def test_eigenvalues(self):
"""Ensure that the characteristic polynomial can be solved."""
A = mechanics.symmetric(np.random.rand(self.n, 3, 3))
lambd = mechanics.eigenvalues(A)
s = np.random.randint(self.n)
for i in range(3):
assert np.allclose(np.linalg.det(A[s] - lambd[s, i] * np.eye(3)),
.0)
def test_eigenvalues_and_vectors(self):
"""Ensure that eigenvalues and -vectors are the solution to the characteristic polynomial."""
A = mechanics.symmetric(np.random.rand(self.n, 3, 3))
lambd = mechanics.eigenvalues(A)
x = mechanics.eigenvectors(A)
s = np.random.randint(self.n)
for i in range(3):
assert np.allclose(
np.dot(A[s] - lambd[s, i] * np.eye(3), x[s, :, i]), .0)
def test_stress_measures(self, function):
"""Ensure that all stress measures are equivalent for no deformation."""
P = np.random.rand(self.n, 3, 3)
assert np.allclose(
function(P, np.broadcast_to(np.eye(3), (self.n, 3, 3))),
mechanics.symmetric(P))
def test_spherical_no_shear(self):
"""Ensure that sherical stress has max shear of 0.0."""
A = mechanics.spherical_part(
mechanics.symmetric(np.random.rand(self.n, 3, 3)), True)
assert np.allclose(mechanics.maximum_shear(A), 0.0)
def test_eigenvectors_RHS(self):
"""Ensure that RHS coordinate system does only change sign of determinant."""
A = mechanics.symmetric(np.random.rand(self.n, 3, 3))
LRHS = np.linalg.det(mechanics.eigenvectors(A, RHS=False))
RHS = np.linalg.det(mechanics.eigenvectors(A, RHS=True))
assert np.allclose(np.abs(LRHS), RHS)
def test_transpose(self):
"""Ensure that a symmetric tensor equals its transpose."""
x = mechanics.symmetric(np.random.rand(self.n, 3, 3))
assert np.allclose(mechanics.transpose(x), x)
def test_symmetric(self):
"""Ensure that a symmetric tensor is half of the sum of a tensor and its transpose."""
x = np.random.rand(self.n, 3, 3)
assert np.allclose(
mechanics.symmetric(x) * 2.0,
mechanics.transpose(x) + x)