def __new__(cls, strain_matrix, dfm=None):
"""
Create a Strain object. Note that the constructor uses __new__
rather than __init__ according to the standard method of
subclassing numpy ndarrays. Note also that the default constructor
does not include the deformation gradient
Args:
strain_matrix (3x3 array-like): the 3x3 array-like
representing the Green-Lagrange strain
"""
obj = SquareTensor(strain_matrix).view(cls)
obj._dfm = dfm
if not obj.is_symmetric():
raise ValueError("Strain objects must be initialized "
"with a symmetric array-like.")
if dfm is None:
warnings.warn(
"Constructing a strain object without a deformation "
"matrix makes many methods unusable. Use "
"Strain.from_deformation to construct a Strain object"
" from a deformation gradient.")
elif (np.array(dfm) - obj < 1e-5).all():
warnings.warn("Warning: deformation matrix does not correspond "
"to input strain_matrix value")
return obj
def __new__(cls, strain_matrix, dfm=None):
"""
Create a Strain object. Note that the constructor uses __new__
rather than __init__ according to the standard method of
subclassing numpy ndarrays. Note also that the default constructor
does not include the deformation gradient
Args:
strain_matrix (3x3 array-like): the 3x3 array-like
representing the Green-Lagrange strain
"""
obj = SquareTensor(strain_matrix).view(cls)
obj._dfm = dfm
if not obj.is_symmetric():
raise ValueError("Strain objects must be initialized "
"with a symmetric array-like.")
if dfm is None:
warnings.warn("Constructing a strain object without a deformation "
"matrix makes many methods unusable. Use "
"Strain.from_deformation to construct a Strain object"
" from a deformation gradient.")
elif (np.array(dfm) - obj < 1e-5).all():
warnings.warn("Warning: deformation matrix does not correspond "
"to input strain_matrix value")
return obj
def thermal_expansion_coeff(self, structure, temperature, mode="debye"):
"""
Gets thermal expansion coefficient from third-order constants.
Args:
temperature (float): Temperature in kelvin, if not specified
will return non-cv-normalized value
structure (Structure): Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified
mode (string): mode for finding average heat-capacity,
current supported modes are 'debye' and 'dulong-petit'
"""
soec = ElasticTensor(self[0])
v0 = (structure.volume * 1e-30 / structure.num_sites)
if mode == "debye":
td = soec.debye_temperature(structure)
t_ratio = temperature / td
integrand = lambda x: (x**4 * np.exp(x)) / (np.exp(x) - 1)**2
cv = 9 * 8.314 * t_ratio**3 * quad(integrand, 0, t_ratio**-1)[0]
elif mode == "dulong-petit":
cv = 3 * 8.314
else:
raise ValueError("Mode must be debye or dulong-petit")
tgt = self.get_tgt(temperature, structure)
alpha = np.einsum('ijkl,ij', soec.compliance_tensor, tgt)
alpha *= cv / (1e9 * v0 * 6.022e23)
return SquareTensor(alpha)
def convert_strain_to_deformation(strain):
strain = SquareTensor(strain)
ftdotf = 2 * strain + np.eye(3)
eigs, eigvecs = np.linalg.eigh(ftdotf)
rotated = ftdotf.rotate(np.transpose(eigvecs))
rotated = rotated.round(10)
defo = Deformation(np.sqrt(rotated))
result = defo.rotate(eigvecs)
return result
def test_rotate(self):
self.assertArrayEqual(
self.vec.rotate([[0, -1, 0], [1, 0, 0], [0, 0, 1]]), [0, 1, 0])
self.assertArrayAlmostEqual(self.non_symm.rotate(self.rotation),
SquareTensor([[0.531, 0.485, 0.271],
[0.700, 0.5, 0.172],
[0.171, 0.233, 0.068]]),
decimal=3)
self.assertRaises(ValueError, self.non_symm.rotate, self.symm_rank2)
def test_properties(self):
# transpose
self.assertArrayEqual(self.non_symm.trans,
SquareTensor([[0.1, 0.4, 0.2],
[0.2, 0.5, 0.5],
[0.3, 0.6, 0.5]]))
self.assertArrayEqual(self.rand_sqtensor.trans,
np.transpose(self.rand_sqtensor))
self.assertArrayEqual(self.symm_sqtensor,
self.symm_sqtensor.trans)
# inverse
self.assertArrayEqual(self.non_symm.inv,
np.linalg.inv(self.non_symm))
with self.assertRaises(ValueError):
self.non_invertible.inv
# determinant
self.assertEqual(self.rand_sqtensor.det,
np.linalg.det(self.rand_sqtensor))
self.assertEqual(self.non_invertible.det,
0.0)
self.assertEqual(self.non_symm.det, 0.009)
# symmetrized
self.assertArrayEqual(self.rand_sqtensor.symmetrized,
0.5 * (self.rand_sqtensor + self.rand_sqtensor.trans))
self.assertArrayEqual(self.symm_sqtensor,
self.symm_sqtensor.symmetrized)
self.assertArrayAlmostEqual(self.non_symm.symmetrized,
SquareTensor([[0.1, 0.3, 0.25],
[0.3, 0.5, 0.55],
[0.25, 0.55, 0.5]]))
# invariants
i1 = np.trace(self.rand_sqtensor)
i2 = self.rand_sqtensor[0, 0] * self.rand_sqtensor[1, 1] + \
self.rand_sqtensor[1, 1] * self.rand_sqtensor[2, 2] + \
self.rand_sqtensor[2, 2] * self.rand_sqtensor[0, 0] - \
self.rand_sqtensor[0, 1] * self.rand_sqtensor[1, 0] - \
self.rand_sqtensor[0, 2] * self.rand_sqtensor[2, 0] - \
self.rand_sqtensor[2, 1] * self.rand_sqtensor[1, 2]
i3 = np.linalg.det(self.rand_sqtensor)
self.assertArrayAlmostEqual([i1, i2, i3],
self.rand_sqtensor.principal_invariants)
def generate_elastic_workflow(structure, tags=None):
"""
Generates a standard production workflow.
Notes:
Uses a primitive structure transformed into
the conventional basis (for equivalent deformations).
