63 lines
2.0 KiB
Python
63 lines
2.0 KiB
Python
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from sympy.core import symbols, S
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from sympy.matrices.expressions import MatrixSymbol, Inverse, MatPow, ZeroMatrix, OneMatrix
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from sympy.matrices.common import NonInvertibleMatrixError, NonSquareMatrixError
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from sympy.matrices import eye, Identity
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from sympy.testing.pytest import raises
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from sympy.assumptions.ask import Q
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from sympy.assumptions.refine import refine
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n, m, l = symbols('n m l', integer=True)
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A = MatrixSymbol('A', n, m)
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B = MatrixSymbol('B', m, l)
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C = MatrixSymbol('C', n, n)
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D = MatrixSymbol('D', n, n)
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E = MatrixSymbol('E', m, n)
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def test_inverse():
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assert Inverse(C).args == (C, S.NegativeOne)
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assert Inverse(C).shape == (n, n)
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assert Inverse(A*E).shape == (n, n)
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assert Inverse(E*A).shape == (m, m)
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assert Inverse(C).inverse() == C
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assert Inverse(Inverse(C)).doit() == C
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assert isinstance(Inverse(Inverse(C)), Inverse)
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assert Inverse(*Inverse(E*A).args) == Inverse(E*A)
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assert C.inverse().inverse() == C
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assert C.inverse()*C == Identity(C.rows)
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assert Identity(n).inverse() == Identity(n)
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assert (3*Identity(n)).inverse() == Identity(n)/3
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# Simplifies Muls if possible (i.e. submatrices are square)
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assert (C*D).inverse() == D.I*C.I
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# But still works when not possible
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assert isinstance((A*E).inverse(), Inverse)
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assert Inverse(C*D).doit(inv_expand=False) == Inverse(C*D)
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assert Inverse(eye(3)).doit() == eye(3)
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assert Inverse(eye(3)).doit(deep=False) == eye(3)
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assert OneMatrix(1, 1).I == Identity(1)
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assert isinstance(OneMatrix(n, n).I, Inverse)
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def test_inverse_non_invertible():
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raises(NonInvertibleMatrixError, lambda: ZeroMatrix(n, n).I)
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raises(NonInvertibleMatrixError, lambda: OneMatrix(2, 2).I)
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def test_refine():
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assert refine(C.I, Q.orthogonal(C)) == C.T
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def test_inverse_matpow_canonicalization():
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A = MatrixSymbol('A', 3, 3)
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assert Inverse(MatPow(A, 3)).doit() == MatPow(Inverse(A), 3).doit()
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def test_nonsquare_error():
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A = MatrixSymbol('A', 3, 4)
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raises(NonSquareMatrixError, lambda: Inverse(A))
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