def test_rotated_spheroid_equals_rotated_light(material, atol):
"""cross-sections are the same if a spheroid is rotated or if the light is rotated"""
theta = 1.3
phi = 0.7
source = miepy.sources.plane_wave([1,0], theta=theta, phi=phi)
z_oriented = miepy.cluster(particles=miepy.spheroid([0,0,0], radius, 2*radius, material),
source=source,
wavelength=wavelength,
lmax=lmax,
medium=medium)
C1 = z_oriented.cross_sections()
source = miepy.sources.plane_wave([1,0])
q = miepy.quaternion.from_spherical_coords(theta, phi).inverse()
oriented = miepy.cluster(particles=miepy.spheroid([0,0,0], radius, 2*radius, material, orientation=q),
source=source,
wavelength=wavelength,
lmax=lmax,
medium=medium)
C2 = oriented.cross_sections()
assert np.allclose(C1, C2, rtol=0, atol=atol)
def test_ellipsoid_equal_spheroid_z_oriented():
"""An (rx, ry, rz) ellipsoid should equal a z-oriented (rxy, rz) spheroid"""
e = miepy.spheroid([0, 0, 0], rx, rz, material)
T1 = e.compute_tmatrix(lmax, wavelength, 1.0)
e = miepy.ellipsoid([0, 0, 0], rx, ry, rz, material)
T2 = e.compute_tmatrix(lmax, wavelength, 1.0)
assert np.allclose(T1, T2, atol=2e-5)
def test_tmatrix_spheroid_is_sphere(material, atol):
"""tmatrix of spheroid with aspect ratio 1 is equal to tmatrix of sphere"""
sphere = miepy.sphere([0,0,0], radius, material)
spheroid = miepy.spheroid([0,0,0], radius, radius, material, tmatrix_lmax=4)
T1 = sphere.compute_tmatrix(lmax, wavelength, eps_b)
T2 = spheroid.compute_tmatrix(lmax, wavelength, eps_b)
print(np.max(np.abs(T1-T2)))
assert np.allclose(T1, T2, rtol=0, atol=atol)
def test_ellipsoid_equal_spheroid_y_oriented():
"""An (rx, rz, ry) ellipsoid should equal a y-oriented (rxy, rz) spheroid"""
q = miepy.quaternion.from_spherical_coords(np.pi / 2, np.pi / 2)
e = miepy.spheroid([0, 0, 0], rx, rz, material, orientation=q)
T1 = e.compute_tmatrix(lmax, wavelength, 1.0)
e = miepy.ellipsoid([0, 0, 0], rx, rz, ry, material)
T2 = e.compute_tmatrix(lmax, wavelength, 1.0)
assert np.allclose(T1, T2, atol=5e-5)
def tests(Nmax, step=1):
Nparticles = np.arange(1, Nmax+1, step)
t_force, t_flux, t_build, t_solve, t_expand, t_tmatrix = [np.zeros_like(Nparticles, dtype=float) for i in range(6)]
for i,N in enumerate(Nparticles):
print(N, Nmax)
positions = [[n*separation, 0, 0] for n in range(N)]
particles = [miepy.spheroid(pos, radius, 0.5*radius, Ag) for pos in positions]
mie = miepy.cluster(particles=particles,
source=source,
wavelength=600*nm,
lmax=2)
t_force[i] = time_function(mie.force)
t_flux[i] = time_function(mie.cross_sections)
t_build[i] = time_function(partial(miepy.interactions.particle_aggregate_tmatrix,
mie.position, mie.tmatrix, mie.material_data.k_b))
A = miepy.interactions.particle_aggregate_tmatrix(mie.position, mie.tmatrix, k=mie.material_data.k_b)
t_solve[i] = time_function(partial(solve_linear_system, A, mie.p_src, method=miepy.solver.bicgstab))
t_tmatrix[i] = time_function(partial(tmatrix_time, mie))
x = np.linspace(0, N*separation, 1)
y = 2*radius*np.ones_like(x)
z = np.zeros_like(x)
t_expand[i] = time_function(partial(mie.E_field, x, y, z))
fig, ax = plt.subplots()
ax.plot(Nparticles, t_force, label='force')
ax.plot(Nparticles, t_flux, label='flux')
ax.plot(Nparticles, t_build, label='build')
ax.plot(Nparticles, t_solve, label='solve')
ax.plot(Nparticles, t_expand, label='expand')
ax.plot(Nparticles, t_tmatrix, label='tmatrix')
ax.legend()
ax.set(xlabel='number of particles', ylabel='runtime (s)')
plt.show()
import miepy S = miepy.spheroid([0, 0, 0], 1, 1, miepy.constant_material(2)) T = S.compute_tmatrix(2, 5, 1) print(T)
dr_phi = -rad**3 * np.sin(phi) * np.cos(phi) * np.sin(theta) * (1 / b**2 -
1 / a**2)
rhat, that, phat = miepy.coordinates.sph_basis_vectors(theta, phi)
sigma = (rhat - 1 / rad * dr_theta * that -
1 / rad * dr_phi * phat) * rad**2 * np.sin(theta)
return rad, sigma
rad, dS = ellipsoid_dS(1 * radius, 1.3 * radius, 1.6 * radius, THETA, PHI)
T = get_tmatrix(rad, dS, eps, 1, wavelength, lmax)
print(T[1, :, 0, 0])
T1 = np.copy(T)
spheroid = miepy.spheroid([0, 0, 0], radius, 1.3 * radius, material)
spheroid = miepy.ellipsoid([0, 0, 0], radius, 1.3 * radius, 1.6 * radius,
material)
T = spheroid.compute_tmatrix(lmax, wavelength, 1)
print(T[1, :, 0, 0])
T2 = np.copy(T)
import matplotlib.pyplot as plt
rmax = lmax * (lmax + 2)
T1 = np.reshape(T1, [2 * rmax, 2 * rmax])
T2 = np.reshape(T2, [2 * rmax, 2 * rmax])
y = np.abs(T1 - T2)
y /= np.max(y)
plt.pcolormesh(y, vmax=.1)
plt.gca().set_aspect('equal')