Adds the "minimal" category to the minimal portion
of the workflow necessary to generate the elastic tensor,
and the "minimal_full_stencil" category to the portion that
includes all of the strain stencil, but is symmetrically complete
"""
if tags == None:
tags = []
# transform the structure
ieee_rot = Tensor.get_ieee_rotation(structure)
if not SquareTensor(ieee_rot).is_rotation(tol=0.005):
raise ValueError("Rotation matrix does not satisfy rotation conditions")
symm_op = SymmOp.from_rotation_and_translation(ieee_rot)
ieee_structure = structure.copy()
ieee_structure.apply_operation(symm_op)
# construct workflow
wf = wf_elastic_constant(ieee_structure)
# Set categories, starting with optimization
opt_fws = get_fws_and_tasks(wf, fw_name_constraint="optimization")
wf.fws[opt_fws[0][0]].spec['elastic_category'] = "minimal"
# find minimal set of fireworks using symmetry reduction
fws_by_strain = {Strain(fw.tasks[-1]['pass_dict']['strain']): n
for n, fw in enumerate(wf.fws) if 'deformation' in fw.name}
unique_tensors = symmetry_reduce(list(fws_by_strain.keys()), ieee_structure)
for unique_tensor in unique_tensors:
fw_index = get_tkd_value(fws_by_strain, unique_tensor)
if np.isclose(unique_tensor, 0.005).any():
wf.fws[fw_index].spec['elastic_category'] = "minimal"
else:
wf.fws[fw_index].spec['elastic_category'] = "minimal_full_stencil"
# Add tags
if tags:
wf = add_tags(wf, tags)
wf = add_modify_incar(wf)
priority = 500 - structure.num_sites
wf = add_priority(wf, priority)
for fw in wf.fws:
if fw.spec.get('elastic_category') == 'minimal':
fw.spec['_priority'] += 2000
elif fw.spec.get('elastic_category') == 'minimal_full_stencil':
fw.spec['_priority'] += 1000
return wf
def piola_kirchoff_1(self, def_grad):
"""
calculates the first Piola-Kirchoff stress
Args:
def_grad (3x3 array-like): deformation gradient tensor
"""
if not self.is_symmetric:
raise ValueError("The stress tensor is not symmetric, \
PK stress is based on a symmetric stress tensor.")
def_grad = SquareTensor(def_grad)
return def_grad.det * np.dot(self, def_grad.inv.trans)
def __new__(cls, stress_matrix):
"""
Create a Stress object. Note that the constructor uses __new__
rather than __init__ according to the standard method of
subclassing numpy ndarrays.
Args:
stress_matrix (3x3 array-like): the 3x3 array-like
representing the stress
"""
obj = SquareTensor(stress_matrix).view(cls)
return obj
def setUp(self):
self.rand_sqtensor = SquareTensor(np.random.randn(3, 3))
self.symm_sqtensor = SquareTensor([[0.1, 0.3, 0.4],
[0.3, 0.5, 0.2],
[0.4, 0.2, 0.6]])
self.non_invertible = SquareTensor([[0.1, 0, 0],
[0.2, 0, 0],
[0, 0, 0]])
self.non_symm = SquareTensor([[0.1, 0.2, 0.3],
[0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.low_val = SquareTensor([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.low_val_2 = SquareTensor([[1e-6, -1 - 1e-6, 1e-6],
[1 + 1e-7, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-6]])
a = 3.14 * 42.5 / 180
self.rotation = SquareTensor([[math.cos(a), 0, math.sin(a)],
[0, 1, 0],
[-math.sin(a), 0, math.cos(a)]])
def convert_strain_to_deformation(strain, tol=1e-5):
strain = SquareTensor(strain)
ftdotf = 2 * strain + np.eye(3)
eigs, eigvecs = np.linalg.eig(ftdotf)
rotated = ftdotf.rotate(np.transpose(eigvecs))
rotated = rotated.round(10)
defo = Deformation(np.sqrt(rotated))
result = defo.rotate(eigvecs)
rd = np.abs(strain - 0.5 *
(np.dot(np.transpose(result), result) - np.eye(3)))
assert (rd < tol).all(), "Strain-generated deformation is not valid!"
return result
def __new__(cls, deformation_gradient):
"""
Create a Deformation object. Note that the constructor uses __new__
rather than __init__ according to the standard method of subclassing
numpy ndarrays.
Args:
deformation_gradient (3x3 array-like): the 3x3 array-like
representing the deformation gradient
"""
obj = SquareTensor(deformation_gradient).view(cls)
return obj
def piola_kirchoff_2(self, def_grad):
"""
calculates the second Piola-Kirchoff stress
Args:
def_grad (3x3 array-like): rate of deformation tensor
"""
def_grad = SquareTensor(def_grad)
if not self.is_symmetric:
raise ValueError("The stress tensor is not symmetric, \
PK stress is based on a symmetric stress tensor.")
return def_grad.det * np.dot(np.dot(def_grad.inv, self),
def_grad.inv.trans)
def convert_strain_to_deformation(strain):
"""
This function converts a strain to a deformation gradient that will
produce that strain
Args:
strain (3x3 array-like): strain matrix
"""
strain = SquareTensor(strain)
ftdotf = 2*strain + np.eye(3)
eigs, eigvecs = np.linalg.eigh(ftdotf)
rotated = ftdotf.rotate(np.transpose(eigvecs))
rotated = rotated.round(10)
defo = Deformation(np.sqrt(rotated))
result = defo.rotate(eigvecs)
return result
def get_tgt(self, temperature=None, structure=None, quad=None):
"""
Gets the thermodynamic Gruneisen tensor (TGT) by via an
integration of the GGT weighted by the directional heat
capacity.
