index, value = mat._minor_reduce(min_or_max)
+        not_full = np.diff(mat.indptr)[major_index] < N
+        value[not_full] = min_or_max(value[not_full], 0)
+
+        mask = value != 0
+        major_index = np.compress(mask, major_index)
+        value = np.compress(mask, value)
+
+        from . import coo_matrix
+        if axis == 0:
+            return coo_matrix((value, (np.zeros(len(value)), major_index)),
+                              dtype=self.dtype, shape=(1, M))
+        else:
+            return coo_matrix((value, (major_index, np.zeros(len(value)))),
+                              dtype=self.dtype, shape=(M, 1))
+
+    def _min_or_max(self, axis, out, min_or_max):
+        if out is not None:
+            raise ValueError(("Sparse matrices do not support "
+                              "an 'out' parameter."))
+
+        validateaxis(axis)
+
+        if axis is None:
+            if 0 in self.shape:
+                raise ValueError("zero-size array to reduction operation")
+
+            zero = self.dtype.type(0)
+            if self.nnz == 0:
+                return zero
+            m = min_or_max.reduce(self._deduped_data().ravel())
+            if self.nnz != np.prod(self.shape):
+                m = min_or_max(zero, m)
+            return m
+
+        if axis < 0:
+            axis += 2
+
+        if (axis == 0) or (axis == 1):
+            return self._min_or_max_axis(axis, min_or_max)
+        else:
+            raise ValueError("axis out of range")
+
+    def _arg_min_or_max_axis(self, axis, op, compare):
+        if self.shape[axis] == 0:
+            raise ValueError("Can't apply the operation along a zero-sized "
+                             "dimension.")
+
+        if axis < 0:
+            axis += 2
+
+        zero = self.dtype.type(0)
+
+        mat = self.tocsc() if axis == 0 else self.tocsr()
+        mat.sum_duplicates()
+
+        ret_size, line_size = mat._swap(mat.shape)
+        ret = np.zeros(ret_size, dtype=int)
+
+        nz_lines, = np.nonzero(np.diff(mat.indptr))
+        for i in nz_lines:
+            p, q = mat.indptr[i:i + 2]
+            data = mat.data[p:q]
+            indices = mat.indices[p:q]
+            am = op(data)
+            m = data[am]
+            if compare(m, zero) or q - p == line_size:
+                ret[i] = indices[am]
+            else:
+                zero_ind = _find_missing_index(indices, line_size)
+                if m == zero:
+                    ret[i] = min(am, zero_ind)
+                else:
+                    ret[i] = zero_ind
+
+        if axis == 1:
+            ret = ret.reshape(-1, 1)
+
+        return matrix(ret)
+
+    def _arg_min_or_max(self, axis, out, op, compare):
+        if out is not None:
+            raise ValueError("Sparse matrices do not support "
+                             "an 'out' parameter.")
+
+        validateaxis(axis)
+
+        if axis is None:
+            if 0 in self.shape:
+                raise ValueError("Can't apply the operation to "
+                                 "an empty matrix.")
+
+            if self.nnz == 0:
+                return 0
+            else:
+                zero = self.dtype.type(0)
+                mat = self.tocoo()
+                mat.sum_duplicates()
+                am = op(mat.data)
+                m = mat.data[am]
+
+                if compare(m, zero):
+                    return mat.row[am] * mat.shape[1] + mat.col[am]
+                else:
+                    size = np.prod(mat.shape)
+                    if size == mat.nnz:
+                        return am
+                    else:
+                        ind = mat.row * mat.shape[1] + mat.col
+                        zero_ind = _find_missing_index(ind, size)
+                        if m == zero:
+                            return min(zero_ind, am)
+                        else:
+                            return zero_ind
+
+        return self._arg_min_or_max_axis(axis, op, compare)
+
+    def max(self, axis=None, out=None):
+        """
+        Return the maximum of the matrix or maximum along an axis.
+        This takes all elements into account, not just the non-zero ones.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the sum is computed. The default is to
+            compute the maximum over all the matrix elements, returning
+            a scalar (i.e., `axis` = `None`).
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except
+            for the default value, as this argument is not used.
+
+        Returns
+        -------
+        amax : coo_matrix or scalar
+            Maximum of `a`. If `axis` is None, the result is a scalar value.
+            If `axis` is given, the result is a sparse.coo_matrix of dimension
+            ``a.ndim - 1``.
+
+        See Also
+        --------
+        min : The minimum value of a sparse matrix along a given axis.
+        numpy.matrix.max : NumPy's implementation of 'max' for matrices
+
+        """
+        return self._min_or_max(axis, out, np.maximum)
+
+    def min(self, axis=None, out=None):
+        """
+        Return the minimum of the matrix or maximum along an axis.
+        This takes all elements into account, not just the non-zero ones.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None} optional
+            Axis along which the sum is computed. The default is to
+            compute the minimum over all the matrix elements, returning
+            a scalar (i.e., `axis` = `None`).
+
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except for
+            the default value, as this argument is not used.
+
+        Returns
+        -------
+        amin : coo_matrix or scalar
+            Minimum of `a`. If `axis` is None, the result is a scalar value.
+            If `axis` is given, the result is a sparse.coo_matrix of dimension
+            ``a.ndim - 1``.
+
+        See Also
+        --------
+        max : The maximum value of a sparse matrix along a given axis.
+        numpy.matrix.min : NumPy's implementation of 'min' for matrices
+
+        """
+        return self._min_or_max(axis, out, np.minimum)
+
+    def argmax(self, axis=None, out=None):
+        """Return indices of maximum elements along an axis.
+
+        Implicit zero elements are also taken into account. If there are
+        several maximum values, the index of the first occurrence is returned.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None}, optional
+            Axis along which the argmax is computed. If None (default), index
+            of the maximum element in the flatten data is returned.
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except for
+            the default value, as this argument is not used.
+
+        Returns
+        -------
+        ind : numpy.matrix or int
+            Indices of maximum elements. If matrix, its size along `axis` is 1.
+        """
+        return self._arg_min_or_max(axis, out, np.argmax, np.greater)
+
+    def argmin(self, axis=None, out=None):
+        """Return indices of minimum elements along an axis.
+
+        Implicit zero elements are also taken into account. If there are
+        several minimum values, the index of the first occurrence is returned.
+
+        Parameters
+        ----------
+        axis : {-2, -1, 0, 1, None}, optional
+            Axis along which the argmin is computed. If None (default), index
+            of the minimum element in the flatten data is returned.
+        out : None, optional
+            This argument is in the signature *solely* for NumPy
+            compatibility reasons. Do not pass in anything except for
+            the default value, as this argument is not used.
+
+        Returns
+        -------
+         ind : numpy.matrix or int
+            Indices of minimum elements. If matrix, its size along `axis` is 1.
+        """
+        return self._arg_min_or_max(axis, out, np.argmin, np.less)

venv/Lib/site-packages/scipy/sparse/dia.py

@@ -0,0 +1,431 @@
+"""Sparse DIAgonal format"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['dia_matrix', 'isspmatrix_dia']
+
+import numpy as np
+
+from .base import isspmatrix, _formats, spmatrix
+from .data import _data_matrix
+from .sputils import (isshape, upcast_char, getdtype, get_index_dtype,
+                      get_sum_dtype, validateaxis, check_shape, matrix)
+from ._sparsetools import dia_matvec
+
+
+class dia_matrix(_data_matrix):
+    """Sparse matrix with DIAgonal storage
+
+    This can be instantiated in several ways:
+        dia_matrix(D)
+            with a dense matrix
+
+        dia_matrix(S)
+            with another sparse matrix S (equivalent to S.todia())
+
+        dia_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N),
+            dtype is optional, defaulting to dtype='d'.
+
+        dia_matrix((data, offsets), shape=(M, N))
+            where the ``data[k,:]`` stores the diagonal entries for
+            diagonal ``offsets[k]`` (See example below)
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    nnz
+        Number of stored values, including explicit zeros
+    data
+        DIA format data array of the matrix
+    offsets
+        DIA format offset array of the matrix
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> from scipy.sparse import dia_matrix
+    >>> dia_matrix((3, 4), dtype=np.int8).toarray()
+    array([[0, 0, 0, 0],
+           [0, 0, 0, 0],
+           [0, 0, 0, 0]], dtype=int8)
+
+    >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
+    >>> offsets = np.array([0, -1, 2])
+    >>> dia_matrix((data, offsets), shape=(4, 4)).toarray()
+    array([[1, 0, 3, 0],
+           [1, 2, 0, 4],
+           [0, 2, 3, 0],
+           [0, 0, 3, 4]])
+
+    >>> from scipy.sparse import dia_matrix
+    >>> n = 10
+    >>> ex = np.ones(n)
+    >>> data = np.array([ex, 2 * ex, ex])
+    >>> offsets = np.array([-1, 0, 1])
+    >>> dia_matrix((data, offsets), shape=(n, n)).toarray()
+    array([[2., 1., 0., ..., 0., 0., 0.],
+           [1., 2., 1., ..., 0., 0., 0.],
+           [0., 1., 2., ..., 0., 0., 0.],
+           ...,
+           [0., 0., 0., ..., 2., 1., 0.],
+           [0., 0., 0., ..., 1., 2., 1.],
+           [0., 0., 0., ..., 0., 1., 2.]])
+    """
+    format = 'dia'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False):
+        _data_matrix.__init__(self)
+
+        if isspmatrix_dia(arg1):
+            if copy:
+                arg1 = arg1.copy()
+            self.data = arg1.data
+            self.offsets = arg1.offsets
+            self._shape = check_shape(arg1.shape)
+        elif isspmatrix(arg1):
+            if isspmatrix_dia(arg1) and copy:
+                A = arg1.copy()
+            else:
+                A = arg1.todia()
+            self.data = A.data
+            self.offsets = A.offsets
+            self._shape = check_shape(A.shape)
+        elif isinstance(arg1, tuple):
+            if isshape(arg1):
+                # It's a tuple of matrix dimensions (M, N)
+                # create empty matrix
+                self._shape = check_shape(arg1)
+                self.data = np.zeros((0,0), getdtype(dtype, default=float))
+                idx_dtype = get_index_dtype(maxval=max(self.shape))
+                self.offsets = np.zeros((0), dtype=idx_dtype)
+            else:
+                try:
+                    # Try interpreting it as (data, offsets)
+                    data, offsets = arg1
+                except Exception:
+                    raise ValueError('unrecognized form for dia_matrix constructor')
+                else:
+                    if shape is None:
+                        raise ValueError('expected a shape argument')
+                    self.data = np.atleast_2d(np.array(arg1[0], dtype=dtype, copy=copy))
+                    self.offsets = np.atleast_1d(np.array(arg1[1],
+                                                          dtype=get_index_dtype(maxval=max(shape)),
+                                                          copy=copy))
+                    self._shape = check_shape(shape)
+        else:
+            #must be dense, convert to COO first, then to DIA
+            try:
+                arg1 = np.asarray(arg1)
+            except Exception:
+                raise ValueError("unrecognized form for"
+                        " %s_matrix constructor" % self.format)
+            from .coo import coo_matrix
+            A = coo_matrix(arg1, dtype=dtype, shape=shape).todia()
+            self.data = A.data
+            self.offsets = A.offsets
+            self._shape = check_shape(A.shape)
+
+        if dtype is not None:
+            self.data = self.data.astype(dtype)
+
+        #check format
+        if self.offsets.ndim != 1:
+            raise ValueError('offsets array must have rank 1')
+
+        if self.data.ndim != 2:
+            raise ValueError('data array must have rank 2')
+
+        if self.data.shape[0] != len(self.offsets):
+            raise ValueError('number of diagonals (%d) '
+                    'does not match the number of offsets (%d)'
+                    % (self.data.shape[0], len(self.offsets)))
+
+        if len(np.unique(self.offsets)) != len(self.offsets):
+            raise ValueError('offset array contains duplicate values')
+
+    def __repr__(self):
+        format = _formats[self.getformat()][1]
+        return "<%dx%d sparse matrix of type '%s'\n" \
+               "\twith %d stored elements (%d diagonals) in %s format>" % \
+               (self.shape + (self.dtype.type, self.nnz, self.data.shape[0],
+                              format))
+
+    def _data_mask(self):
+        """Returns a mask of the same shape as self.data, where
+        mask[i,j] is True when data[i,j] corresponds to a stored element."""
+        num_rows, num_cols = self.shape
+        offset_inds = np.arange(self.data.shape[1])
+        row = offset_inds - self.offsets[:,None]
+        mask = (row >= 0)
+        mask &= (row < num_rows)
+        mask &= (offset_inds < num_cols)
+        return mask
+
+    def count_nonzero(self):
+        mask = self._data_mask()
+        return np.count_nonzero(self.data[mask])
+
+    def getnnz(self, axis=None):
+        if axis is not None:
+            raise NotImplementedError("getnnz over an axis is not implemented "
+                                      "for DIA format")
+        M,N = self.shape
+        nnz = 0
+        for k in self.offsets:
+            if k > 0:
+                nnz += min(M,N-k)
+            else:
+                nnz += min(M+k,N)
+        return int(nnz)
+
+    getnnz.__doc__ = spmatrix.getnnz.__doc__
+    count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
+
+    def sum(self, axis=None, dtype=None, out=None):
+        validateaxis(axis)
+
+        if axis is not None and axis < 0:
+            axis += 2
+
+        res_dtype = get_sum_dtype(self.dtype)
+        num_rows, num_cols = self.shape
+        ret = None
+
+        if axis == 0:
+            mask = self._data_mask()
+            x = (self.data * mask).sum(axis=0)
+            if x.shape[0] == num_cols:
+                res = x
+            else:
+                res = np.zeros(num_cols, dtype=x.dtype)
+                res[:x.shape[0]] = x
+            ret = matrix(res, dtype=res_dtype)
+
+        else:
+            row_sums = np.zeros(num_rows, dtype=res_dtype)
+            one = np.ones(num_cols, dtype=res_dtype)
+            dia_matvec(num_rows, num_cols, len(self.offsets),
+                       self.data.shape[1], self.offsets, self.data, one, row_sums)
+
+            row_sums = matrix(row_sums)
+
+            if axis is None:
+                return row_sums.sum(dtype=dtype, out=out)
+
+            if axis is not None:
+                row_sums = row_sums.T
+
+            ret = matrix(row_sums.sum(axis=axis))
+
+        if out is not None and out.shape != ret.shape:
+            raise ValueError("dimensions do not match")
+
+        return ret.sum(axis=(), dtype=dtype, out=out)
+
+    sum.__doc__ = spmatrix.sum.__doc__
+
+    def _mul_vector(self, other):
+        x = other
+
+        y = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
+                                                       x.dtype.char))
+
+        L = self.data.shape[1]
+
+        M,N = self.shape
+
+        dia_matvec(M,N, len(self.offsets), L, self.offsets, self.data, x.ravel(), y.ravel())
+
+        return y
+
+    def _mul_multimatrix(self, other):
+        return np.hstack([self._mul_vector(col).reshape(-1,1) for col in other.T])
+
+    def _setdiag(self, values, k=0):
+        M, N = self.shape
+
+        if values.ndim == 0:
+            # broadcast
+            values_n = np.inf
+        else:
+            values_n = len(values)
+
+        if k < 0:
+            n = min(M + k, N, values_n)
+            min_index = 0
+            max_index = n
+        else:
+            n = min(M, N - k, values_n)
+            min_index = k
+            max_index = k + n
+
+        if values.ndim != 0:
+            # allow also longer sequences
+            values = values[:n]
+
+        if k in self.offsets:
+            self.data[self.offsets == k, min_index:max_index] = values
+        else:
+            self.offsets = np.append(self.offsets, self.offsets.dtype.type(k))
+            m = max(max_index, self.data.shape[1])
+            data = np.zeros((self.data.shape[0]+1, m), dtype=self.data.dtype)
+            data[:-1,:self.data.shape[1]] = self.data
+            data[-1, min_index:max_index] = values
+            self.data = data
+
+    def todia(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    todia.__doc__ = spmatrix.todia.__doc__
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None:
+            raise ValueError(("Sparse matrices do not support "
+                              "an 'axes' parameter because swapping "
+                              "dimensions is the only logical permutation."))
+
+        num_rows, num_cols = self.shape
+        max_dim = max(self.shape)
+
+        # flip diagonal offsets
+        offsets = -self.offsets
+
+        # re-align the data matrix
+        r = np.arange(len(offsets), dtype=np.intc)[:, None]
+        c = np.arange(num_rows, dtype=np.intc) - (offsets % max_dim)[:, None]
+        pad_amount = max(0, max_dim-self.data.shape[1])
+        data = np.hstack((self.data, np.zeros((self.data.shape[0], pad_amount),
+                                              dtype=self.data.dtype)))
+        data = data[r, c]
+        return dia_matrix((data, offsets), shape=(
+            num_cols, num_rows), copy=copy)
+
+    transpose.__doc__ = spmatrix.transpose.__doc__
+
+    def diagonal(self, k=0):
+        rows, cols = self.shape
+        if k <= -rows or k >= cols:
+            return np.empty(0, dtype=self.data.dtype)
+        idx, = np.nonzero(self.offsets == k)
+        first_col, last_col = max(0, k), min(rows + k, cols)
+        if idx.size == 0:
+            return np.zeros(last_col - first_col, dtype=self.data.dtype)
+        return self.data[idx[0], first_col:last_col]
+
+    diagonal.__doc__ = spmatrix.diagonal.__doc__
+
+    def tocsc(self, copy=False):
+        from .csc import csc_matrix
+        if self.nnz == 0:
+            return csc_matrix(self.shape, dtype=self.dtype)
+
+        num_rows, num_cols = self.shape
+        num_offsets, offset_len = self.data.shape
+        offset_inds = np.arange(offset_len)
+
+        row = offset_inds - self.offsets[:,None]
+        mask = (row >= 0)
+        mask &= (row < num_rows)
+        mask &= (offset_inds < num_cols)
+        mask &= (self.data != 0)
+
+        idx_dtype = get_index_dtype(maxval=max(self.shape))
+        indptr = np.zeros(num_cols + 1, dtype=idx_dtype)
+        indptr[1:offset_len+1] = np.cumsum(mask.sum(axis=0))
+        indptr[offset_len+1:] = indptr[offset_len]
+        indices = row.T[mask.T].astype(idx_dtype, copy=False)
+        data = self.data.T[mask.T]
+        return csc_matrix((data, indices, indptr), shape=self.shape,
+                          dtype=self.dtype)
+
+    tocsc.__doc__ = spmatrix.tocsc.__doc__
+
+    def tocoo(self, copy=False):
+        num_rows, num_cols = self.shape
+        num_offsets, offset_len = self.data.shape
+        offset_inds = np.arange(offset_len)
+
+        row = offset_inds - self.offsets[:,None]
+        mask = (row >= 0)
+        mask &= (row < num_rows)
+        mask &= (offset_inds < num_cols)
+        mask &= (self.data != 0)
+        row = row[mask]
+        col = np.tile(offset_inds, num_offsets)[mask.ravel()]
+        data = self.data[mask]
+
+        from .coo import coo_matrix
+        A = coo_matrix((data,(row,col)), shape=self.shape, dtype=self.dtype)
+        A.has_canonical_format = True
+        return A
+
+    tocoo.__doc__ = spmatrix.tocoo.__doc__
+
+    # needed by _data_matrix
+    def _with_data(self, data, copy=True):
+        """Returns a matrix with the same sparsity structure as self,
+        but with different data.  By default the structure arrays are copied.
+        """
+        if copy:
+            return dia_matrix((data, self.offsets.copy()), shape=self.shape)
+        else:
+            return dia_matrix((data,self.offsets), shape=self.shape)
+
+    def resize(self, *shape):
+        shape = check_shape(shape)
+        M, N = shape
+        # we do not need to handle the case of expanding N
+        self.data = self.data[:, :N]
+
+        if (M > self.shape[0] and
+                np.any(self.offsets + self.shape[0] < self.data.shape[1])):
+            # explicitly clear values that were previously hidden
+            mask = (self.offsets[:, None] + self.shape[0] <=
+                    np.arange(self.data.shape[1]))
+            self.data[mask] = 0
+
+        self._shape = shape
+
+    resize.__doc__ = spmatrix.resize.__doc__
+
+
+def isspmatrix_dia(x):
+    """Is x of dia_matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a dia matrix
+
+    Returns
+    -------
+    bool
+        True if x is a dia matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import dia_matrix, isspmatrix_dia
+    >>> isspmatrix_dia(dia_matrix([[5]]))
+    True
+
+    >>> from scipy.sparse import dia_matrix, csr_matrix, isspmatrix_dia
+    >>> isspmatrix_dia(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, dia_matrix)

