def test_normalization(self):
# test normalization results for extreme case of isotropic scattering.
# this is done by testing for different geometries the following cases:
# Isotropic := 1/pi = CosineLobe(i=0) = HenyeyGreenstein(t=0)
N = 20
t_0 = np.random.random(N) * np.pi
t_ex = np.random.random(N) * np.pi
p_0 = np.pi / 4.
p_ex = np.pi / 4.
for i in range(N):
I = Isotropic()
self.assertTrue(
np.allclose(I.brdf(t_0[i], t_ex[i], p_0, p_ex), 1. / np.pi))
ncoefs = 10
C = CosineLobe(ncoefs=ncoefs, i=0)
self.assertTrue(
np.allclose(C.brdf(t_0[i], t_ex[i], p_0, p_ex), 1. / np.pi))
H = HenyeyGreenstein(t=0, ncoefs=5)
self.assertTrue(
np.allclose(H.brdf(t_0[i], t_ex[i], p_0, p_ex), 1. / np.pi))
LCH = LinCombSRF([[.5, HenyeyGreenstein(t=0, ncoefs=5)],
[.5, HenyeyGreenstein(t=0, ncoefs=5)]])
self.assertTrue(
np.allclose(LCH.brdf(t_0[i], t_ex[i], p_0, p_ex), 1. / np.pi))
def test_expansion_cosine_lobe(self):
# theta_i = np.pi/2.
# theta_s = 0.234234
# phi_i = np.pi/2.
# phi_s = 0.
# reference solution based on first N Legrende polynomials
ncoefs = 10
# means coefficients 0...9; i=5 is for the example in the paper
S = CosineLobe(ncoefs=ncoefs, i=5)
# input parameters are set in a way that COS_THETA = 1
# and therefore only the legendre coefficients should be returned
# which is always 1 in case that cos_THETA=1
t_0 = 0.1234
t_ex = np.pi / 2.
p_0 = 0.3456
p_ex = 0.
r = S._eval_legpoly(t_0, t_ex, p_0, p_ex, geometry='ffff')
# calculate reference solution
refs = []
for k in range(ncoefs):
refs.append(S._get_legcoef(k) * 1.)
ref = np.array(refs).sum()
self.assertAlmostEqual(r, ref, 15)
def test_cosine_coeff(self):
# test legcoefs for example in paper
n = 10
S = CosineLobe(ncoefs=n, i=5)
for i in range(n):
z1 = 120. * (1. / 128. + i / 64.) / np.sqrt(np.pi)
z2 = sc.gamma((7. - i) * 0.5) * sc.gamma((8. + i) * 0.5)
self.assertAlmostEqual(S._get_legcoef(i), z1 / z2)
self.assertAlmostEqual(
S._get_legcoef(0),
15. / (16. * sc.gamma(3.5) * sc.gamma(4.) * np.sqrt(np.pi)))
self.assertAlmostEqual(
S._get_legcoef(2),
75. / (16. * sc.gamma(2.5) * sc.gamma(5.) * np.sqrt(np.pi)))
def test_fn_coefficients_RayCosine(self):
# test if calculation of fn coefficients is correct
# for a cosine lobe with reduced number of coefficients
# this is done by comparing the obtained coefficients
# against the analytical solution using a Rayleigh volume
# and isotropic surface scattering phase function
S = CosineLobe(ncoefs=1, i=5)
V = Rayleigh(tau=0.7, omega=0.3)
# --> cosTHETA = 0.
# tests are using full Volume phase function, but only
# ncoef times the coefficients from the surface
t_0 = np.pi / 2.
t_ex = 0.234234
p_0 = np.pi / 2.
p_ex = 0.