See refs:
R. N. Thurston and K. Brugger, Phys. Rev. 113, A1604 (1964).
K. Brugger Phys. Rev. 137, A1826 (1965).
Args:
temperature (float): Temperature in kelvin, if not specified
will return non-cv-normalized value
structure (float): Structure to be used in directional heat
capacity determination, only necessary if temperature
is specified
quad (dict): quadrature for integration, should be
dictionary with "points" and "weights" keys defaults
to quadpy.sphere.Lebedev(19) as read from file
"""
if temperature and not structure:
raise ValueError("If using temperature input, you must also "
"include structure")
if not quad:
quad = loadfn(
os.path.join(os.path.dirname(__file__), "quad_data.json"))
points = quad['points']
weights = quad['weights']
num, denom, c = np.zeros((3, 3)), 0, 1
for p, w in zip(points, weights):
gk = ElasticTensor(self[0]).green_kristoffel(p)
rho_wsquareds, us = np.linalg.eigh(gk)
us = [u / np.linalg.norm(u) for u in np.transpose(us)]
for u in us:
# TODO: this should be benchmarked
if temperature:
c = self.get_heat_capacity(temperature, structure, p, u)
num += c * self.get_ggt(p, u) * w
denom += c * w
return SquareTensor(num / denom)
def convert_strain_to_deformation(strain, shape="upper"):
"""
This function converts a strain to a deformation gradient that will
produce that strain. Supports three methods:
Args:
strain (3x3 array-like): strain matrix
shape: (string): method for determining deformation, supports
"upper" produces an upper triangular defo
"lower" produces a lower triangular defo
"symmetric" produces a symmetric defo
"""
strain = SquareTensor(strain)
ftdotf = 2 * strain + np.eye(3)
if shape == "upper":
result = scipy.linalg.cholesky(ftdotf)
elif shape == "symmetric":
result = scipy.linalg.sqrtm(ftdotf)
else:
raise ValueError("shape must be \"upper\" or \"symmetric\"")
return Deformation(result)
def setUp(self):
self.vec = TensorBase([1., 0., 0.])
self.rand_rank2 = TensorBase(np.random.randn(3,3))
self.rand_rank3 = TensorBase(np.random.randn(3,3,3))
self.rand_rank4 = TensorBase(np.random.randn(3,3,3,3))
a = 3.14 * 42.5 / 180
self.non_symm = SquareTensor([[0.1, 0.2, 0.3],
[0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.rotation = SquareTensor([[math.cos(a), 0, math.sin(a)],
[0, 1, 0],
[-math.sin(a), 0, math.cos(a)]])
self.low_val = TensorBase([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.symm_rank2 = TensorBase([[1, 2, 3],
[2, 4, 5],
[3, 5, 6]])
self.symm_rank3 = TensorBase([[[1, 2, 3],
[2, 4, 5],
[3, 5, 6]],
[[2, 4, 5],
[4, 7, 8],
[5, 8, 9]],
[[3, 5, 6],
[5, 8, 9],
[6, 9, 10]]])
self.symm_rank4 = TensorBase([[[[1.2, 0.4, -0.92],
[0.4, 0.05, 0.11],
[-0.92, 0.11, -0.02]],
[[0.4, 0.05, 0.11],
[0.05, -0.47, 0.09],
[0.11, 0.09, -0.]],
[[-0.92, 0.11, -0.02],
[0.11, 0.09, 0.],
[-0.02, 0., -0.3]]],
[[[0.4, 0.05, 0.11],
[0.05, -0.47, 0.09],
[0.11, 0.09, 0.]],
[[0.05, -0.47, 0.09],
[-0.47, 0.17, 0.62],
[0.09, 0.62, 0.3]],
[[0.11, 0.09, 0.],
[0.09, 0.62, 0.3],
[0., 0.3, -0.18]]],
[[[-0.92, 0.11, -0.02],
[0.11, 0.09, 0.],
[-0.02, 0, -0.3]],
[[0.11, 0.09, 0.],
[0.09, 0.62, 0.3],
[0., 0.3, -0.18]],
[[-0.02, 0., -0.3],
[0., 0.3, -0.18],
[-0.3, -0.18, -0.51]]]])
# Structural symmetries tested using BaNiO3 piezo/elastic tensors
self.fit_r3 = TensorBase([[[0., 0., 0.03839],
[0., 0., 0.],
[0.03839, 0., 0.]],
[[0., 0., 0.],
[0., 0., 0.03839],
[0., 0.03839, 0.]],
[[6.89822, 0., 0.],
[0., 6.89822, 0.],
[0., 0., 27.4628]]])
self.fit_r4 = TensorBase([[[[157.9, 0., 0.],
[0., 63.1, 0.],
[0., 0., 29.4]],
[[0., 47.4, 0.],
[47.4, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.3],
[0., 0., 0.],
[4.3, 0., 0.]]],
[[[0., 47.4, 0.],
[47.4, 0., 0.],
[0., 0., 0.]],
[[63.1, 0., 0.],
[0., 157.9, 0.],
[0., 0., 29.4]],
[[0., 0., 0.],
[0., 0., 4.3],
[0., 4.3, 0.]]],
[[[0., 0., 4.3],
[0., 0., 0.],
[4.3, 0., 0.]],
[[0., 0., 0.],
[0., 0., 4.3],
[0., 4.3, 0.]],
[[29.4, 0., 0.],
[0., 29.4, 0.],
[0., 0., 207.6]]]])
self.unfit4 = TensorBase([[[[161.26, 0., 0.],
[0., 62.76, 0.],
[0., 0., 30.18]],
[[0., 47.08, 0.],
[47.08, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.23],
[0., 0., 0.],
[4.23, 0., 0.]]],
[[[0., 47.08, 0.],
[47.08, 0., 0.],
[0., 0., 0.]],
[[62.76, 0., 0.],
[0., 155.28, -0.06],
[0., -0.06, 28.53]],
[[0., 0., 0.],
[0., -0.06, 4.44],
[0., 4.44, 0.]]],
