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_eigenvalues(rnd_data1, rnd_data2, rnd_data3, rnd_data4,
rnd_data5, rnd_data6):
"""
Comparison of eigenvalue calculation for xi from random complex material
data. Comparing polynomial calculation from determinant, from quadratic
eigenvalue problem and analytical calculation from sympy.
"""
lc = LocalCoordinates("1")
myeps = np.zeros((3, 3), dtype=complex)
myeps[0:2, 0:2] = rnd_data1 + complex(0, 1) * rnd_data2
myeps[2, 2] = rnd_data3 + complex(0, 1) * rnd_data4
((epsxx, epsxy, _), (epsyx, epsyy, _), (_, _, epszz)) = \
tuple(myeps)
m = AnisotropicMaterial(lc, myeps)
#n = n/np.sqrt(np.sum(n*n, axis=0))
n = np.zeros((3, 1))
n[2, :] = 1
x = np.zeros((3, 1))
k = rnd_data5 + complex(0, 1) * rnd_data6
kpa = k - np.sum(n * k, axis=0) * n
(eigenvalues, _) = m.calcXiEigenvectorsNorm(x, n, kpa)
xiarray = m.calcXiNormZeros(x, n, kpa)
# sympy check with analytical solution
kx, ky, xi = sympy.symbols('k_x k_y xi')
exx, exy, _, eyx, eyy, _, _, _, ezz \
= sympy.symbols('e_xx e_xy e_xz e_yx e_yy e_yz e_zx e_zy e_zz')
#eps = Matrix([[exx, exy, exz], [eyx, eyy, eyz], [ezx, ezy, ezz]])
eps = sympy.Matrix([[exx, exy, 0], [eyx, eyy, 0], [0, 0, ezz]])
v = sympy.Matrix([[kx, ky, xi]])
m = -(v * v.T)[0] * sympy.eye(3) + v.T * v + eps
detm = m.det().collect(xi)
soldetm = sympy.solve(detm, xi)
subsdict = {
kx: kpa[0, 0],
ky: kpa[1, 0],
exx: epsxx,
exy: epsxy,
eyx: epsyx,
eyy: epsyy,
ezz: epszz,
sympy.I: complex(0, 1)
}
analytical_solution = np.sort_complex(
np.array([sol.evalf(subs=subsdict) for sol in soldetm], dtype=complex))
numerical_solution1 = np.sort_complex(xiarray[:, 0])
numerical_solution2 = np.sort_complex(eigenvalues[:, 0])
assert np.allclose(analytical_solution - numerical_solution1, 0)
assert np.allclose(analytical_solution - numerical_solution2, 0)