DAMASK_EICMD/python/tests/test_tensor.py

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import pytest
import numpy as np
from damask import tensor
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def deviatoric(T):
return T - spherical(T)
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
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def spherical(T,tensor=True):
sph = np.trace(T)/3.0
return sph if not tensor else np.eye(3)*sph
class TestTensor:
n = 1000
c = np.random.randint(n)
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@pytest.mark.parametrize('vectorized,single',[(tensor.deviatoric, deviatoric),
(tensor.eigenvalues, eigenvalues),
(tensor.eigenvectors, eigenvectors),
(tensor.symmetric, symmetric),
(tensor.transpose, transpose),
(tensor.spherical, spherical),
])
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)
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def test_spherical_deviatoric_part(self):
"""Ensure that full tensor is sum of spherical and deviatoric part."""
x = np.random.rand(self.n,3,3)
assert np.allclose(tensor.spherical(x,True) + tensor.deviatoric(x),
x)
def test_spherical_mapping(self):
"""Ensure that mapping to tensor is correct."""
x = np.random.rand(self.n,3,3)
tnsr = tensor.spherical(x,True)
scalar = tensor.spherical(x,False)
assert np.allclose(np.linalg.det(tnsr),
scalar**3.0)
def test_deviatoric(self):
I_n = np.broadcast_to(np.eye(3),(self.n,3,3))
r = np.logical_not(I_n)*np.random.rand(self.n,3,3)
assert np.allclose(tensor.deviatoric(I_n+r),r)