70 lines
1.9 KiB
Python
70 lines
1.9 KiB
Python
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from sympy.functions import adjoint, conjugate, transpose
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from sympy.matrices.expressions import MatrixSymbol, Adjoint, trace, Transpose
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from sympy.matrices import eye, Matrix
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from sympy.assumptions.ask import Q
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from sympy.assumptions.refine import refine
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from sympy.core.singleton import S
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from sympy.core.symbol import symbols
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n, m, l, k, p = symbols('n m l k p', 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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def test_transpose():
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Sq = MatrixSymbol('Sq', n, n)
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assert transpose(A) == Transpose(A)
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assert Transpose(A).shape == (m, n)
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assert Transpose(A*B).shape == (l, n)
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assert transpose(Transpose(A)) == A
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assert isinstance(Transpose(Transpose(A)), Transpose)
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assert adjoint(Transpose(A)) == Adjoint(Transpose(A))
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assert conjugate(Transpose(A)) == Adjoint(A)
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assert Transpose(eye(3)).doit() == eye(3)
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assert Transpose(S(5)).doit() == S(5)
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assert Transpose(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])
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assert transpose(trace(Sq)) == trace(Sq)
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assert trace(Transpose(Sq)) == trace(Sq)
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assert Transpose(Sq)[0, 1] == Sq[1, 0]
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assert Transpose(A*B).doit() == Transpose(B) * Transpose(A)
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def test_transpose_MatAdd_MatMul():
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# Issue 16807
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from sympy.functions.elementary.trigonometric import cos
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x = symbols('x')
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M = MatrixSymbol('M', 3, 3)
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N = MatrixSymbol('N', 3, 3)
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assert (N + (cos(x) * M)).T == cos(x)*M.T + N.T
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def test_refine():
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assert refine(C.T, Q.symmetric(C)) == C
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def test_transpose1x1():
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m = MatrixSymbol('m', 1, 1)
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assert m == refine(m.T)
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assert m == refine(m.T.T)
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def test_issue_9817():
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from sympy.matrices.expressions import Identity
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v = MatrixSymbol('v', 3, 1)
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A = MatrixSymbol('A', 3, 3)
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x = Matrix([i + 1 for i in range(3)])
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X = Identity(3)
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quadratic = v.T * A * v
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subbed = quadratic.xreplace({v:x, A:X})
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assert subbed.as_explicit() == Matrix([[14]])
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