def test_zero_power():
z1 = ZeroMatrix(n, n)
assert MatPow(z1, 3).doit() == z1
pytest.raises(ValueError, lambda: MatPow(z1, -1).doit())
assert MatPow(z1, 0).doit() == Identity(n)
assert MatPow(z1, n).doit() == z1
pytest.raises(ValueError, lambda: MatPow(z1, -2).doit())
z2 = ZeroMatrix(4, 4)
assert MatPow(z2, n).doit() == z2
pytest.raises(ValueError, lambda: MatPow(z2, -3).doit())
assert MatPow(z2, 2).doit() == z2
assert MatPow(z2, 0).doit() == Identity(4)
pytest.raises(ValueError, lambda: MatPow(z2, -1).doit())
def test_Zero_power():
z1 = ZeroMatrix(n, n)
assert z1**4 == z1
pytest.raises(ValueError, lambda: z1**-2)
assert z1**0 == Identity(n)
assert MatPow(z1, 2).doit() == z1**2
pytest.raises(ValueError, lambda: MatPow(z1, -2).doit())
z2 = ZeroMatrix(3, 3)
assert MatPow(z2, 4).doit() == z2**4
pytest.raises(ValueError, lambda: z2**-3)
assert z2**3 == MatPow(z2, 3).doit()
assert z2**0 == Identity(3)
pytest.raises(ValueError, lambda: MatPow(z2, -1).doit())
def test_addition():
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('B', n, m)
assert isinstance(A + B, MatAdd)
assert (A + B).shape == A.shape
assert isinstance(A - A + 2 * B, MatMul)
pytest.raises(ShapeError, lambda: A + B.T)
pytest.raises(TypeError, lambda: A + 1)
pytest.raises(TypeError, lambda: 5 + A)
pytest.raises(TypeError, lambda: 5 - A)
assert A + ZeroMatrix(n, m) - A == ZeroMatrix(n, m)
with pytest.raises(TypeError):
ZeroMatrix(n, m) + Integer(0)
def test_ZeroMatrix():
A = MatrixSymbol('A', n, m)
Z = ZeroMatrix(n, m)
assert A + Z == A
assert A*Z.T == ZeroMatrix(n, n)
assert Z*A.T == ZeroMatrix(n, n)
assert A - A == ZeroMatrix(*A.shape)
assert not Z
assert transpose(Z) == ZeroMatrix(m, n)
assert Z.conjugate() == Z
assert ZeroMatrix(n, n)**0 == Identity(n)
with pytest.raises(ShapeError):
Z**0
with pytest.raises(ShapeError):
Z**2
def test_multiplication():
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('B', m, l)
C = MatrixSymbol('C', n, n)
assert (2 * A * B).shape == (n, l)
assert (A * 0 * B) == ZeroMatrix(n, l)
pytest.raises(ShapeError, lambda: B * A)
assert (2 * A).shape == A.shape
assert A * ZeroMatrix(m, m) * B == ZeroMatrix(n, l)
assert C * Identity(n) * C.inverse() == Identity(n)
assert B / 2 == Rational(1, 2) * B
pytest.raises(NotImplementedError, lambda: 2 / B)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, n)
assert Identity(n) * (A + B) == A + B
def test_ZeroMatrix():
A = MatrixSymbol('A', n, m)
Z = ZeroMatrix(n, m)
assert A + Z == A
assert A * Z.T == ZeroMatrix(n, n)
assert Z * A.T == ZeroMatrix(n, n)
assert A - A == ZeroMatrix(*A.shape)
assert not Z
assert transpose(Z) == ZeroMatrix(m, n)
assert Z.conjugate() == Z
assert ZeroMatrix(n, n)**0 == Identity(n)
with pytest.raises(ShapeError):
Z**0
with pytest.raises(ShapeError):
Z**2
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_ZeroMatrix_doit():
Znn = ZeroMatrix(Add(n, n, evaluate=False), n)
assert isinstance(Znn.rows, Add)
assert Znn.doit() == ZeroMatrix(2 * n, n)
assert isinstance(Znn.doit().rows, Mul)
def test_matexpr():
assert (x * A).shape == A.shape
assert (x * A).__class__ == MatMul
assert 2 * A - A - A == ZeroMatrix(*A.shape)
assert (A * B).shape == (n, l)
def test_ZeroMatrix_doit():
Znn = ZeroMatrix(Add(n, n, evaluate=False), n)
assert isinstance(Znn.rows, Add)
assert Znn.doit() == ZeroMatrix(2*n, n)
assert isinstance(Znn.doit().rows, Mul)
def test_any_zeros():
assert any_zeros(MatMul(A, ZeroMatrix(m, k), evaluate=False)) == \
ZeroMatrix(n, k)
