Пример #1
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def test_transpose():
    Sq = MatrixSymbol('Sq', n, n)

    assert transpose(A) == Transpose(A)
    assert Transpose(A).shape == (m, n)
    assert Transpose(A * B).shape == (l, n)
    assert transpose(Transpose(A)) == A
    assert isinstance(Transpose(Transpose(A)), Transpose)

    assert adjoint(Transpose(A)) == Adjoint(Transpose(A))
    assert conjugate(Transpose(A)) == Adjoint(A)

    assert Transpose(eye(3)).doit() == eye(3)

    assert Transpose(S(5)).doit() == S(5)

    assert Transpose(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3],
                                                                 [2, 4]])

    assert transpose(trace(Sq)) == trace(Sq)
    assert trace(Transpose(Sq)) == trace(Sq)

    assert Transpose(Sq)[0, 1] == Sq[1, 0]

    assert Transpose(A * B).doit() == Transpose(B) * Transpose(A)
Пример #2
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def test_trace():
    assert isinstance(Trace(A), Trace)
    assert not isinstance(Trace(A), MatrixExpr)
    raises(ShapeError, lambda: Trace(C))
    assert Trace(eye(3)) == 3
    assert Trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15

    assert adjoint(Trace(A)) == Trace(Adjoint(A))
    assert conjugate(Trace(A)) == Trace(Adjoint(A))
    assert transpose(Trace(A)) == Trace(A)

    A / Trace(A)  # Make sure this is possible

    # Some easy simplifications
    assert Trace(Identity(5)) == 5
    assert Trace(ZeroMatrix(5, 5)) == 0
    assert Trace(2 * A * B) == 2 * Trace(A * B)
    assert Trace(A.T) == Trace(A)

    i, j = symbols('i j')
    F = FunctionMatrix(3, 3, Lambda((i, j), i + j))
    assert Trace(F).doit() == (0 + 0) + (1 + 1) + (2 + 2)

    raises(TypeError, lambda: Trace(S.One))

    assert Trace(A).arg is A
Пример #3
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def test_adjoint():
    assert adjoint(A * B) == Adjoint(B) * Adjoint(A)
    assert adjoint(2 * A * B) == 2 * Adjoint(B) * Adjoint(A)
    assert adjoint(2 * I * C) == -2 * I * Adjoint(C)

    M = Matrix(2, 2, [1, 2 + I, 3, 4])
    MA = Matrix(2, 2, [1, 3, 2 - I, 4])
    assert adjoint(M) == MA
    assert adjoint(2 * M) == 2 * MA
    assert adjoint(MatMul(2, M)) == MatMul(2, MA).doit()
Пример #4
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def test_adjoint():
    Sq = MatrixSymbol('Sq', n, n)

    assert Adjoint(A).shape == (m, n)
    assert Adjoint(A * B).shape == (l, n)
    assert Adjoint(Adjoint(A)) == A

    assert Adjoint(eye(3)) == eye(3)

    assert Adjoint(S(5)) == S(5)

    assert Adjoint(Matrix([[1, 2], [3, 4]])) == Matrix([[1, 3], [2, 4]])

    assert Adjoint(Trace(Sq)) == conjugate(Trace(Sq))
    assert Trace(Adjoint(Sq)) == conjugate(Trace(Sq))

    assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])
Пример #5
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def test_adjoint():
    Sq = MatrixSymbol("Sq", n, n)

    assert Adjoint(A).shape == (m, n)
    assert Adjoint(A * B).shape == (l, n)
    assert adjoint(Adjoint(A)) == A
    assert isinstance(Adjoint(Adjoint(A)), Adjoint)

    assert conjugate(Adjoint(A)) == Transpose(A)
    assert transpose(Adjoint(A)) == Adjoint(Transpose(A))

    assert Adjoint(eye(3)).doit() == eye(3)

    assert Adjoint(S(5)).doit() == S(5)

    assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])

    assert adjoint(trace(Sq)) == conjugate(trace(Sq))
    assert trace(adjoint(Sq)) == conjugate(trace(Sq))

    assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])

    assert Adjoint(A * B).doit() == Adjoint(B) * Adjoint(A)