venv/Lib/site-packages/scipy/sparse/dok.py

@@ -0,0 +1,453 @@
+"""Dictionary Of Keys based matrix"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['dok_matrix', 'isspmatrix_dok']
+
+import itertools
+import numpy as np
+
+from .base import spmatrix, isspmatrix
+from ._index import IndexMixin
+from .sputils import (isdense, getdtype, isshape, isintlike, isscalarlike,
+                      upcast, upcast_scalar, get_index_dtype, check_shape)
+
+try:
+    from operator import isSequenceType as _is_sequence
+except ImportError:
+    def _is_sequence(x):
+        return (hasattr(x, '__len__') or hasattr(x, '__next__')
+                or hasattr(x, 'next'))
+
+
+class dok_matrix(spmatrix, IndexMixin, dict):
+    """
+    Dictionary Of Keys based sparse matrix.
+
+    This is an efficient structure for constructing sparse
+    matrices incrementally.
+
+    This can be instantiated in several ways:
+        dok_matrix(D)
+            with a dense matrix, D
+
+        dok_matrix(S)
+            with a sparse matrix, S
+
+        dok_matrix((M,N), [dtype])
+            create the matrix with initial shape (M,N)
+            dtype is optional, defaulting to dtype='d'
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    nnz
+        Number of nonzero elements
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Allows for efficient O(1) access of individual elements.
+    Duplicates are not allowed.
+    Can be efficiently converted to a coo_matrix once constructed.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.sparse import dok_matrix
+    >>> S = dok_matrix((5, 5), dtype=np.float32)
+    >>> for i in range(5):
+    ...     for j in range(5):
+    ...         S[i, j] = i + j    # Update element
+
+    """
+    format = 'dok'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False):
+        dict.__init__(self)
+        spmatrix.__init__(self)
+
+        self.dtype = getdtype(dtype, default=float)
+        if isinstance(arg1, tuple) and isshape(arg1):  # (M,N)
+            M, N = arg1
+            self._shape = check_shape((M, N))
+        elif isspmatrix(arg1):  # Sparse ctor
+            if isspmatrix_dok(arg1) and copy:
+                arg1 = arg1.copy()
+            else:
+                arg1 = arg1.todok()
+
+            if dtype is not None:
+                arg1 = arg1.astype(dtype, copy=False)
+
+            dict.update(self, arg1)
+            self._shape = check_shape(arg1.shape)
+            self.dtype = arg1.dtype
+        else:  # Dense ctor
+            try:
+                arg1 = np.asarray(arg1)
+            except Exception:
+                raise TypeError('Invalid input format.')
+
+            if len(arg1.shape) != 2:
+                raise TypeError('Expected rank <=2 dense array or matrix.')
+
+            from .coo import coo_matrix
+            d = coo_matrix(arg1, dtype=dtype).todok()
+            dict.update(self, d)
+            self._shape = check_shape(arg1.shape)
+            self.dtype = d.dtype
+
+    def update(self, val):
+        # Prevent direct usage of update
+        raise NotImplementedError("Direct modification to dok_matrix element "
+                                  "is not allowed.")
+
+    def _update(self, data):
+        """An update method for dict data defined for direct access to
+        `dok_matrix` data. Main purpose is to be used for effcient conversion
+        from other spmatrix classes. Has no checking if `data` is valid."""
+        return dict.update(self, data)
+
+    def set_shape(self, shape):
+        new_matrix = self.reshape(shape, copy=False).asformat(self.format)
+        self.__dict__ = new_matrix.__dict__
+        dict.clear(self)
+        dict.update(self, new_matrix)
+
+    shape = property(fget=spmatrix.get_shape, fset=set_shape)
+
+    def getnnz(self, axis=None):
+        if axis is not None:
+            raise NotImplementedError("getnnz over an axis is not implemented "
+                                      "for DOK format.")
+        return dict.__len__(self)
+
+    def count_nonzero(self):
+        return sum(x != 0 for x in self.values())
+
+    getnnz.__doc__ = spmatrix.getnnz.__doc__
+    count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
+
+    def __len__(self):
+        return dict.__len__(self)
+
+    def get(self, key, default=0.):
+        """This overrides the dict.get method, providing type checking
+        but otherwise equivalent functionality.
+        """
+        try:
+            i, j = key
+            assert isintlike(i) and isintlike(j)
+        except (AssertionError, TypeError, ValueError):
+            raise IndexError('Index must be a pair of integers.')
+        if (i < 0 or i >= self.shape[0] or j < 0 or j >= self.shape[1]):
+            raise IndexError('Index out of bounds.')
+        return dict.get(self, key, default)
+
+    def _get_intXint(self, row, col):
+        return dict.get(self, (row, col), self.dtype.type(0))
+
+    def _get_intXslice(self, row, col):
+        return self._get_sliceXslice(slice(row, row+1), col)
+
+    def _get_sliceXint(self, row, col):
+        return self._get_sliceXslice(row, slice(col, col+1))
+
+    def _get_sliceXslice(self, row, col):
+        row_start, row_stop, row_step = row.indices(self.shape[0])
+        col_start, col_stop, col_step = col.indices(self.shape[1])
+        row_range = range(row_start, row_stop, row_step)
+        col_range = range(col_start, col_stop, col_step)
+        shape = (len(row_range), len(col_range))
+        # Switch paths only when advantageous
+        # (count the iterations in the loops, adjust for complexity)
+        if len(self) >= 2 * shape[0] * shape[1]:
+            # O(nr*nc) path: loop over <row x col>
+            return self._get_columnXarray(row_range, col_range)
+        # O(nnz) path: loop over entries of self
+        newdok = dok_matrix(shape, dtype=self.dtype)
+        for key in self.keys():
+            i, ri = divmod(int(key[0]) - row_start, row_step)
+            if ri != 0 or i < 0 or i >= shape[0]:
+                continue
+            j, rj = divmod(int(key[1]) - col_start, col_step)
+            if rj != 0 or j < 0 or j >= shape[1]:
+                continue
+            x = dict.__getitem__(self, key)
+            dict.__setitem__(newdok, (i, j), x)
+        return newdok
+
+    def _get_intXarray(self, row, col):
+        return self._get_columnXarray([row], col)
+
+    def _get_arrayXint(self, row, col):
+        return self._get_columnXarray(row, [col])
+
+    def _get_sliceXarray(self, row, col):
+        row = list(range(*row.indices(self.shape[0])))
+        return self._get_columnXarray(row, col)
+
+    def _get_arrayXslice(self, row, col):
+        col = list(range(*col.indices(self.shape[1])))
+        return self._get_columnXarray(row, col)
+
+    def _get_columnXarray(self, row, col):
+        # outer indexing
+        newdok = dok_matrix((len(row), len(col)), dtype=self.dtype)
+
+        for i, r in enumerate(row):
+            for j, c in enumerate(col):
+                v = dict.get(self, (r, c), 0)
+                if v:
+                    dict.__setitem__(newdok, (i, j), v)
+        return newdok
+
+    def _get_arrayXarray(self, row, col):
+        # inner indexing
+        i, j = map(np.atleast_2d, np.broadcast_arrays(row, col))
+        newdok = dok_matrix(i.shape, dtype=self.dtype)
+
+        for key in itertools.product(range(i.shape[0]), range(i.shape[1])):
+            v = dict.get(self, (i[key], j[key]), 0)
+            if v:
+                dict.__setitem__(newdok, key, v)
+        return newdok
+
+    def _set_intXint(self, row, col, x):
+        key = (row, col)
+        if x:
+            dict.__setitem__(self, key, x)
+        elif dict.__contains__(self, key):
+            del self[key]
+
+    def _set_arrayXarray(self, row, col, x):
+        row = list(map(int, row.ravel()))
+        col = list(map(int, col.ravel()))
+        x = x.ravel()
+        dict.update(self, zip(zip(row, col), x))
+
+        for i in np.nonzero(x == 0)[0]:
+            key = (row[i], col[i])
+            if dict.__getitem__(self, key) == 0:
+                # may have been superseded by later update
+                del self[key]
+
+    def __add__(self, other):
+        if isscalarlike(other):
+            res_dtype = upcast_scalar(self.dtype, other)
+            new = dok_matrix(self.shape, dtype=res_dtype)
+            # Add this scalar to every element.
+            M, N = self.shape
+            for key in itertools.product(range(M), range(N)):
+                aij = dict.get(self, (key), 0) + other
+                if aij:
+                    new[key] = aij
+            # new.dtype.char = self.dtype.char
+        elif isspmatrix_dok(other):
+            if other.shape != self.shape:
+                raise ValueError("Matrix dimensions are not equal.")
+            # We could alternatively set the dimensions to the largest of
+            # the two matrices to be summed.  Would this be a good idea?
+            res_dtype = upcast(self.dtype, other.dtype)
+            new = dok_matrix(self.shape, dtype=res_dtype)
+            dict.update(new, self)
+            with np.errstate(over='ignore'):
+                dict.update(new,
+                           ((k, new[k] + other[k]) for k in other.keys()))
+        elif isspmatrix(other):
+            csc = self.tocsc()
+            new = csc + other
+        elif isdense(other):
+            new = self.todense() + other
+        else:
+            return NotImplemented
+        return new
+
+    def __radd__(self, other):
+        if isscalarlike(other):
+            new = dok_matrix(self.shape, dtype=self.dtype)
+            M, N = self.shape
+            for key in itertools.product(range(M), range(N)):
+                aij = dict.get(self, (key), 0) + other
+                if aij:
+                    new[key] = aij
+        elif isspmatrix_dok(other):
+            if other.shape != self.shape:
+                raise ValueError("Matrix dimensions are not equal.")
+            new = dok_matrix(self.shape, dtype=self.dtype)
+            dict.update(new, self)
+            dict.update(new,
+                       ((k, self[k] + other[k]) for k in other.keys()))
+        elif isspmatrix(other):
+            csc = self.tocsc()
+            new = csc + other
+        elif isdense(other):
+            new = other + self.todense()
+        else:
+            return NotImplemented
+        return new
+
+    def __neg__(self):
+        if self.dtype.kind == 'b':
+            raise NotImplementedError('Negating a sparse boolean matrix is not'
+                                      ' supported.')
+        new = dok_matrix(self.shape, dtype=self.dtype)
+        dict.update(new, ((k, -self[k]) for k in self.keys()))
+        return new
+
+    def _mul_scalar(self, other):
+        res_dtype = upcast_scalar(self.dtype, other)
+        # Multiply this scalar by every element.
+        new = dok_matrix(self.shape, dtype=res_dtype)
+        dict.update(new, ((k, v * other) for k, v in self.items()))
+        return new
+
+    def _mul_vector(self, other):
+        # matrix * vector
+        result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype))
+        for (i, j), v in self.items():
+            result[i] += v * other[j]
+        return result
+
+    def _mul_multivector(self, other):
+        # matrix * multivector
+        result_shape = (self.shape[0], other.shape[1])
+        result_dtype = upcast(self.dtype, other.dtype)
+        result = np.zeros(result_shape, dtype=result_dtype)
+        for (i, j), v in self.items():
+            result[i,:] += v * other[j,:]
+        return result
+
+    def __imul__(self, other):
+        if isscalarlike(other):
+            dict.update(self, ((k, v * other) for k, v in self.items()))
+            return self
+        return NotImplemented
+
+    def __truediv__(self, other):
+        if isscalarlike(other):
+            res_dtype = upcast_scalar(self.dtype, other)
+            new = dok_matrix(self.shape, dtype=res_dtype)
+            dict.update(new, ((k, v / other) for k, v in self.items()))
+            return new
+        return self.tocsr() / other
+
+    def __itruediv__(self, other):
+        if isscalarlike(other):
+            dict.update(self, ((k, v / other) for k, v in self.items()))
+            return self
+        return NotImplemented
+
+    def __reduce__(self):
+        # this approach is necessary because __setstate__ is called after
+        # __setitem__ upon unpickling and since __init__ is not called there
+        # is no shape attribute hence it is not possible to unpickle it.
+        return dict.__reduce__(self)
+
+    # What should len(sparse) return? For consistency with dense matrices,
+    # perhaps it should be the number of rows?  For now it returns the number
+    # of non-zeros.
+
+    def transpose(self, axes=None, copy=False):
+        if axes is not None:
+            raise ValueError("Sparse matrices do not support "
+                             "an 'axes' parameter because swapping "
+                             "dimensions is the only logical permutation.")
+
+        M, N = self.shape
+        new = dok_matrix((N, M), dtype=self.dtype, copy=copy)
+        dict.update(new, (((right, left), val)
+                          for (left, right), val in self.items()))
+        return new
+
+    transpose.__doc__ = spmatrix.transpose.__doc__
+
+    def conjtransp(self):
+        """Return the conjugate transpose."""
+        M, N = self.shape
+        new = dok_matrix((N, M), dtype=self.dtype)
+        dict.update(new, (((right, left), np.conj(val))
+                          for (left, right), val in self.items()))
+        return new
+
+    def copy(self):
+        new = dok_matrix(self.shape, dtype=self.dtype)
+        dict.update(new, self)
+        return new
+
+    copy.__doc__ = spmatrix.copy.__doc__
+
+    def tocoo(self, copy=False):
+        from .coo import coo_matrix
+        if self.nnz == 0:
+            return coo_matrix(self.shape, dtype=self.dtype)
+
+        idx_dtype = get_index_dtype(maxval=max(self.shape))
+        data = np.fromiter(self.values(), dtype=self.dtype, count=self.nnz)
+        row = np.fromiter((i for i, _ in self.keys()), dtype=idx_dtype, count=self.nnz)
+        col = np.fromiter((j for _, j in self.keys()), dtype=idx_dtype, count=self.nnz)
+        A = coo_matrix((data, (row, col)), shape=self.shape, dtype=self.dtype)
+        A.has_canonical_format = True
+        return A
+
+    tocoo.__doc__ = spmatrix.tocoo.__doc__
+
+    def todok(self, copy=False):
+        if copy:
+            return self.copy()
+        return self
+
+    todok.__doc__ = spmatrix.todok.__doc__
+
+    def tocsc(self, copy=False):
+        return self.tocoo(copy=False).tocsc(copy=copy)
+
+    tocsc.__doc__ = spmatrix.tocsc.__doc__
+
+    def resize(self, *shape):
+        shape = check_shape(shape)
+        newM, newN = shape
+        M, N = self.shape
+        if newM < M or newN < N:
+            # Remove all elements outside new dimensions
+            for (i, j) in list(self.keys()):
+                if i >= newM or j >= newN:
+                    del self[i, j]
+        self._shape = shape
+
+    resize.__doc__ = spmatrix.resize.__doc__
+
+
+def isspmatrix_dok(x):
+    """Is x of dok_matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a dok matrix
+
+    Returns
+    -------
+    bool
+        True if x is a dok matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import dok_matrix, isspmatrix_dok
+    >>> isspmatrix_dok(dok_matrix([[5]]))
+    True
+
+    >>> from scipy.sparse import dok_matrix, csr_matrix, isspmatrix_dok
+    >>> isspmatrix_dok(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, dok_matrix)

venv/Lib/site-packages/scipy/sparse/extract.py

@@ -0,0 +1,169 @@
+"""Functions to extract parts of sparse matrices
+"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['find', 'tril', 'triu']
+
+
+from .coo import coo_matrix
+
+
+def find(A):
+    """Return the indices and values of the nonzero elements of a matrix
+
+    Parameters
+    ----------
+    A : dense or sparse matrix
+        Matrix whose nonzero elements are desired.
+
+    Returns
+    -------
+    (I,J,V) : tuple of arrays
+        I,J, and V contain the row indices, column indices, and values
+        of the nonzero matrix entries.
+
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_matrix, find
+    >>> A = csr_matrix([[7.0, 8.0, 0],[0, 0, 9.0]])
+    >>> find(A)
+    (array([0, 0, 1], dtype=int32), array([0, 1, 2], dtype=int32), array([ 7.,  8.,  9.]))
+
+    """
+
+    A = coo_matrix(A, copy=True)
+    A.sum_duplicates()
+    # remove explicit zeros
+    nz_mask = A.data != 0
+    return A.row[nz_mask], A.col[nz_mask], A.data[nz_mask]
+
+
+def tril(A, k=0, format=None):
+    """Return the lower triangular portion of a matrix in sparse format
+
+    Returns the elements on or below the k-th diagonal of the matrix A.
+        - k = 0 corresponds to the main diagonal
+        - k > 0 is above the main diagonal
+        - k < 0 is below the main diagonal
+
+    Parameters
+    ----------
+    A : dense or sparse matrix
+        Matrix whose lower trianglar portion is desired.
+    k : integer : optional
+        The top-most diagonal of the lower triangle.
+    format : string
+        Sparse format of the result, e.g. format="csr", etc.
+
+    Returns
+    -------
+    L : sparse matrix
+        Lower triangular portion of A in sparse format.
+
+    See Also
+    --------
+    triu : upper triangle in sparse format
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_matrix, tril
+    >>> A = csr_matrix([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
+    ...                dtype='int32')
+    >>> A.toarray()
+    array([[1, 2, 0, 0, 3],
+           [4, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]])
+    >>> tril(A).toarray()
+    array([[1, 0, 0, 0, 0],
+           [4, 5, 0, 0, 0],
+           [0, 0, 8, 0, 0]])
+    >>> tril(A).nnz
+    4
+    >>> tril(A, k=1).toarray()
+    array([[1, 2, 0, 0, 0],
+           [4, 5, 0, 0, 0],
+           [0, 0, 8, 9, 0]])
+    >>> tril(A, k=-1).toarray()
+    array([[0, 0, 0, 0, 0],
+           [4, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0]])
+    >>> tril(A, format='csc')
+    <3x5 sparse matrix of type '<class 'numpy.int32'>'
+            with 4 stored elements in Compressed Sparse Column format>
+
+    """
+
+    # convert to COOrdinate format where things are easy
+    A = coo_matrix(A, copy=False)
+    mask = A.row + k >= A.col
+    return _masked_coo(A, mask).asformat(format)
+
+
+def triu(A, k=0, format=None):
+    """Return the upper triangular portion of a matrix in sparse format
+
+    Returns the elements on or above the k-th diagonal of the matrix A.
+        - k = 0 corresponds to the main diagonal
+        - k > 0 is above the main diagonal
+        - k < 0 is below the main diagonal
+
+    Parameters
+    ----------
+    A : dense or sparse matrix
+        Matrix whose upper trianglar portion is desired.
+    k : integer : optional
+        The bottom-most diagonal of the upper triangle.
+    format : string
+        Sparse format of the result, e.g. format="csr", etc.
+
+    Returns
+    -------
+    L : sparse matrix
+        Upper triangular portion of A in sparse format.
+
+    See Also
+    --------
+    tril : lower triangle in sparse format
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_matrix, triu
+    >>> A = csr_matrix([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
+    ...                dtype='int32')
+    >>> A.toarray()
+    array([[1, 2, 0, 0, 3],
+           [4, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]])
+    >>> triu(A).toarray()
+    array([[1, 2, 0, 0, 3],
+           [0, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]])
+    >>> triu(A).nnz
+    8
+    >>> triu(A, k=1).toarray()
+    array([[0, 2, 0, 0, 3],
+           [0, 0, 0, 6, 7],
+           [0, 0, 0, 9, 0]])
+    >>> triu(A, k=-1).toarray()
+    array([[1, 2, 0, 0, 3],
+           [4, 5, 0, 6, 7],
+           [0, 0, 8, 9, 0]])
+    >>> triu(A, format='csc')
+    <3x5 sparse matrix of type '<class 'numpy.int32'>'
+            with 8 stored elements in Compressed Sparse Column format>
+
+    """
+
+    # convert to COOrdinate format where things are easy
+    A = coo_matrix(A, copy=False)
+    mask = A.row + k <= A.col
+    return _masked_coo(A, mask).asformat(format)
+
+
+def _masked_coo(A, mask):
+    row = A.row[mask]
+    col = A.col[mask]
+    data = A.data[mask]
+    return coo_matrix((data, (row, col)), shape=A.shape, dtype=A.dtype)

