Fixed database typo and removed unnecessary class identifier.

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)