Beispiel #1
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def test_doit_args():
    A = ImmutableMatrix([[1, 2], [3, 4]])
    B = ImmutableMatrix([[2, 3], [4, 5]])
    assert MatAdd(A, MatPow(B, 2)).doit() == A + B**2
    assert MatAdd(A, MatMul(A, B)).doit() == A + A * B
    assert MatAdd(A, A).doit(deep=False) == 2 * A
    assert (MatAdd(A, X, MatMul(A, B), Y,
                   MatAdd(2 * A, B)).doit() == MatAdd(X, Y, 3 * A + A * B + B))
Beispiel #2
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def test_transpose():
    assert transpose(A * B) == Transpose(B) * Transpose(A)
    assert transpose(2 * A * B) == 2 * Transpose(B) * Transpose(A)
    assert transpose(2 * I * C) == 2 * I * Transpose(C)

    M = Matrix(2, 2, [1, 2 + I, 3, 4]).as_immutable()
    MT = Matrix(2, 2, [1, 3, 2 + I, 4])
    assert transpose(M) == MT
    assert transpose(2 * M) == 2 * MT
    assert transpose(MatMul(2, M)) == MatMul(2, MT).doit()
Beispiel #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]).as_immutable()
    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()
Beispiel #4
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def test_Trace_doit_deep_False():
    X = Matrix([[1, 2], [3, 4]])
    assert Trace(X).doit(deep=False) == 5
    q = MatPow(X, 2)
    assert Trace(q).doit(deep=False).arg == q
    q = MatAdd(X, 2 * X)
    assert Trace(q).doit(deep=False).arg == q
    q = MatMul(X, 2 * X)
    assert Trace(q).doit(deep=False).arg == q
Beispiel #5
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def test_invariants():
    A = MatrixSymbol('A', n, m)
    B = MatrixSymbol('B', m, l)
    X = MatrixSymbol('X', n, n)
    objs = [Identity(n), ZeroMatrix(m, n), MatMul(A, B), MatAdd(A, A),
            Transpose(A), Adjoint(A), Inverse(X), MatPow(X, 2), MatPow(X, -1),
            MatPow(X, 0)]
    for obj in objs:
        assert obj == obj.__class__(*obj.args)
Beispiel #6
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def test_doit_drills_down():
    X = ImmutableMatrix([[1, 2], [3, 4]])
    Y = ImmutableMatrix([[2, 3], [4, 5]])
    assert MatMul(X, MatPow(Y, 2)).doit() == X * Y**2
    assert MatMul(C, Transpose(D * C)).doit().args == (C, C.T, D.T)
Beispiel #7
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def test_doit():
    assert MatMul(C, 2, D).args == (C, 2, D)
    assert MatMul(C, 2, D).doit().args == (2, C, D)
    assert MatMul(C, Transpose(D * C)).args == (C, Transpose(D * C))
    assert MatMul(C, Transpose(D * C)).doit(deep=True).args == (C, C.T, D.T)
Beispiel #8
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def test_unpack():
    assert unpack(MatMul(A, evaluate=False)) == A
    x = MatMul(A, B)
    assert unpack(x) == x
Beispiel #9
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def test_any_zeros():
    assert any_zeros(MatMul(A, ZeroMatrix(m, k), evaluate=False)) == \
        ZeroMatrix(n, k)
Beispiel #10
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def test_doit_deep_false_still_canonical():
    assert (MatMul(C, Transpose(D * C),
                   2).doit(deep=False).args == (2, C, Transpose(D * C)))
Beispiel #11
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def test_matmul_simplify():
    A = MatrixSymbol('A', 1, 1)
    assert simplify(MatMul(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
        MatMul(A, ImmutableMatrix([[1]]))
Beispiel #12
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def test_factor_in_front():
    assert factor_in_front(MatMul(A, 2, B, evaluate=False)) ==\
        MatMul(2, A, B, evaluate=False)
Beispiel #13
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def test_matmul_new():
    pytest.raises(ShapeError, lambda: MatMul(A, C))
    MatMul(A, C, check=False)  # not raises
Beispiel #14
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def test_collapse_MatrixBase():
    A = Matrix([[1, 1], [1, 1]])
    B = Matrix([[1, 2], [3, 4]])
    assert MatMul(A, B).doit() == ImmutableMatrix([[4, 6], [4, 6]])
Beispiel #15
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def test_matmul_sympify():
    assert isinstance(MatMul(eye(1), eye(1)).args[0], Basic)
Beispiel #16
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def test_matmul_scalar_Matrix_doit():
    # Issue sympy/sympy#9053
    X = Matrix([[1, 2], [3, 4]])
    assert MatMul(2, X).doit() == 2 * X
Beispiel #17
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def test_trace_constant_factor():
    # Issue sympy/sympy#9052: gave 2*Trace(MatMul(A)) instead of 2*Trace(A)
    assert trace(2 * A) == 2 * Trace(A)
    X = ImmutableMatrix([[1, 2], [3, 4]])
    assert trace(MatMul(2, X)) == 10
Beispiel #18
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def test_remove_ids():
    assert remove_ids(MatMul(A, Identity(m), B, evaluate=False)) == \
        MatMul(A, B, evaluate=False)
    assert null_safe(remove_ids)(MatMul(Identity(n), evaluate=False)) == \
        MatMul(Identity(n), evaluate=False)
Beispiel #19
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def test_xxinv():
    assert xxinv(MatMul(D, Inverse(D), D, evaluate=False)) == \
        MatMul(Identity(n), D, evaluate=False)
Beispiel #20
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def test_doit_nested_MatrixExpr():
    X = ImmutableMatrix([[1, 2], [3, 4]])
    Y = ImmutableMatrix([[2, 3], [4, 5]])
    assert MatPow(MatMul(X, Y), 2).doit() == (X * Y)**2
    assert MatPow(MatAdd(X, Y), 2).doit() == (X + Y)**2