venv/Lib/site-packages/scipy/sparse/generate_sparsetools.py

@@ -0,0 +1,433 @@
+"""
+python generate_sparsetools.py
+
+Generate manual wrappers for C++ sparsetools code.
+
+Type codes used:
+
+    'i':  integer scalar
+    'I':  integer array
+    'T':  data array
+    'B':  boolean array
+    'V':  std::vector<integer>*
+    'W':  std::vector<data>*
+    '*':  indicates that the next argument is an output argument
+    'v':  void
+    'l':  64-bit integer scalar
+
+See sparsetools.cxx for more details.
+
+"""
+import optparse
+import os
+from distutils.dep_util import newer
+
+#
+# List of all routines and their argument types.
+#
+# The first code indicates the return value, the rest the arguments.
+#
+
+# bsr.h
+BSR_ROUTINES = """
+bsr_diagonal        v iiiiiIIT*T
+bsr_tocsr           v iiiiIIT*I*I*T
+bsr_scale_rows      v iiiiII*TT
+bsr_scale_columns   v iiiiII*TT
+bsr_sort_indices    v iiii*I*I*T
+bsr_transpose       v iiiiIIT*I*I*T
+bsr_matmat          v iiiiiiIITIIT*I*I*T
+bsr_matvec          v iiiiIITT*T
+bsr_matvecs         v iiiiiIITT*T
+bsr_elmul_bsr       v iiiiIITIIT*I*I*T
+bsr_eldiv_bsr       v iiiiIITIIT*I*I*T
+bsr_plus_bsr        v iiiiIITIIT*I*I*T
+bsr_minus_bsr       v iiiiIITIIT*I*I*T
+bsr_maximum_bsr     v iiiiIITIIT*I*I*T
+bsr_minimum_bsr     v iiiiIITIIT*I*I*T
+bsr_ne_bsr          v iiiiIITIIT*I*I*B
+bsr_lt_bsr          v iiiiIITIIT*I*I*B
+bsr_gt_bsr          v iiiiIITIIT*I*I*B
+bsr_le_bsr          v iiiiIITIIT*I*I*B
+bsr_ge_bsr          v iiiiIITIIT*I*I*B
+"""
+
+# csc.h
+CSC_ROUTINES = """
+csc_diagonal        v iiiIIT*T
+csc_tocsr           v iiIIT*I*I*T
+csc_matmat_maxnnz   l iiIIII
+csc_matmat          v iiIITIIT*I*I*T
+csc_matvec          v iiIITT*T
+csc_matvecs         v iiiIITT*T
+csc_elmul_csc       v iiIITIIT*I*I*T
+csc_eldiv_csc       v iiIITIIT*I*I*T
+csc_plus_csc        v iiIITIIT*I*I*T
+csc_minus_csc       v iiIITIIT*I*I*T
+csc_maximum_csc     v iiIITIIT*I*I*T
+csc_minimum_csc     v iiIITIIT*I*I*T
+csc_ne_csc          v iiIITIIT*I*I*B
+csc_lt_csc          v iiIITIIT*I*I*B
+csc_gt_csc          v iiIITIIT*I*I*B
+csc_le_csc          v iiIITIIT*I*I*B
+csc_ge_csc          v iiIITIIT*I*I*B
+"""
+
+# csr.h
+CSR_ROUTINES = """
+csr_matmat_maxnnz   l iiIIII
+csr_matmat          v iiIITIIT*I*I*T
+csr_diagonal        v iiiIIT*T
+csr_tocsc           v iiIIT*I*I*T
+csr_tobsr           v iiiiIIT*I*I*T
+csr_todense         v iiIIT*T
+csr_matvec          v iiIITT*T
+csr_matvecs         v iiiIITT*T
+csr_elmul_csr       v iiIITIIT*I*I*T
+csr_eldiv_csr       v iiIITIIT*I*I*T
+csr_plus_csr        v iiIITIIT*I*I*T
+csr_minus_csr       v iiIITIIT*I*I*T
+csr_maximum_csr     v iiIITIIT*I*I*T
+csr_minimum_csr     v iiIITIIT*I*I*T
+csr_ne_csr          v iiIITIIT*I*I*B
+csr_lt_csr          v iiIITIIT*I*I*B
+csr_gt_csr          v iiIITIIT*I*I*B
+csr_le_csr          v iiIITIIT*I*I*B
+csr_ge_csr          v iiIITIIT*I*I*B
+csr_scale_rows      v iiII*TT
+csr_scale_columns   v iiII*TT
+csr_sort_indices    v iI*I*T
+csr_eliminate_zeros v ii*I*I*T
+csr_sum_duplicates  v ii*I*I*T
+get_csr_submatrix   v iiIITiiii*V*V*W
+csr_row_index       v iIIIT*I*T
+csr_row_slice       v iiiIIT*I*T
+csr_column_index1   v iIiiII*I*I
+csr_column_index2   v IIiIT*I*T
+csr_sample_values   v iiIITiII*T
+csr_count_blocks    i iiiiII
+csr_sample_offsets  i iiIIiII*I
+expandptr           v iI*I
+test_throw_error    i
+csr_has_sorted_indices    i iII
+csr_has_canonical_format  i iII
+"""
+
+# coo.h, dia.h, csgraph.h
+OTHER_ROUTINES = """
+coo_tocsr           v iiiIIT*I*I*T
+coo_todense         v iilIIT*Ti
+coo_matvec          v lIITT*T
+dia_matvec          v iiiiITT*T
+cs_graph_components i iII*I
+"""
+
+# List of compilation units
+COMPILATION_UNITS = [
+    ('bsr', BSR_ROUTINES),
+    ('csr', CSR_ROUTINES),
+    ('csc', CSC_ROUTINES),
+    ('other', OTHER_ROUTINES),
+]
+
+#
+# List of the supported index typenums and the corresponding C++ types
+#
+I_TYPES = [
+    ('NPY_INT32', 'npy_int32'),
+    ('NPY_INT64', 'npy_int64'),
+]
+
+#
+# List of the supported data typenums and the corresponding C++ types
+#
+T_TYPES = [
+    ('NPY_BOOL', 'npy_bool_wrapper'),
+    ('NPY_BYTE', 'npy_byte'),
+    ('NPY_UBYTE', 'npy_ubyte'),
+    ('NPY_SHORT', 'npy_short'),
+    ('NPY_USHORT', 'npy_ushort'),
+    ('NPY_INT', 'npy_int'),
+    ('NPY_UINT', 'npy_uint'),
+    ('NPY_LONG', 'npy_long'),
+    ('NPY_ULONG', 'npy_ulong'),
+    ('NPY_LONGLONG', 'npy_longlong'),
+    ('NPY_ULONGLONG', 'npy_ulonglong'),
+    ('NPY_FLOAT', 'npy_float'),
+    ('NPY_DOUBLE', 'npy_double'),
+    ('NPY_LONGDOUBLE', 'npy_longdouble'),
+    ('NPY_CFLOAT', 'npy_cfloat_wrapper'),
+    ('NPY_CDOUBLE', 'npy_cdouble_wrapper'),
+    ('NPY_CLONGDOUBLE', 'npy_clongdouble_wrapper'),
+]
+
+#
+# Code templates
+#
+
+THUNK_TEMPLATE = """
+static PY_LONG_LONG %(name)s_thunk(int I_typenum, int T_typenum, void **a)
+{
+    %(thunk_content)s
+}
+"""
+
+METHOD_TEMPLATE = """
+NPY_VISIBILITY_HIDDEN PyObject *
+%(name)s_method(PyObject *self, PyObject *args)
+{
+    return call_thunk('%(ret_spec)s', "%(arg_spec)s", %(name)s_thunk, args);
+}
+"""
+
+GET_THUNK_CASE_TEMPLATE = """
+static int get_thunk_case(int I_typenum, int T_typenum)
+{
+    %(content)s;
+    return -1;
+}
+"""
+
+
+#
+# Code generation
+#
+
+def get_thunk_type_set():
+    """
+    Get a list containing cartesian product of data types, plus a getter routine.
+
+    Returns
+    -------
+    i_types : list [(j, I_typenum, None, I_type, None), ...]
+         Pairing of index type numbers and the corresponding C++ types,
+         and an unique index `j`. This is for routines that are parameterized
+         only by I but not by T.
+    it_types : list [(j, I_typenum, T_typenum, I_type, T_type), ...]
+         Same as `i_types`, but for routines parameterized both by T and I.
+    getter_code : str
+         C++ code for a function that takes I_typenum, T_typenum and returns
+         the unique index corresponding to the lists, or -1 if no match was
+         found.
+
+    """
+    it_types = []
+    i_types = []
+
+    j = 0
+
+    getter_code = "    if (0) {}"
+
+    for I_typenum, I_type in I_TYPES:
+        piece = """
+        else if (I_typenum == %(I_typenum)s) {
+            if (T_typenum == -1) { return %(j)s; }"""
+        getter_code += piece % dict(I_typenum=I_typenum, j=j)
+
+        i_types.append((j, I_typenum, None, I_type, None))
+        j += 1
+
+        for T_typenum, T_type in T_TYPES:
+            piece = """
+            else if (T_typenum == %(T_typenum)s) { return %(j)s; }"""
+            getter_code += piece % dict(T_typenum=T_typenum, j=j)
+
+            it_types.append((j, I_typenum, T_typenum, I_type, T_type))
+            j += 1
+
+        getter_code += """
+        }"""
+
+    return i_types, it_types, GET_THUNK_CASE_TEMPLATE % dict(content=getter_code)
+
+
+def parse_routine(name, args, types):
+    """
+    Generate thunk and method code for a given routine.
+
+    Parameters
+    ----------
+    name : str
+        Name of the C++ routine
+    args : str
+        Argument list specification (in format explained above)
+    types : list
+        List of types to instantiate, as returned `get_thunk_type_set`
+
+    """
+
+    ret_spec = args[0]
+    arg_spec = args[1:]
+
+    def get_arglist(I_type, T_type):
+        """
+        Generate argument list for calling the C++ function
+        """
+        args = []
+        next_is_writeable = False
+        j = 0
+        for t in arg_spec:
+            const = '' if next_is_writeable else 'const '
+            next_is_writeable = False
+            if t == '*':
+                next_is_writeable = True
+                continue
+            elif t == 'i':
+                args.append("*(%s*)a[%d]" % (const + I_type, j))
+            elif t == 'I':
+                args.append("(%s*)a[%d]" % (const + I_type, j))
+            elif t == 'T':
+                args.append("(%s*)a[%d]" % (const + T_type, j))
+            elif t == 'B':
+                args.append("(npy_bool_wrapper*)a[%d]" % (j,))
+            elif t == 'V':
+                if const:
+                    raise ValueError("'V' argument must be an output arg")
+                args.append("(std::vector<%s>*)a[%d]" % (I_type, j,))
+            elif t == 'W':
+                if const:
+                    raise ValueError("'W' argument must be an output arg")
+                args.append("(std::vector<%s>*)a[%d]" % (T_type, j,))
+            elif t == 'l':
+                args.append("*(%snpy_int64*)a[%d]" % (const, j))
+            else:
+                raise ValueError("Invalid spec character %r" % (t,))
+            j += 1
+        return ", ".join(args)
+
+    # Generate thunk code: a giant switch statement with different
+    # type combinations inside.
+    thunk_content = """int j = get_thunk_case(I_typenum, T_typenum);
+    switch (j) {"""
+    for j, I_typenum, T_typenum, I_type, T_type in types:
+        arglist = get_arglist(I_type, T_type)
+        if T_type is None:
+            dispatch = "%s" % (I_type,)
+        else:
+            dispatch = "%s,%s" % (I_type, T_type)
+        if 'B' in arg_spec:
+            dispatch += ",npy_bool_wrapper"
+
+        piece = """
+        case %(j)s:"""
+        if ret_spec == 'v':
+            piece += """
+            (void)%(name)s<%(dispatch)s>(%(arglist)s);
+            return 0;"""
+        else:
+            piece += """
+            return %(name)s<%(dispatch)s>(%(arglist)s);"""
+        thunk_content += piece % dict(j=j, I_type=I_type, T_type=T_type,
+                                      I_typenum=I_typenum, T_typenum=T_typenum,
+                                      arglist=arglist, name=name,
+                                      dispatch=dispatch)
+
+    thunk_content += """
+    default:
+        throw std::runtime_error("internal error: invalid argument typenums");
+    }"""
+
+    thunk_code = THUNK_TEMPLATE % dict(name=name,
+                                       thunk_content=thunk_content)
+
+    # Generate method code
+    method_code = METHOD_TEMPLATE % dict(name=name,
+                                         ret_spec=ret_spec,
+                                         arg_spec=arg_spec)
+
+    return thunk_code, method_code
+
+
+def main():
+    p = optparse.OptionParser(usage=(__doc__ or '').strip())
+    p.add_option("--no-force", action="store_false",
+                 dest="force", default=True)
+    options, args = p.parse_args()
+
+    names = []
+
+    i_types, it_types, getter_code = get_thunk_type_set()
+
+    # Generate *_impl.h for each compilation unit
+    for unit_name, routines in COMPILATION_UNITS:
+        thunks = []
+        methods = []
+
+        # Generate thunks and methods for all routines
+        for line in routines.splitlines():
+            line = line.strip()
+            if not line or line.startswith('#'):
+                continue
+
+            try:
+                name, args = line.split(None, 1)
+            except ValueError:
+                raise ValueError("Malformed line: %r" % (line,))
+
+            args = "".join(args.split())
+            if 't' in args or 'T' in args:
+                thunk, method = parse_routine(name, args, it_types)
+            else:
+                thunk, method = parse_routine(name, args, i_types)
+
+            if name in names:
+                raise ValueError("Duplicate routine %r" % (name,))
+
+            names.append(name)
+            thunks.append(thunk)
+            methods.append(method)
+
+        # Produce output
+        dst = os.path.join(os.path.dirname(__file__),
+                           'sparsetools',
+                           unit_name + '_impl.h')
+        if newer(__file__, dst) or options.force:
+            print("[generate_sparsetools] generating %r" % (dst,))
+            with open(dst, 'w') as f:
+                write_autogen_blurb(f)
+                f.write(getter_code)
+                for thunk in thunks:
+                    f.write(thunk)
+                for method in methods:
+                    f.write(method)
+        else:
+            print("[generate_sparsetools] %r already up-to-date" % (dst,))
+
+    # Generate code for method struct
+    method_defs = ""
+    for name in names:
+        method_defs += "NPY_VISIBILITY_HIDDEN PyObject *%s_method(PyObject *, PyObject *);\n" % (name,)
+
+    method_struct = """\nstatic struct PyMethodDef sparsetools_methods[] = {"""
+    for name in names:
+        method_struct += """
+        {"%(name)s", (PyCFunction)%(name)s_method, METH_VARARGS, NULL},""" % dict(name=name)
+    method_struct += """
+        {NULL, NULL, 0, NULL}
+    };"""
+
+    # Produce sparsetools_impl.h
+    dst = os.path.join(os.path.dirname(__file__),
+                       'sparsetools',
+                       'sparsetools_impl.h')
+
+    if newer(__file__, dst) or options.force:
+        print("[generate_sparsetools] generating %r" % (dst,))
+        with open(dst, 'w') as f:
+            write_autogen_blurb(f)
+            f.write(method_defs)
+            f.write(method_struct)
+    else:
+        print("[generate_sparsetools] %r already up-to-date" % (dst,))
+
+
+def write_autogen_blurb(stream):
+    stream.write("""\
+/* This file is autogenerated by generate_sparsetools.py
+ * Do not edit manually or check into VCS.
+ */
+""")
+
+
+if __name__ == "__main__":
+    main()

venv/Lib/site-packages/scipy/sparse/lil.py

@@ -0,0 +1,550 @@
+"""List of Lists sparse matrix class
+"""
+
+__docformat__ = "restructuredtext en"
+
+__all__ = ['lil_matrix', 'isspmatrix_lil']
+
+from bisect import bisect_left
+
+import numpy as np
+
+from .base import spmatrix, isspmatrix
+from ._index import IndexMixin, INT_TYPES, _broadcast_arrays
+from .sputils import (getdtype, isshape, isscalarlike, upcast_scalar,
+                      get_index_dtype, check_shape, check_reshape_kwargs,
+                      asmatrix)
+from . import _csparsetools
+
+
+class lil_matrix(spmatrix, IndexMixin):
+    """Row-based list of lists sparse matrix
+
+    This is a structure for constructing sparse matrices incrementally.
+    Note that inserting a single item can take linear time in the worst case;
+    to construct a matrix efficiently, make sure the items are pre-sorted by
+    index, per row.
+
+    This can be instantiated in several ways:
+        lil_matrix(D)
+            with a dense matrix or rank-2 ndarray D
+
+        lil_matrix(S)
+            with another sparse matrix S (equivalent to S.tolil())
+
+        lil_matrix((M, N), [dtype])
+            to construct an empty matrix with shape (M, N)
+            dtype is optional, defaulting to dtype='d'.
+
+    Attributes
+    ----------
+    dtype : dtype
+        Data type of the matrix
+    shape : 2-tuple
+        Shape of the matrix
+    ndim : int
+        Number of dimensions (this is always 2)
+    nnz
+        Number of stored values, including explicit zeros
+    data
+        LIL format data array of the matrix
+    rows
+        LIL format row index array of the matrix
+
+    Notes
+    -----
+
+    Sparse matrices can be used in arithmetic operations: they support
+    addition, subtraction, multiplication, division, and matrix power.
+
+    Advantages of the LIL format
+        - supports flexible slicing
+        - changes to the matrix sparsity structure are efficient
+
+    Disadvantages of the LIL format
+        - arithmetic operations LIL + LIL are slow (consider CSR or CSC)
+        - slow column slicing (consider CSC)
+        - slow matrix vector products (consider CSR or CSC)
+
+    Intended Usage
+        - LIL is a convenient format for constructing sparse matrices
+        - once a matrix has been constructed, convert to CSR or
+          CSC format for fast arithmetic and matrix vector operations
+        - consider using the COO format when constructing large matrices
+
+    Data Structure
+        - An array (``self.rows``) of rows, each of which is a sorted
+          list of column indices of non-zero elements.
+        - The corresponding nonzero values are stored in similar
+          fashion in ``self.data``.
+
+
+    """
+    format = 'lil'
+
+    def __init__(self, arg1, shape=None, dtype=None, copy=False):
+        spmatrix.__init__(self)
+        self.dtype = getdtype(dtype, arg1, default=float)
+
+        # First get the shape
+        if isspmatrix(arg1):
+            if isspmatrix_lil(arg1) and copy:
+                A = arg1.copy()
+            else:
+                A = arg1.tolil()
+
+            if dtype is not None:
+                A = A.astype(dtype, copy=False)
+
+            self._shape = check_shape(A.shape)
+            self.dtype = A.dtype
+            self.rows = A.rows
+            self.data = A.data
+        elif isinstance(arg1,tuple):
+            if isshape(arg1):
+                if shape is not None:
+                    raise ValueError('invalid use of shape parameter')
+                M, N = arg1
+                self._shape = check_shape((M, N))
+                self.rows = np.empty((M,), dtype=object)
+                self.data = np.empty((M,), dtype=object)
+                for i in range(M):
+                    self.rows[i] = []
+                    self.data[i] = []
+            else:
+                raise TypeError('unrecognized lil_matrix constructor usage')
+        else:
+            # assume A is dense
+            try:
+                A = asmatrix(arg1)
+            except TypeError:
+                raise TypeError('unsupported matrix type')
+            else:
+                from .csr import csr_matrix
+                A = csr_matrix(A, dtype=dtype).tolil()
+
+                self._shape = check_shape(A.shape)
+                self.dtype = A.dtype
+                self.rows = A.rows
+                self.data = A.data
+
+    def __iadd__(self,other):
+        self[:,:] = self + other
+        return self
+
+    def __isub__(self,other):
+        self[:,:] = self - other
+        return self
+
+    def __imul__(self,other):
+        if isscalarlike(other):
+            self[:,:] = self * other
+            return self
+        else:
+            return NotImplemented
+
+    def __itruediv__(self,other):
+        if isscalarlike(other):
+            self[:,:] = self / other
+            return self
+        else:
+            return NotImplemented
+
+    # Whenever the dimensions change, empty lists should be created for each
+    # row
+
+    def getnnz(self, axis=None):
+        if axis is None:
+            return sum([len(rowvals) for rowvals in self.data])
+        if axis < 0:
+            axis += 2
+        if axis == 0:
+            out = np.zeros(self.shape[1], dtype=np.intp)
+            for row in self.rows:
+                out[row] += 1
+            return out
+        elif axis == 1:
+            return np.array([len(rowvals) for rowvals in self.data], dtype=np.intp)
+        else:
+            raise ValueError('axis out of bounds')
+
+    def count_nonzero(self):
+        return sum(np.count_nonzero(rowvals) for rowvals in self.data)
+
+    getnnz.__doc__ = spmatrix.getnnz.__doc__
+    count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
+
+    def __str__(self):
+        val = ''
+        for i, row in enumerate(self.rows):
+            for pos, j in enumerate(row):
+                val += "  %s\t%s\n" % (str((i, j)), str(self.data[i][pos]))
+        return val[:-1]
+
+    def getrowview(self, i):
+        """Returns a view of the 'i'th row (without copying).
+        """
+        new = lil_matrix((1, self.shape[1]), dtype=self.dtype)
+        new.rows[0] = self.rows[i]
+        new.data[0] = self.data[i]
+        return new
+
+    def getrow(self, i):
+        """Returns a copy of the 'i'th row.
+        """
+        M, N = self.shape
+        if i < 0:
+            i += M
+        if i < 0 or i >= M:
+            raise IndexError('row index out of bounds')
+        new = lil_matrix((1, N), dtype=self.dtype)
+        new.rows[0] = self.rows[i][:]
+        new.data[0] = self.data[i][:]
+        return new
+
+    def __getitem__(self, key):
+        # Fast path for simple (int, int) indexing.
+        if (isinstance(key, tuple) and len(key) == 2 and
+                isinstance(key[0], INT_TYPES) and
+                isinstance(key[1], INT_TYPES)):
+            # lil_get1 handles validation for us.
+            return self._get_intXint(*key)
+        # Everything else takes the normal path.
+        return IndexMixin.__getitem__(self, key)
+
+    def _asindices(self, idx, N):
+        # LIL routines handle bounds-checking for us, so don't do it here.
+        try:
+            x = np.asarray(idx)
+        except (ValueError, TypeError, MemoryError):
+            raise IndexError('invalid index')
+        if x.ndim not in (1, 2):
+            raise IndexError('Index dimension must be <= 2')
+        return x
+
+    def _get_intXint(self, row, col):
+        v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows,
+                                   self.data, row, col)
+        return self.dtype.type(v)
+
+    def _get_sliceXint(self, row, col):
+        row = range(*row.indices(self.shape[0]))
+        return self._get_row_ranges(row, slice(col, col+1))
+
+    def _get_arrayXint(self, row, col):
+        return self._get_row_ranges(row, slice(col, col+1))
+
+    def _get_intXslice(self, row, col):
+        return self._get_row_ranges((row,), col)
+
+    def _get_sliceXslice(self, row, col):
+        row = range(*row.indices(self.shape[0]))
+        return self._get_row_ranges(row, col)
+
+    def _get_arrayXslice(self, row, col):
+        return self._get_row_ranges(row, col)
+
+    def _get_intXarray(self, row, col):
+        row = np.array(row, dtype=col.dtype, ndmin=1)
+        return self._get_columnXarray(row, col)
+
+    def _get_sliceXarray(self, row, col):
+        row = np.arange(*row.indices(self.shape[0]))
+        return self._get_columnXarray(row, col)
+
+    def _get_columnXarray(self, row, col):
+        # outer indexing
+        row, col = _broadcast_arrays(row[:,None], col)
+        return self._get_arrayXarray(row, col)
+
+    def _get_arrayXarray(self, row, col):
+        # inner indexing
+        i, j = map(np.atleast_2d, _prepare_index_for_memoryview(row, col))
+        new = lil_matrix(i.shape, dtype=self.dtype)
+        _csparsetools.lil_fancy_get(self.shape[0], self.shape[1],
+                                    self.rows, self.data,
+                                    new.rows, new.data,
+                                    i, j)
+        return new
+
+    def _get_row_ranges(self, rows, col_slice):
+        """
+        Fast path for indexing in the case where column index is slice.
+
+        This gains performance improvement over brute force by more
+        efficient skipping of zeros, by accessing the elements
+        column-wise in order.
+
+        Parameters
+        ----------
+        rows : sequence or range
+            Rows indexed. If range, must be within valid bounds.
+        col_slice : slice
+            Columns indexed
+
+        """
+        j_start, j_stop, j_stride = col_slice.indices(self.shape[1])
+        col_range = range(j_start, j_stop, j_stride)
+        nj = len(col_range)
+        new = lil_matrix((len(rows), nj), dtype=self.dtype)
+
+        _csparsetools.lil_get_row_ranges(self.shape[0], self.shape[1],
+                                         self.rows, self.data,
+                                         new.rows, new.data,
+                                         rows,
+                                         j_start, j_stop, j_stride, nj)
+
+        return new
+
+    def _set_intXint(self, row, col, x):
+        _csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows,
+                                 self.data, row, col, x)
+
+    def _set_arrayXarray(self, row, col, x):
+        i, j, x = map(np.atleast_2d, _prepare_index_for_memoryview(row, col, x))
+        _csparsetools.lil_fancy_set(self.shape[0], self.shape[1],
+                                    self.rows, self.data,
+                                    i, j, x)
+
+    def _set_arrayXarray_sparse(self, row, col, x):
+        # Special case: full matrix assignment
+        if (x.shape == self.shape and
+                isinstance(row, slice) and row == slice(None) and
+                isinstance(col, slice) and col == slice(None)):
+            x = lil_matrix(x, dtype=self.dtype)
+            self.rows = x.rows
+            self.data = x.data
+            return
+        # Fall back to densifying x
+        x = np.asarray(x.toarray(), dtype=self.dtype)
+        x, _ = _broadcast_arrays(x, row)
+        self._set_arrayXarray(row, col, x)
+
+    def __setitem__(self, key, x):
+        # Fast path for simple (int, int) indexing.
+        if (isinstance(key, tuple) and len(key) == 2 and
+                isinstance(key[0], INT_TYPES) and
+                isinstance(key[1], INT_TYPES)):
+            x = self.dtype.type(x)
+            if x.size > 1:
+                raise ValueError("Trying to assign a sequence to an item")
+            return self._set_intXint(key[0], key[1], x)
+        # Everything else takes the normal path.
+        IndexMixin.__setitem__(self, key, x)
+
+    def _mul_scalar(self, other):
+        if other == 0:
+            # Multiply by zero: return the zero matrix
+            new = lil_matrix(self.shape, dtype=self.dtype)
+        else:
+            res_dtype = upcast_scalar(self.dtype, other)
+
+            new = self.copy()
+            new = new.astype(res_dtype)
+            # Multiply this scalar by every element.
+            for j, rowvals in enumerate(new.data):
+                new.data[j] = [val*other for val in rowvals]
+        return new
+
+    def __truediv__(self, other):           # self / other
+        if isscalarlike(other):
+            new = self.copy()
+            # Divide every element by this scalar
+            for j, rowvals in enumerate(new.data):
+                new.data[j] = [val/other for val in rowvals]
+            return new
+        else:
+            return self.tocsr() / other
+
+    def copy(self):
+        M, N = self.shape
+        new = lil_matrix(self.shape, dtype=self.dtype)
+        # This is ~14x faster than calling deepcopy() on rows and data.
+        _csparsetools.lil_get_row_ranges(M, N, self.rows, self.data,
+                                         new.rows, new.data, range(M),
+                                         0, N, 1, N)
+        return new
+
+    copy.__doc__ = spmatrix.copy.__doc__
+
+    def reshape(self, *args, **kwargs):
+        shape = check_shape(args, self.shape)
+        order, copy = check_reshape_kwargs(kwargs)
+
+        # Return early if reshape is not required
+        if shape == self.shape:
+            if copy:
+                return self.copy()
+            else:
+                return self
+
+        new = lil_matrix(shape, dtype=self.dtype)
+
+        if order == 'C':
+            ncols = self.shape[1]
+            for i, row in enumerate(self.rows):
+                for col, j in enumerate(row):
+                    new_r, new_c = np.unravel_index(i * ncols + j, shape)
+                    new[new_r, new_c] = self[i, j]
+        elif order == 'F':
+            nrows = self.shape[0]
+            for i, row in enumerate(self.rows):
+                for col, j in enumerate(row):
+                    new_r, new_c = np.unravel_index(i + j * nrows, shape, order)
+                    new[new_r, new_c] = self[i, j]
+        else:
+            raise ValueError("'order' must be 'C' or 'F'")
+
+        return new
+
+    reshape.__doc__ = spmatrix.reshape.__doc__
+
+    def resize(self, *shape):
+        shape = check_shape(shape)
+        new_M, new_N = shape
+        M, N = self.shape
+
+        if new_M < M:
+            self.rows = self.rows[:new_M]
+            self.data = self.data[:new_M]
+        elif new_M > M:
+            self.rows = np.resize(self.rows, new_M)
+            self.data = np.resize(self.data, new_M)
+            for i in range(M, new_M):
+                self.rows[i] = []
+                self.data[i] = []
+
+        if new_N < N:
+            for row, data in zip(self.rows, self.data):
+                trunc = bisect_left(row, new_N)
+                del row[trunc:]
+                del data[trunc:]
+
+        self._shape = shape
+
+    resize.__doc__ = spmatrix.resize.__doc__
+
+    def toarray(self, order=None, out=None):
+        d = self._process_toarray_args(order, out)
+        for i, row in enumerate(self.rows):
+            for pos, j in enumerate(row):
+                d[i, j] = self.data[i][pos]
+        return d
+
+    toarray.__doc__ = spmatrix.toarray.__doc__
+
+    def transpose(self, axes=None, copy=False):
+        return self.tocsr(copy=copy).transpose(axes=axes, copy=False).tolil(copy=False)
+
+    transpose.__doc__ = spmatrix.transpose.__doc__
+
+    def tolil(self, copy=False):
+        if copy:
+            return self.copy()
+        else:
+            return self
+
+    tolil.__doc__ = spmatrix.tolil.__doc__
+
+    def tocsr(self, copy=False):
+        from .csr import csr_matrix
+
+        M, N = self.shape
+        if M == 0 or N == 0:
+            return csr_matrix((M, N), dtype=self.dtype)
+
+        # construct indptr array
+        if M*N <= np.iinfo(np.int32).max:
+            # fast path: it is known that 64-bit indexing will not be needed.
+            idx_dtype = np.int32
+            indptr = np.empty(M + 1, dtype=idx_dtype)
+            indptr[0] = 0
+            _csparsetools.lil_get_lengths(self.rows, indptr[1:])
+            np.cumsum(indptr, out=indptr)
+            nnz = indptr[-1]
+        else:
+            idx_dtype = get_index_dtype(maxval=N)
+            lengths = np.empty(M, dtype=idx_dtype)
+            _csparsetools.lil_get_lengths(self.rows, lengths)
+            nnz = lengths.sum()
+            idx_dtype = get_index_dtype(maxval=max(N, nnz))
+            indptr = np.empty(M + 1, dtype=idx_dtype)
+            indptr[0] = 0
+            np.cumsum(lengths, dtype=idx_dtype, out=indptr[1:])
+
+        indices = np.empty(nnz, dtype=idx_dtype)
+        data = np.empty(nnz, dtype=self.dtype)
+        _csparsetools.lil_flatten_to_array(self.rows, indices)
+        _csparsetools.lil_flatten_to_array(self.data, data)
+
+        # init csr matrix
+        return csr_matrix((data, indices, indptr), shape=self.shape)
+
+    tocsr.__doc__ = spmatrix.tocsr.__doc__
+
+
+def _prepare_index_for_memoryview(i, j, x=None):
+    """
+    Convert index and data arrays to form suitable for passing to the
+    Cython fancy getset routines.
+
+    The conversions are necessary since to (i) ensure the integer
+    index arrays are in one of the accepted types, and (ii) to ensure
+    the arrays are writable so that Cython memoryview support doesn't
+    choke on them.
+
+    Parameters
+    ----------
+    i, j
+        Index arrays
+    x : optional
+        Data arrays
+
+    Returns
+    -------
+    i, j, x
+        Re-formatted arrays (x is omitted, if input was None)
+
+    """
+    if i.dtype > j.dtype:
+        j = j.astype(i.dtype)
+    elif i.dtype < j.dtype:
+        i = i.astype(j.dtype)
+
+    if not i.flags.writeable or i.dtype not in (np.int32, np.int64):
+        i = i.astype(np.intp)
+    if not j.flags.writeable or j.dtype not in (np.int32, np.int64):
+        j = j.astype(np.intp)
+
+    if x is not None:
+        if not x.flags.writeable:
+            x = x.copy()
+        return i, j, x
+    else:
+        return i, j
+
+
+def isspmatrix_lil(x):
+    """Is x of lil_matrix type?
+
+    Parameters
+    ----------
+    x
+        object to check for being a lil matrix
+
+    Returns
+    -------
+    bool
+        True if x is a lil matrix, False otherwise
+
+    Examples
+    --------
+    >>> from scipy.sparse import lil_matrix, isspmatrix_lil
+    >>> isspmatrix_lil(lil_matrix([[5]]))
+    True
+
+    >>> from scipy.sparse import lil_matrix, csr_matrix, isspmatrix_lil
+    >>> isspmatrix_lil(csr_matrix([[5]]))
+    False
+    """
+    return isinstance(x, lil_matrix)

