DAMASK_EICMD/python/tests/test_tensor.py

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import pytest
import numpy as np
from damask import tensor
def eigenvalues(T_sym):
return np.linalg.eigvalsh(symmetric(T_sym))
def eigenvectors(T_sym,RHS=False):
(u,v) = np.linalg.eigh(symmetric(T_sym))
if RHS:
if np.linalg.det(v) < 0.0: v[:,2] *= -1.0
return v
def symmetric(T):
return (T+transpose(T))*0.5
def transpose(T):
return T.T
class TestTensor:
n = 1000
c = np.random.randint(n)
@pytest.mark.parametrize('vectorized,single',[(tensor.eigenvalues , eigenvalues ),
(tensor.eigenvectors , eigenvectors ),
(tensor.symmetric , symmetric ),
(tensor.transpose , transpose ),
])
def test_vectorize_1_arg(self,vectorized,single):
epsilon = np.random.rand(self.n,3,3)
epsilon_vec = np.reshape(epsilon,(self.n//10,10,3,3))
for i,v in enumerate(np.reshape(vectorized(epsilon_vec),vectorized(epsilon).shape)):
assert np.allclose(single(epsilon[i]),v)
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(tensor.symmetric(x)*2.0,tensor.transpose(x)+x)
def test_transpose(self):
"""Ensure that a symmetric tensor equals its transpose."""
x = tensor.symmetric(np.random.rand(self.n,3,3))
assert np.allclose(tensor.transpose(x),x)
def test_eigenvalues(self):
"""Ensure that the characteristic polynomial can be solved."""
A = tensor.symmetric(np.random.rand(self.n,3,3))
lambd = tensor.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 = 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)