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_MatPow():
A = MatrixSymbol('A', n, n)
AA = MatPow(A, 2)
assert AA.exp == 2
assert AA.base == A
assert (A**n).exp == n
assert A**0 == Identity(n)
assert A**1 == A
assert A**2 == AA
assert A**-1 == Inverse(A)
assert A**Rational(1, 2) == sqrt(A)
pytest.raises(ShapeError, lambda: MatrixSymbol('B', 3, 2)**2)
def test_xxinv():
assert xxinv(MatMul(D, Inverse(D), D, evaluate=False)) == \
MatMul(Identity(n), D, evaluate=False)
def test_inverse():
pytest.raises(ShapeError, lambda: Inverse(A))
pytest.raises(ShapeError, lambda: Inverse(A * B))
pytest.raises(TypeError, lambda: Inverse(1))
assert Inverse(C).shape == (n, n)
assert Inverse(A * E).shape == (n, n)
assert Inverse(E * A).shape == (m, m)
assert Inverse(C).inverse() == C
assert isinstance(Inverse(Inverse(C)), Inverse)
assert C.inverse().inverse() == C
assert C.inverse() * C == Identity(C.rows)
assert Identity(n).inverse() == Identity(n)
assert (3 * Identity(n)).inverse() == Identity(n) / 3
# Simplifies Muls if possible (i.e. submatrices are square)
assert (C * D).inverse() == D.inverse() * C.inverse()
# But still works when not possible
assert isinstance((A * E).inverse(), Inverse)
assert Inverse(eye(3)).doit() == eye(3)
assert Inverse(eye(3)).doit(deep=False) == eye(3)
assert det(Inverse(C)) == 1 / det(C)