venv/Lib/site-packages/scipy/sparse/linalg/__init__.py

@@ -0,0 +1,124 @@
+"""
+Sparse linear algebra (:mod:`scipy.sparse.linalg`)
+==================================================
+
+.. currentmodule:: scipy.sparse.linalg
+
+Abstract linear operators
+-------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   LinearOperator -- abstract representation of a linear operator
+   aslinearoperator -- convert an object to an abstract linear operator
+
+Matrix Operations
+-----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   inv -- compute the sparse matrix inverse
+   expm -- compute the sparse matrix exponential
+   expm_multiply -- compute the product of a matrix exponential and a matrix
+
+Matrix norms
+------------
+
+.. autosummary::
+   :toctree: generated/
+
+   norm -- Norm of a sparse matrix
+   onenormest -- Estimate the 1-norm of a sparse matrix
+
+Solving linear problems
+-----------------------
+
+Direct methods for linear equation systems:
+
+.. autosummary::
+   :toctree: generated/
+
+   spsolve -- Solve the sparse linear system Ax=b
+   spsolve_triangular -- Solve the sparse linear system Ax=b for a triangular matrix
+   factorized -- Pre-factorize matrix to a function solving a linear system
+   MatrixRankWarning -- Warning on exactly singular matrices
+   use_solver -- Select direct solver to use
+
+Iterative methods for linear equation systems:
+
+.. autosummary::
+   :toctree: generated/
+
+   bicg -- Use BIConjugate Gradient iteration to solve A x = b
+   bicgstab -- Use BIConjugate Gradient STABilized iteration to solve A x = b
+   cg -- Use Conjugate Gradient iteration to solve A x = b
+   cgs -- Use Conjugate Gradient Squared iteration to solve A x = b
+   gmres -- Use Generalized Minimal RESidual iteration to solve A x = b
+   lgmres -- Solve a matrix equation using the LGMRES algorithm
+   minres -- Use MINimum RESidual iteration to solve Ax = b
+   qmr -- Use Quasi-Minimal Residual iteration to solve A x = b
+   gcrotmk -- Solve a matrix equation using the GCROT(m,k) algorithm
+
+Iterative methods for least-squares problems:
+
+.. autosummary::
+   :toctree: generated/
+
+   lsqr -- Find the least-squares solution to a sparse linear equation system
+   lsmr -- Find the least-squares solution to a sparse linear equation system
+
+Matrix factorizations
+---------------------
+
+Eigenvalue problems:
+
+.. autosummary::
+   :toctree: generated/
+
+   eigs -- Find k eigenvalues and eigenvectors of the square matrix A
+   eigsh -- Find k eigenvalues and eigenvectors of a symmetric matrix
+   lobpcg -- Solve symmetric partial eigenproblems with optional preconditioning
+
+Singular values problems:
+
+.. autosummary::
+   :toctree: generated/
+
+   svds -- Compute k singular values/vectors for a sparse matrix
+
+Complete or incomplete LU factorizations
+
+.. autosummary::
+   :toctree: generated/
+
+   splu -- Compute a LU decomposition for a sparse matrix
+   spilu -- Compute an incomplete LU decomposition for a sparse matrix
+   SuperLU -- Object representing an LU factorization
+
+Exceptions
+----------
+
+.. autosummary::
+   :toctree: generated/
+
+   ArpackNoConvergence
+   ArpackError
+
+"""
+
+from .isolve import *
+from .dsolve import *
+from .interface import *
+from .eigen import *
+from .matfuncs import *
+from ._onenormest import *
+from ._norm import *
+from ._expm_multiply import *
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

venv/Lib/site-packages/scipy/sparse/linalg/_expm_multiply.py

@@ -0,0 +1,711 @@
+"""Compute the action of the matrix exponential.
+"""
+
+import numpy as np
+
+import scipy.linalg
+import scipy.sparse.linalg
+from scipy.sparse.linalg import aslinearoperator
+from scipy.sparse.sputils import is_pydata_spmatrix
+
+__all__ = ['expm_multiply']
+
+
+def _exact_inf_norm(A):
+    # A compatibility function which should eventually disappear.
+    if scipy.sparse.isspmatrix(A):
+        return max(abs(A).sum(axis=1).flat)
+    elif is_pydata_spmatrix(A):
+        return max(abs(A).sum(axis=1))
+    else:
+        return np.linalg.norm(A, np.inf)
+
+
+def _exact_1_norm(A):
+    # A compatibility function which should eventually disappear.
+    if scipy.sparse.isspmatrix(A):
+        return max(abs(A).sum(axis=0).flat)
+    elif is_pydata_spmatrix(A):
+        return max(abs(A).sum(axis=0))
+    else:
+        return np.linalg.norm(A, 1)
+
+
+def _trace(A):
+    # A compatibility function which should eventually disappear.
+    if scipy.sparse.isspmatrix(A):
+        return A.diagonal().sum()
+    elif is_pydata_spmatrix(A):
+        return A.to_scipy_sparse().diagonal().sum()
+    else:
+        return np.trace(A)
+
+
+def _ident_like(A):
+    # A compatibility function which should eventually disappear.
+    if scipy.sparse.isspmatrix(A):
+        return scipy.sparse.construct.eye(A.shape[0], A.shape[1],
+                dtype=A.dtype, format=A.format)
+    elif is_pydata_spmatrix(A):
+        import sparse
+        return sparse.eye(A.shape[0], A.shape[1], dtype=A.dtype)
+    else:
+        return np.eye(A.shape[0], A.shape[1], dtype=A.dtype)
+
+
+def expm_multiply(A, B, start=None, stop=None, num=None, endpoint=None):
+    """
+    Compute the action of the matrix exponential of A on B.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose exponential is of interest.
+    B : ndarray
+        The matrix or vector to be multiplied by the matrix exponential of A.
+    start : scalar, optional
+        The starting time point of the sequence.
+    stop : scalar, optional
+        The end time point of the sequence, unless `endpoint` is set to False.
+        In that case, the sequence consists of all but the last of ``num + 1``
+        evenly spaced time points, so that `stop` is excluded.
+        Note that the step size changes when `endpoint` is False.
+    num : int, optional
+        Number of time points to use.
+    endpoint : bool, optional
+        If True, `stop` is the last time point.  Otherwise, it is not included.
+
+    Returns
+    -------
+    expm_A_B : ndarray
+         The result of the action :math:`e^{t_k A} B`.
+
+    Notes
+    -----
+    The optional arguments defining the sequence of evenly spaced time points
+    are compatible with the arguments of `numpy.linspace`.
+
+    The output ndarray shape is somewhat complicated so I explain it here.
+    The ndim of the output could be either 1, 2, or 3.
+    It would be 1 if you are computing the expm action on a single vector
+    at a single time point.
+    It would be 2 if you are computing the expm action on a vector
+    at multiple time points, or if you are computing the expm action
+    on a matrix at a single time point.
+    It would be 3 if you want the action on a matrix with multiple
+    columns at multiple time points.
+    If multiple time points are requested, expm_A_B[0] will always
+    be the action of the expm at the first time point,
+    regardless of whether the action is on a vector or a matrix.
+
+    References
+    ----------
+    .. [1] Awad H. Al-Mohy and Nicholas J. Higham (2011)
+           "Computing the Action of the Matrix Exponential,
+           with an Application to Exponential Integrators."
+           SIAM Journal on Scientific Computing,
+           33 (2). pp. 488-511. ISSN 1064-8275
+           http://eprints.ma.man.ac.uk/1591/
+
+    .. [2] Nicholas J. Higham and Awad H. Al-Mohy (2010)
+           "Computing Matrix Functions."
+           Acta Numerica,
+           19. 159-208. ISSN 0962-4929
+           http://eprints.ma.man.ac.uk/1451/
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_matrix
+    >>> from scipy.sparse.linalg import expm, expm_multiply
+    >>> A = csc_matrix([[1, 0], [0, 1]])
+    >>> A.todense()
+    matrix([[1, 0],
+            [0, 1]], dtype=int64)
+    >>> B = np.array([np.exp(-1.), np.exp(-2.)])
+    >>> B
+    array([ 0.36787944,  0.13533528])
+    >>> expm_multiply(A, B, start=1, stop=2, num=3, endpoint=True)
+    array([[ 1.        ,  0.36787944],
+           [ 1.64872127,  0.60653066],
+           [ 2.71828183,  1.        ]])
+    >>> expm(A).dot(B)                  # Verify 1st timestep
+    array([ 1.        ,  0.36787944])
+    >>> expm(1.5*A).dot(B)              # Verify 2nd timestep
+    array([ 1.64872127,  0.60653066])
+    >>> expm(2*A).dot(B)                # Verify 3rd timestep
+    array([ 2.71828183,  1.        ])
+    """
+    if all(arg is None for arg in (start, stop, num, endpoint)):
+        X = _expm_multiply_simple(A, B)
+    else:
+        X, status = _expm_multiply_interval(A, B, start, stop, num, endpoint)
+    return X
+
+
+def _expm_multiply_simple(A, B, t=1.0, balance=False):
+    """
+    Compute the action of the matrix exponential at a single time point.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose exponential is of interest.
+    B : ndarray
+        The matrix to be multiplied by the matrix exponential of A.
+    t : float
+        A time point.
+    balance : bool
+        Indicates whether or not to apply balancing.
+
+    Returns
+    -------
+    F : ndarray
+        :math:`e^{t A} B`
+
+    Notes
+    -----
+    This is algorithm (3.2) in Al-Mohy and Higham (2011).
+
+    """
+    if balance:
+        raise NotImplementedError
+    if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+        raise ValueError('expected A to be like a square matrix')
+    if A.shape[1] != B.shape[0]:
+        raise ValueError('the matrices A and B have incompatible shapes')
+    ident = _ident_like(A)
+    n = A.shape[0]
+    if len(B.shape) == 1:
+        n0 = 1
+    elif len(B.shape) == 2:
+        n0 = B.shape[1]
+    else:
+        raise ValueError('expected B to be like a matrix or a vector')
+    u_d = 2**-53
+    tol = u_d
+    mu = _trace(A) / float(n)
+    A = A - mu * ident
+    A_1_norm = _exact_1_norm(A)
+    if t*A_1_norm == 0:
+        m_star, s = 0, 1
+    else:
+        ell = 2
+        norm_info = LazyOperatorNormInfo(t*A, A_1_norm=t*A_1_norm, ell=ell)
+        m_star, s = _fragment_3_1(norm_info, n0, tol, ell=ell)
+    return _expm_multiply_simple_core(A, B, t, mu, m_star, s, tol, balance)
+
+
+def _expm_multiply_simple_core(A, B, t, mu, m_star, s, tol=None, balance=False):
+    """
+    A helper function.
+    """
+    if balance:
+        raise NotImplementedError
+    if tol is None:
+        u_d = 2 ** -53
+        tol = u_d
+    F = B
+    eta = np.exp(t*mu / float(s))
+    for i in range(s):
+        c1 = _exact_inf_norm(B)
+        for j in range(m_star):
+            coeff = t / float(s*(j+1))
+            B = coeff * A.dot(B)
+            c2 = _exact_inf_norm(B)
+            F = F + B
+            if c1 + c2 <= tol * _exact_inf_norm(F):
+                break
+            c1 = c2
+        F = eta * F
+        B = F
+    return F
+
+
+# This table helps to compute bounds.
+# They seem to have been difficult to calculate, involving symbolic
+# manipulation of equations, followed by numerical root finding.
+_theta = {
+        # The first 30 values are from table A.3 of Computing Matrix Functions.
+        1: 2.29e-16,
+        2: 2.58e-8,
+        3: 1.39e-5,
+        4: 3.40e-4,
+        5: 2.40e-3,
+        6: 9.07e-3,
+        7: 2.38e-2,
+        8: 5.00e-2,
+        9: 8.96e-2,
+        10: 1.44e-1,
+        # 11
+        11: 2.14e-1,
+        12: 3.00e-1,
+        13: 4.00e-1,
+        14: 5.14e-1,
+        15: 6.41e-1,
+        16: 7.81e-1,
+        17: 9.31e-1,
+        18: 1.09,
+        19: 1.26,
+        20: 1.44,
+        # 21
+        21: 1.62,
+        22: 1.82,
+        23: 2.01,
+        24: 2.22,
+        25: 2.43,
+        26: 2.64,
+        27: 2.86,
+        28: 3.08,
+        29: 3.31,
+        30: 3.54,
+        # The rest are from table 3.1 of
+        # Computing the Action of the Matrix Exponential.
+        35: 4.7,
+        40: 6.0,
+        45: 7.2,
+        50: 8.5,
+        55: 9.9,
+        }
+
+
+def _onenormest_matrix_power(A, p,
+        t=2, itmax=5, compute_v=False, compute_w=False):
+    """
+    Efficiently estimate the 1-norm of A^p.
+
+    Parameters
+    ----------
+    A : ndarray
+        Matrix whose 1-norm of a power is to be computed.
+    p : int
+        Non-negative integer power.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+        Larger values take longer and use more memory
+        but give more accurate output.
+    itmax : int, optional
+        Use at most this many iterations.
+    compute_v : bool, optional
+        Request a norm-maximizing linear operator input vector if True.
+    compute_w : bool, optional
+        Request a norm-maximizing linear operator output vector if True.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse matrix.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+
+    """
+    #XXX Eventually turn this into an API function in the  _onenormest module,
+    #XXX and remove its underscore,
+    #XXX but wait until expm_multiply goes into scipy.
+    return scipy.sparse.linalg.onenormest(aslinearoperator(A) ** p)
+
+class LazyOperatorNormInfo:
+    """
+    Information about an operator is lazily computed.
+
+    The information includes the exact 1-norm of the operator,
+    in addition to estimates of 1-norms of powers of the operator.
+    This uses the notation of Computing the Action (2011).
+    This class is specialized enough to probably not be of general interest
+    outside of this module.
+
+    """
+    def __init__(self, A, A_1_norm=None, ell=2, scale=1):
+        """
+        Provide the operator and some norm-related information.
+
+        Parameters
+        ----------
+        A : linear operator
+            The operator of interest.
+        A_1_norm : float, optional
+            The exact 1-norm of A.
+        ell : int, optional
+            A technical parameter controlling norm estimation quality.
+        scale : int, optional
+            If specified, return the norms of scale*A instead of A.
+
+        """
+        self._A = A
+        self._A_1_norm = A_1_norm
+        self._ell = ell
+        self._d = {}
+        self._scale = scale
+
+    def set_scale(self,scale):
+        """
+        Set the scale parameter.
+        """
+        self._scale = scale
+
+    def onenorm(self):
+        """
+        Compute the exact 1-norm.
+        """
+        if self._A_1_norm is None:
+            self._A_1_norm = _exact_1_norm(self._A)
+        return self._scale*self._A_1_norm
+
+    def d(self, p):
+        """
+        Lazily estimate d_p(A) ~= || A^p ||^(1/p) where ||.|| is the 1-norm.
+        """
+        if p not in self._d:
+            est = _onenormest_matrix_power(self._A, p, self._ell)
+            self._d[p] = est ** (1.0 / p)
+        return self._scale*self._d[p]
+
+    def alpha(self, p):
+        """
+        Lazily compute max(d(p), d(p+1)).
+        """
+        return max(self.d(p), self.d(p+1))
+
+def _compute_cost_div_m(m, p, norm_info):
+    """
+    A helper function for computing bounds.
+
+    This is equation (3.10).
+    It measures cost in terms of the number of required matrix products.
+
+    Parameters
+    ----------
+    m : int
+        A valid key of _theta.
+    p : int
+        A matrix power.
+    norm_info : LazyOperatorNormInfo
+        Information about 1-norms of related operators.
+
+    Returns
+    -------
+    cost_div_m : int
+        Required number of matrix products divided by m.
+
+    """
+    return int(np.ceil(norm_info.alpha(p) / _theta[m]))
+
+
+def _compute_p_max(m_max):
+    """
+    Compute the largest positive integer p such that p*(p-1) <= m_max + 1.
+
+    Do this in a slightly dumb way, but safe and not too slow.
+
+    Parameters
+    ----------
+    m_max : int
+        A count related to bounds.
+
+    """
+    sqrt_m_max = np.sqrt(m_max)
+    p_low = int(np.floor(sqrt_m_max))
+    p_high = int(np.ceil(sqrt_m_max + 1))
+    return max(p for p in range(p_low, p_high+1) if p*(p-1) <= m_max + 1)
+
+
+def _fragment_3_1(norm_info, n0, tol, m_max=55, ell=2):
+    """
+    A helper function for the _expm_multiply_* functions.
+
+    Parameters
+    ----------
+    norm_info : LazyOperatorNormInfo
+        Information about norms of certain linear operators of interest.
+    n0 : int
+        Number of columns in the _expm_multiply_* B matrix.
+    tol : float
+        Expected to be
+        :math:`2^{-24}` for single precision or
+        :math:`2^{-53}` for double precision.
+    m_max : int
+        A value related to a bound.
+    ell : int
+        The number of columns used in the 1-norm approximation.
+        This is usually taken to be small, maybe between 1 and 5.
+
+    Returns
+    -------
+    best_m : int
+        Related to bounds for error control.
+    best_s : int
+        Amount of scaling.
+
+    Notes
+    -----
+    This is code fragment (3.1) in Al-Mohy and Higham (2011).
+    The discussion of default values for m_max and ell
+    is given between the definitions of equation (3.11)
+    and the definition of equation (3.12).
+
+    """
+    if ell < 1:
+        raise ValueError('expected ell to be a positive integer')
+    best_m = None
+    best_s = None
+    if _condition_3_13(norm_info.onenorm(), n0, m_max, ell):
+        for m, theta in _theta.items():
+            s = int(np.ceil(norm_info.onenorm() / theta))
+            if best_m is None or m * s < best_m * best_s:
+                best_m = m
+                best_s = s
+    else:
+        # Equation (3.11).
+        for p in range(2, _compute_p_max(m_max) + 1):
+            for m in range(p*(p-1)-1, m_max+1):
+                if m in _theta:
+                    s = _compute_cost_div_m(m, p, norm_info)
+                    if best_m is None or m * s < best_m * best_s:
+                        best_m = m
+                        best_s = s
+        best_s = max(best_s, 1)
+    return best_m, best_s
+
+
+def _condition_3_13(A_1_norm, n0, m_max, ell):
+    """
+    A helper function for the _expm_multiply_* functions.
+
+    Parameters
+    ----------
+    A_1_norm : float
+        The precomputed 1-norm of A.
+    n0 : int
+        Number of columns in the _expm_multiply_* B matrix.
+    m_max : int
+        A value related to a bound.
+    ell : int
+        The number of columns used in the 1-norm approximation.
+        This is usually taken to be small, maybe between 1 and 5.
+
+    Returns
+    -------
+    value : bool
+        Indicates whether or not the condition has been met.
+
+    Notes
+    -----
+    This is condition (3.13) in Al-Mohy and Higham (2011).
+
+    """
+
+    # This is the rhs of equation (3.12).
+    p_max = _compute_p_max(m_max)
+    a = 2 * ell * p_max * (p_max + 3)
+
+    # Evaluate the condition (3.13).
+    b = _theta[m_max] / float(n0 * m_max)
+    return A_1_norm <= a * b
+
+
+def _expm_multiply_interval(A, B, start=None, stop=None,
+        num=None, endpoint=None, balance=False, status_only=False):
+    """
+    Compute the action of the matrix exponential at multiple time points.
+
+    Parameters
+    ----------
+    A : transposable linear operator
+        The operator whose exponential is of interest.
+    B : ndarray
+        The matrix to be multiplied by the matrix exponential of A.
+    start : scalar, optional
+        The starting time point of the sequence.
+    stop : scalar, optional
+        The end time point of the sequence, unless `endpoint` is set to False.
+        In that case, the sequence consists of all but the last of ``num + 1``
+        evenly spaced time points, so that `stop` is excluded.
+        Note that the step size changes when `endpoint` is False.
+    num : int, optional
+        Number of time points to use.
+    endpoint : bool, optional
+        If True, `stop` is the last time point. Otherwise, it is not included.
+    balance : bool
+        Indicates whether or not to apply balancing.
+    status_only : bool
+        A flag that is set to True for some debugging and testing operations.
+
+    Returns
+    -------
+    F : ndarray
+        :math:`e^{t_k A} B`
+    status : int
+        An integer status for testing and debugging.
+
+    Notes
+    -----
+    This is algorithm (5.2) in Al-Mohy and Higham (2011).
+
+    There seems to be a typo, where line 15 of the algorithm should be
+    moved to line 6.5 (between lines 6 and 7).
+
+    """
+    if balance:
+        raise NotImplementedError
+    if len(A.shape) != 2 or A.shape[0] != A.shape[1]:
+        raise ValueError('expected A to be like a square matrix')
+    if A.shape[1] != B.shape[0]:
+        raise ValueError('the matrices A and B have incompatible shapes')
+    ident = _ident_like(A)
+    n = A.shape[0]
+    if len(B.shape) == 1:
+        n0 = 1
+    elif len(B.shape) == 2:
+        n0 = B.shape[1]
+    else:
+        raise ValueError('expected B to be like a matrix or a vector')
+    u_d = 2**-53
+    tol = u_d
+    mu = _trace(A) / float(n)
+
+    # Get the linspace samples, attempting to preserve the linspace defaults.
+    linspace_kwargs = {'retstep': True}
+    if num is not None:
+        linspace_kwargs['num'] = num
+    if endpoint is not None:
+        linspace_kwargs['endpoint'] = endpoint
+    samples, step = np.linspace(start, stop, **linspace_kwargs)
+
+    # Convert the linspace output to the notation used by the publication.
+    nsamples = len(samples)
+    if nsamples < 2:
+        raise ValueError('at least two time points are required')
+    q = nsamples - 1
+    h = step
+    t_0 = samples[0]
+    t_q = samples[q]
+
+    # Define the output ndarray.
+    # Use an ndim=3 shape, such that the last two indices
+    # are the ones that may be involved in level 3 BLAS operations.
+    X_shape = (nsamples,) + B.shape
+    X = np.empty(X_shape, dtype=np.result_type(A.dtype, B.dtype, float))
+    t = t_q - t_0
+    A = A - mu * ident
+    A_1_norm = _exact_1_norm(A)
+    ell = 2
+    norm_info = LazyOperatorNormInfo(t*A, A_1_norm=t*A_1_norm, ell=ell)
+    if t*A_1_norm == 0:
+        m_star, s = 0, 1
+    else:
+        m_star, s = _fragment_3_1(norm_info, n0, tol, ell=ell)
+
+    # Compute the expm action up to the initial time point.
+    X[0] = _expm_multiply_simple_core(A, B, t_0, mu, m_star, s)
+
+    # Compute the expm action at the rest of the time points.
+    if q <= s:
+        if status_only:
+            return 0
+        else:
+            return _expm_multiply_interval_core_0(A, X,
+                    h, mu, q, norm_info, tol, ell,n0)
+    elif not (q % s):
+        if status_only:
+            return 1
+        else:
+            return _expm_multiply_interval_core_1(A, X,
+                    h, mu, m_star, s, q, tol)
+    elif (q % s):
+        if status_only:
+            return 2
+        else:
+            return _expm_multiply_interval_core_2(A, X,
+                    h, mu, m_star, s, q, tol)
+    else:
+        raise Exception('internal error')
+
+
+def _expm_multiply_interval_core_0(A, X, h, mu, q, norm_info, tol, ell, n0):
+    """
+    A helper function, for the case q <= s.
+    """
+
+    # Compute the new values of m_star and s which should be applied
+    # over intervals of size t/q
+    if norm_info.onenorm() == 0:
+        m_star, s = 0, 1
+    else:
+        norm_info.set_scale(1./q)
+        m_star, s = _fragment_3_1(norm_info, n0, tol, ell=ell)
+        norm_info.set_scale(1)
+
+    for k in range(q):
+        X[k+1] = _expm_multiply_simple_core(A, X[k], h, mu, m_star, s)
+    return X, 0
+
+
+def _expm_multiply_interval_core_1(A, X, h, mu, m_star, s, q, tol):
+    """
+    A helper function, for the case q > s and q % s == 0.
+    """
+    d = q // s
+    input_shape = X.shape[1:]
+    K_shape = (m_star + 1, ) + input_shape
+    K = np.empty(K_shape, dtype=X.dtype)
+    for i in range(s):
+        Z = X[i*d]
+        K[0] = Z
+        high_p = 0
+        for k in range(1, d+1):
+            F = K[0]
+            c1 = _exact_inf_norm(F)
+            for p in range(1, m_star+1):
+                if p > high_p:
+                    K[p] = h * A.dot(K[p-1]) / float(p)
+                coeff = float(pow(k, p))
+                F = F + coeff * K[p]
+                inf_norm_K_p_1 = _exact_inf_norm(K[p])
+                c2 = coeff * inf_norm_K_p_1
+                if c1 + c2 <= tol * _exact_inf_norm(F):
+                    break
+                c1 = c2
+            X[k + i*d] = np.exp(k*h*mu) * F
+    return X, 1
+
+
+def _expm_multiply_interval_core_2(A, X, h, mu, m_star, s, q, tol):
+    """
+    A helper function, for the case q > s and q % s > 0.
+    """
+    d = q // s
+    j = q // d
+    r = q - d * j
+    input_shape = X.shape[1:]
+    K_shape = (m_star + 1, ) + input_shape
+    K = np.empty(K_shape, dtype=X.dtype)
+    for i in range(j + 1):
+        Z = X[i*d]
+        K[0] = Z
+        high_p = 0
+        if i < j:
+            effective_d = d
+        else:
+            effective_d = r
+        for k in range(1, effective_d+1):
+            F = K[0]
+            c1 = _exact_inf_norm(F)
+            for p in range(1, m_star+1):
+                if p == high_p + 1:
+                    K[p] = h * A.dot(K[p-1]) / float(p)
+                    high_p = p
+                coeff = float(pow(k, p))
+                F = F + coeff * K[p]
+                inf_norm_K_p_1 = _exact_inf_norm(K[p])
+                c2 = coeff * inf_norm_K_p_1
+                if c1 + c2 <= tol * _exact_inf_norm(F):
+                    break
+                c1 = c2
+            X[k + i*d] = np.exp(k*h*mu) * F
+    return X, 2

