def test_rayleigh(self):
V = Rayleigh(omega=0.2, tau=1.7)
t_0 = np.pi / 2.
t_ex = 0.234234
p_0 = np.pi / 2.
p_ex = 0.
p = V.p(t_0, t_ex, p_0, p_ex) # cos=0
self.assertEqual(p, (3. / (16. * np.pi)))
def test_volume(self):
t_0 = np.deg2rad(60.)
t_ex = np.deg2rad(60.)
V = Rayleigh(tau=0., omega=0.0)
RT = RT1(self.I0, t_0, t_ex, self.p_0, self.p_ex, V=V, SRF=self.S)
Itot, Isurf, Ivol, Iint = RT.calc()
self.assertEqual(Ivol, 0.)
def test_calc(self):
# just try to get it running simply without further testing
RT = RT1(self.I0,
self.t_0,
self.t_ex,
self.p_0,
self.p_ex,
V=self.V,
SRF=self.S)
Itot, Isurf, Ivol, Iint = RT.calc()
self.assertTrue(np.allclose(Itot, Isurf + Ivol + Iint))
V = Rayleigh(tau=0., omega=0.)
RT = RT1(self.I0,
self.t_0,
self.t_ex,
self.p_0,
self.p_ex,
V=V,
SRF=self.S)
Itot, Isurf, Ivol, Iint = RT.calc()
self.assertEqual(Ivol, 0.)
self.assertEqual(Iint, 0.) # todo gives nan
self.assertEqual(Itot, Isurf)
self.assertTrue(Isurf > 0.)
def setUp(self):
self.I0 = 1.
self.t_0 = np.deg2rad(60.)
self.t_ex = np.deg2rad(60.)
self.p_0 = np.ones_like(self.t_0) * 0.
self.p_ex = np.ones_like(self.t_0) * 0.
self.V = Rayleigh(tau=0.7, omega=0.3)
self.S = Isotropic()
def setUp(self):
self.I0 = 1.
self.t_0 = np.deg2rad(60.)
self.t_ex = np.deg2rad(60.)
self.p_0 = np.ones_like(self.t_0) * 0.
self.p_ex = np.ones_like(self.t_0) * 0.
self.V = Rayleigh(tau=np.array([0.7]), omega=np.array([0.3]))
self.S = Isotropic()
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_fn_coefficients_RayIso(self):
# test if calculation of fn coefficients is correct
# this is done by comparing the obtained coefficients
# against the analytical solution using a Rayleigh volume
# and isotropic surface scattering phase function
S = Isotropic()
V = Rayleigh(tau=0.7, omega=0.3)
t_0 = np.deg2rad(60.)
t_ex = np.deg2rad(60.)
p_0 = 0.
RT = RT1(self.I0, t_0, t_ex, p_0, self.p_ex, V=V, SRF=S)
# the reference solutions should be (see rayleighisocoefficients.pdf)
f0 = 3. / (16. * np.pi) * (3. - np.cos(t_0)**2.)
f1 = 0.
f2 = 3. / (16. * np.pi) * (3. * np.cos(t_0)**2. - 1.)
# and all others are 0.
self.assertTrue(
np.allclose([f0, f1, f2], RT._fnevals(t_0, p_0, t_ex, self.p_ex)))
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_surface(self):
V = Rayleigh(tau=0., omega=0.)
t_0 = np.deg2rad(60.)
RT = RT1(4., t_0, self.t_ex, self.p_0, self.p_ex, V=V, SRF=self.S)
Itot, Isurf, Ivol, Iint = RT.calc()
self.assertTrue(np.allclose(Isurf, 2. / np.pi, 15))
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)
def performfit(
self,
sig0,
dB,
Nmeasurements,
mininc,
maxinc,
minincnum,
maxincnum,
omin,
omax,
taumin,
taumax,
rmin,
rmax,
tmin,
tmax,
):
'''
fucntion adapted from doc/examples/examples_fitting.py
the values are generated using np.random.seed(0) for all
calls of np.random...
