def test_eigenvalues_and_vectors(self):
"""Ensure that eigenvalues and -vectors are the solution to the characteristic polynomial."""
A = tensor.symmetric(np.random.rand(self.n, 3, 3))
lambd = tensor.eigenvalues(A)
x = tensor.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_eigenvectors_RHS(self):
"""Ensure that RHS coordinate system does only change sign of determinant."""
A = tensor.symmetric(np.random.rand(self.n, 3, 3))
LRHS = np.linalg.det(tensor.eigenvectors(A, RHS=False))
RHS = np.linalg.det(tensor.eigenvectors(A, RHS=True))
assert np.allclose(np.abs(LRHS), RHS)
def test_add_eigenvector(self, default, eigenvalue, idx):
default.add_stress_Cauchy('P', 'F')
default.add_eigenvector('sigma', eigenvalue)
in_memory = tensor.eigenvectors(default.place('sigma'))[:, idx]
in_file = default.place(f'v_{eigenvalue}(sigma)')
assert np.allclose(in_memory, in_file)