[[[0., 0., 4.23],
[0., 0., 0.],
[4.23, 0., 0.]],
[[0., 0., 0.],
[0., -0.06, 4.44],
[0., 4.44, 0.]],
[[30.18, 0., 0.],
[0., 28.53, 0.],
[0., 0., 207.57]]]])
self.structure = self.get_structure('BaNiO3')
ieee_file_path = os.path.join(test_dir, "ieee_conversion_data.json")
with open(ieee_file_path) as f:
self.ieee_data = json.load(f)
def setUp(self):
self.rand_sqtensor = SquareTensor(np.random.randn(3, 3))
self.symm_sqtensor = SquareTensor([[0.1, 0.3, 0.4], [0.3, 0.5, 0.2],
[0.4, 0.2, 0.6]])
self.non_invertible = SquareTensor([[0.1, 0, 0], [0.2, 0, 0],
[0, 0, 0]])
self.non_symm = SquareTensor([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.low_val = SquareTensor([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.low_val_2 = SquareTensor([[1e-6, -1 - 1e-6, 1e-6],
[1 + 1e-7, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-6]])
a = 3.14 * 42.5 / 180
self.rotation = SquareTensor([[math.cos(a), 0,
math.sin(a)], [0, 1, 0],
[-math.sin(a), 0,
math.cos(a)]])
def test_get_scaled(self):
self.assertArrayEqual(self.non_symm.get_scaled(10.),
SquareTensor([[1, 2, 3], [4, 5, 6], [2, 5, 5]]))
class SquareTensorTest(PymatgenTest):
def setUp(self):
self.rand_sqtensor = SquareTensor(np.random.randn(3, 3))
self.symm_sqtensor = SquareTensor([[0.1, 0.3, 0.4], [0.3, 0.5, 0.2],
[0.4, 0.2, 0.6]])
self.non_invertible = SquareTensor([[0.1, 0, 0], [0.2, 0, 0],
[0, 0, 0]])
self.non_symm = SquareTensor([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.low_val = SquareTensor([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.low_val_2 = SquareTensor([[1e-6, -1 - 1e-6, 1e-6],
[1 + 1e-7, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-6]])
a = 3.14 * 42.5 / 180
self.rotation = SquareTensor([[math.cos(a), 0,
math.sin(a)], [0, 1, 0],
[-math.sin(a), 0,
math.cos(a)]])
def test_new(self):
non_sq_matrix = [[0.1, 0.2, 0.1], [0.1, 0.2, 0.3], [0.1, 0.2, 0.3],
[0.1, 0.1, 0.1]]
bad_matrix = [[0.1, 0.2], [0.2, 0.3, 0.4], [0.2, 0.3, 0.5]]
too_high_rank = np.zeros((3, 3, 3))
self.assertRaises(ValueError, SquareTensor, non_sq_matrix)
self.assertRaises(ValueError, SquareTensor, bad_matrix)
self.assertRaises(ValueError, SquareTensor, too_high_rank)
def test_properties(self):
# transpose
self.assertArrayEqual(
self.non_symm.trans,
SquareTensor([[0.1, 0.4, 0.2], [0.2, 0.5, 0.5], [0.3, 0.6, 0.5]]))
self.assertArrayEqual(self.rand_sqtensor.trans,
np.transpose(self.rand_sqtensor))
self.assertArrayEqual(self.symm_sqtensor, self.symm_sqtensor.trans)
# inverse
self.assertArrayEqual(self.non_symm.inv, np.linalg.inv(self.non_symm))
with self.assertRaises(ValueError):
self.non_invertible.inv
# determinant
self.assertEqual(self.rand_sqtensor.det,
np.linalg.det(self.rand_sqtensor))
self.assertEqual(self.non_invertible.det, 0.0)
self.assertEqual(self.non_symm.det, 0.009)
# symmetrized
self.assertArrayEqual(
self.rand_sqtensor.symmetrized,
0.5 * (self.rand_sqtensor + self.rand_sqtensor.trans))
self.assertArrayEqual(self.symm_sqtensor,
self.symm_sqtensor.symmetrized)
self.assertArrayAlmostEqual(
self.non_symm.symmetrized,
SquareTensor([[0.1, 0.3, 0.25], [0.3, 0.5, 0.55],
[0.25, 0.55, 0.5]]))
# invariants
i1 = np.trace(self.rand_sqtensor)
i2 = self.rand_sqtensor[0, 0] * self.rand_sqtensor[1, 1] + \
self.rand_sqtensor[1, 1] * self.rand_sqtensor[2, 2] + \
self.rand_sqtensor[2, 2] * self.rand_sqtensor[0, 0] - \
self.rand_sqtensor[0, 1] * self.rand_sqtensor[1, 0] - \
self.rand_sqtensor[0, 2] * self.rand_sqtensor[2, 0] - \
self.rand_sqtensor[2, 1] * self.rand_sqtensor[1, 2]
i3 = np.linalg.det(self.rand_sqtensor)
self.assertArrayAlmostEqual([i1, i2, i3],
self.rand_sqtensor.principal_invariants)
def test_is_rotation(self):
self.assertTrue(self.rotation.is_rotation())
self.assertFalse(self.symm_sqtensor.is_rotation())
self.assertTrue(self.low_val_2.is_rotation())
self.assertFalse(self.low_val_2.is_rotation(tol=1e-8))
def test_get_scaled(self):
self.assertArrayEqual(self.non_symm.get_scaled(10.),
SquareTensor([[1, 2, 3], [4, 5, 6], [2, 5, 5]]))
def test_polar_decomposition(self):
u, p = self.rand_sqtensor.polar_decomposition()
self.assertArrayAlmostEqual(np.dot(u, p), self.rand_sqtensor)
self.assertArrayAlmostEqual(np.eye(3),
np.dot(u, np.conjugate(np.transpose(u))))
def setUp(self):
self.vec = TensorBase([1., 0., 0.])