'''
# ---------------------------------------------------------------------
# ------------------------- DATA-GENERATION ---------------------------
# generate N arrays of incidence-angles that contain maxincnum
# values between mininc and maxinc
inc = np.array([np.deg2rad(np.linspace(mininc, maxinc, maxincnum))] *
Nmeasurements)
np.random.seed(0) # reset seed to have a reproducible test
# generate random samples of parameters
omegadata = np.random.uniform(low=omin,
high=omax,
size=(Nmeasurements, ))
np.random.seed(0) # reset seed to have a reproducible test
taudata = np.random.uniform(low=taumin,
high=taumax,
size=(Nmeasurements, ))
np.random.seed(0) # reset seed to have a reproducible test
rdata = np.random.uniform(low=rmin, high=rmax, size=(Nmeasurements, ))
np.random.seed(0) # reset seed to have a reproducible test
tdata = np.random.uniform(low=tmin, high=tmax, size=(Nmeasurements, ))
# set tau of Neq measurements to be equal and fit only a single param.
# for tau to all datasets
# choose a random number of equal datasets
if Nmeasurements == 1:
Neq = 0
equal_tau_selects = [0]
else:
Neq = int(Nmeasurements / 5)
np.random.seed(0) # reset seed to have a reproducible test
equal_tau_selects = np.random.choice(range(Nmeasurements),
size=Neq + 1,
replace=False)
for i in equal_tau_selects:
# for i in [1,3,5,7,9,11,14,16,17]:
taudata[i] = taudata[equal_tau_selects[0]]
# define model that is used to generate the data
# the choices for tau, omega and NormBRDF have no effect on the
# dataset since they will be changed to randomly generated values!
V_data = Rayleigh(tau=0.1, omega=0.1)
SRF_data = HGsurface(ncoefs=10, t=sp.var('t_data'), a=[1., 1., 1.])
# setup rt1-object
# (since the fn-coefficients must still be calculated, one must
# specify the arrays for the parameters afterwards)
R_data = RT1(1.,
0.,
0.,
0.,
0.,
V=V_data,
SRF=SRF_data,
geometry='mono',
param_dict={'t_data': .5})
# specify parameters and incidence-angles
R_data.t_0 = inc
R_data.p_0 = np.zeros_like(inc)
R_data.V.omega = omegadata[:, np.newaxis]
R_data.V.tau = taudata[:, np.newaxis]
R_data.SRF.NormBRDF = rdata[:, np.newaxis]
R_data.param_dict = {'t_data': tdata[:, np.newaxis]}
# calculate the data and add some random noise
data = R_data.calc()[0]
np.random.seed(0) # reset seed to have a reproducible test
noise = np.random.uniform(low=-np.max(data) / 50.,
high=np.max(data) / 50.,
size=data.shape)
data = data + noise
if sig0 is True:
# convert the calculated results do sigma0
signorm = 4. * np.pi * np.cos(inc)
data = signorm * data
if dB is True:
# convert the calculated results to dB
data = 10. * np.log10(data)
# define the mask for selecting non-rectangular arrays of data (this is
# done to show that fitting also works for non-rectangular datasets)
np.random.seed(0) # reset seed to have a reproducible test
inc_lengths = np.random.randint(minincnum, maxincnum, Nmeasurements)
selects = []
for i in range(Nmeasurements):
np.random.seed(0) # reset seed to have a reproducible test
selects += [
np.random.choice(range(maxincnum),
inc_lengths[i],
replace=False)
]
# generate dataset of the shape [ [inc_0, data_0], [inc_1, data_1], ..]
# with inc_i and data_i being arrays of varying length
dfindex = [nsel for nsel, i in enumerate(selects) for j in i]
dfinc = [j for i, inc_i in enumerate(inc) for j in inc_i[selects[i]]]
dfsig = [
j for i, data_i in enumerate(data) for j in data_i[selects[i]]
]
dataset = pd.DataFrame({
'inc': dfinc,
'sig': dfsig
},
index=pd.to_datetime(dfindex, unit='D'))
# ---------------------------------------------------------------------
# ------------------------------- FITTING -----------------------------
def set_V_SRF(t1, N, tau, omega, **kwargs):
V = Rayleigh(omega=omega, tau=tau)
SRF = HGsurface(ncoefs=10, t=t1, NormBRDF=N, a=[1., 1., 1.])
