def weighted_delta_tracking_no_absorption(lambda_):
"""
pg. 111:5, Algorithm 1. (rhs).
Modified as per Sec. 5.1.3.
Removal of volume absorption/emission events.
"""
sigma_t_majorante_lambda = ms.sigma_t_majorante[lambda_]
x = 0.
w = 1.
while True:
x += exp_sample(sigma_t_majorante_lambda)
if x > ms.domain_length:
return (x, 0.)
else:
sigma_s = ms.get_sigma_s(x)[lambda_]
sigma_a = ms.get_sigma_a(x)[lambda_]
sigma_n = sigma_t_majorante_lambda - sigma_s - sigma_a
ps = sigma_s / (sigma_s + abs(sigma_n))
pn = abs(sigma_n) / (sigma_s + abs(sigma_n))
r = random.uniform(0.,1.)
if r < ps:
w *= sigma_s / sigma_t_majorante_lambda / ps * ms.get_integrand(x)[lambda_]
return (x, w)
else:
w *= sigma_n / sigma_t_majorante_lambda / pn
def ratio_tracking():
"""
pg. 111:16, Eq (41)
"""
sigma_t_majorante = ms.sigma_t_majorante_across_channels
x = 0.
weight = np.ones(2, np.float32)
while True:
x += exp_sample(sigma_t_majorante)
if x > ms.domain_length:
return weight
else:
sigma_s = ms.get_sigma_s(x)
sigma_a = ms.get_sigma_a(x)
sigma_n = sigma_t_majorante - sigma_s - sigma_a
weight *= sigma_n / sigma_t_majorante
def single_lambda_ratio_tracking(lambda_):
"""
pg. 111:16, Eq (41)
"""
sigma_t_majorante_lambda = ms.sigma_t_majorante[lambda_]
x = 0.
weight = 1.
while True:
x += exp_sample(sigma_t_majorante_lambda)
if x > ms.domain_length:
return weight
else:
sigma_s = ms.get_sigma_s(x)[lambda_]
sigma_a = ms.get_sigma_a(x)[lambda_]
sigma_n = sigma_t_majorante_lambda - sigma_s - sigma_a
weight *= sigma_n / sigma_t_majorante_lambda
def weighted_next_flight_estimator():
"""
pg. 111:16, Eq (39)
More variance than ratio tracking?!
"""
sigma_t_majorante = ms.sigma_t_majorante_across_channels
x = 0.
weight_product = np.ones(2, np.float32)
weight = np.zeros(2, np.float32)
while True:
weight += np.exp(sigma_t_majorante * (x - ms.domain_length)) * weight_product
x += exp_sample(sigma_t_majorante)
if x > ms.domain_length:
return weight
else:
sigma_s = ms.get_sigma_s(x)
sigma_a = ms.get_sigma_a(x)
sigma_n = sigma_t_majorante - sigma_s - sigma_a
weight_product *= sigma_n / sigma_t_majorante
def delta_tracking(lambda_):
"""
pg. 111:5, Algorithm 1. (lhs). Although this is a very
well known algorithm. Also known as woodcock tracking.
"""
sigma_t_majorante_lambda = ms.sigma_t_majorante[lambda_]
x = 0.
while True:
x += exp_sample(sigma_t_majorante_lambda)
if x > ms.domain_length:
return (x, 0.)
else:
sigma_s = ms.get_sigma_s(x)[lambda_]
sigma_a = ms.get_sigma_a(x)[lambda_]
sigma_n = sigma_t_majorante_lambda - sigma_s - sigma_a
r = random.uniform(0.,1.)
if r < (sigma_a / sigma_t_majorante_lambda):
return (x, 0.)
elif r < (1. - (sigma_n / sigma_t_majorante_lambda)):
return (x, ms.get_integrand(x)[lambda_])
else:
pass # Null collision
def spectral_tracking_no_absorption(x = 0, weights = None):
"""
pg. 111:10, Algorithm 4.
Modified as per Sec. 5.1.3.
Removal of volume absorption/emission events.
"""
weights = weights.copy() if weights is not None else np.ones(2, np.float32)
while True:
x += exp_sample(ms.sigma_t_majorante_across_channels)
if x > ms.domain_length:
return (x, weights)
else:
sigma_s = ms.get_sigma_s(x)
sigma_a = ms.get_sigma_a(x)
sigma_n = ms.sigma_t_majorante_across_channels - sigma_s - sigma_a
pt, pn = the_probability_scheme(weights, sigma_s, sigma_n)
r = random.uniform(0.,1.)
if r < pt:
weights *= sigma_s / ms.sigma_t_majorante_across_channels * ms.get_integrand(x) / pt
return (x, weights)
else:
weights *= sigma_n / ms.sigma_t_majorante_across_channels / pn
def spectral_tracking():
"""
pg. 111:10, Algorithm 4
"""
weights = np.ones(2, np.float32)
x = 0.
while True:
x += exp_sample(ms.sigma_t_majorante_across_channels)
if x > ms.domain_length:
return (x, weights)
else:
sigma_s = ms.get_sigma_s(x)
sigma_a = ms.get_sigma_a(x)
sigma_n = ms.sigma_t_majorante_across_channels - sigma_s - sigma_a
ps, pa, pn = the_probability_scheme(weights, sigma_s, sigma_a, sigma_n)
r = random.uniform(0.,1.)
if r < pa:
return (x, np.zeros(2, np.float32))
elif r < 1. - pn:
weights *= sigma_s / ms.sigma_t_majorante_across_channels * ms.get_integrand(x) / ps
return (x, weights)
else:
weights *= sigma_n / ms.sigma_t_majorante_across_channels / pn
def construct_piecewise_constant_transmittance():
"""
By ratio tracking.
We have positions xi, and associated weight wi. If we want to obtain
an estimate of the transmittance of some point y, T(y) we look up
the next xi which comes afterwards and use the estimate T^(y) = wi.
In expectation T^(y) equals the true transmittance T(y).
"""
sigma_t_majorante = ms.sigma_t_majorante_across_channels
x = 0.
weight = np.ones(2, np.float32)
points_and_weights = [c_(x, weight)]
while True:
x += exp_sample(sigma_t_majorante)
if x > ms.domain_length:
points_and_weights += [c_(x,weight)]
break
else:
points_and_weights += [c_(x, weight)]
sigma_s = ms.get_sigma_s(x)
sigma_a = ms.get_sigma_a(x)
sigma_n = sigma_t_majorante - sigma_s - sigma_a
weight *= sigma_n / sigma_t_majorante
term_criterion = np.amax(weight)
# Russian roulette termination. Otherwise I would have to traverse
# through the entire domain which would be very inefficient if the
# mean free path length is short
r = random.uniform(0., 1.)
survival_probability = term_criterion
if r < survival_probability: # live on
weight /= survival_probability
else:
points_and_weights += [c_(ms.domain_length*1.1,np.zeros_like(weight))]
break
return np.asarray(points_and_weights)