self.rand_rank2 = TensorBase(np.random.randn(3, 3))
self.rand_rank3 = TensorBase(np.random.randn(3, 3, 3))
self.rand_rank4 = TensorBase(np.random.randn(3, 3, 3, 3))
a = 3.14 * 42.5 / 180
self.non_symm = SquareTensor([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.rotation = SquareTensor([[math.cos(a), 0,
math.sin(a)], [0, 1, 0],
[-math.sin(a), 0,
math.cos(a)]])
self.low_val = TensorBase([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.symm_rank2 = TensorBase([[1, 2, 3], [2, 4, 5], [3, 5, 6]])
self.symm_rank3 = TensorBase([[[1, 2, 3], [2, 4, 5], [3, 5, 6]],
[[2, 4, 5], [4, 7, 8], [5, 8, 9]],
[[3, 5, 6], [5, 8, 9], [6, 9, 10]]])
self.symm_rank4 = TensorBase([[[[1.2, 0.4, -0.92], [0.4, 0.05, 0.11],
[-0.92, 0.11, -0.02]],
[[0.4, 0.05, 0.11], [0.05, -0.47, 0.09],
[0.11, 0.09, -0.]],
[[-0.92, 0.11, -0.02], [0.11, 0.09, 0.],
[-0.02, 0., -0.3]]],
[[[0.4, 0.05, 0.11], [0.05, -0.47, 0.09],
[0.11, 0.09, 0.]],
[[0.05, -0.47,
0.09], [-0.47, 0.17, 0.62],
[0.09, 0.62, 0.3]],
[[0.11, 0.09, 0.], [0.09, 0.62, 0.3],
[0., 0.3, -0.18]]],
[[[-0.92, 0.11, -0.02], [0.11, 0.09, 0.],
[-0.02, 0, -0.3]],
[[0.11, 0.09, 0.], [0.09, 0.62, 0.3],
[0., 0.3, -0.18]],
[[-0.02, 0., -0.3], [0., 0.3, -0.18],
[-0.3, -0.18, -0.51]]]])
# Structural symmetries tested using BaNiO3 piezo/elastic tensors
self.fit_r3 = TensorBase([[[0., 0., 0.03839], [0., 0., 0.],
[0.03839, 0., 0.]],
[[0., 0., 0.], [0., 0., 0.03839],
[0., 0.03839, 0.]],
[[6.89822, 0., 0.], [0., 6.89822, 0.],
[0., 0., 27.4628]]])
self.fit_r4 = TensorBase([[[[157.9, 0., 0.], [0., 63.1, 0.],
[0., 0., 29.4]],
[[0., 47.4, 0.], [47.4, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.3], [0., 0., 0.], [4.3, 0.,
0.]]],
[[[0., 47.4, 0.], [47.4, 0., 0.],
[0., 0., 0.]],
[[63.1, 0., 0.], [0., 157.9, 0.],
[0., 0., 29.4]],
[[0., 0., 0.], [0., 0., 4.3], [0., 4.3,
0.]]],
[[[0., 0., 4.3], [0., 0., 0.], [4.3, 0.,
0.]],
[[0., 0., 0.], [0., 0., 4.3], [0., 4.3,
0.]],
[[29.4, 0., 0.], [0., 29.4, 0.],
[0., 0., 207.6]]]])
self.unfit4 = TensorBase([[[[161.26, 0., 0.], [0., 62.76, 0.],
[0., 0., 30.18]],
[[0., 47.08, 0.], [47.08, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.23], [0., 0., 0.],
[4.23, 0., 0.]]],
[[[0., 47.08, 0.], [47.08, 0., 0.],
[0., 0., 0.]],
[[62.76, 0., 0.], [0., 155.28, -0.06],
[0., -0.06, 28.53]],
[[0., 0., 0.], [0., -0.06, 4.44],
[0., 4.44, 0.]]],
[[[0., 0., 4.23], [0., 0., 0.],
[4.23, 0., 0.]],
[[0., 0., 0.], [0., -0.06, 4.44],
[0., 4.44, 0.]],
[[30.18, 0., 0.], [0., 28.53, 0.],
[0., 0., 207.57]]]])
self.structure = self.get_structure('BaNiO3')
ieee_file_path = os.path.join(test_dir, "ieee_conversion_data.json")
with open(ieee_file_path) as f:
self.ieee_data = json.load(f)
class TensorBaseTest(PymatgenTest):
def setUp(self):
self.vec = TensorBase([1., 0., 0.])
self.rand_rank2 = TensorBase(np.random.randn(3, 3))
self.rand_rank3 = TensorBase(np.random.randn(3, 3, 3))
self.rand_rank4 = TensorBase(np.random.randn(3, 3, 3, 3))
a = 3.14 * 42.5 / 180
self.non_symm = SquareTensor([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.rotation = SquareTensor([[math.cos(a), 0,
math.sin(a)], [0, 1, 0],
[-math.sin(a), 0,
math.cos(a)]])
self.low_val = TensorBase([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.symm_rank2 = TensorBase([[1, 2, 3], [2, 4, 5], [3, 5, 6]])
self.symm_rank3 = TensorBase([[[1, 2, 3], [2, 4, 5], [3, 5, 6]],
[[2, 4, 5], [4, 7, 8], [5, 8, 9]],
[[3, 5, 6], [5, 8, 9], [6, 9, 10]]])
self.symm_rank4 = TensorBase([[[[1.2, 0.4, -0.92], [0.4, 0.05, 0.11],
[-0.92, 0.11, -0.02]],
[[0.4, 0.05, 0.11], [0.05, -0.47, 0.09],
[0.11, 0.09, -0.]],
[[-0.92, 0.11, -0.02], [0.11, 0.09, 0.],
[-0.02, 0., -0.3]]],
[[[0.4, 0.05, 0.11], [0.05, -0.47, 0.09],
[0.11, 0.09, 0.]],
[[0.05, -0.47,
0.09], [-0.47, 0.17, 0.62],
[0.09, 0.62, 0.3]],
[[0.11, 0.09, 0.], [0.09, 0.62, 0.3],
[0., 0.3, -0.18]]],
[[[-0.92, 0.11, -0.02], [0.11, 0.09, 0.],
[-0.02, 0, -0.3]],
[[0.11, 0.09, 0.], [0.09, 0.62, 0.3],
[0., 0.3, -0.18]],
[[-0.02, 0., -0.3], [0., 0.3, -0.18],
[-0.3, -0.18, -0.51]]]])
# Structural symmetries tested using BaNiO3 piezo/elastic tensors
self.fit_r3 = TensorBase([[[0., 0., 0.03839], [0., 0., 0.],
[0.03839, 0., 0.]],
[[0., 0., 0.], [0., 0., 0.03839],
[0., 0.03839, 0.]],