return V, SRF
# specify additional arguments for scipy.least_squares
lsq_kwargs = {
'ftol': 1e-8,
'gtol': 1e-8,
'xtol': 1e-8,
'max_nfev': 500,
'method': 'trf',
'tr_solver': 'lsmr',
'x_scale': 'jac'
}
# select random numbers within the boundaries as sart-values
np.random.seed(0) # reset seed to have a reproducible test
ostart = (omax - omin) * np.random.random() + omin
np.random.seed(0) # reset seed to have a reproducible test
tstart = (tmax - tmin) * np.random.random() + tmin
taustart = (taumax - taumin) * np.random.random() + taumin
# fit only a single parameter to the datasets that have equal tau
_, fittau_dyn = np.unique(dataset.index, return_inverse=True)
fittau_dyn[np.isin(fittau_dyn, equal_tau_selects)] = \
fittau_dyn[np.isin(fittau_dyn, equal_tau_selects)][0]
# add manual parameter dynamics for tau
dataset['tau_dyn'] = fittau_dyn
# specify the treatment of the parameters in the retrieval procedure
defdict = {
't1': [True, tstart, 'D', ([tmin], [tmax])],
'N': [False, 'auxiliary'],
'tau': [True, taustart, 'manual', ([taumin], [taumax])],
'omega': [True, ostart, None, ([omin], [omax])],
'bsf': [False, 0.]
}
# append auxiliary datasets
N_auxdata = pd.DataFrame({
'N': rdata
}, pd.unique(dataset.index)).loc[dataset.index]
dataset['N'] = N_auxdata
# initialize fit-class
testfit = Fits(sig0=sig0,
dB=dB,
dataset=dataset,
defdict=defdict,
set_V_SRF=set_V_SRF,
lsq_kwargs=lsq_kwargs,
setindex='mean',
int_Q=True,
verbose=2)
# print model definition
testfit.model_definition
# perform the fit
testfit.performfit(print_progress=True)
# check if _calc_slope_curv is working
# TODO this only tests if a result is obtained, not if the result
# is actually correct !!
slops, curvs = testfit._calc_slope_curv()
# provide true-values for comparison of fitted results
truevals = {
'tau': taudata,
'omega': omegadata,
't1': tdata,
}
# ----------- calculate R^2 values and errors of parameters -----------
# sicne fit[0].fun gives the residuals weighted with respect to
# weights, the model calculation can be gained via
# estimates = fit[0].fun/weights + measurements
# apply mask
measures = testfit.data[~testfit.mask]
estimates = testfit.fit_output.fun + measures
# evaluate linear regression to get r-value etc.
slope, intercept, r_value, p_value, std_err = linregress(
estimates, measures)
# calculate R^2 value
r2 = r_value**2
# check if r^2 between original and fitted data is > 0.95
self.assertTrue(r2 > 0.95, msg=f'r^2 condition not met , R={r2:4f}')
# set mean-error values for the derived parameters
if sig0 is True and dB is False:
errdict = {'tau': 0.03, 'omega': 0.008, 't1': 0.05}
if sig0 is False and dB is False:
errdict = {'tau': 0.03, 'omega': 0.01, 't1': 0.08}
if sig0 is True and dB is True:
errdict = {'tau': 0.03, 'omega': 0.01, 't1': 0.09}
if sig0 is False and dB is True:
errdict = {'tau': 0.03, 'omega': 0.01, 't1': 0.09}
fittedvals = testfit.res_df
for key in truevals:
err = abs(fittedvals[key] - truevals[key]).mean()
self.assertTrue(err < errdict[key],
msg='derived error' + str(err) + 'too high for ' +
str(key))
return truevals, r2
equal_tau_selects = [0]
else:
Neq = int(Nmeasurements / 5)
equal_tau_selects = np.random.choice(range(Nmeasurements),
size=Neq + 1,
replace=False)
for i in equal_tau_selects:
# for i in [1,3,5,7,9,11,14,16,17]:
taudata[i] = taudata[equal_tau_selects[0]]
# define model that is used to generate the data
# the choices for tau, omega and NormBRDF have no effect on the generated data
# since they will be changed to randomly generated values!
V_data = Rayleigh(tau=0.1, omega=0.1)
SRF_data = HGsurface(ncoefs=15, t=sp.var('t_data'), a=[1., 1., 1.])
