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test_operators.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import numpy as np
import pprint
import mechkit
from mechkit.operators import Sym_Fourth_Order_Special
import pytest
import itertools
con = mechkit.notation.Converter()
@pytest.fixture(name="tensor4")
def create_random_fourth_order_tensor():
return np.random.rand(3, 3, 3, 3)
def has_sym_left(A):
for iii in range(3):
for jjj in range(3):
for kkk in range(3):
for lll in range(3):
assert A[iii, jjj, kkk, lll] == A[jjj, iii, kkk, lll]
def has_sym_right(A):
for iii in range(3):
for jjj in range(3):
for kkk in range(3):
for lll in range(3):
assert A[iii, jjj, kkk, lll] == A[iii, jjj, lll, kkk]
def has_sym_major(A):
for iii in range(3):
for jjj in range(3):
for kkk in range(3):
for lll in range(3):
assert A[iii, jjj, kkk, lll] == A[kkk, lll, iii, jjj]
def has_sym_minor(A):
for iii in range(3):
for jjj in range(3):
for kkk in range(3):
for lll in range(3):
np.allclose(
A[iii, jjj, kkk, lll],
A[jjj, iii, kkk, lll],
rtol=1e-8,
atol=1e-8,
)
np.allclose(
A[iii, jjj, kkk, lll],
A[iii, jjj, lll, kkk],
rtol=1e-8,
atol=1e-8,
)
def has_sym_inner(A):
for iii in range(3):
for jjj in range(3):
for kkk in range(3):
for lll in range(3):
print(iii, jjj, kkk, lll)
assert np.isclose(A[iii, jjj, kkk, lll], A[jjj, iii, kkk, lll])
assert np.isclose(A[iii, jjj, kkk, lll], A[iii, jjj, lll, kkk])
assert np.isclose(A[iii, jjj, kkk, lll], A[kkk, lll, iii, jjj])
def has_sym_complete(A):
for iii in range(3):
for jjj in range(3):
for kkk in range(3):
for lll in range(3):
print(iii, jjj, kkk, lll)
assert np.isclose(A[iii, jjj, kkk, lll], A[jjj, iii, kkk, lll])
assert np.isclose(A[iii, jjj, kkk, lll], A[iii, jjj, lll, kkk])
assert np.isclose(A[iii, jjj, kkk, lll], A[kkk, lll, iii, jjj])
assert np.isclose(A[iii, jjj, kkk, lll], A[lll, kkk, jjj, iii])
class Test_Sym_Fourth_Order_Special:
def test_check_sym_by_loop_left(self, tensor4):
t_sym = Sym_Fourth_Order_Special(label="left")(tensor4)
pprint.pprint(con.to_mandel9(t_sym))
has_sym_left(t_sym)
def test_check_sym_by_loop_right(self, tensor4):
t_sym = Sym_Fourth_Order_Special(label="right")(tensor4)
pprint.pprint(con.to_mandel9(t_sym))
has_sym_right(t_sym)
def test_check_sym_by_loop_major(self, tensor4):
t_sym = Sym_Fourth_Order_Special(label="major")(tensor4)
pprint.pprint(con.to_mandel9(t_sym))
has_sym_major(t_sym)
def test_check_sym_by_loop_minor(self, tensor4):
t_sym = Sym_Fourth_Order_Special(label="minor")(tensor4)
pprint.pprint(con.to_mandel9(t_sym))
has_sym_minor(t_sym)
def test_check_sym_by_loop_inner_mandel(self, tensor4):
t_sym = Sym_Fourth_Order_Special(label="inner_mandel")(tensor4)
pprint.pprint(con.to_mandel9(t_sym))
has_sym_inner(t_sym)
def test_check_sym_by_loop_inner(self, tensor4):
t_sym = Sym_Fourth_Order_Special(label="inner")(tensor4)
pprint.pprint(con.to_mandel9(t_sym))
has_sym_inner(t_sym)
def test_check_sym_by_loop_complete(tensor4):
t_sym = mechkit.operators.Sym()(tensor4)
pprint.pprint(con.to_mandel9(t_sym))
has_sym_complete(t_sym)
def test_check_sym_by_loop_alternative_implementation(tensor4):
t_sym = mechkit.operators.Sym()(tensor4)
def sym(tensor, sym_axes=None):
"""
Symmetrize selected axes of tensor.