[[6.89822, 0., 0.], [0., 6.89822, 0.],
[0., 0., 27.4628]]])
self.fit_r4 = TensorBase([[[[157.9, 0., 0.], [0., 63.1, 0.],
[0., 0., 29.4]],
[[0., 47.4, 0.], [47.4, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.3], [0., 0., 0.], [4.3, 0.,
0.]]],
[[[0., 47.4, 0.], [47.4, 0., 0.],
[0., 0., 0.]],
[[63.1, 0., 0.], [0., 157.9, 0.],
[0., 0., 29.4]],
[[0., 0., 0.], [0., 0., 4.3], [0., 4.3,
0.]]],
[[[0., 0., 4.3], [0., 0., 0.], [4.3, 0.,
0.]],
[[0., 0., 0.], [0., 0., 4.3], [0., 4.3,
0.]],
[[29.4, 0., 0.], [0., 29.4, 0.],
[0., 0., 207.6]]]])
self.unfit4 = TensorBase([[[[161.26, 0., 0.], [0., 62.76, 0.],
[0., 0., 30.18]],
[[0., 47.08, 0.], [47.08, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.23], [0., 0., 0.],
[4.23, 0., 0.]]],
[[[0., 47.08, 0.], [47.08, 0., 0.],
[0., 0., 0.]],
[[62.76, 0., 0.], [0., 155.28, -0.06],
[0., -0.06, 28.53]],
[[0., 0., 0.], [0., -0.06, 4.44],
[0., 4.44, 0.]]],
[[[0., 0., 4.23], [0., 0., 0.],
[4.23, 0., 0.]],
[[0., 0., 0.], [0., -0.06, 4.44],
[0., 4.44, 0.]],
[[30.18, 0., 0.], [0., 28.53, 0.],
[0., 0., 207.57]]]])
self.structure = self.get_structure('BaNiO3')
ieee_file_path = os.path.join(test_dir, "ieee_conversion_data.json")
with open(ieee_file_path) as f:
self.ieee_data = json.load(f)
def test_new(self):
bad_2 = np.zeros((4, 4))
bad_3 = np.zeros((4, 4, 4))
self.assertRaises(ValueError, TensorBase, bad_2)
self.assertRaises(ValueError, TensorBase, bad_3)
self.assertEqual(self.rand_rank2.rank, 2)
self.assertEqual(self.rand_rank3.rank, 3)
self.assertEqual(self.rand_rank4.rank, 4)
def test_zeroed(self):
self.assertArrayEqual(
self.low_val.zeroed(),
TensorBase([[0, 1 + 1e-5, 0], [1 + 1e-6, 0, 0], [0, 0, 1 + 1e-5]]))
self.assertArrayEqual(
self.low_val.zeroed(tol=1e-6),
TensorBase([[1e-6, 1 + 1e-5, 1e-6], [1 + 1e-6, 1e-6, 1e-6],
[0, 0, 1 + 1e-5]]))
self.assertArrayEqual(
TensorBase([[1e-6, -30, 1], [1e-7, 1, 0], [1e-8, 0, 1]]).zeroed(),
TensorBase([[0, -30, 1], [0, 1, 0], [0, 0, 1]]))
def test_transform(self):
# Rank 3
tensor = TensorBase(np.arange(0, 27).reshape(3, 3, 3))
symm_op = SymmOp.from_axis_angle_and_translation([0, 0, 1], 30, False,
[0, 0, 1])
new_tensor = tensor.transform(symm_op)
self.assertArrayAlmostEqual(
new_tensor, [[[-0.871, -2.884, -1.928], [-2.152, -6.665, -4.196],
[-1.026, -2.830, -1.572]],
[[0.044, 1.531, 1.804], [4.263, 21.008, 17.928],
[5.170, 23.026, 18.722]],
[[1.679, 7.268, 5.821], [9.268, 38.321, 29.919],
[8.285, 33.651, 26.000]]], 3)
def test_rotate(self):
self.assertArrayEqual(
self.vec.rotate([[0, -1, 0], [1, 0, 0], [0, 0, 1]]), [0, 1, 0])
self.assertArrayAlmostEqual(self.non_symm.rotate(self.rotation),
SquareTensor([[0.531, 0.485, 0.271],
[0.700, 0.5, 0.172],
[0.171, 0.233, 0.068]]),
decimal=3)
self.assertRaises(ValueError, self.non_symm.rotate, self.symm_rank2)
def test_symmetrized(self):
self.assertTrue(self.rand_rank2.symmetrized.is_symmetric())
self.assertTrue(self.rand_rank3.symmetrized.is_symmetric())
self.assertTrue(self.rand_rank4.symmetrized.is_symmetric())
def test_is_symmetric(self):
self.assertTrue(self.symm_rank2.is_symmetric())
self.assertTrue(self.symm_rank3.is_symmetric())
self.assertTrue(self.symm_rank4.is_symmetric())
tol_test = self.symm_rank4
tol_test[0, 1, 2, 2] += 1e-6
self.assertFalse(self.low_val.is_symmetric(tol=1e-8))
def test_fit_to_structure(self):
new_fit = self.unfit4.fit_to_structure(self.structure)
self.assertArrayAlmostEqual(new_fit, self.fit_r4, 1)
def test_is_fit_to_structure(self):
self.assertFalse(self.unfit4.is_fit_to_structure(self.structure))
self.assertTrue(self.fit_r3.is_fit_to_structure(self.structure))
self.assertTrue(self.fit_r4.is_fit_to_structure(self.structure))
def test_convert_to_ieee(self):
for xtal in self.ieee_data.keys():
orig = TensorBase(self.ieee_data[xtal]['original_tensor'])
ieee = TensorBase(self.ieee_data[xtal]['ieee_tensor'])
struct = Structure.from_dict(self.ieee_data[xtal]['structure'])
diff = np.max(abs(ieee - orig.convert_to_ieee(struct)))
err_msg = "{} IEEE conversion failed with max diff {}".format(
xtal, diff)
self.assertArrayAlmostEqual(ieee,
orig.convert_to_ieee(struct),
err_msg=err_msg,
decimal=3)
class TensorBaseTest(PymatgenTest):
def setUp(self):
self.vec = TensorBase([1., 0., 0.])
