def test_invertible_BlockMatrix():
assert ask(Q.invertible(BlockMatrix([Identity(3)]))) == True
assert ask(Q.invertible(BlockMatrix([ZeroMatrix(3, 3)]))) == False
X = Matrix([[1, 2, 3], [3, 5, 4]])
Y = Matrix([[4, 2, 7], [2, 3, 5]])
# non-invertible A block
assert ask(
Q.invertible(
BlockMatrix([
[Matrix.ones(3, 3), Y.T],
[X, Matrix.eye(2)],
]))) == True
# non-invertible B block
assert ask(
Q.invertible(
BlockMatrix([
[Y.T, Matrix.ones(3, 3)],
[Matrix.eye(2), X],
]))) == True
# non-invertible C block
assert ask(
Q.invertible(
BlockMatrix([
[X, Matrix.eye(2)],
[Matrix.ones(3, 3), Y.T],
]))) == True
# non-invertible D block
assert ask(
Q.invertible(
BlockMatrix([
[Matrix.eye(2), X],
[Y.T, Matrix.ones(3, 3)],
]))) == True
def test_TensorProduct_construction():
assert TensorProduct(3, 4) == 12
assert isinstance(TensorProduct(A, A), TensorProduct)
expr = TensorProduct(TensorProduct(x, y), z)
assert expr == x * y * z
expr = TensorProduct(TensorProduct(A, B), C)
assert expr == TensorProduct(A, B, C)
expr = TensorProduct(Matrix.eye(2), [[0, -1], [1, 0]])
assert expr == Array([[[[0, -1], [1, 0]], [[0, 0], [0, 0]]],
[[[0, 0], [0, 0]], [[0, -1], [1, 0]]]])
def test_TensorProduct_shape():
expr = TensorProduct(3, 4, evaluate=False)
assert expr.shape == ()
assert expr.rank() == 0
expr = TensorProduct(Array([1, 2]), Array([x, y]), evaluate=False)
assert expr.shape == (2, 2)
assert expr.rank() == 2
expr = TensorProduct(expr, expr, evaluate=False)
assert expr.shape == (2, 2, 2, 2)
assert expr.rank() == 4
expr = TensorProduct(Matrix.eye(2), Array([[0, -1], [1, 0]]), evaluate=False)
assert expr.shape == (2, 2, 2, 2)
assert expr.rank() == 4
def test_issue_2827_trigsimp_methods():
measure1 = lambda expr: len(str(expr))
measure2 = lambda expr: -count_ops(expr)
# Return the most complicated result
expr = (x + 1) / (x + sin(x)**2 + cos(x)**2)
ans = Matrix([1])
M = Matrix([expr])
assert trigsimp(M, method='fu', measure=measure1) == ans
assert trigsimp(M, method='fu', measure=measure2) != ans
# all methods should work with Basic expressions even if they
# aren't Expr
M = Matrix.eye(1)
assert all(
trigsimp(M, method=m) == M for m in 'fu matching groebner old'.split())
# watch for E in exptrigsimp, not only exp()
eq = 1 / sqrt(E) + E
assert exptrigsimp(eq) == eq