RT = RT1(self.I0, t_0, t_ex, p_0, p_ex, V=V, SRF=S, geometry='vvvv')
res = RT._fnevals(t_0, p_0, t_ex, p_ex)
# ncoefs = 1
# analtytical solution for ncoefs = 1 --> n=0
a0 = (3. / (16. * np.pi)) * (4. / 3.)
a2 = (3. / (16. * np.pi)) * (2. / 3.)
b0 = (15. * np.sqrt(np.pi)) / (16. * gamma(3.5) * gamma(4.))
# print 'a0:', a0, V._get_legcoef(0)
# print 'a2:', a2, V._get_legcoef(2)
# print 'b0: ', b0, S._get_legcoef(0)
ref0 = 1. / 4. * b0 * (8. * a0 - a2 - 3. * a2 * np.cos(2. * t_0))
ref2 = 3. / 4. * a2 * b0 * (1. + 3. * np.cos(2. * t_0))
self.assertTrue(np.allclose([ref0, ref2], [res[0], res[2]]))
# ncoefs = 2
# first and third coef should be the same as for ncoefs=1
S = CosineLobe(ncoefs=2, i=5, NormBRDF=np.pi)
RT = RT1(self.I0, t_0, t_ex, p_0, p_ex, V=V, SRF=S, geometry='ffff')
res2 = RT._fnevals(t_0, p_0, t_ex, p_ex)
self.assertTrue(np.allclose([ref0, ref2], [res2[0], res2[2]]))
def test_example_2_int(self):
print('Testing Example 2 ...')
inc = self.inc2
# ---- evaluation of second example
V = HenyeyGreenstein(tau=0.7, omega=0.3, t=0.7, ncoefs=20)
SRF = CosineLobe(ncoefs=10, i=5, NormBRDF=np.pi)
R = RT1(1.,
np.deg2rad(inc),
np.deg2rad(inc),
np.zeros_like(inc),
np.full_like(inc, np.pi),
V=V,
SRF=SRF,
geometry='mono')
self.assertTrue(np.allclose(self.int_num_2, R.calc()[3], atol=1e-6))
def test_example_1_int(self):
print('Testing Example 1 ...')
inc = self.inc1
# ---- evaluation of first example
V = Rayleigh(tau=np.array([0.7]), omega=np.array([0.3]))
# 11 instead of 10 coefficients used to assure 7 digit precision
SRF = CosineLobe(ncoefs=11, i=5, NormBRDF=np.array([np.pi]))
R = RT1(1.,
np.deg2rad(inc),
np.deg2rad(inc),
np.zeros_like(inc),
np.full_like(inc, np.pi),
V=V,
SRF=SRF,
geometry='mono')
self.assertTrue(np.allclose(self.int_num_1, R.calc()[3]))
def test_example1_fn(self):
S = CosineLobe(
ncoefs=10, i=5, NormBRDF=np.pi
) # somehow this is only working for ncoefs=1 at the moment!
V = Rayleigh(tau=0.7, omega=0.3)
I0 = 1.
phi_0 = 0.
#~ phi_0 = np.pi/2.
phi_ex = np.pi # backscatter case
fn = None
for i in range(0, len(self.inc), self.step):
#~ if self.n[i] % 2 == 1:
#~ continue # todo skipping odds at the moment
t_0 = self.inc[i]
t_ex = t_0 * 1.
RT = RT1(I0, t_0, t_ex, phi_0, phi_ex, RV=V, SRF=S, fn=fn)
self.assertAlmostEqual(self.inc[i], RT.theta_0)
mysol = RT._get_fn(int(self.n[i]), RT.theta_0, phi_0)
print('inc,n,fnref,mysol:', RT.t_0, self.n[i], self.fn[i], mysol)
fn = RT.fn
self.assertEqual(
self.tau[i], V.tau
) # check that tau for reference is the same as used for Volume object
if self.fn[i] == 0.:
self.assertEqual(mysol, self.fn[i])
else:
#~ if np.abs(self.fn[i]) > 1.E-:
#~ thres = 1.E-3 ## 1 promille threshold
#~ else:
thres = 1.E-8 # one percent threshold for very small numbers
ratio = mysol / self.fn[i]
self.assertTrue(np.abs(1. - ratio) < thres)
def test_example1_Fint(self):
# backscatter case
S = CosineLobe(ncoefs=10, i=5, NormBRDF=np.pi)
V = Rayleigh(tau=0.7, omega=0.3)
I0 = 1.
