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122 lines
4.1 KiB
Python
122 lines
4.1 KiB
Python
5 years ago
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from __future__ import division, print_function, absolute_import
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import numpy as np
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from numpy.testing import assert_equal
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from scipy.sparse.csgraph import (reverse_cuthill_mckee,
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maximum_bipartite_matching, structural_rank)
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from scipy.sparse import diags, csc_matrix, csr_matrix, coo_matrix
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def test_graph_reverse_cuthill_mckee():
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A = np.array([[1, 0, 0, 0, 1, 0, 0, 0],
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[0, 1, 1, 0, 0, 1, 0, 1],
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[0, 1, 1, 0, 1, 0, 0, 0],
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[0, 0, 0, 1, 0, 0, 1, 0],
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[1, 0, 1, 0, 1, 0, 0, 0],
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[0, 1, 0, 0, 0, 1, 0, 1],
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[0, 0, 0, 1, 0, 0, 1, 0],
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[0, 1, 0, 0, 0, 1, 0, 1]], dtype=int)
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graph = csr_matrix(A)
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perm = reverse_cuthill_mckee(graph)
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correct_perm = np.array([6, 3, 7, 5, 1, 2, 4, 0])
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assert_equal(perm, correct_perm)
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# Test int64 indices input
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graph.indices = graph.indices.astype('int64')
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graph.indptr = graph.indptr.astype('int64')
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perm = reverse_cuthill_mckee(graph, True)
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assert_equal(perm, correct_perm)
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def test_graph_reverse_cuthill_mckee_ordering():
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data = np.ones(63,dtype=int)
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rows = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2,
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2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5,
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6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9,
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9, 10, 10, 10, 10, 10, 11, 11, 11, 11,
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12, 12, 12, 13, 13, 13, 13, 14, 14, 14,
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14, 15, 15, 15, 15, 15])
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cols = np.array([0, 2, 5, 8, 10, 1, 3, 9, 11, 0, 2,
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7, 10, 1, 3, 11, 4, 6, 12, 14, 0, 7, 13,
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15, 4, 6, 14, 2, 5, 7, 15, 0, 8, 10, 13,
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1, 9, 11, 0, 2, 8, 10, 15, 1, 3, 9, 11,
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4, 12, 14, 5, 8, 13, 15, 4, 6, 12, 14,
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5, 7, 10, 13, 15])
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graph = coo_matrix((data, (rows,cols))).tocsr()
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perm = reverse_cuthill_mckee(graph)
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correct_perm = np.array([12, 14, 4, 6, 10, 8, 2, 15,
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0, 13, 7, 5, 9, 11, 1, 3])
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assert_equal(perm, correct_perm)
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def test_graph_maximum_bipartite_matching():
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A = diags(np.ones(25), offsets=0, format='csc')
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rand_perm = np.random.permutation(25)
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rand_perm2 = np.random.permutation(25)
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Rrow = np.arange(25)
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Rcol = rand_perm
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Rdata = np.ones(25,dtype=int)
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Rmat = coo_matrix((Rdata,(Rrow,Rcol))).tocsc()
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Crow = rand_perm2
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Ccol = np.arange(25)
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Cdata = np.ones(25,dtype=int)
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Cmat = coo_matrix((Cdata,(Crow,Ccol))).tocsc()
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# Randomly permute identity matrix
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B = Rmat*A*Cmat
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# Row permute
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perm = maximum_bipartite_matching(B,perm_type='row')
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Rrow = np.arange(25)
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Rcol = perm
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Rdata = np.ones(25,dtype=int)
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Rmat = coo_matrix((Rdata,(Rrow,Rcol))).tocsc()
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C1 = Rmat*B
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# Column permute
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perm2 = maximum_bipartite_matching(B,perm_type='column')
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Crow = perm2
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Ccol = np.arange(25)
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Cdata = np.ones(25,dtype=int)
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Cmat = coo_matrix((Cdata,(Crow,Ccol))).tocsc()
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C2 = B*Cmat
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# Should get identity matrix back
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assert_equal(any(C1.diagonal() == 0), False)
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assert_equal(any(C2.diagonal() == 0), False)
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# Test int64 indices input
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B.indices = B.indices.astype('int64')
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B.indptr = B.indptr.astype('int64')
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perm = maximum_bipartite_matching(B,perm_type='row')
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Rrow = np.arange(25)
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Rcol = perm
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Rdata = np.ones(25,dtype=int)
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Rmat = coo_matrix((Rdata,(Rrow,Rcol))).tocsc()
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C3 = Rmat*B
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assert_equal(any(C3.diagonal() == 0), False)
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def test_graph_structural_rank():
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# Test square matrix #1
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A = csc_matrix([[1, 1, 0],
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[1, 0, 1],
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[0, 1, 0]])
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assert_equal(structural_rank(A), 3)
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# Test square matrix #2
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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])
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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])
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data = np.ones_like(rows)
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B = coo_matrix((data,(rows,cols)), shape=(8,8))
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assert_equal(structural_rank(B), 6)
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#Test non-square matrix
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C = csc_matrix([[1, 0, 2, 0],
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[2, 0, 4, 0]])
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assert_equal(structural_rank(C), 2)
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#Test tall matrix
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assert_equal(structural_rank(C.T), 2)
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