If no sym_axes are specified, all axes are symmetrized
"""
base_axis = np.array(range(len(tensor.shape)))
sym_axes = base_axis if sym_axes is None else sym_axes
perms = itertools.permutations(sym_axes)
axes = list()
for perm in perms:
axis = base_axis.copy()
axis[sym_axes] = perm
axes.append(axis)
return 1.0 / len(axes) * sum(tensor.transpose(axis) for axis in axes)
np.allclose(sym(tensor4), t_sym)
def test_compare_sym_inner_inner_mandel(tensor4):
t_sym_inner = Sym_Fourth_Order_Special(label="inner")(tensor4)
t_sym_inner_mandel = Sym_Fourth_Order_Special(label="inner_mandel")(tensor4)
print("t_sym_inner")
pprint.pprint(con.to_mandel9(t_sym_inner))
print("t_sym_inner_mandel")
pprint.pprint(con.to_mandel9(t_sym_inner_mandel))
np.allclose(t_sym_inner, t_sym_inner_mandel)
def test_sym_minor_mandel(tensor4):
"""Converting to Mandel6 and back should be identical to
Sym(label=\'minor\')
"""
t_sym_mandel = con.to_tensor(con.to_mandel6(tensor4))
t_sym_label = Sym_Fourth_Order_Special(label="minor")(tensor4)
print(con.to_mandel9(t_sym_mandel))
print(con.to_mandel9(t_sym_label))
assert np.allclose(t_sym_mandel, t_sym_label)
def test_sym_axes_label_left(tensor4):
"""Two implementation should do the same job"""
sym_axes = mechkit.operators.Sym(axes=[0, 1])(tensor4)
sym_label = Sym_Fourth_Order_Special(label="left")(tensor4)
print(sym_axes)
print(sym_label)
assert np.allclose(sym_axes, sym_label)
def test_sym_axes_label_right(tensor4):
"""Two implementation should do the same job"""
sym_axes = mechkit.operators.Sym(axes=[2, 3])(tensor4)
sym_label = Sym_Fourth_Order_Special(label="right")(tensor4)
print(sym_axes)
print(sym_label)
assert np.allclose(sym_axes, sym_label)
####################################################################
@pytest.fixture(name="tensors")
def create_random_tensors_with_minor_symmetries():
tensors = {
"hooke": mechkit.operators.Sym_Fourth_Order_Special(label="inner")(
np.random.rand(3, 3, 3, 3)
),
"complete": mechkit.operators.Sym_Fourth_Order_Special(label="complete")(
np.random.rand(3, 3, 3, 3)
),
}
return tensors
alternatives = mechkit.operators.Alternative_Deviator_Formulations()
class Test_Deviators:
def test_deviator_part_of_4_tensor_is_deviator(self, tensors):
for key in ["hooke", "complete"]:
deviator = alternatives.dev_t4_spencer1970(tensors[key])
# Is symmetric
sym = mechkit.operators.Sym()
assert np.allclose(deviator, sym(deviator))
# Is traceless (as it is already symmetric, one trace tested is sufficient)
assert np.allclose(np.einsum("ijkk->ij", deviator), np.zeros((3, 3)))
def test_deviator_part_of_4_tensor_implementations_spencer_boehlke(self, tensors):
for key in ["hooke", "complete"]:
D_spencer = alternatives.dev_t4_spencer1970(tensors[key])
D_boehlke = alternatives.dev_t4_boehlke2001(tensors[key])
assert np.allclose(D_spencer, D_boehlke)
def test_deviator_part_of_4_tensor_implementations_spencer_simple(self, tensors):
for key in ["hooke", "complete"]:
D_spencer = alternatives.dev_t4_spencer1970(tensors[key])
D_simple = mechkit.operators.dev_tensor_4th_order_simple(tensors[key])
assert np.allclose(D_spencer, D_simple)