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()
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()
def bc_matmul(expr):
factor, matrices = expr.as_coeff_matrices()
i = 0
while (i + 1 < len(matrices)):
A, B = matrices[i:i + 2]
if isinstance(A, BlockMatrix) and isinstance(B, BlockMatrix):
matrices[i] = A._blockmul(B)
matrices.pop(i + 1)
elif isinstance(A, BlockMatrix):
matrices[i] = A._blockmul(BlockMatrix([[B]]))
matrices.pop(i + 1)
elif isinstance(B, BlockMatrix):
matrices[i] = BlockMatrix([[A]])._blockmul(B)
matrices.pop(i + 1)
else:
i += 1
return MatMul(factor, *matrices).doit()
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)
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)
def test_unpack():
assert unpack(MatMul(A, evaluate=False)) == A
x = MatMul(A, B)
assert unpack(x) == x
def test_any_zeros():
assert any_zeros(MatMul(A, ZeroMatrix(m, k), evaluate=False)) == \
ZeroMatrix(n, k)
def test_xxinv():
assert xxinv(MatMul(D, Inverse(D), D, evaluate=False)) == \
MatMul(Identity(n), D, evaluate=False)
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)
def test_factor_in_front():
assert factor_in_front(MatMul(A, 2, B, evaluate=False)) ==\
MatMul(2, A, B, evaluate=False)
def test_matmul_new():
pytest.raises(ShapeError, lambda: MatMul(A, C))
MatMul(A, C, check=False) # not raises
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]])
def test_matmul_sympify():
assert isinstance(MatMul(eye(1), eye(1)).args[0], Basic)
def test_matmul_scalar_Matrix_doit():
# Issue sympy/sympy#9053
X = Matrix([[1, 2], [3, 4]])
assert MatMul(2, X).doit() == 2*X
def test_doit_deep_false_still_canonical():
assert (MatMul(C, Transpose(D*C), 2).doit(deep=False).args ==
(2, C, Transpose(D*C)))