venv/Lib/site-packages/scipy/sparse/linalg/_norm.py

@@ -0,0 +1,182 @@
+"""Sparse matrix norms.
+
+"""
+import numpy as np
+from scipy.sparse import issparse
+
+from numpy import Inf, sqrt, abs
+
+__all__ = ['norm']
+
+
+def _sparse_frobenius_norm(x):
+    if np.issubdtype(x.dtype, np.complexfloating):
+        sqnorm = abs(x).power(2).sum()
+    else:
+        sqnorm = x.power(2).sum()
+    return sqrt(sqnorm)
+
+
+def norm(x, ord=None, axis=None):
+    """
+    Norm of a sparse matrix
+
+    This function is able to return one of seven different matrix norms,
+    depending on the value of the ``ord`` parameter.
+
+    Parameters
+    ----------
+    x : a sparse matrix
+        Input sparse matrix.
+    ord : {non-zero int, inf, -inf, 'fro'}, optional
+        Order of the norm (see table under ``Notes``). inf means numpy's
+        `inf` object.
+    axis : {int, 2-tuple of ints, None}, optional
+        If `axis` is an integer, it specifies the axis of `x` along which to
+        compute the vector norms.  If `axis` is a 2-tuple, it specifies the
+        axes that hold 2-D matrices, and the matrix norms of these matrices
+        are computed.  If `axis` is None then either a vector norm (when `x`
+        is 1-D) or a matrix norm (when `x` is 2-D) is returned.
+
+    Returns
+    -------
+    n : float or ndarray
+
+    Notes
+    -----
+    Some of the ord are not implemented because some associated functions like,
+    _multi_svd_norm, are not yet available for sparse matrix.
+
+    This docstring is modified based on numpy.linalg.norm.
+    https://github.com/numpy/numpy/blob/master/numpy/linalg/linalg.py
+
+    The following norms can be calculated:
+
+    =====  ============================
+    ord    norm for sparse matrices
+    =====  ============================
+    None   Frobenius norm
+    'fro'  Frobenius norm
+    inf    max(sum(abs(x), axis=1))
+    -inf   min(sum(abs(x), axis=1))
+    0      abs(x).sum(axis=axis)
+    1      max(sum(abs(x), axis=0))
+    -1     min(sum(abs(x), axis=0))
+    2      Not implemented
+    -2     Not implemented
+    other  Not implemented
+    =====  ============================
+
+    The Frobenius norm is given by [1]_:
+
+        :math:`||A||_F = [\\sum_{i,j} abs(a_{i,j})^2]^{1/2}`
+
+    References
+    ----------
+    .. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*,
+        Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15
+
+    Examples
+    --------
+    >>> from scipy.sparse import *
+    >>> import numpy as np
+    >>> from scipy.sparse.linalg import norm
+    >>> a = np.arange(9) - 4
+    >>> a
+    array([-4, -3, -2, -1, 0, 1, 2, 3, 4])
+    >>> b = a.reshape((3, 3))
+    >>> b
+    array([[-4, -3, -2],
+           [-1, 0, 1],
+           [ 2, 3, 4]])
+
+    >>> b = csr_matrix(b)
+    >>> norm(b)
+    7.745966692414834
+    >>> norm(b, 'fro')
+    7.745966692414834
+    >>> norm(b, np.inf)
+    9
+    >>> norm(b, -np.inf)
+    2
+    >>> norm(b, 1)
+    7
+    >>> norm(b, -1)
+    6
+
+    """
+    if not issparse(x):
+        raise TypeError("input is not sparse. use numpy.linalg.norm")
+
+    # Check the default case first and handle it immediately.
+    if axis is None and ord in (None, 'fro', 'f'):
+        return _sparse_frobenius_norm(x)
+
+    # Some norms require functions that are not implemented for all types.
+    x = x.tocsr()
+
+    if axis is None:
+        axis = (0, 1)
+    elif not isinstance(axis, tuple):
+        msg = "'axis' must be None, an integer or a tuple of integers"
+        try:
+            int_axis = int(axis)
+        except TypeError:
+            raise TypeError(msg)
+        if axis != int_axis:
+            raise TypeError(msg)
+        axis = (int_axis,)
+
+    nd = 2
+    if len(axis) == 2:
+        row_axis, col_axis = axis
+        if not (-nd <= row_axis < nd and -nd <= col_axis < nd):
+            raise ValueError('Invalid axis %r for an array with shape %r' %
+                             (axis, x.shape))
+        if row_axis % nd == col_axis % nd:
+            raise ValueError('Duplicate axes given.')
+        if ord == 2:
+            raise NotImplementedError
+            #return _multi_svd_norm(x, row_axis, col_axis, amax)
+        elif ord == -2:
+            raise NotImplementedError
+            #return _multi_svd_norm(x, row_axis, col_axis, amin)
+        elif ord == 1:
+            return abs(x).sum(axis=row_axis).max(axis=col_axis)[0,0]
+        elif ord == Inf:
+            return abs(x).sum(axis=col_axis).max(axis=row_axis)[0,0]
+        elif ord == -1:
+            return abs(x).sum(axis=row_axis).min(axis=col_axis)[0,0]
+        elif ord == -Inf:
+            return abs(x).sum(axis=col_axis).min(axis=row_axis)[0,0]
+        elif ord in (None, 'f', 'fro'):
+            # The axis order does not matter for this norm.
+            return _sparse_frobenius_norm(x)
+        else:
+            raise ValueError("Invalid norm order for matrices.")
+    elif len(axis) == 1:
+        a, = axis
+        if not (-nd <= a < nd):
+            raise ValueError('Invalid axis %r for an array with shape %r' %
+                             (axis, x.shape))
+        if ord == Inf:
+            M = abs(x).max(axis=a)
+        elif ord == -Inf:
+            M = abs(x).min(axis=a)
+        elif ord == 0:
+            # Zero norm
+            M = (x != 0).sum(axis=a)
+        elif ord == 1:
+            # special case for speedup
+            M = abs(x).sum(axis=a)
+        elif ord in (2, None):
+            M = sqrt(abs(x).power(2).sum(axis=a))
+        else:
+            try:
+                ord + 1
+            except TypeError:
+                raise ValueError('Invalid norm order for vectors.')
+            M = np.power(abs(x).power(ord).sum(axis=a), 1 / ord)
+        return M.A.ravel()
+    else:
+        raise ValueError("Improper number of dimensions to norm.")

