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