phi_0 = 0.
phi_ex = np.pi # backscatter case
for i in range(0, len(self.inc), self.step):
print('i,n:', i, self.n[i])
t_0 = self.inc[i]
t_ex = t_0 * 1.
RT = RT1(I0, t_0, t_ex, phi_0, phi_ex, RV=V, SRF=S)
self.assertEqual(
self.tau[i], V.tau
) # check that tau for reference is the same as used for Volume object
Fint1 = RT._calc_Fint(t_0, t_ex, phi_0,
phi_ex) # todo clairfy usage of phi!!!
Fint2 = RT._calc_Fint(t_ex, t_0, phi_ex, phi_0)
self.assertEqual(Fint1, Fint2)
def test_cosine(self):
S = CosineLobe(ncoefs=10, i=5)
t_0 = np.pi / 2.
t_ex = 0.234234
p_0 = np.pi / 2.
p_ex = 0.
self.assertAlmostEqual(S.scat_angle(t_0, t_ex, p_0, p_ex, S.a), 0., 15)
self.assertAlmostEqual(S.brdf(t_0, t_ex, p_0, p_ex), 0., 20)
t_0 = 0.
t_ex = np.deg2rad(60.)
p_0 = 0.
p_ex = 0.
self.assertAlmostEqual(S.scat_angle(t_0, t_ex, p_0, p_ex, S.a), 0.5,
15)
self.assertAlmostEqual(S.brdf(t_0, t_ex, p_0, p_ex), 0.5**5. / np.pi,
10)
possible choices for example = ?
1 : example 1 from the paper
2 : example 2 from the paper
3 : example using a linear-combination for p and the BRDF
'''
example = 3
# ----------- definition of examples -----------
if example == 1:
# define incidence-angle range for generation of backscatter-plots
inc = np.arange(1., 89., 1.)
# Example 1
V = Rayleigh(tau=0.55, omega=0.24)
SRF = CosineLobe(ncoefs=15, i=6, a=[.28, 1., 1.])
label = 'Example 1'
elif example == 2:
# define incidence-angle range for generation of backscatter-plots
inc = np.arange(1., 89., 1.)
V = HenyeyGreenstein(tau=0.7, omega=0.3, t=0.7, ncoefs=20)
SRF = CosineLobe(ncoefs=10, i=5)
label = 'Example 2'
elif example == 3:
# define incidence-angle range for generation of backscatter-plots
inc = np.arange(1., 89., 1.)
# list of volume-scattering phase-functions to be combined
phasechoices = [
# forward-scattering-peak
HenyeyGreenstein(t=0.5, ncoefs=10, a=[-1., 1., 1.]),
import sys
sys.path.append('..')
from rt1.rt1 import RT1
from rt1.volume import Rayleigh
from rt1.surface import CosineLobe
import numpy as np
import time
# some speed benchmarking ...
S = CosineLobe(ncoefs=10, i=5)
V = Rayleigh(tau=0.7, omega=0.3)
I0 = 1.
theta_i = np.pi / 2.
theta_ex = 0.234234
phi_i = np.pi / 2.
phi_ex = 0.
RT = RT1(I0, theta_i, theta_ex, phi_i, phi_ex, RV=V, SRF=S, geometry='vvvv')
#~ print RT.fn
#~ print len(RT.fn)
#~ start = time.time()
#~ for i in xrange(10):
#~ for n in xrange(len(RT.fn)):
#~ RT._get_fn(n, theta_i, phi_i, theta_ex, phi_ex)