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| from sympy.combinatorics import Permutation | |
| from sympy.core.symbol import symbols | |
| from sympy.matrices import Matrix | |
| from sympy.matrices.expressions import ( | |
| PermutationMatrix, BlockDiagMatrix, BlockMatrix) | |
| def test_connected_components(): | |
| a, b, c, d, e, f, g, h, i, j, k, l, m = symbols('a:m') | |
| M = Matrix([ | |
| [a, 0, 0, 0, b, 0, 0, 0, 0, 0, c, 0, 0], | |
| [0, d, 0, 0, 0, e, 0, 0, 0, 0, 0, f, 0], | |
| [0, 0, g, 0, 0, 0, h, 0, 0, 0, 0, 0, i], | |
| [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], | |
| [m, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], | |
| [0, m, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], | |
| [0, 0, m, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], | |
| [j, 0, 0, 0, k, 0, 0, 1, 0, 0, l, 0, 0], | |
| [0, j, 0, 0, 0, k, 0, 0, 1, 0, 0, l, 0], | |
| [0, 0, j, 0, 0, 0, k, 0, 0, 1, 0, 0, l], | |
| [0, 0, 0, 0, d, 0, 0, 0, 0, 0, 1, 0, 0], | |
| [0, 0, 0, 0, 0, d, 0, 0, 0, 0, 0, 1, 0], | |
| [0, 0, 0, 0, 0, 0, d, 0, 0, 0, 0, 0, 1]]) | |
| cc = M.connected_components() | |
| assert cc == [[0, 4, 7, 10], [1, 5, 8, 11], [2, 6, 9, 12], [3]] | |
| P, B = M.connected_components_decomposition() | |
| p = Permutation([0, 4, 7, 10, 1, 5, 8, 11, 2, 6, 9, 12, 3]) | |
| assert P == PermutationMatrix(p) | |
| B0 = Matrix([ | |
| [a, b, 0, c], | |
| [m, 1, 0, 0], | |
| [j, k, 1, l], | |
| [0, d, 0, 1]]) | |
| B1 = Matrix([ | |
| [d, e, 0, f], | |
| [m, 1, 0, 0], | |
| [j, k, 1, l], | |
| [0, d, 0, 1]]) | |
| B2 = Matrix([ | |
| [g, h, 0, i], | |
| [m, 1, 0, 0], | |
| [j, k, 1, l], | |
| [0, d, 0, 1]]) | |
| B3 = Matrix([[1]]) | |
| assert B == BlockDiagMatrix(B0, B1, B2, B3) | |
| def test_strongly_connected_components(): | |
| M = Matrix([ | |
| [11, 14, 10, 0, 15, 0], | |
| [0, 44, 0, 0, 45, 0], | |
| [1, 4, 0, 0, 5, 0], | |
| [0, 0, 0, 22, 0, 23], | |
| [0, 54, 0, 0, 55, 0], | |
| [0, 0, 0, 32, 0, 33]]) | |
| scc = M.strongly_connected_components() | |
| assert scc == [[1, 4], [0, 2], [3, 5]] | |
| P, B = M.strongly_connected_components_decomposition() | |
| p = Permutation([1, 4, 0, 2, 3, 5]) | |
| assert P == PermutationMatrix(p) | |
| assert B == BlockMatrix([ | |
| [ | |
| Matrix([[44, 45], [54, 55]]), | |
| Matrix.zeros(2, 2), | |
| Matrix.zeros(2, 2) | |
| ], | |
| [ | |
| Matrix([[14, 15], [4, 5]]), | |
| Matrix([[11, 10], [1, 0]]), | |
| Matrix.zeros(2, 2) | |
| ], | |
| [ | |
| Matrix.zeros(2, 2), | |
| Matrix.zeros(2, 2), | |
| Matrix([[22, 23], [32, 33]]) | |
| ] | |
| ]) | |
| P = P.as_explicit() | |
| B = B.as_explicit() | |
| assert P.T * B * P == M | |
| P, B = M.strongly_connected_components_decomposition(lower=False) | |
| p = Permutation([3, 5, 0, 2, 1, 4]) | |
| assert P == PermutationMatrix(p) | |
| assert B == BlockMatrix([ | |
| [ | |
| Matrix([[22, 23], [32, 33]]), | |
| Matrix.zeros(2, 2), | |
| Matrix.zeros(2, 2) | |
| ], | |
| [ | |
| Matrix.zeros(2, 2), | |
| Matrix([[11, 10], [1, 0]]), | |
| Matrix([[14, 15], [4, 5]]) | |
| ], | |
| [ | |
| Matrix.zeros(2, 2), | |
| Matrix.zeros(2, 2), | |
| Matrix([[44, 45], [54, 55]]) | |
| ] | |
| ]) | |
| P = P.as_explicit() | |
| B = B.as_explicit() | |
| assert P.T * B * P == M | |