def test_anisotropic_xi_eigenvectors(rnd_data1, rnd_data2, rnd_data3,
rnd_data4, rnd_data5):
"""
Check whether eigenvectors fulfill the QEVP.
"""
lc = LocalCoordinates("1")
myeps = rnd_data1 + complex(0, 1) * rnd_data2
# ((epsxx, epsxy, epsxz), (epsyx, epsyy, epsyz), (epszx, epszy, epszz)) = \
# tuple(myeps)
m = AnisotropicMaterial(lc, myeps)
n = rnd_data3
n = n / np.sqrt(np.sum(n * n, axis=0))
x = np.zeros((3, 5))
k = rnd_data4 + complex(0, 1) * rnd_data5
kpa = k - np.sum(n * k, axis=0) * n
((_, _), (Mmatrix, Cmatrix, Kmatrix)) \
= m.calcXiQEVMatricesNorm(x, n, kpa)
(eigenvalues, eigenvectors) = m.calcXiEigenvectorsNorm(x, n, kpa)
#print(eigenvalues)
should_be_zero = np.ones((4, 3, 5), dtype=complex)
for j in range(5):
for k in range(4):
should_be_zero[k, :, j] = np.dot(
(Mmatrix[:, :, j] * eigenvalues[k, j]**2 +
Cmatrix[:, :, j] * eigenvalues[k, j] + Kmatrix[:, :, j]),
eigenvectors[k, :, j])
assert np.allclose(should_be_zero, 0)
def test_anisotropic_xi_determinants(rnd_data1, rnd_data2, rnd_data3,
rnd_data4, rnd_data5):
"""
Check whether xi zeros from polynomial fulfill the QEVP and the
associated GLEVP. This also verifies whether A6x6 and B6x6 are
constructed correctly.
"""
lc = LocalCoordinates("1")
myeps = rnd_data1 + complex(0, 1) * rnd_data2
# ((epsxx, epsxy, epsxz), (epsyx, epsyy, epsyz), (epszx, epszy, epszz)) = \
# tuple(myeps)
m = AnisotropicMaterial(lc, myeps)
n = rnd_data3
n = n / np.sqrt(np.sum(n * n, axis=0))
x = np.zeros((3, 5))
k = rnd_data4 + complex(0, 1) * rnd_data5
kpa = k - np.sum(n * k, axis=0) * n
xiarray = m.calcXiNormZeros(x, n, kpa)
((Amatrix6x6, Bmatrix6x6), (Mmatrix, Cmatrix, Kmatrix)) \
= m.calcXiQEVMatricesNorm(x, n, kpa)
should_be_zero_1 = np.ones((4, 5), dtype=complex)
should_be_zero_2 = np.ones((4, 5), dtype=complex)
for j in range(5):
for xi_num in range(4):
should_be_zero_1[xi_num, j] = np.linalg.det(
(Mmatrix[:, :, j] * xiarray[xi_num, j]**2 +
Cmatrix[:, :, j] * xiarray[xi_num, j] + Kmatrix[:, :, j]))
should_be_zero_2[xi_num, j] = np.linalg.det(
(Amatrix6x6[:, :, j] -
Bmatrix6x6[:, :, j] * xiarray[xi_num, j]))
assert np.allclose(should_be_zero_1, 0)
assert np.allclose(should_be_zero_2, 0)