# setup rt1-object
# (since the fn-coefficients must still be calculated, one must
# specify the arrays for the parameters afterwards)
R_data = RT1(1.,
t_0=inc,
p_0=np.zeros_like(inc),
t_ex=None,
p_ex=None,
V=V_data,
SRF=SRF_data,
geometry='mono',
param_dict={'t_data': .5},
lambda_backend='cse_seng_sp_newlambdify',
def performfit(
self,
sig0,
dB,
Nmeasurements,
mininc,
maxinc,
minincnum,
maxincnum,
omin,
omax,
taumin,
taumax,
rmin,
rmax,
tmin,
tmax,
):
'''
fucntion adapted from doc/examples/examples_fitting.py
the values are generated using np.random.seed(0) for all
calls of np.random...
'''
# ---------------------------------------------------------------------
# ------------------------- DATA-GENERATION ---------------------------
# generate N arrays of incidence-angles that contain maxincnum
# values between mininc and maxinc
inc = np.array([np.deg2rad(np.linspace(mininc, maxinc, maxincnum))] *
Nmeasurements)
np.random.seed(0) # reset seed to have a reproducible test
# generate random samples of parameters
omegadata = np.random.uniform(low=omin,
high=omax,
size=(Nmeasurements, ))
np.random.seed(0) # reset seed to have a reproducible test
taudata = np.random.uniform(low=taumin,
high=taumax,
size=(Nmeasurements, ))
np.random.seed(0) # reset seed to have a reproducible test
rdata = np.random.uniform(low=rmin, high=rmax, size=(Nmeasurements, ))
np.random.seed(0) # reset seed to have a reproducible test
tdata = np.random.uniform(low=tmin, high=tmax, size=(Nmeasurements, ))
# set tau of Neq measurements to be equal and fit only a single param.
# for tau to all datasets
# choose a random number of equal datasets
if Nmeasurements == 1:
Neq = 0
equal_tau_selects = [0]
else:
Neq = int(Nmeasurements / 5)
np.random.seed(0) # reset seed to have a reproducible test
equal_tau_selects = np.random.choice(range(Nmeasurements),
size=Neq + 1,
replace=False)
for i in equal_tau_selects:
# for i in [1,3,5,7,9,11,14,16,17]:
taudata[i] = taudata[equal_tau_selects[0]]
# define model that is used to generate the data
# the choices for tau, omega and NormBRDF have no effect on the
# dataset since they will be changed to randomly generated values!
V_data = Rayleigh(tau=0.1, omega=0.1)
SRF_data = HGsurface(ncoefs=10, t=sp.var('t_data'), a=[1., 1., 1.])
# setup rt1-object
# (since the fn-coefficients must still be calculated, one must
# specify the arrays for the parameters afterwards)
R_data = RT1(1.,
0.,
0.,
0.,
0.,
V=V_data,
SRF=SRF_data,
geometry='mono',
param_dict={'t_data': .5})
# specify parameters and incidence-angles
R_data.t_0 = inc
R_data.p_0 = np.zeros_like(inc)
R_data.V.omega = omegadata
R_data.V.tau = taudata
R_data.SRF.NormBRDF = rdata
R_data.param_dict = {'t_data': tdata[:, np.newaxis]}
# calculate the data and add some random noise
data = R_data.calc()[0]
np.random.seed(0) # reset seed to have a reproducible test
noise = np.random.uniform(low=-np.max(data) / 50.,
high=np.max(data) / 50.,
size=data.shape)
data = data + noise
if sig0 is True:
# convert the calculated results do sigma0
signorm = 4. * np.pi * np.cos(inc)
data = signorm * data
if dB is True:
# convert the calculated results to dB
data = 10. * np.log10(data)
# define the mask for selecting non-rectangular arrays of data (this is
# done to show that fitting also works for non-rectangular datasets)
np.random.seed(0) # reset seed to have a reproducible test
inc_lengths = np.random.randint(minincnum, maxincnum, Nmeasurements)
selects = []
for i in range(Nmeasurements):
np.random.seed(0) # reset seed to have a reproducible test
selects += [
np.random.choice(range(maxincnum),
inc_lengths[i],
replace=False)
]
# generate dataset of the shape [ [inc_0, data_0], [inc_1, data_1], ..]
# with inc_i and data_i being arrays of varying length
dataset = []
for i, row in enumerate(inc):
dataset = dataset + [[inc[i][selects[i]], data[i][selects[i]]]]
# ---------------------------------------------------------------------
# ------------------------------- FITTING -----------------------------
# initialize fit-class
testfit = Fits(sig0=sig0, dB=dB)
# define sympy-symbols for definition of V and SRF
t1 = sp.Symbol('t1')
V = Rayleigh(omega=0.1, tau=0.1)
# values for NormBRDF are set to known values (i.e. rdata)
SRF = HGsurface(ncoefs=10, t=t1, NormBRDF=rdata, a=[1., 1., 1.])