venv/Lib/site-packages/scipy/sparse/linalg/_onenormest.py

@@ -0,0 +1,466 @@
+"""Sparse block 1-norm estimator.
+"""
+
+import numpy as np
+from scipy.sparse.linalg import aslinearoperator
+
+
+__all__ = ['onenormest']
+
+
+def onenormest(A, t=2, itmax=5, compute_v=False, compute_w=False):
+    """
+    Compute a lower bound of the 1-norm of a sparse matrix.
+
+    Parameters
+    ----------
+    A : ndarray or other linear operator
+        A linear operator that can be transposed and that can
+        produce matrix products.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+        Larger values take longer and use more memory
+        but give more accurate output.
+    itmax : int, optional
+        Use at most this many iterations.
+    compute_v : bool, optional
+        Request a norm-maximizing linear operator input vector if True.
+    compute_w : bool, optional
+        Request a norm-maximizing linear operator output vector if True.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse matrix.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+
+    Notes
+    -----
+    This is algorithm 2.4 of [1].
+
+    In [2] it is described as follows.
+    "This algorithm typically requires the evaluation of
+    about 4t matrix-vector products and almost invariably
+    produces a norm estimate (which is, in fact, a lower
+    bound on the norm) correct to within a factor 3."
+
+    .. versionadded:: 0.13.0
+
+    References
+    ----------
+    .. [1] Nicholas J. Higham and Francoise Tisseur (2000),
+           "A Block Algorithm for Matrix 1-Norm Estimation,
+           with an Application to 1-Norm Pseudospectra."
+           SIAM J. Matrix Anal. Appl. Vol. 21, No. 4, pp. 1185-1201.
+
+    .. [2] Awad H. Al-Mohy and Nicholas J. Higham (2009),
+           "A new scaling and squaring algorithm for the matrix exponential."
+           SIAM J. Matrix Anal. Appl. Vol. 31, No. 3, pp. 970-989.
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_matrix
+    >>> from scipy.sparse.linalg import onenormest
+    >>> A = csc_matrix([[1., 0., 0.], [5., 8., 2.], [0., -1., 0.]], dtype=float)
+    >>> A.todense()
+    matrix([[ 1.,  0.,  0.],
+            [ 5.,  8.,  2.],
+            [ 0., -1.,  0.]])
+    >>> onenormest(A)
+    9.0
+    >>> np.linalg.norm(A.todense(), ord=1)
+    9.0
+    """
+
+    # Check the input.
+    A = aslinearoperator(A)
+    if A.shape[0] != A.shape[1]:
+        raise ValueError('expected the operator to act like a square matrix')
+
+    # If the operator size is small compared to t,
+    # then it is easier to compute the exact norm.
+    # Otherwise estimate the norm.
+    n = A.shape[1]
+    if t >= n:
+        A_explicit = np.asarray(aslinearoperator(A).matmat(np.identity(n)))
+        if A_explicit.shape != (n, n):
+            raise Exception('internal error: ',
+                    'unexpected shape ' + str(A_explicit.shape))
+        col_abs_sums = abs(A_explicit).sum(axis=0)
+        if col_abs_sums.shape != (n, ):
+            raise Exception('internal error: ',
+                    'unexpected shape ' + str(col_abs_sums.shape))
+        argmax_j = np.argmax(col_abs_sums)
+        v = elementary_vector(n, argmax_j)
+        w = A_explicit[:, argmax_j]
+        est = col_abs_sums[argmax_j]
+    else:
+        est, v, w, nmults, nresamples = _onenormest_core(A, A.H, t, itmax)
+
+    # Report the norm estimate along with some certificates of the estimate.
+    if compute_v or compute_w:
+        result = (est,)
+        if compute_v:
+            result += (v,)
+        if compute_w:
+            result += (w,)
+        return result
+    else:
+        return est
+
+
+def _blocked_elementwise(func):
+    """
+    Decorator for an elementwise function, to apply it blockwise along
+    first dimension, to avoid excessive memory usage in temporaries.
+    """
+    block_size = 2**20
+
+    def wrapper(x):
+        if x.shape[0] < block_size:
+            return func(x)
+        else:
+            y0 = func(x[:block_size])
+            y = np.zeros((x.shape[0],) + y0.shape[1:], dtype=y0.dtype)
+            y[:block_size] = y0
+            del y0
+            for j in range(block_size, x.shape[0], block_size):
+                y[j:j+block_size] = func(x[j:j+block_size])
+            return y
+    return wrapper
+
+
+@_blocked_elementwise
+def sign_round_up(X):
+    """
+    This should do the right thing for both real and complex matrices.
+
+    From Higham and Tisseur:
+    "Everything in this section remains valid for complex matrices
+    provided that sign(A) is redefined as the matrix (aij / |aij|)
+    (and sign(0) = 1) transposes are replaced by conjugate transposes."
+
+    """
+    Y = X.copy()
+    Y[Y == 0] = 1
+    Y /= np.abs(Y)
+    return Y
+
+
+@_blocked_elementwise
+def _max_abs_axis1(X):
+    return np.max(np.abs(X), axis=1)
+
+
+def _sum_abs_axis0(X):
+    block_size = 2**20
+    r = None
+    for j in range(0, X.shape[0], block_size):
+        y = np.sum(np.abs(X[j:j+block_size]), axis=0)
+        if r is None:
+            r = y
+        else:
+            r += y
+    return r
+
+
+def elementary_vector(n, i):
+    v = np.zeros(n, dtype=float)
+    v[i] = 1
+    return v
+
+
+def vectors_are_parallel(v, w):
+    # Columns are considered parallel when they are equal or negative.
+    # Entries are required to be in {-1, 1},
+    # which guarantees that the magnitudes of the vectors are identical.
+    if v.ndim != 1 or v.shape != w.shape:
+        raise ValueError('expected conformant vectors with entries in {-1,1}')
+    n = v.shape[0]
+    return np.dot(v, w) == n
+
+
+def every_col_of_X_is_parallel_to_a_col_of_Y(X, Y):
+    for v in X.T:
+        if not any(vectors_are_parallel(v, w) for w in Y.T):
+            return False
+    return True
+
+
+def column_needs_resampling(i, X, Y=None):
+    # column i of X needs resampling if either
+    # it is parallel to a previous column of X or
+    # it is parallel to a column of Y
+    n, t = X.shape
+    v = X[:, i]
+    if any(vectors_are_parallel(v, X[:, j]) for j in range(i)):
+        return True
+    if Y is not None:
+        if any(vectors_are_parallel(v, w) for w in Y.T):
+            return True
+    return False
+
+
+def resample_column(i, X):
+    X[:, i] = np.random.randint(0, 2, size=X.shape[0])*2 - 1
+
+
+def less_than_or_close(a, b):
+    return np.allclose(a, b) or (a < b)
+
+
+def _algorithm_2_2(A, AT, t):
+    """
+    This is Algorithm 2.2.
+
+    Parameters
+    ----------
+    A : ndarray or other linear operator
+        A linear operator that can produce matrix products.
+    AT : ndarray or other linear operator
+        The transpose of A.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+
+    Returns
+    -------
+    g : sequence
+        A non-negative decreasing vector
+        such that g[j] is a lower bound for the 1-norm
+        of the column of A of jth largest 1-norm.
+        The first entry of this vector is therefore a lower bound
+        on the 1-norm of the linear operator A.
+        This sequence has length t.
+    ind : sequence
+        The ith entry of ind is the index of the column A whose 1-norm
+        is given by g[i].
+        This sequence of indices has length t, and its entries are
+        chosen from range(n), possibly with repetition,
+        where n is the order of the operator A.
+
+    Notes
+    -----
+    This algorithm is mainly for testing.
+    It uses the 'ind' array in a way that is similar to
+    its usage in algorithm 2.4. This algorithm 2.2 may be easier to test,
+    so it gives a chance of uncovering bugs related to indexing
+    which could have propagated less noticeably to algorithm 2.4.
+
+    """
+    A_linear_operator = aslinearoperator(A)
+    AT_linear_operator = aslinearoperator(AT)
+    n = A_linear_operator.shape[0]
+
+    # Initialize the X block with columns of unit 1-norm.
+    X = np.ones((n, t))
+    if t > 1:
+        X[:, 1:] = np.random.randint(0, 2, size=(n, t-1))*2 - 1
+    X /= float(n)
+
+    # Iteratively improve the lower bounds.
+    # Track extra things, to assert invariants for debugging.
+    g_prev = None
+    h_prev = None
+    k = 1
+    ind = range(t)
+    while True:
+        Y = np.asarray(A_linear_operator.matmat(X))
+        g = _sum_abs_axis0(Y)
+        best_j = np.argmax(g)
+        g.sort()
+        g = g[::-1]
+        S = sign_round_up(Y)
+        Z = np.asarray(AT_linear_operator.matmat(S))
+        h = _max_abs_axis1(Z)
+
+        # If this algorithm runs for fewer than two iterations,
+        # then its return values do not have the properties indicated
+        # in the description of the algorithm.
+        # In particular, the entries of g are not 1-norms of any
+        # column of A until the second iteration.
+        # Therefore we will require the algorithm to run for at least
+        # two iterations, even though this requirement is not stated
+        # in the description of the algorithm.
+        if k >= 2:
+            if less_than_or_close(max(h), np.dot(Z[:, best_j], X[:, best_j])):
+                break
+        ind = np.argsort(h)[::-1][:t]
+        h = h[ind]
+        for j in range(t):
+            X[:, j] = elementary_vector(n, ind[j])
+
+        # Check invariant (2.2).
+        if k >= 2:
+            if not less_than_or_close(g_prev[0], h_prev[0]):
+                raise Exception('invariant (2.2) is violated')
+            if not less_than_or_close(h_prev[0], g[0]):
+                raise Exception('invariant (2.2) is violated')
+
+        # Check invariant (2.3).
+        if k >= 3:
+            for j in range(t):
+                if not less_than_or_close(g[j], g_prev[j]):
+                    raise Exception('invariant (2.3) is violated')
+
+        # Update for the next iteration.
+        g_prev = g
+        h_prev = h
+        k += 1
+
+    # Return the lower bounds and the corresponding column indices.
+    return g, ind
+
+
+def _onenormest_core(A, AT, t, itmax):
+    """
+    Compute a lower bound of the 1-norm of a sparse matrix.
+
+    Parameters
+    ----------
+    A : ndarray or other linear operator
+        A linear operator that can produce matrix products.
+    AT : ndarray or other linear operator
+        The transpose of A.
+    t : int, optional
+        A positive parameter controlling the tradeoff between
+        accuracy versus time and memory usage.
+    itmax : int, optional
+        Use at most this many iterations.
+
+    Returns
+    -------
+    est : float
+        An underestimate of the 1-norm of the sparse matrix.
+    v : ndarray, optional
+        The vector such that ||Av||_1 == est*||v||_1.
+        It can be thought of as an input to the linear operator
+        that gives an output with particularly large norm.
+    w : ndarray, optional
+        The vector Av which has relatively large 1-norm.
+        It can be thought of as an output of the linear operator
+        that is relatively large in norm compared to the input.
+    nmults : int, optional
+        The number of matrix products that were computed.
+    nresamples : int, optional
+        The number of times a parallel column was observed,
+        necessitating a re-randomization of the column.
+
+    Notes
+    -----
+    This is algorithm 2.4.
+
+    """
+    # This function is a more or less direct translation
+    # of Algorithm 2.4 from the Higham and Tisseur (2000) paper.
+    A_linear_operator = aslinearoperator(A)
+    AT_linear_operator = aslinearoperator(AT)
+    if itmax < 2:
+        raise ValueError('at least two iterations are required')
+    if t < 1:
+        raise ValueError('at least one column is required')
+    n = A.shape[0]
+    if t >= n:
+        raise ValueError('t should be smaller than the order of A')
+    # Track the number of big*small matrix multiplications
+    # and the number of resamplings.
+    nmults = 0
+    nresamples = 0
+    # "We now explain our choice of starting matrix.  We take the first
+    # column of X to be the vector of 1s [...] This has the advantage that
+    # for a matrix with nonnegative elements the algorithm converges
+    # with an exact estimate on the second iteration, and such matrices
+    # arise in applications [...]"
+    X = np.ones((n, t), dtype=float)
+    # "The remaining columns are chosen as rand{-1,1},
+    # with a check for and correction of parallel columns,
+    # exactly as for S in the body of the algorithm."
+    if t > 1:
+        for i in range(1, t):
+            # These are technically initial samples, not resamples,
+            # so the resampling count is not incremented.
+            resample_column(i, X)
+        for i in range(t):
+            while column_needs_resampling(i, X):
+                resample_column(i, X)
+                nresamples += 1
+    # "Choose starting matrix X with columns of unit 1-norm."
+    X /= float(n)
+    # "indices of used unit vectors e_j"
+    ind_hist = np.zeros(0, dtype=np.intp)
+    est_old = 0
+    S = np.zeros((n, t), dtype=float)
+    k = 1
+    ind = None
+    while True:
+        Y = np.asarray(A_linear_operator.matmat(X))
+        nmults += 1
+        mags = _sum_abs_axis0(Y)
+        est = np.max(mags)
+        best_j = np.argmax(mags)
+        if est > est_old or k == 2:
+            if k >= 2:
+                ind_best = ind[best_j]
+            w = Y[:, best_j]
+        # (1)
+        if k >= 2 and est <= est_old:
+            est = est_old
+            break
+        est_old = est
+        S_old = S
+        if k > itmax:
+            break
+        S = sign_round_up(Y)
+        del Y
+        # (2)
+        if every_col_of_X_is_parallel_to_a_col_of_Y(S, S_old):
+            break
+        if t > 1:
+            # "Ensure that no column of S is parallel to another column of S
+            # or to a column of S_old by replacing columns of S by rand{-1,1}."
+            for i in range(t):
+                while column_needs_resampling(i, S, S_old):
+                    resample_column(i, S)
+                    nresamples += 1
+        del S_old
+        # (3)
+        Z = np.asarray(AT_linear_operator.matmat(S))
+        nmults += 1
+        h = _max_abs_axis1(Z)
+        del Z
+        # (4)
+        if k >= 2 and max(h) == h[ind_best]:
+            break
+        # "Sort h so that h_first >= ... >= h_last
+        # and re-order ind correspondingly."
+        #
+        # Later on, we will need at most t+len(ind_hist) largest
+        # entries, so drop the rest
+        ind = np.argsort(h)[::-1][:t+len(ind_hist)].copy()
+        del h
+        if t > 1:
+            # (5)
+            # Break if the most promising t vectors have been visited already.
+            if np.in1d(ind[:t], ind_hist).all():
+                break
+            # Put the most promising unvisited vectors at the front of the list
+            # and put the visited vectors at the end of the list.
+            # Preserve the order of the indices induced by the ordering of h.
+            seen = np.in1d(ind, ind_hist)
+            ind = np.concatenate((ind[~seen], ind[seen]))
+        for j in range(t):
+            X[:, j] = elementary_vector(n, ind[j])
+
+        new_ind = ind[:t][~np.in1d(ind[:t], ind_hist)]
+        ind_hist = np.concatenate((ind_hist, new_ind))
+        k += 1
+    v = elementary_vector(n, ind_best)
+    return est, v, w, nmults, nresamples

venv/Lib/site-packages/scipy/sparse/linalg/dsolve/SuperLU/License.txt

@@ -0,0 +1,29 @@
+Copyright (c) 2003, The Regents of the University of California, through
+Lawrence Berkeley National Laboratory (subject to receipt of any required 
+approvals from U.S. Dept. of Energy) 
+
+All rights reserved. 
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met: 
+
+(1) Redistributions of source code must retain the above copyright notice,
+this list of conditions and the following disclaimer. 
+(2) Redistributions in binary form must reproduce the above copyright notice,
+this list of conditions and the following disclaimer in the documentation
+and/or other materials provided with the distribution. 
+(3) Neither the name of Lawrence Berkeley National Laboratory, U.S. Dept. of
+Energy nor the names of its contributors may be used to endorse or promote
+products derived from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 

venv/Lib/site-packages/scipy/sparse/linalg/dsolve/__init__.py

@@ -0,0 +1,66 @@
+"""
+Linear Solvers
+==============
+
+The default solver is SuperLU (included in the scipy distribution),
+which can solve real or complex linear systems in both single and
+double precisions.  It is automatically replaced by UMFPACK, if
+available.  Note that UMFPACK works in double precision only, so
+switch it off by::
+
+    >>> use_solver(useUmfpack=False)
+
+to solve in the single precision. See also use_solver documentation.
+
+Example session::
+
+    >>> from scipy.sparse import csc_matrix, spdiags
+    >>> from numpy import array
+    >>> from scipy.sparse.linalg import spsolve, use_solver
+    >>>
+    >>> print("Inverting a sparse linear system:")
+    >>> print("The sparse matrix (constructed from diagonals):")
+    >>> a = spdiags([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1], 5, 5)
+    >>> b = array([1, 2, 3, 4, 5])
+    >>> print("Solve: single precision complex:")
+    >>> use_solver( useUmfpack = False )
+    >>> a = a.astype('F')
+    >>> x = spsolve(a, b)
+    >>> print(x)
+    >>> print("Error: ", a*x-b)
+    >>>
+    >>> print("Solve: double precision complex:")
+    >>> use_solver( useUmfpack = True )
+    >>> a = a.astype('D')
+    >>> x = spsolve(a, b)
+    >>> print(x)
+    >>> print("Error: ", a*x-b)
+    >>>
+    >>> print("Solve: double precision:")
+    >>> a = a.astype('d')
+    >>> x = spsolve(a, b)
+    >>> print(x)
+    >>> print("Error: ", a*x-b)
+    >>>
+    >>> print("Solve: single precision:")
+    >>> use_solver( useUmfpack = False )
+    >>> a = a.astype('f')
+    >>> x = spsolve(a, b.astype('f'))
+    >>> print(x)
+    >>> print("Error: ", a*x-b)
+
+"""
+
+#import umfpack
+#__doc__ = '\n\n'.join( (__doc__,  umfpack.__doc__) )
+#del umfpack
+
+from .linsolve import *
+from ._superlu import SuperLU
+from . import _add_newdocs
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

venv/Lib/site-packages/scipy/sparse/linalg/dsolve/_add_newdocs.py

@@ -0,0 +1,152 @@
+from numpy.lib import add_newdoc
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU',
+    """
+    LU factorization of a sparse matrix.
+
+    Factorization is represented as::
+
+        Pr * A * Pc = L * U
+
+    To construct these `SuperLU` objects, call the `splu` and `spilu`
+    functions.
+
+    Attributes
+    ----------
+    shape
+    nnz
+    perm_c
+    perm_r
+    L
+    U
+
+    Methods
+    -------
+    solve
+
+    Notes
+    -----
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    The LU decomposition can be used to solve matrix equations. Consider:
+
+    >>> import numpy as np
+    >>> from scipy.sparse import csc_matrix, linalg as sla
+    >>> A = csc_matrix([[1,2,0,4],[1,0,0,1],[1,0,2,1],[2,2,1,0.]])
+
+    This can be solved for a given right-hand side:
+
+    >>> lu = sla.splu(A)
+    >>> b = np.array([1, 2, 3, 4])
+    >>> x = lu.solve(b)
+    >>> A.dot(x)
+    array([ 1.,  2.,  3.,  4.])
+
+    The ``lu`` object also contains an explicit representation of the
+    decomposition. The permutations are represented as mappings of
+    indices:
+
+    >>> lu.perm_r
+    array([0, 2, 1, 3], dtype=int32)
+    >>> lu.perm_c
+    array([2, 0, 1, 3], dtype=int32)
+
+    The L and U factors are sparse matrices in CSC format:
+
+    >>> lu.L.A
+    array([[ 1. ,  0. ,  0. ,  0. ],
+           [ 0. ,  1. ,  0. ,  0. ],
+           [ 0. ,  0. ,  1. ,  0. ],
+           [ 1. ,  0.5,  0.5,  1. ]])
+    >>> lu.U.A
+    array([[ 2.,  0.,  1.,  4.],
+           [ 0.,  2.,  1.,  1.],
+           [ 0.,  0.,  1.,  1.],
+           [ 0.,  0.,  0., -5.]])
+
+    The permutation matrices can be constructed:
+
+    >>> Pr = csc_matrix((np.ones(4), (lu.perm_r, np.arange(4))))
+    >>> Pc = csc_matrix((np.ones(4), (np.arange(4), lu.perm_c)))
+
+    We can reassemble the original matrix:
+
+    >>> (Pr.T * (lu.L * lu.U) * Pc.T).A
+    array([[ 1.,  2.,  0.,  4.],
+           [ 1.,  0.,  0.,  1.],
+           [ 1.,  0.,  2.,  1.],
+           [ 2.,  2.,  1.,  0.]])
+    """)
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('solve',
+    """
+    solve(rhs[, trans])
+
+    Solves linear system of equations with one or several right-hand sides.
+
+    Parameters
+    ----------
+    rhs : ndarray, shape (n,) or (n, k)
+        Right hand side(s) of equation
+    trans : {'N', 'T', 'H'}, optional
+        Type of system to solve::
+
+            'N':   A   * x == rhs  (default)
+            'T':   A^T * x == rhs
+            'H':   A^H * x == rhs
+
+        i.e., normal, transposed, and hermitian conjugate.
+
+    Returns
+    -------
+    x : ndarray, shape ``rhs.shape``
+        Solution vector(s)
+    """))
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('L',
+    """
+    Lower triangular factor with unit diagonal as a
+    `scipy.sparse.csc_matrix`.
+
+    .. versionadded:: 0.14.0
+    """))
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('U',
+    """
+    Upper triangular factor as a `scipy.sparse.csc_matrix`.
+
+    .. versionadded:: 0.14.0
+    """))
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('shape',
+    """
+    Shape of the original matrix as a tuple of ints.
+    """))
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('nnz',
+    """
+    Number of nonzero elements in the matrix.
+    """))
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('perm_c',
+    """
+    Permutation Pc represented as an array of indices.
+
+    The column permutation matrix can be reconstructed via:
+
+    >>> Pc = np.zeros((n, n))
+    >>> Pc[np.arange(n), perm_c] = 1
+    """))
+
+add_newdoc('scipy.sparse.linalg.dsolve._superlu', 'SuperLU', ('perm_r',
+    """
+    Permutation Pr represented as an array of indices.
+
+    The row permutation matrix can be reconstructed via:
+
+    >>> Pr = np.zeros((n, n))
+    >>> Pr[perm_r, np.arange(n)] = 1
+    """))

