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)
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)
def test_dft():
assert DFT(4).shape == (4, 4)
assert Abs(simplify(det(Matrix(DFT(4))))) == 1
assert DFT(n) * IDFT(n) == Identity(n)
assert DFT(n)[i, j] == exp(-2 * S.Pi * I / n)**(i * j) / sqrt(n)
def test_dft():
assert DFT(4).shape == (4, 4)
assert Abs(simplify(det(Matrix(DFT(4))))) == 1
assert DFT(n)*IDFT(n) == Identity(n)
assert DFT(n)[i, j] == exp(-2*pi*I/n)**(i*j) / sqrt(n)
assert DFT(n).inverse() == IDFT(n)