# select random numbers within the boundaries as sart-values
np.random.seed(0) # reset seed to have a reproducible test
ostart = (omax - omin) * np.random.random() + omin
np.random.seed(0) # reset seed to have a reproducible test
tstart = (tmax - tmin) * np.random.random() + tmin
taustart = (taumax - taumin) * np.random.random() + taumin
# define which parameter should be fitted
param_dict = {
'tau': [taustart] * (Nmeasurements - Neq),
'omega': ostart,
't1': [tstart] * (Nmeasurements)
}
# optionally define fixed parameters
fixed_dict = {'NormBRDF': rdata}
# define boundary-conditions
bounds_dict = {
't1': ([tmin] * (Nmeasurements), [tmax] * (Nmeasurements)),
'tau': ([taumin] * (Nmeasurements - Neq),
[taumax] * (Nmeasurements - Neq)),
'omega': ([omin], [omax])
}
# setup param_dyn_dict
param_dyn_dict = {}
for key in param_dict:
param_dyn_dict[key] = np.linspace(
1, len(np.atleast_1d(param_dict[key])), Nmeasurements)
# fit only a single parameter to the datasets that have equal tau
for i in equal_tau_selects:
param_dyn_dict['tau'][i] = param_dyn_dict['tau'][
equal_tau_selects[0]]
# provide true-values for comparison of fitted results
truevals = {
'tau': taudata,
'omega': omegadata,
't1': tdata,
}
# perform fit
fit = testfit.monofit(V=V,
SRF=SRF,
dataset=dataset,
param_dict=param_dict,
bounds_dict=bounds_dict,
fixed_dict=fixed_dict,
param_dyn_dict=param_dyn_dict,
verbose=2,
ftol=1.e-8,
xtol=1.e-8,
gtol=1.e-8,
x_scale='jac',
max_nfev=500)
# ----------- calculate R^2 values and errors of parameters -----------
# scatterplot, r2 = testfit.printscatter(fit, pointsize=4,
# c=fit[3][~fit[4]],
# cmap='coolwarm',
# regression=True)
(res_lsq, R, data, inc, mask, weights, res_dict, start_dict,
fixed_dict) = fit
# sicne fit[0].fun gives the residuals weighted with respect to
# weights, the model calculation can be gained via
# estimates = fit[0].fun/weights + measurements
estimates = np.reshape(fit[0].fun / weights, data.shape)
# apply mask
measures = data[~mask]
estimates = estimates[~mask] + measures
# evaluate linear regression to get r-value etc.
slope, intercept, r_value, p_value, std_err = linregress(
estimates, measures)
# calculate R^2 value
r2 = r_value**2
# check if r^2 between original and fitted data is > 0.95
self.assertTrue(r2 > 0.95, msg='r^2 condition not met')
# set mean-error values for the derived parameters
if sig0 is True and dB is False:
errdict = {'tau': 0.03, 'omega': 0.008, 't1': 0.05}
if sig0 is False and dB is False:
errdict = {'tau': 0.03, 'omega': 0.01, 't1': 0.08}
if sig0 is True and dB is True:
errdict = {'tau': 0.03, 'omega': 0.01, 't1': 0.09}
if sig0 is False and dB is True:
errdict = {'tau': 0.03, 'omega': 0.01, 't1': 0.09}
for key in truevals:
err = abs(fit[6][key] - truevals[key]).mean()
self.assertTrue(err < errdict[key],
msg='derived error' + str(err) + 'too high for ' +
str(key))
return truevals, fit, r2
'''
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
def set_V_SRF(t1, N, tau, omega, **kwargs):
V = Rayleigh(omega=omega, tau=tau)
SRF = HGsurface(ncoefs=10, t=t1, NormBRDF=N, a=[1., 1., 1.])
return V, SRF