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))
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 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_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
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)
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_doit_deep_false_still_canonical():
assert (MatMul(C, Transpose(D * C),
2).doit(deep=False).args == (2, C, Transpose(D * C)))
def test_matmul_simplify():
A = MatrixSymbol('A', 1, 1)
assert simplify(MatMul(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
MatMul(A, ImmutableMatrix([[1]]))
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_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
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_xxinv():
assert xxinv(MatMul(D, Inverse(D), D, evaluate=False)) == \
MatMul(Identity(n), D, evaluate=False)
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