self.rand_rank2 = TensorBase(np.random.randn(3,3))
self.rand_rank3 = TensorBase(np.random.randn(3,3,3))
self.rand_rank4 = TensorBase(np.random.randn(3,3,3,3))
a = 3.14 * 42.5 / 180
self.non_symm = SquareTensor([[0.1, 0.2, 0.3],
[0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.rotation = SquareTensor([[math.cos(a), 0, math.sin(a)],
[0, 1, 0],
[-math.sin(a), 0, math.cos(a)]])
self.low_val = TensorBase([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.symm_rank2 = TensorBase([[1, 2, 3],
[2, 4, 5],
[3, 5, 6]])
self.symm_rank3 = TensorBase([[[1, 2, 3],
[2, 4, 5],
[3, 5, 6]],
[[2, 4, 5],
[4, 7, 8],
[5, 8, 9]],
[[3, 5, 6],
[5, 8, 9],
[6, 9, 10]]])
self.symm_rank4 = TensorBase([[[[1.2, 0.4, -0.92],
[0.4, 0.05, 0.11],
[-0.92, 0.11, -0.02]],
[[0.4, 0.05, 0.11],
[0.05, -0.47, 0.09],
[0.11, 0.09, -0.]],
[[-0.92, 0.11, -0.02],
[0.11, 0.09, 0.],
[-0.02, 0., -0.3]]],
[[[0.4, 0.05, 0.11],
[0.05, -0.47, 0.09],
[0.11, 0.09, 0.]],
[[0.05, -0.47, 0.09],
[-0.47, 0.17, 0.62],
[0.09, 0.62, 0.3]],
[[0.11, 0.09, 0.],
[0.09, 0.62, 0.3],
[0., 0.3, -0.18]]],
[[[-0.92, 0.11, -0.02],
[0.11, 0.09, 0.],
[-0.02, 0, -0.3]],
[[0.11, 0.09, 0.],
[0.09, 0.62, 0.3],
[0., 0.3, -0.18]],
[[-0.02, 0., -0.3],
[0., 0.3, -0.18],
[-0.3, -0.18, -0.51]]]])
# Structural symmetries tested using BaNiO3 piezo/elastic tensors
self.fit_r3 = TensorBase([[[0., 0., 0.03839],
[0., 0., 0.],
[0.03839, 0., 0.]],
[[0., 0., 0.],
[0., 0., 0.03839],
[0., 0.03839, 0.]],
[[6.89822, 0., 0.],
[0., 6.89822, 0.],
[0., 0., 27.4628]]])
self.fit_r4 = TensorBase([[[[157.9, 0., 0.],
[0., 63.1, 0.],
[0., 0., 29.4]],
[[0., 47.4, 0.],
[47.4, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.3],
[0., 0., 0.],
[4.3, 0., 0.]]],
[[[0., 47.4, 0.],
[47.4, 0., 0.],
[0., 0., 0.]],
[[63.1, 0., 0.],
[0., 157.9, 0.],
[0., 0., 29.4]],
[[0., 0., 0.],
[0., 0., 4.3],
[0., 4.3, 0.]]],
[[[0., 0., 4.3],
[0., 0., 0.],
[4.3, 0., 0.]],
[[0., 0., 0.],
[0., 0., 4.3],
[0., 4.3, 0.]],
[[29.4, 0., 0.],
[0., 29.4, 0.],
[0., 0., 207.6]]]])
self.unfit4 = TensorBase([[[[161.26, 0., 0.],
[0., 62.76, 0.],
[0., 0., 30.18]],
[[0., 47.08, 0.],
[47.08, 0., 0.],
[0., 0., 0.]],
[[0., 0., 4.23],
[0., 0., 0.],
[4.23, 0., 0.]]],
[[[0., 47.08, 0.],
[47.08, 0., 0.],
[0., 0., 0.]],
[[62.76, 0., 0.],
[0., 155.28, -0.06],
[0., -0.06, 28.53]],
[[0., 0., 0.],
[0., -0.06, 4.44],
[0., 4.44, 0.]]],
[[[0., 0., 4.23],
[0., 0., 0.],
[4.23, 0., 0.]],
[[0., 0., 0.],
[0., -0.06, 4.44],
[0., 4.44, 0.]],
[[30.18, 0., 0.],
[0., 28.53, 0.],
[0., 0., 207.57]]]])
self.structure = self.get_structure('BaNiO3')
ieee_file_path = os.path.join(test_dir, "ieee_conversion_data.json")
with open(ieee_file_path) as f:
self.ieee_data = json.load(f)
def test_new(self):
bad_2 = np.zeros((4, 4))
bad_3 = np.zeros((4, 4, 4))
self.assertRaises(ValueError, TensorBase, bad_2)
self.assertRaises(ValueError, TensorBase, bad_3)
self.assertEqual(self.rand_rank2.rank, 2)
self.assertEqual(self.rand_rank3.rank, 3)
self.assertEqual(self.rand_rank4.rank, 4)
def test_zeroed(self):
self.assertArrayEqual(self.low_val.zeroed(),
TensorBase([[0, 1 + 1e-5, 0],
[1 + 1e-6, 0, 0],
[0, 0, 1 + 1e-5]]))
self.assertArrayEqual(self.low_val.zeroed(tol=1e-6),
TensorBase([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[0, 0, 1 + 1e-5]]))
self.assertArrayEqual(TensorBase([[1e-6, -30, 1],
[1e-7, 1, 0],
[1e-8, 0, 1]]).zeroed(),
TensorBase([[0, -30, 1],
[0, 1, 0],
[0, 0, 1]]))
def test_transform(self):
# Rank 3
tensor = TensorBase(np.arange(0, 27).reshape(3, 3, 3))
symm_op = SymmOp.from_axis_angle_and_translation([0, 0, 1], 30,
False, [0, 0, 1])
new_tensor = tensor.transform(symm_op)
self.assertArrayAlmostEqual(new_tensor,
[[[-0.871, -2.884, -1.928],
[-2.152, -6.665, -4.196],
[-1.026, -2.830, -1.572]],
[[0.044, 1.531, 1.804],
[4.263, 21.008, 17.928],
[5.170, 23.026, 18.722]],
[[1.679, 7.268, 5.821],
[9.268, 38.321, 29.919],
[8.285, 33.651, 26.000]]], 3)
def test_rotate(self):
self.assertArrayEqual(self.vec.rotate([[0, -1, 0],
[1, 0, 0],
[0, 0, 1]]),
[0, 1, 0])
self.assertArrayAlmostEqual(self.non_symm.rotate(self.rotation),
SquareTensor([[0.531, 0.485, 0.271],
[0.700, 0.5, 0.172],
[0.171, 0.233, 0.068]]),
decimal=3)
self.assertRaises(ValueError, self.non_symm.rotate,
self.symm_rank2)
def test_symmetrized(self):
self.assertTrue(self.rand_rank2.symmetrized.is_symmetric())
self.assertTrue(self.rand_rank3.symmetrized.is_symmetric())