venv/Lib/site-packages/scipy/sparse/linalg/dsolve/linsolve.py

@@ -0,0 +1,626 @@
+from warnings import warn
+
+import numpy as np
+from numpy import asarray
+from scipy.sparse import (isspmatrix_csc, isspmatrix_csr, isspmatrix,
+                          SparseEfficiencyWarning, csc_matrix, csr_matrix)
+from scipy.sparse.sputils import is_pydata_spmatrix
+from scipy.linalg import LinAlgError
+import copy
+
+from . import _superlu
+
+noScikit = False
+try:
+    import scikits.umfpack as umfpack
+except ImportError:
+    noScikit = True
+
+useUmfpack = not noScikit
+
+__all__ = ['use_solver', 'spsolve', 'splu', 'spilu', 'factorized',
+           'MatrixRankWarning', 'spsolve_triangular']
+
+
+class MatrixRankWarning(UserWarning):
+    pass
+
+
+def use_solver(**kwargs):
+    """
+    Select default sparse direct solver to be used.
+
+    Parameters
+    ----------
+    useUmfpack : bool, optional
+        Use UMFPACK over SuperLU. Has effect only if scikits.umfpack is
+        installed. Default: True
+    assumeSortedIndices : bool, optional
+        Allow UMFPACK to skip the step of sorting indices for a CSR/CSC matrix.
+        Has effect only if useUmfpack is True and scikits.umfpack is installed.
+        Default: False
+
+    Notes
+    -----
+    The default sparse solver is umfpack when available
+    (scikits.umfpack is installed). This can be changed by passing
+    useUmfpack = False, which then causes the always present SuperLU
+    based solver to be used.
+
+    Umfpack requires a CSR/CSC matrix to have sorted column/row indices. If
+    sure that the matrix fulfills this, pass ``assumeSortedIndices=True``
+    to gain some speed.
+
+    """
+    if 'useUmfpack' in kwargs:
+        globals()['useUmfpack'] = kwargs['useUmfpack']
+    if useUmfpack and 'assumeSortedIndices' in kwargs:
+        umfpack.configure(assumeSortedIndices=kwargs['assumeSortedIndices'])
+
+def _get_umf_family(A):
+    """Get umfpack family string given the sparse matrix dtype."""
+    _families = {
+        (np.float64, np.int32): 'di',
+        (np.complex128, np.int32): 'zi',
+        (np.float64, np.int64): 'dl',
+        (np.complex128, np.int64): 'zl'
+    }
+
+    f_type = np.sctypeDict[A.dtype.name]
+    i_type = np.sctypeDict[A.indices.dtype.name]
+
+    try:
+        family = _families[(f_type, i_type)]
+
+    except KeyError:
+        msg = 'only float64 or complex128 matrices with int32 or int64' \
+            ' indices are supported! (got: matrix: %s, indices: %s)' \
+            % (f_type, i_type)
+        raise ValueError(msg)
+
+    # See gh-8278. Considered converting only if
+    # A.shape[0]*A.shape[1] > np.iinfo(np.int32).max,
+    # but that didn't always fix the issue.
+    family = family[0] + "l"
+    A_new = copy.copy(A)
+    A_new.indptr = np.array(A.indptr, copy=False, dtype=np.int64)
+    A_new.indices = np.array(A.indices, copy=False, dtype=np.int64)
+
+    return family, A_new
+
+def spsolve(A, b, permc_spec=None, use_umfpack=True):
+    """Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
+
+    Parameters
+    ----------
+    A : ndarray or sparse matrix
+        The square matrix A will be converted into CSC or CSR form
+    b : ndarray or sparse matrix
+        The matrix or vector representing the right hand side of the equation.
+        If a vector, b.shape must be (n,) or (n, 1).
+    permc_spec : str, optional
+        How to permute the columns of the matrix for sparsity preservation.
+        (default: 'COLAMD')
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering
+    use_umfpack : bool, optional
+        if True (default) then use umfpack for the solution.  This is
+        only referenced if b is a vector and ``scikit-umfpack`` is installed.
+
+    Returns
+    -------
+    x : ndarray or sparse matrix
+        the solution of the sparse linear equation.
+        If b is a vector, then x is a vector of size A.shape[1]
+        If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1])
+
+    Notes
+    -----
+    For solving the matrix expression AX = B, this solver assumes the resulting
+    matrix X is sparse, as is often the case for very sparse inputs.  If the
+    resulting X is dense, the construction of this sparse result will be
+    relatively expensive.  In that case, consider converting A to a dense
+    matrix and using scipy.linalg.solve or its variants.
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_matrix
+    >>> from scipy.sparse.linalg import spsolve
+    >>> A = csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
+    >>> B = csc_matrix([[2, 0], [-1, 0], [2, 0]], dtype=float)
+    >>> x = spsolve(A, B)
+    >>> np.allclose(A.dot(x).todense(), B.todense())
+    True
+    """
+
+    if is_pydata_spmatrix(A):
+        A = A.to_scipy_sparse().tocsc()
+
+    if not (isspmatrix_csc(A) or isspmatrix_csr(A)):
+        A = csc_matrix(A)
+        warn('spsolve requires A be CSC or CSR matrix format',
+                SparseEfficiencyWarning)
+
+    # b is a vector only if b have shape (n,) or (n, 1)
+    b_is_sparse = isspmatrix(b) or is_pydata_spmatrix(b)
+    if not b_is_sparse:
+        b = asarray(b)
+    b_is_vector = ((b.ndim == 1) or (b.ndim == 2 and b.shape[1] == 1))
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+    A = A.asfptype()  # upcast to a floating point format
+    result_dtype = np.promote_types(A.dtype, b.dtype)
+    if A.dtype != result_dtype:
+        A = A.astype(result_dtype)
+    if b.dtype != result_dtype:
+        b = b.astype(result_dtype)
+
+    # validate input shapes
+    M, N = A.shape
+    if (M != N):
+        raise ValueError("matrix must be square (has shape %s)" % ((M, N),))
+
+    if M != b.shape[0]:
+        raise ValueError("matrix - rhs dimension mismatch (%s - %s)"
+                         % (A.shape, b.shape[0]))
+
+    use_umfpack = use_umfpack and useUmfpack
+
+    if b_is_vector and use_umfpack:
+        if b_is_sparse:
+            b_vec = b.toarray()
+        else:
+            b_vec = b
+        b_vec = asarray(b_vec, dtype=A.dtype).ravel()
+
+        if noScikit:
+            raise RuntimeError('Scikits.umfpack not installed.')
+
+        if A.dtype.char not in 'dD':
+            raise ValueError("convert matrix data to double, please, using"
+                  " .astype(), or set linsolve.useUmfpack = False")
+
+        umf_family, A = _get_umf_family(A)
+        umf = umfpack.UmfpackContext(umf_family)
+        x = umf.linsolve(umfpack.UMFPACK_A, A, b_vec,
+                         autoTranspose=True)
+    else:
+        if b_is_vector and b_is_sparse:
+            b = b.toarray()
+            b_is_sparse = False
+
+        if not b_is_sparse:
+            if isspmatrix_csc(A):
+                flag = 1  # CSC format
+            else:
+                flag = 0  # CSR format
+
+            options = dict(ColPerm=permc_spec)
+            x, info = _superlu.gssv(N, A.nnz, A.data, A.indices, A.indptr,
+                                    b, flag, options=options)
+            if info != 0:
+                warn("Matrix is exactly singular", MatrixRankWarning)
+                x.fill(np.nan)
+            if b_is_vector:
+                x = x.ravel()
+        else:
+            # b is sparse
+            Afactsolve = factorized(A)
+
+            if not (isspmatrix_csc(b) or is_pydata_spmatrix(b)):
+                warn('spsolve is more efficient when sparse b '
+                     'is in the CSC matrix format', SparseEfficiencyWarning)
+                b = csc_matrix(b)
+
+            # Create a sparse output matrix by repeatedly applying
+            # the sparse factorization to solve columns of b.
+            data_segs = []
+            row_segs = []
+            col_segs = []
+            for j in range(b.shape[1]):
+                bj = np.asarray(b[:, j].todense()).ravel()
+                xj = Afactsolve(bj)
+                w = np.flatnonzero(xj)
+                segment_length = w.shape[0]
+                row_segs.append(w)
+                col_segs.append(np.full(segment_length, j, dtype=int))
+                data_segs.append(np.asarray(xj[w], dtype=A.dtype))
+            sparse_data = np.concatenate(data_segs)
+            sparse_row = np.concatenate(row_segs)
+            sparse_col = np.concatenate(col_segs)
+            x = A.__class__((sparse_data, (sparse_row, sparse_col)),
+                           shape=b.shape, dtype=A.dtype)
+
+            if is_pydata_spmatrix(b):
+                x = b.__class__(x)
+
+    return x
+
+
+def splu(A, permc_spec=None, diag_pivot_thresh=None,
+         relax=None, panel_size=None, options=dict()):
+    """
+    Compute the LU decomposition of a sparse, square matrix.
+
+    Parameters
+    ----------
+    A : sparse matrix
+        Sparse matrix to factorize. Should be in CSR or CSC format.
+    permc_spec : str, optional
+        How to permute the columns of the matrix for sparsity preservation.
+        (default: 'COLAMD')
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering
+
+    diag_pivot_thresh : float, optional
+        Threshold used for a diagonal entry to be an acceptable pivot.
+        See SuperLU user's guide for details [1]_
+    relax : int, optional
+        Expert option for customizing the degree of relaxing supernodes.
+        See SuperLU user's guide for details [1]_
+    panel_size : int, optional
+        Expert option for customizing the panel size.
+        See SuperLU user's guide for details [1]_
+    options : dict, optional
+        Dictionary containing additional expert options to SuperLU.
+        See SuperLU user guide [1]_ (section 2.4 on the 'Options' argument)
+        for more details. For example, you can specify
+        ``options=dict(Equil=False, IterRefine='SINGLE'))``
+        to turn equilibration off and perform a single iterative refinement.
+
+    Returns
+    -------
+    invA : scipy.sparse.linalg.SuperLU
+        Object, which has a ``solve`` method.
+
+    See also
+    --------
+    spilu : incomplete LU decomposition
+
+    Notes
+    -----
+    This function uses the SuperLU library.
+
+    References
+    ----------
+    .. [1] SuperLU http://crd.lbl.gov/~xiaoye/SuperLU/
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_matrix
+    >>> from scipy.sparse.linalg import splu
+    >>> A = csc_matrix([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float)
+    >>> B = splu(A)
+    >>> x = np.array([1., 2., 3.], dtype=float)
+    >>> B.solve(x)
+    array([ 1. , -3. , -1.5])
+    >>> A.dot(B.solve(x))
+    array([ 1.,  2.,  3.])
+    >>> B.solve(A.dot(x))
+    array([ 1.,  2.,  3.])
+    """
+
+    if is_pydata_spmatrix(A):
+        csc_construct_func = lambda *a, cls=type(A): cls(csc_matrix(*a))
+        A = A.to_scipy_sparse().tocsc()
+    else:
+        csc_construct_func = csc_matrix
+
+    if not isspmatrix_csc(A):
+        A = csc_matrix(A)
+        warn('splu requires CSC matrix format', SparseEfficiencyWarning)
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+    A = A.asfptype()  # upcast to a floating point format
+
+    M, N = A.shape
+    if (M != N):
+        raise ValueError("can only factor square matrices")  # is this true?
+
+    _options = dict(DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
+                    PanelSize=panel_size, Relax=relax)
+    if options is not None:
+        _options.update(options)
+
+    # Ensure that no column permutations are applied
+    if (_options["ColPerm"] == "NATURAL"):
+        _options["SymmetricMode"] = True
+
+    return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
+                          csc_construct_func=csc_construct_func,
+                          ilu=False, options=_options)
+
+
+def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None, permc_spec=None,
+          diag_pivot_thresh=None, relax=None, panel_size=None, options=None):
+    """
+    Compute an incomplete LU decomposition for a sparse, square matrix.
+
+    The resulting object is an approximation to the inverse of `A`.
+
+    Parameters
+    ----------
+    A : (N, N) array_like
+        Sparse matrix to factorize
+    drop_tol : float, optional
+        Drop tolerance (0 <= tol <= 1) for an incomplete LU decomposition.
+        (default: 1e-4)
+    fill_factor : float, optional
+        Specifies the fill ratio upper bound (>= 1.0) for ILU. (default: 10)
+    drop_rule : str, optional
+        Comma-separated string of drop rules to use.
+        Available rules: ``basic``, ``prows``, ``column``, ``area``,
+        ``secondary``, ``dynamic``, ``interp``. (Default: ``basic,area``)
+
+        See SuperLU documentation for details.
+
+    Remaining other options
+        Same as for `splu`
+
+    Returns
+    -------
+    invA_approx : scipy.sparse.linalg.SuperLU
+        Object, which has a ``solve`` method.
+
+    See also
+    --------
+    splu : complete LU decomposition
+
+    Notes
+    -----
+    To improve the better approximation to the inverse, you may need to
+    increase `fill_factor` AND decrease `drop_tol`.
+
+    This function uses the SuperLU library.
+
+    Examples
+    --------
+    >>> from scipy.sparse import csc_matrix
+    >>> from scipy.sparse.linalg import spilu
+    >>> A = csc_matrix([[1., 0., 0.], [5., 0., 2.], [0., -1., 0.]], dtype=float)
+    >>> B = spilu(A)
+    >>> x = np.array([1., 2., 3.], dtype=float)
+    >>> B.solve(x)
+    array([ 1. , -3. , -1.5])
+    >>> A.dot(B.solve(x))
+    array([ 1.,  2.,  3.])
+    >>> B.solve(A.dot(x))
+    array([ 1.,  2.,  3.])
+    """
+
+    if is_pydata_spmatrix(A):
+        csc_construct_func = lambda *a, cls=type(A): cls(csc_matrix(*a))
+        A = A.to_scipy_sparse().tocsc()
+    else:
+        csc_construct_func = csc_matrix
+
+    if not isspmatrix_csc(A):
+        A = csc_matrix(A)
+        warn('splu requires CSC matrix format', SparseEfficiencyWarning)
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+    A = A.asfptype()  # upcast to a floating point format
+
+    M, N = A.shape
+    if (M != N):
+        raise ValueError("can only factor square matrices")  # is this true?
+
+    _options = dict(ILU_DropRule=drop_rule, ILU_DropTol=drop_tol,
+                    ILU_FillFactor=fill_factor,
+                    DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
+                    PanelSize=panel_size, Relax=relax)
+    if options is not None:
+        _options.update(options)
+
+    # Ensure that no column permutations are applied
+    if (_options["ColPerm"] == "NATURAL"):
+        _options["SymmetricMode"] = True
+
+    return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
+                          csc_construct_func=csc_construct_func,
+                          ilu=True, options=_options)
+
+
+def factorized(A):
+    """
+    Return a function for solving a sparse linear system, with A pre-factorized.
+
+    Parameters
+    ----------
+    A : (N, N) array_like
+        Input.
+
+    Returns
+    -------
+    solve : callable
+        To solve the linear system of equations given in `A`, the `solve`
+        callable should be passed an ndarray of shape (N,).
+
+    Examples
+    --------
+    >>> from scipy.sparse.linalg import factorized
+    >>> A = np.array([[ 3. ,  2. , -1. ],
+    ...               [ 2. , -2. ,  4. ],
+    ...               [-1. ,  0.5, -1. ]])
+    >>> solve = factorized(A) # Makes LU decomposition.
+    >>> rhs1 = np.array([1, -2, 0])
+    >>> solve(rhs1) # Uses the LU factors.
+    array([ 1., -2., -2.])
+
+    """
+    if is_pydata_spmatrix(A):
+        A = A.to_scipy_sparse().tocsc()
+
+    if useUmfpack:
+        if noScikit:
+            raise RuntimeError('Scikits.umfpack not installed.')
+
+        if not isspmatrix_csc(A):
+            A = csc_matrix(A)
+            warn('splu requires CSC matrix format', SparseEfficiencyWarning)
+
+        A = A.asfptype()  # upcast to a floating point format
+
+        if A.dtype.char not in 'dD':
+            raise ValueError("convert matrix data to double, please, using"
+                  " .astype(), or set linsolve.useUmfpack = False")
+
+        umf_family, A = _get_umf_family(A)
+        umf = umfpack.UmfpackContext(umf_family)
+
+        # Make LU decomposition.
+        umf.numeric(A)
+
+        def solve(b):
+            return umf.solve(umfpack.UMFPACK_A, A, b, autoTranspose=True)
+
+        return solve
+    else:
+        return splu(A).solve
+
+
+def spsolve_triangular(A, b, lower=True, overwrite_A=False, overwrite_b=False,
+                       unit_diagonal=False):
+    """
+    Solve the equation `A x = b` for `x`, assuming A is a triangular matrix.
+
+    Parameters
+    ----------
+    A : (M, M) sparse matrix
+        A sparse square triangular matrix. Should be in CSR format.
+    b : (M,) or (M, N) array_like
+        Right-hand side matrix in `A x = b`
+    lower : bool, optional
+        Whether `A` is a lower or upper triangular matrix.
+        Default is lower triangular matrix.
+    overwrite_A : bool, optional
+        Allow changing `A`. The indices of `A` are going to be sorted and zero
+        entries are going to be removed.
+        Enabling gives a performance gain. Default is False.
+    overwrite_b : bool, optional
+        Allow overwriting data in `b`.
+        Enabling gives a performance gain. Default is False.
+        If `overwrite_b` is True, it should be ensured that
+        `b` has an appropriate dtype to be able to store the result.
+    unit_diagonal : bool, optional
+        If True, diagonal elements of `a` are assumed to be 1 and will not be
+        referenced.
+
+        .. versionadded:: 1.4.0
+
+    Returns
+    -------
+    x : (M,) or (M, N) ndarray
+        Solution to the system `A x = b`. Shape of return matches shape of `b`.
+
+    Raises
+    ------
+    LinAlgError
+        If `A` is singular or not triangular.
+    ValueError
+        If shape of `A` or shape of `b` do not match the requirements.
+
+    Notes
+    -----
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+    >>> from scipy.sparse import csr_matrix
+    >>> from scipy.sparse.linalg import spsolve_triangular
+    >>> A = csr_matrix([[3, 0, 0], [1, -1, 0], [2, 0, 1]], dtype=float)
+    >>> B = np.array([[2, 0], [-1, 0], [2, 0]], dtype=float)
+    >>> x = spsolve_triangular(A, B)
+    >>> np.allclose(A.dot(x), B)
+    True
+    """
+
+    if is_pydata_spmatrix(A):
+        A = A.to_scipy_sparse().tocsr()
+
+    # Check the input for correct type and format.
+    if not isspmatrix_csr(A):
+        warn('CSR matrix format is required. Converting to CSR matrix.',
+             SparseEfficiencyWarning)
+        A = csr_matrix(A)
+    elif not overwrite_A:
+        A = A.copy()
+
+    if A.shape[0] != A.shape[1]:
+        raise ValueError(
+            'A must be a square matrix but its shape is {}.'.format(A.shape))
+
+    # sum duplicates for non-canonical format
+    A.sum_duplicates()
+
+    b = np.asanyarray(b)
+
+    if b.ndim not in [1, 2]:
+        raise ValueError(
+            'b must have 1 or 2 dims but its shape is {}.'.format(b.shape))
+    if A.shape[0] != b.shape[0]:
+        raise ValueError(
+            'The size of the dimensions of A must be equal to '
+            'the size of the first dimension of b but the shape of A is '
+            '{} and the shape of b is {}.'.format(A.shape, b.shape))
+
+    # Init x as (a copy of) b.
+    x_dtype = np.result_type(A.data, b, np.float64)
+    if overwrite_b:
+        if np.can_cast(b.dtype, x_dtype, casting='same_kind'):
+            x = b
+        else:
+            raise ValueError(
+                'Cannot overwrite b (dtype {}) with result '
+                'of type {}.'.format(b.dtype, x_dtype))
+    else:
+        x = b.astype(x_dtype, copy=True)
+
+    # Choose forward or backward order.
+    if lower:
+        row_indices = range(len(b))
+    else:
+        row_indices = range(len(b) - 1, -1, -1)
+
+    # Fill x iteratively.
+    for i in row_indices:
+
+        # Get indices for i-th row.
+        indptr_start = A.indptr[i]
+        indptr_stop = A.indptr[i + 1]
+        if lower:
+            A_diagonal_index_row_i = indptr_stop - 1
+            A_off_diagonal_indices_row_i = slice(indptr_start, indptr_stop - 1)
+        else:
+            A_diagonal_index_row_i = indptr_start
+            A_off_diagonal_indices_row_i = slice(indptr_start + 1, indptr_stop)
+
+        # Check regularity and triangularity of A.
+        if not unit_diagonal and (indptr_stop <= indptr_start
+                                  or A.indices[A_diagonal_index_row_i] < i):
+            raise LinAlgError(
+                'A is singular: diagonal {} is zero.'.format(i))
+        if A.indices[A_diagonal_index_row_i] > i:
+            raise LinAlgError(
+                'A is not triangular: A[{}, {}] is nonzero.'
+                ''.format(i, A.indices[A_diagonal_index_row_i]))
+
+        # Incorporate off-diagonal entries.
+        A_column_indices_in_row_i = A.indices[A_off_diagonal_indices_row_i]
+        A_values_in_row_i = A.data[A_off_diagonal_indices_row_i]
+        x[i] -= np.dot(x[A_column_indices_in_row_i].T, A_values_in_row_i)
+
+        # Compute i-th entry of x.
+        if not unit_diagonal:
+            x[i] /= A.data[A_diagonal_index_row_i]
+
+    return x

venv/Lib/site-packages/scipy/sparse/linalg/dsolve/setup.py

@@ -0,0 +1,53 @@
+from os.path import join, dirname
+import sys
+import glob
+
+
+def configuration(parent_package='',top_path=None):
+    from numpy.distutils.misc_util import Configuration
+    from scipy._build_utils.system_info import get_info
+    from scipy._build_utils import numpy_nodepr_api
+
+    config = Configuration('dsolve',parent_package,top_path)
+    config.add_data_dir('tests')
+
+    lapack_opt = get_info('lapack_opt',notfound_action=2)
+    if sys.platform == 'win32':
+        superlu_defs = [('NO_TIMER',1)]
+    else:
+        superlu_defs = []
+    superlu_defs.append(('USE_VENDOR_BLAS',1))
+
+    superlu_src = join(dirname(__file__), 'SuperLU', 'SRC')
+
+    sources = sorted(glob.glob(join(superlu_src, '*.c')))
+    headers = list(glob.glob(join(superlu_src, '*.h')))
+
+    config.add_library('superlu_src',
+                       sources=sources,
+                       macros=superlu_defs,
+                       include_dirs=[superlu_src],
+                       )
+
+    # Extension
+    ext_sources = ['_superlumodule.c',
+                   '_superlu_utils.c',
+                   '_superluobject.c']
+
+    config.add_extension('_superlu',
+                         sources=ext_sources,
+                         libraries=['superlu_src'],
+                         depends=(sources + headers),
+                         extra_info=lapack_opt,
+                         **numpy_nodepr_api
+                         )
+
+    # Add license files
+    config.add_data_files('SuperLU/License.txt')
+
+    return config
+
+
+if __name__ == '__main__':
+    from numpy.distutils.core import setup
+    setup(**configuration(top_path='').todict())

