def test_anisotropic_xi_calculation_det(rnd_data1, rnd_data2, rnd_data3,
rnd_data4, rnd_data5, rnd_data6):
"""
Random epsilon tensor, Random k vector and n unit vector in z direction.
Determinant of the propagator from numerical calculations
via np.einsum and from analytical expression given below should coincide.
The test should work for real and complex epsilon and k values.
"""
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 = np.zeros((3, 5))
n[2, :] = 1.
x = np.zeros((3, 5))
k = rnd_data3 + complex(0, 1) * rnd_data4
xi = rnd_data5 + complex(0, 1) * rnd_data6
kpa = k - np.sum(n * k, axis=0) * n
kx = kpa[0]
ky = kpa[1]
# TODO: Maybe generalize to arbitrary n vectors
det_analytical = xi**4*epszz \
+ xi**3*((epsxz + epszx)*kx + (epsyz + epszy)*ky)\
+ xi**2*(epsxz*epszx + epsyz*epszy - (epsxx + epsyy)*epszz\
+ (epsxx + epszz)*kx**2 + (epsxy + epsyx)*kx*ky\
+ (epsyy + epszz)*ky**2)\
+ xi*((epsxz + epszx)*kx**3\
+ (epsxz*epsyx + epsxy*epszx - epsxx*(epsyz + epszy))*ky\
+ (epsyz + epszy)*kx**2*ky + (epsyz + epszy)*ky**3\
+ kx*(-(epsxz*epsyy) + epsxy*epsyz - epsyy*epszx\
+ epsyx*epszy + (epsxz + epszx)*ky**2))\
-(epsxz*epsyy*epszx) + epsxy*epsyz*epszx\
+ epsxz*epsyx*epszy - epsxx*epsyz*epszy\
- epsxy*epsyx*epszz + epsxx*epsyy*epszz + epsxx*kx**4\
+ (epsxy + epsyx)*kx**3*ky \
+ (epsxy*epsyx - epsxx*epsyy + epsyz*epszy - epsyy*epszz)*ky**2 \
+ epsyy*ky**4 + kx**2*(epsxy*epsyx + epsxz*epszx \
- epsxx*(epsyy + epszz) + (epsxx + epsyy)*ky**2)\
+ kx*((epsyz*epszx + epsxz*epszy \
- (epsxy + epsyx)*epszz)*ky + (epsxy + epsyx)*ky**3)
should_be_zero = det_analytical - m.calcXiDetNorm(xi, x, n, kpa)
assert np.allclose(should_be_zero, 0)
def test_anisotropic_xi_calculation_polynomial_zeros(rnd_data1, rnd_data2,
rnd_data3, rnd_data4,
rnd_data5):
"""
Random epsilon tensor, random k vector and random n unit vector.
Check whether the roots calculated give really zero for the determinant.
The test should work for real and complex epsilon and k values.
"""
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
should_be_zero = np.ones((4, 5), dtype=complex)
xiarray = m.calcXiNormZeros(x, n, kpa)
for i in range(4):
should_be_zero[i, :] = m.calcXiDetNorm(xiarray[i], x, n, kpa)
assert np.allclose(should_be_zero, 0)