self.assertTrue(self.rand_rank4.symmetrized.is_symmetric())
def test_is_symmetric(self):
self.assertTrue(self.symm_rank2.is_symmetric())
self.assertTrue(self.symm_rank3.is_symmetric())
self.assertTrue(self.symm_rank4.is_symmetric())
tol_test = self.symm_rank4
tol_test[0, 1, 2, 2] += 1e-6
self.assertFalse(self.low_val.is_symmetric(tol=1e-8))
def test_fit_to_structure(self):
new_fit = self.unfit4.fit_to_structure(self.structure)
self.assertArrayAlmostEqual(new_fit, self.fit_r4, 1)
def test_is_fit_to_structure(self):
self.assertFalse(self.unfit4.is_fit_to_structure(self.structure))
self.assertTrue(self.fit_r3.is_fit_to_structure(self.structure))
self.assertTrue(self.fit_r4.is_fit_to_structure(self.structure))
def test_convert_to_ieee(self):
for xtal in self.ieee_data.keys():
orig = TensorBase(self.ieee_data[xtal]['original_tensor'])
ieee = TensorBase(self.ieee_data[xtal]['ieee_tensor'])
struct = Structure.from_dict(self.ieee_data[xtal]['structure'])
diff = np.max(abs(ieee - orig.convert_to_ieee(struct)))
err_msg = "{} IEEE conversion failed with max diff {}".format(
xtal, diff)
self.assertArrayAlmostEqual(ieee, orig.convert_to_ieee(struct),
err_msg = err_msg, decimal=3)
class SquareTensorTest(PymatgenTest):
def setUp(self):
self.rand_sqtensor = SquareTensor(np.random.randn(3, 3))
self.symm_sqtensor = SquareTensor([[0.1, 0.3, 0.4],
[0.3, 0.5, 0.2],
[0.4, 0.2, 0.6]])
self.non_invertible = SquareTensor([[0.1, 0, 0],
[0.2, 0, 0],
[0, 0, 0]])
self.non_symm = SquareTensor([[0.1, 0.2, 0.3],
[0.4, 0.5, 0.6],
[0.2, 0.5, 0.5]])
self.low_val = SquareTensor([[1e-6, 1 + 1e-5, 1e-6],
[1 + 1e-6, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-5]])
self.low_val_2 = SquareTensor([[1e-6, -1 - 1e-6, 1e-6],
[1 + 1e-7, 1e-6, 1e-6],
[1e-7, 1e-7, 1 + 1e-6]])
a = 3.14 * 42.5 / 180
self.rotation = SquareTensor([[math.cos(a), 0, math.sin(a)],
[0, 1, 0],
[-math.sin(a), 0, math.cos(a)]])
def test_new(self):
non_sq_matrix = [[0.1, 0.2, 0.1],
[0.1, 0.2, 0.3],
[0.1, 0.2, 0.3],
[0.1, 0.1, 0.1]]
bad_matrix = [[0.1, 0.2],
[0.2, 0.3, 0.4],
[0.2, 0.3, 0.5]]
too_high_rank = np.zeros((3,3,3))
self.assertRaises(ValueError, SquareTensor, non_sq_matrix)
self.assertRaises(ValueError, SquareTensor, bad_matrix)
self.assertRaises(ValueError, SquareTensor, too_high_rank)
def test_properties(self):
# transpose
self.assertArrayEqual(self.non_symm.trans,
SquareTensor([[0.1, 0.4, 0.2],
[0.2, 0.5, 0.5],
[0.3, 0.6, 0.5]]))
self.assertArrayEqual(self.rand_sqtensor.trans,
np.transpose(self.rand_sqtensor))
self.assertArrayEqual(self.symm_sqtensor,
self.symm_sqtensor.trans)
# inverse
self.assertArrayEqual(self.non_symm.inv,
np.linalg.inv(self.non_symm))
with self.assertRaises(ValueError):
self.non_invertible.inv
# determinant
self.assertEqual(self.rand_sqtensor.det,
np.linalg.det(self.rand_sqtensor))
self.assertEqual(self.non_invertible.det,
0.0)
self.assertEqual(self.non_symm.det, 0.009)
# symmetrized
self.assertArrayEqual(self.rand_sqtensor.symmetrized,
0.5 * (self.rand_sqtensor + self.rand_sqtensor.trans))
self.assertArrayEqual(self.symm_sqtensor,
self.symm_sqtensor.symmetrized)
self.assertArrayAlmostEqual(self.non_symm.symmetrized,
SquareTensor([[0.1, 0.3, 0.25],
[0.3, 0.5, 0.55],
[0.25, 0.55, 0.5]]))
# invariants
i1 = np.trace(self.rand_sqtensor)
i2 = self.rand_sqtensor[0, 0] * self.rand_sqtensor[1, 1] + \
self.rand_sqtensor[1, 1] * self.rand_sqtensor[2, 2] + \
self.rand_sqtensor[2, 2] * self.rand_sqtensor[0, 0] - \
self.rand_sqtensor[0, 1] * self.rand_sqtensor[1, 0] - \
self.rand_sqtensor[0, 2] * self.rand_sqtensor[2, 0] - \
self.rand_sqtensor[2, 1] * self.rand_sqtensor[1, 2]
i3 = np.linalg.det(self.rand_sqtensor)
self.assertArrayAlmostEqual([i1, i2, i3],
self.rand_sqtensor.principal_invariants)
def test_is_rotation(self):
self.assertTrue(self.rotation.is_rotation())
self.assertFalse(self.symm_sqtensor.is_rotation())
self.assertTrue(self.low_val_2.is_rotation())
self.assertFalse(self.low_val_2.is_rotation(tol=1e-8))
def test_get_scaled(self):
self.assertArrayEqual(self.non_symm.get_scaled(10.),
SquareTensor([[1, 2, 3], [4, 5, 6], [2, 5, 5]]))
def test_polar_decomposition(self):
u, p = self.rand_sqtensor.polar_decomposition()
self.assertArrayAlmostEqual(np.dot(u, p), self.rand_sqtensor)
self.assertArrayAlmostEqual(np.eye(3),
np.dot(u, np.conjugate(np.transpose(u))))