venv/Lib/site-packages/scipy/sparse/linalg/dsolve/tests/test_linsolve.py

@@ -0,0 +1,777 @@
+import sys
+import threading
+
+import numpy as np
+from numpy import array, finfo, arange, eye, all, unique, ones, dot
+import numpy.random as random
+from numpy.testing import (
+        assert_array_almost_equal, assert_almost_equal,
+        assert_equal, assert_array_equal, assert_, assert_allclose,
+        assert_warns, suppress_warnings)
+import pytest
+from pytest import raises as assert_raises
+
+import scipy.linalg
+from scipy.linalg import norm, inv
+from scipy.sparse import (spdiags, SparseEfficiencyWarning, csc_matrix,
+        csr_matrix, identity, isspmatrix, dok_matrix, lil_matrix, bsr_matrix)
+from scipy.sparse.linalg import SuperLU
+from scipy.sparse.linalg.dsolve import (spsolve, use_solver, splu, spilu,
+        MatrixRankWarning, _superlu, spsolve_triangular, factorized)
+import scipy.sparse
+
+from scipy._lib._testutils import check_free_memory
+
+
+sup_sparse_efficiency = suppress_warnings()
+sup_sparse_efficiency.filter(SparseEfficiencyWarning)
+
+# scikits.umfpack is not a SciPy dependency but it is optionally used in
+# dsolve, so check whether it's available
+try:
+    import scikits.umfpack as umfpack
+    has_umfpack = True
+except ImportError:
+    has_umfpack = False
+
+def toarray(a):
+    if isspmatrix(a):
+        return a.toarray()
+    else:
+        return a
+
+
+def setup_bug_8278():
+    N = 2 ** 6
+    h = 1/N
+    Ah1D = scipy.sparse.diags([-1, 2, -1], [-1, 0, 1],
+                              shape=(N-1, N-1))/(h**2)
+    eyeN = scipy.sparse.eye(N - 1)
+    A = (scipy.sparse.kron(eyeN, scipy.sparse.kron(eyeN, Ah1D))
+         + scipy.sparse.kron(eyeN, scipy.sparse.kron(Ah1D, eyeN))
+         + scipy.sparse.kron(Ah1D, scipy.sparse.kron(eyeN, eyeN)))
+    b = np.random.rand((N-1)**3)
+    return A, b
+
+
+class TestFactorized(object):
+    def setup_method(self):
+        n = 5
+        d = arange(n) + 1
+        self.n = n
+        self.A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n).tocsc()
+        random.seed(1234)
+
+    def _check_singular(self):
+        A = csc_matrix((5,5), dtype='d')
+        b = ones(5)
+        assert_array_almost_equal(0. * b, factorized(A)(b))
+
+    def _check_non_singular(self):
+        # Make a diagonal dominant, to make sure it is not singular
+        n = 5
+        a = csc_matrix(random.rand(n, n))
+        b = ones(n)
+
+        expected = splu(a).solve(b)
+        assert_array_almost_equal(factorized(a)(b), expected)
+
+    def test_singular_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        with assert_raises(RuntimeError, match="Factor is exactly singular"):
+            self._check_singular()
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_singular_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "divide by zero encountered in double_scalars")
+            assert_warns(umfpack.UmfpackWarning, self._check_singular)
+
+    def test_non_singular_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        self._check_non_singular()
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_non_singular_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        self._check_non_singular()
+
+    def test_cannot_factorize_nonsquare_matrix_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        msg = "can only factor square matrices"
+        with assert_raises(ValueError, match=msg):
+            factorized(self.A[:, :4])
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_factorizes_nonsquare_matrix_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        # does not raise
+        factorized(self.A[:,:4])
+
+    def test_call_with_incorrectly_sized_matrix_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        solve = factorized(self.A)
+        b = random.rand(4)
+        B = random.rand(4, 3)
+        BB = random.rand(self.n, 3, 9)
+
+        with assert_raises(ValueError, match="is of incompatible size"):
+            solve(b)
+        with assert_raises(ValueError, match="is of incompatible size"):
+            solve(B)
+        with assert_raises(ValueError,
+                           match="object too deep for desired array"):
+            solve(BB)
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_call_with_incorrectly_sized_matrix_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        solve = factorized(self.A)
+        b = random.rand(4)
+        B = random.rand(4, 3)
+        BB = random.rand(self.n, 3, 9)
+
+        # does not raise
+        solve(b)
+        msg = "object too deep for desired array"
+        with assert_raises(ValueError, match=msg):
+            solve(B)
+        with assert_raises(ValueError, match=msg):
+            solve(BB)
+
+    def test_call_with_cast_to_complex_without_umfpack(self):
+        use_solver(useUmfpack=False)
+        solve = factorized(self.A)
+        b = random.rand(4)
+        for t in [np.complex64, np.complex128]:
+            with assert_raises(TypeError, match="Cannot cast array data"):
+                solve(b.astype(t))
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_call_with_cast_to_complex_with_umfpack(self):
+        use_solver(useUmfpack=True)
+        solve = factorized(self.A)
+        b = random.rand(4)
+        for t in [np.complex64, np.complex128]:
+            assert_warns(np.ComplexWarning, solve, b.astype(t))
+
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_assume_sorted_indices_flag(self):
+        # a sparse matrix with unsorted indices
+        unsorted_inds = np.array([2, 0, 1, 0])
+        data = np.array([10, 16, 5, 0.4])
+        indptr = np.array([0, 1, 2, 4])
+        A = csc_matrix((data, unsorted_inds, indptr), (3, 3))
+        b = ones(3)
+
+        # should raise when incorrectly assuming indices are sorted
+        use_solver(useUmfpack=True, assumeSortedIndices=True)
+        with assert_raises(RuntimeError,
+                           match="UMFPACK_ERROR_invalid_matrix"):
+            factorized(A)
+
+        # should sort indices and succeed when not assuming indices are sorted
+        use_solver(useUmfpack=True, assumeSortedIndices=False)
+        expected = splu(A.copy()).solve(b)
+
+        assert_equal(A.has_sorted_indices, 0)
+        assert_array_almost_equal(factorized(A)(b), expected)
+
+    @pytest.mark.slow
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_bug_8278(self):
+        check_free_memory(8000)
+        use_solver(useUmfpack=True)
+        A, b = setup_bug_8278()
+        A = A.tocsc()
+        f = factorized(A)
+        x = f(b)
+        assert_array_almost_equal(A @ x, b)
+
+
+class TestLinsolve(object):
+    def setup_method(self):
+        use_solver(useUmfpack=False)
+
+    def test_singular(self):
+        A = csc_matrix((5,5), dtype='d')
+        b = array([1, 2, 3, 4, 5],dtype='d')
+        with suppress_warnings() as sup:
+            sup.filter(MatrixRankWarning, "Matrix is exactly singular")
+            x = spsolve(A, b)
+        assert_(not np.isfinite(x).any())
+
+    def test_singular_gh_3312(self):
+        # "Bad" test case that leads SuperLU to call LAPACK with invalid
+        # arguments. Check that it fails moderately gracefully.
+        ij = np.array([(17, 0), (17, 6), (17, 12), (10, 13)], dtype=np.int32)
+        v = np.array([0.284213, 0.94933781, 0.15767017, 0.38797296])
+        A = csc_matrix((v, ij.T), shape=(20, 20))
+        b = np.arange(20)
+
+        try:
+            # should either raise a runtimeerror or return value
+            # appropriate for singular input
+            x = spsolve(A, b)
+            assert_(not np.isfinite(x).any())
+        except RuntimeError:
+            pass
+
+    def test_twodiags(self):
+        A = spdiags([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1], 5, 5)
+        b = array([1, 2, 3, 4, 5])
+
+        # condition number of A
+        cond_A = norm(A.todense(),2) * norm(inv(A.todense()),2)
+
+        for t in ['f','d','F','D']:
+            eps = finfo(t).eps  # floating point epsilon
+            b = b.astype(t)
+
+            for format in ['csc','csr']:
+                Asp = A.astype(t).asformat(format)
+
+                x = spsolve(Asp,b)
+
+                assert_(norm(b - Asp*x) < 10 * cond_A * eps)
+
+    def test_bvector_smoketest(self):
+        Adense = array([[0., 1., 1.],
+                        [1., 0., 1.],
+                        [0., 0., 1.]])
+        As = csc_matrix(Adense)
+        random.seed(1234)
+        x = random.randn(3)
+        b = As*x
+        x2 = spsolve(As, b)
+
+        assert_array_almost_equal(x, x2)
+
+    def test_bmatrix_smoketest(self):
+        Adense = array([[0., 1., 1.],
+                        [1., 0., 1.],
+                        [0., 0., 1.]])
+        As = csc_matrix(Adense)
+        random.seed(1234)
+        x = random.randn(3, 4)
+        Bdense = As.dot(x)
+        Bs = csc_matrix(Bdense)
+        x2 = spsolve(As, Bs)
+        assert_array_almost_equal(x, x2.todense())
+
+    @sup_sparse_efficiency
+    def test_non_square(self):
+        # A is not square.
+        A = ones((3, 4))
+        b = ones((4, 1))
+        assert_raises(ValueError, spsolve, A, b)
+        # A2 and b2 have incompatible shapes.
+        A2 = csc_matrix(eye(3))
+        b2 = array([1.0, 2.0])
+        assert_raises(ValueError, spsolve, A2, b2)
+
+    @sup_sparse_efficiency
+    def test_example_comparison(self):
+        row = array([0,0,1,2,2,2])
+        col = array([0,2,2,0,1,2])
+        data = array([1,2,3,-4,5,6])
+        sM = csr_matrix((data,(row,col)), shape=(3,3), dtype=float)
+        M = sM.todense()
+
+        row = array([0,0,1,1,0,0])
+        col = array([0,2,1,1,0,0])
+        data = array([1,1,1,1,1,1])
+        sN = csr_matrix((data, (row,col)), shape=(3,3), dtype=float)
+        N = sN.todense()
+
+        sX = spsolve(sM, sN)
+        X = scipy.linalg.solve(M, N)
+
+        assert_array_almost_equal(X, sX.todense())
+
+    @sup_sparse_efficiency
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_shape_compatibility(self):
+        use_solver(useUmfpack=True)
+        A = csc_matrix([[1., 0], [0, 2]])
+        bs = [
+            [1, 6],
+            array([1, 6]),
+            [[1], [6]],
+            array([[1], [6]]),
+            csc_matrix([[1], [6]]),
+            csr_matrix([[1], [6]]),
+            dok_matrix([[1], [6]]),
+            bsr_matrix([[1], [6]]),
+            array([[1., 2., 3.], [6., 8., 10.]]),
+            csc_matrix([[1., 2., 3.], [6., 8., 10.]]),
+            csr_matrix([[1., 2., 3.], [6., 8., 10.]]),
+            dok_matrix([[1., 2., 3.], [6., 8., 10.]]),
+            bsr_matrix([[1., 2., 3.], [6., 8., 10.]]),
+            ]
+
+        for b in bs:
+            x = np.linalg.solve(A.toarray(), toarray(b))
+            for spmattype in [csc_matrix, csr_matrix, dok_matrix, lil_matrix]:
+                x1 = spsolve(spmattype(A), b, use_umfpack=True)
+                x2 = spsolve(spmattype(A), b, use_umfpack=False)
+
+                # check solution
+                if x.ndim == 2 and x.shape[1] == 1:
+                    # interprets also these as "vectors"
+                    x = x.ravel()
+
+                assert_array_almost_equal(toarray(x1), x, err_msg=repr((b, spmattype, 1)))
+                assert_array_almost_equal(toarray(x2), x, err_msg=repr((b, spmattype, 2)))
+
+                # dense vs. sparse output  ("vectors" are always dense)
+                if isspmatrix(b) and x.ndim > 1:
+                    assert_(isspmatrix(x1), repr((b, spmattype, 1)))
+                    assert_(isspmatrix(x2), repr((b, spmattype, 2)))
+                else:
+                    assert_(isinstance(x1, np.ndarray), repr((b, spmattype, 1)))
+                    assert_(isinstance(x2, np.ndarray), repr((b, spmattype, 2)))
+
+                # check output shape
+                if x.ndim == 1:
+                    # "vector"
+                    assert_equal(x1.shape, (A.shape[1],))
+                    assert_equal(x2.shape, (A.shape[1],))
+                else:
+                    # "matrix"
+                    assert_equal(x1.shape, x.shape)
+                    assert_equal(x2.shape, x.shape)
+
+        A = csc_matrix((3, 3))
+        b = csc_matrix((1, 3))
+        assert_raises(ValueError, spsolve, A, b)
+
+    @sup_sparse_efficiency
+    def test_ndarray_support(self):
+        A = array([[1., 2.], [2., 0.]])
+        x = array([[1., 1.], [0.5, -0.5]])
+        b = array([[2., 0.], [2., 2.]])
+
+        assert_array_almost_equal(x, spsolve(A, b))
+
+    def test_gssv_badinput(self):
+        N = 10
+        d = arange(N) + 1.0
+        A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), N, N)
+
+        for spmatrix in (csc_matrix, csr_matrix):
+            A = spmatrix(A)
+            b = np.arange(N)
+
+            def not_c_contig(x):
+                return x.repeat(2)[::2]
+
+            def not_1dim(x):
+                return x[:,None]
+
+            def bad_type(x):
+                return x.astype(bool)
+
+            def too_short(x):
+                return x[:-1]
+
+            badops = [not_c_contig, not_1dim, bad_type, too_short]
+
+            for badop in badops:
+                msg = "%r %r" % (spmatrix, badop)
+                # Not C-contiguous
+                assert_raises((ValueError, TypeError), _superlu.gssv,
+                              N, A.nnz, badop(A.data), A.indices, A.indptr,
+                              b, int(spmatrix == csc_matrix), err_msg=msg)
+                assert_raises((ValueError, TypeError), _superlu.gssv,
+                              N, A.nnz, A.data, badop(A.indices), A.indptr,
+                              b, int(spmatrix == csc_matrix), err_msg=msg)
+                assert_raises((ValueError, TypeError), _superlu.gssv,
+                              N, A.nnz, A.data, A.indices, badop(A.indptr),
+                              b, int(spmatrix == csc_matrix), err_msg=msg)
+
+    def test_sparsity_preservation(self):
+        ident = csc_matrix([
+            [1, 0, 0],
+            [0, 1, 0],
+            [0, 0, 1]])
+        b = csc_matrix([
+            [0, 1],
+            [1, 0],
+            [0, 0]])
+        x = spsolve(ident, b)
+        assert_equal(ident.nnz, 3)
+        assert_equal(b.nnz, 2)
+        assert_equal(x.nnz, 2)
+        assert_allclose(x.A, b.A, atol=1e-12, rtol=1e-12)
+
+    def test_dtype_cast(self):
+        A_real = scipy.sparse.csr_matrix([[1, 2, 0],
+                                          [0, 0, 3],
+                                          [4, 0, 5]])
+        A_complex = scipy.sparse.csr_matrix([[1, 2, 0],
+                                             [0, 0, 3],
+                                             [4, 0, 5 + 1j]])
+        b_real = np.array([1,1,1])
+        b_complex = np.array([1,1,1]) + 1j*np.array([1,1,1])
+        x = spsolve(A_real, b_real)
+        assert_(np.issubdtype(x.dtype, np.floating))
+        x = spsolve(A_real, b_complex)
+        assert_(np.issubdtype(x.dtype, np.complexfloating))
+        x = spsolve(A_complex, b_real)
+        assert_(np.issubdtype(x.dtype, np.complexfloating))
+        x = spsolve(A_complex, b_complex)
+        assert_(np.issubdtype(x.dtype, np.complexfloating))
+
+    @pytest.mark.slow
+    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
+    def test_bug_8278(self):
+        check_free_memory(8000)
+        use_solver(useUmfpack=True)
+        A, b = setup_bug_8278()
+        x = spsolve(A, b)
+        assert_array_almost_equal(A @ x, b)
+
+
+class TestSplu(object):
+    def setup_method(self):
+        use_solver(useUmfpack=False)
+        n = 40
+        d = arange(n) + 1
+        self.n = n
+        self.A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n)
+        random.seed(1234)
+
+    def _smoketest(self, spxlu, check, dtype):
+        if np.issubdtype(dtype, np.complexfloating):
+            A = self.A + 1j*self.A.T
+        else:
+            A = self.A
+
+        A = A.astype(dtype)
+        lu = spxlu(A)
+
+        rng = random.RandomState(1234)
+
+        # Input shapes
+        for k in [None, 1, 2, self.n, self.n+2]:
+            msg = "k=%r" % (k,)
+
+            if k is None:
+                b = rng.rand(self.n)
+            else:
+                b = rng.rand(self.n, k)
+
+            if np.issubdtype(dtype, np.complexfloating):
+                b = b + 1j*rng.rand(*b.shape)
+            b = b.astype(dtype)
+
+            x = lu.solve(b)
+            check(A, b, x, msg)
+
+            x = lu.solve(b, 'T')
+            check(A.T, b, x, msg)
+
+            x = lu.solve(b, 'H')
+            check(A.T.conj(), b, x, msg)
+
+    @sup_sparse_efficiency
+    def test_splu_smoketest(self):
+        self._internal_test_splu_smoketest()
+
+    def _internal_test_splu_smoketest(self):
+        # Check that splu works at all
+        def check(A, b, x, msg=""):
+            eps = np.finfo(A.dtype).eps
+            r = A * x
+            assert_(abs(r - b).max() < 1e3*eps, msg)
+
+        self._smoketest(splu, check, np.float32)
+        self._smoketest(splu, check, np.float64)
+        self._smoketest(splu, check, np.complex64)
+        self._smoketest(splu, check, np.complex128)
+
+    @sup_sparse_efficiency
+    def test_spilu_smoketest(self):
+        self._internal_test_spilu_smoketest()
+
+    def _internal_test_spilu_smoketest(self):
+        errors = []
+
+        def check(A, b, x, msg=""):
+            r = A * x
+            err = abs(r - b).max()
+            assert_(err < 1e-2, msg)
+            if b.dtype in (np.float64, np.complex128):
+                errors.append(err)
+
+        self._smoketest(spilu, check, np.float32)
+        self._smoketest(spilu, check, np.float64)
+        self._smoketest(spilu, check, np.complex64)
+        self._smoketest(spilu, check, np.complex128)
+
+        assert_(max(errors) > 1e-5)
+
+    @sup_sparse_efficiency
+    def test_spilu_drop_rule(self):
+        # Test passing in the drop_rule argument to spilu.
+        A = identity(2)
+
+        rules = [
+            b'basic,area'.decode('ascii'),  # unicode
+            b'basic,area',  # ascii
+            [b'basic', b'area'.decode('ascii')]
+        ]
+        for rule in rules:
+            # Argument should be accepted
+            assert_(isinstance(spilu(A, drop_rule=rule), SuperLU))
+
+    def test_splu_nnz0(self):
+        A = csc_matrix((5,5), dtype='d')
+        assert_raises(RuntimeError, splu, A)
+
+    def test_spilu_nnz0(self):
+        A = csc_matrix((5,5), dtype='d')
+        assert_raises(RuntimeError, spilu, A)
+
+    def test_splu_basic(self):
+        # Test basic splu functionality.
+        n = 30
+        rng = random.RandomState(12)
+        a = rng.rand(n, n)
+        a[a < 0.95] = 0
+        # First test with a singular matrix
+        a[:, 0] = 0
+        a_ = csc_matrix(a)
+        # Matrix is exactly singular
+        assert_raises(RuntimeError, splu, a_)
+
+        # Make a diagonal dominant, to make sure it is not singular
+        a += 4*eye(n)
+        a_ = csc_matrix(a)
+        lu = splu(a_)
+        b = ones(n)
+        x = lu.solve(b)
+        assert_almost_equal(dot(a, x), b)
+
+    def test_splu_perm(self):
+        # Test the permutation vectors exposed by splu.
+        n = 30
+        a = random.random((n, n))
+        a[a < 0.95] = 0
+        # Make a diagonal dominant, to make sure it is not singular
+        a += 4*eye(n)
+        a_ = csc_matrix(a)
+        lu = splu(a_)
+        # Check that the permutation indices do belong to [0, n-1].
+        for perm in (lu.perm_r, lu.perm_c):
+            assert_(all(perm > -1))
+            assert_(all(perm < n))
+            assert_equal(len(unique(perm)), len(perm))
+
+        # Now make a symmetric, and test that the two permutation vectors are
+        # the same
+        # Note: a += a.T relies on undefined behavior.
+        a = a + a.T
+        a_ = csc_matrix(a)
+        lu = splu(a_)
+        assert_array_equal(lu.perm_r, lu.perm_c)
+
+    @pytest.mark.parametrize("splu_fun, rtol", [(splu, 1e-7), (spilu, 1e-1)])
+    def test_natural_permc(self, splu_fun, rtol):
+        # Test that the "NATURAL" permc_spec does not permute the matrix
+        np.random.seed(42)
+        n = 500
+        p = 0.01
+        A = scipy.sparse.random(n, n, p)
+        x = np.random.rand(n)
+        # Make A diagonal dominant to make sure it is not singular
+        A += (n+1)*scipy.sparse.identity(n)
+        A_ = csc_matrix(A)
+        b = A_ @ x
+
+        # without permc_spec, permutation is not identity
+        lu = splu_fun(A_)
+        assert_(np.any(lu.perm_c != np.arange(n)))
+
+        # with permc_spec="NATURAL", permutation is identity
+        lu = splu_fun(A_, permc_spec="NATURAL")
+        assert_array_equal(lu.perm_c, np.arange(n))
+
+        # Also, lu decomposition is valid
+        x2 = lu.solve(b)
+        assert_allclose(x, x2, rtol=rtol)
+
+    @pytest.mark.skipif(not hasattr(sys, 'getrefcount'), reason="no sys.getrefcount")
+    def test_lu_refcount(self):
+        # Test that we are keeping track of the reference count with splu.
+        n = 30
+        a = random.random((n, n))
+        a[a < 0.95] = 0
+        # Make a diagonal dominant, to make sure it is not singular
+        a += 4*eye(n)
+        a_ = csc_matrix(a)
+        lu = splu(a_)
+
+        # And now test that we don't have a refcount bug
+        rc = sys.getrefcount(lu)
+        for attr in ('perm_r', 'perm_c'):
+            perm = getattr(lu, attr)
+            assert_equal(sys.getrefcount(lu), rc + 1)
+            del perm
+            assert_equal(sys.getrefcount(lu), rc)
+
+    def test_bad_inputs(self):
+        A = self.A.tocsc()
+
+        assert_raises(ValueError, splu, A[:,:4])
+        assert_raises(ValueError, spilu, A[:,:4])
+
+        for lu in [splu(A), spilu(A)]:
+            b = random.rand(42)
+            B = random.rand(42, 3)
+            BB = random.rand(self.n, 3, 9)
+            assert_raises(ValueError, lu.solve, b)
+            assert_raises(ValueError, lu.solve, B)
+            assert_raises(ValueError, lu.solve, BB)
+            assert_raises(TypeError, lu.solve,
+                          b.astype(np.complex64))
+            assert_raises(TypeError, lu.solve,
+                          b.astype(np.complex128))
+
+    @sup_sparse_efficiency
+    def test_superlu_dlamch_i386_nan(self):
+        # SuperLU 4.3 calls some functions returning floats without
+        # declaring them. On i386@linux call convention, this fails to
+        # clear floating point registers after call. As a result, NaN
+        # can appear in the next floating point operation made.
+        #
+        # Here's a test case that triggered the issue.
+        n = 8
+        d = np.arange(n) + 1
+        A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n)
+        A = A.astype(np.float32)
+        spilu(A)
+        A = A + 1j*A
+        B = A.A
+        assert_(not np.isnan(B).any())
+
+    @sup_sparse_efficiency
+    def test_lu_attr(self):
+
+        def check(dtype, complex_2=False):
+            A = self.A.astype(dtype)
+
+            if complex_2:
+                A = A + 1j*A.T
+
+            n = A.shape[0]
+            lu = splu(A)
+
+            # Check that the decomposition is as advertized
+
+            Pc = np.zeros((n, n))
+            Pc[np.arange(n), lu.perm_c] = 1
+
+            Pr = np.zeros((n, n))
+            Pr[lu.perm_r, np.arange(n)] = 1
+
+            Ad = A.toarray()
+            lhs = Pr.dot(Ad).dot(Pc)
+            rhs = (lu.L * lu.U).toarray()
+
+            eps = np.finfo(dtype).eps
+
+            assert_allclose(lhs, rhs, atol=100*eps)
+
+        check(np.float32)
+        check(np.float64)
+        check(np.complex64)
+        check(np.complex128)
+        check(np.complex64, True)
+        check(np.complex128, True)
+
+    @pytest.mark.slow
+    @sup_sparse_efficiency
+    def test_threads_parallel(self):
+        oks = []
+
+        def worker():
+            try:
+                self.test_splu_basic()
+                self._internal_test_splu_smoketest()
+                self._internal_test_spilu_smoketest()
+                oks.append(True)
+            except Exception:
+                pass
+
+        threads = [threading.Thread(target=worker)
+                   for k in range(20)]
+        for t in threads:
+            t.start()
+        for t in threads:
+            t.join()
+
+        assert_equal(len(oks), 20)
+
+
+class TestSpsolveTriangular(object):
+    def setup_method(self):
+        use_solver(useUmfpack=False)
+
+    def test_singular(self):
+        n = 5
+        A = csr_matrix((n, n))
+        b = np.arange(n)
+        for lower in (True, False):
+            assert_raises(scipy.linalg.LinAlgError, spsolve_triangular, A, b, lower=lower)
+
+    @sup_sparse_efficiency
+    def test_bad_shape(self):
+        # A is not square.
+        A = np.zeros((3, 4))
+        b = ones((4, 1))
+        assert_raises(ValueError, spsolve_triangular, A, b)
+        # A2 and b2 have incompatible shapes.
+        A2 = csr_matrix(eye(3))
+        b2 = array([1.0, 2.0])
+        assert_raises(ValueError, spsolve_triangular, A2, b2)
+
+    @sup_sparse_efficiency
+    def test_input_types(self):
+        A = array([[1., 0.], [1., 2.]])
+        b = array([[2., 0.], [2., 2.]])
+        for matrix_type in (array, csc_matrix, csr_matrix):
+            x = spsolve_triangular(matrix_type(A), b, lower=True)
+            assert_array_almost_equal(A.dot(x), b)
+
+    @pytest.mark.slow
+    @sup_sparse_efficiency
+    def test_random(self):
+        def random_triangle_matrix(n, lower=True):
+            A = scipy.sparse.random(n, n, density=0.1, format='coo')
+            if lower:
+                A = scipy.sparse.tril(A)
+            else:
+                A = scipy.sparse.triu(A)
+            A = A.tocsr(copy=False)
+            for i in range(n):
+                A[i, i] = np.random.rand() + 1
+            return A
+
+        np.random.seed(1234)
+        for lower in (True, False):
+            for n in (10, 10**2, 10**3):
+                A = random_triangle_matrix(n, lower=lower)
+                for m in (1, 10):
+                    for b in (np.random.rand(n, m),
+                              np.random.randint(-9, 9, (n, m)),
+                              np.random.randint(-9, 9, (n, m)) +
+                              np.random.randint(-9, 9, (n, m)) * 1j):
+                        x = spsolve_triangular(A, b, lower=lower)
+                        assert_array_almost_equal(A.dot(x), b)
+                        x = spsolve_triangular(A, b, lower=lower,
+                                               unit_diagonal=True)
+                        A.setdiag(1)
+                        assert_array_almost_equal(A.dot(x), b)

venv/Lib/site-packages/scipy/sparse/linalg/eigen/__init__.py

@@ -0,0 +1,16 @@
+"""
+Sparse Eigenvalue Solvers
+-------------------------
+
+The submodules of sparse.linalg.eigen:
+    1. lobpcg: Locally Optimal Block Preconditioned Conjugate Gradient Method
+
+"""
+from .arpack import *
+from .lobpcg import *
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester