def calc_J(rays, n_mu_pts, n_depth_pts, mu_grid):
I_mu = np.zeros(n_mu_pts)
J_lam = np.zeros(n_depth_pts)
for i in range(n_depth_pts):
for j, each_ray in enumerate(rays):
I_mu[j] = each_ray.I_lam[get_ray_index_for_grid_point(each_ray, i, n_depth_pts)]
J_lam[i] = 0.5 * simps(I_mu, mu_grid)
return (J_lam)
def calc_J(rays, n_mu_pts, n_depth_pts, mu_grid):
I_mu = np.zeros(n_mu_pts)
J_lam = np.zeros(n_depth_pts)
for i in range(n_depth_pts):
for j, each_ray in enumerate(rays):
I_mu[j] = each_ray.I_lam[get_ray_index_for_grid_point(
each_ray, i, n_depth_pts)]
J_lam[i] = 0.5 * simps(I_mu, mu_grid)
return (J_lam)
def calc_Lambda_star(Lambda_star, n_depth_pts, n_mu_pts, rays, mu_grid):
inorm_tmp = np.zeros([n_depth_pts, n_mu_pts])
for l in range(1, n_depth_pts-1):
inorm_tmp[:, :] = 0
for j, each_ray in enumerate(rays):
# get ray index corresponding to physical grid index l
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
# get physical grid indices corresponding to i+1 and i-1 along the ray
grid_idx_lim1 = get_grid_index_for_ray_point(each_ray, ray_idx_l-1, n_depth_pts)
grid_idx_lip1 = get_grid_index_for_ray_point(each_ray, ray_idx_l+1, n_depth_pts)
inorm_tmp[grid_idx_lim1, j] = each_ray.gamma(ray_idx_l-1)
inorm_tmp[l, j] = each_ray.gamma(ray_idx_l-1) * exp(-each_ray.Delta_tau(ray_idx_l-1)) + each_ray.beta(ray_idx_l)
inorm_tmp[grid_idx_lip1, j] = (each_ray.gamma(ray_idx_l-1) * exp(-each_ray.Delta_tau(ray_idx_l-1)) + each_ray.beta(ray_idx_l)) * exp(-each_ray.Delta_tau(ray_idx_l)) + each_ray.alpha(ray_idx_l+1)
# TODO: these +1/-1 offsets are hard-coded, works in 1-D plane parallel,
# but won't work in more complex geometries
Lambda_star[l-1, l] = 0.5 * simps(inorm_tmp[l-1, :], x=mu_grid)
Lambda_star[l , l] = 0.5 * simps(inorm_tmp[l , :], x=mu_grid)
Lambda_star[l+1, l] = 0.5 * simps(inorm_tmp[l+1, :], x=mu_grid)
# boundary cases.
# surface
l = 0
inorm_tmp[:, :] = 0
for j, each_ray in enumerate(rays):
# at the surface, outgoing rays (those with mu > 0) only have i-1 and i components, no i+1
if each_ray.mu > 0:
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lim1 = get_grid_index_for_ray_point(each_ray, ray_idx_l-1, n_depth_pts)
inorm_tmp[grid_idx_lim1, j] = each_ray.gamma(ray_idx_l-1)
inorm_tmp[l, j] = each_ray.gamma(ray_idx_l-1) * exp(-each_ray.Delta_tau(ray_idx_l-1)) + each_ray.beta(ray_idx_l)
else:
# at the surface we don't have an "i-1" term on incoming rays (those with mu < 0)
# no illumination from the surface, so incoming rays at the surface have I(surface) = 0
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lip1 = get_grid_index_for_ray_point(each_ray, ray_idx_l+1, n_depth_pts)
inorm_tmp[l, j] = 0
inorm_tmp[grid_idx_lip1, j] = each_ray.alpha(ray_idx_l+1)
Lambda_star[l, l] = 0.5 * simps(inorm_tmp[l , :], x=mu_grid)
Lambda_star[l+1, l] = 0.5 * simps(inorm_tmp[l+1, :], x=mu_grid)
inorm_tmp[:, :] = 0
# depth
l = n_depth_pts-1
for j, each_ray in enumerate(rays):
# at depth, we don't have an "i-1" term on rays with mu > 0 because they start at depth
if (each_ray.mu < 0):
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lim1 = get_grid_index_for_ray_point(each_ray, ray_idx_l-1, n_depth_pts)
inorm_tmp[grid_idx_lim1, j] = each_ray.gamma(ray_idx_l-1)
inorm_tmp[l, j] = each_ray.gamma(ray_idx_l-1) * exp(-each_ray.Delta_tau(ray_idx_l-1)) + each_ray.beta(ray_idx_l)
else:
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lip1 = get_grid_index_for_ray_point(each_ray, ray_idx_l+1, n_depth_pts)
inorm_tmp[l, j] = 0.0
inorm_tmp[grid_idx_lip1, j] = each_ray.alpha(ray_idx_l+1)
Lambda_star[l-1, l] = 0.5 * simps(inorm_tmp[l-1, :], x=mu_grid)
Lambda_star[l , l] = 0.5 * simps(inorm_tmp[l , :], x=mu_grid)
return(Lambda_star)
def calc_Lambda_star(Lambda_star, n_depth_pts, n_mu_pts, rays, mu_grid):
inorm_tmp = np.zeros([n_depth_pts, n_mu_pts])
for l in range(1, n_depth_pts - 1):
inorm_tmp[:, :] = 0
for j, each_ray in enumerate(rays):
# get ray index corresponding to physical grid index l
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
# get physical grid indices corresponding to i+1 and i-1 along the ray
grid_idx_lim1 = get_grid_index_for_ray_point(
each_ray, ray_idx_l - 1, n_depth_pts)
grid_idx_lip1 = get_grid_index_for_ray_point(
each_ray, ray_idx_l + 1, n_depth_pts)
inorm_tmp[grid_idx_lim1, j] = each_ray.gamma(ray_idx_l - 1)
inorm_tmp[l, j] = each_ray.gamma(ray_idx_l - 1) * exp(
-each_ray.Delta_tau(ray_idx_l - 1)) + each_ray.beta(ray_idx_l)
inorm_tmp[
grid_idx_lip1,
j] = (each_ray.gamma(ray_idx_l - 1) *
exp(-each_ray.Delta_tau(ray_idx_l - 1)) +
each_ray.beta(ray_idx_l)) * exp(-each_ray.Delta_tau(
ray_idx_l)) + each_ray.alpha(ray_idx_l + 1)
# TODO: these +1/-1 offsets are hard-coded, works in 1-D plane parallel,
# but won't work in more complex geometries
Lambda_star[l - 1, l] = 0.5 * simps(inorm_tmp[l - 1, :], x=mu_grid)
Lambda_star[l, l] = 0.5 * simps(inorm_tmp[l, :], x=mu_grid)
Lambda_star[l + 1, l] = 0.5 * simps(inorm_tmp[l + 1, :], x=mu_grid)
# boundary cases.
# surface
l = 0
inorm_tmp[:, :] = 0
for j, each_ray in enumerate(rays):
# at the surface, outgoing rays (those with mu > 0) only have i-1 and i components, no i+1
if each_ray.mu > 0:
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lim1 = get_grid_index_for_ray_point(
each_ray, ray_idx_l - 1, n_depth_pts)
inorm_tmp[grid_idx_lim1, j] = each_ray.gamma(ray_idx_l - 1)
inorm_tmp[l, j] = each_ray.gamma(ray_idx_l - 1) * exp(
-each_ray.Delta_tau(ray_idx_l - 1)) + each_ray.beta(ray_idx_l)
else:
# at the surface we don't have an "i-1" term on incoming rays (those with mu < 0)
# no illumination from the surface, so incoming rays at the surface have I(surface) = 0
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lip1 = get_grid_index_for_ray_point(
each_ray, ray_idx_l + 1, n_depth_pts)
inorm_tmp[l, j] = 0
inorm_tmp[grid_idx_lip1, j] = each_ray.alpha(ray_idx_l + 1)
Lambda_star[l, l] = 0.5 * simps(inorm_tmp[l, :], x=mu_grid)
Lambda_star[l + 1, l] = 0.5 * simps(inorm_tmp[l + 1, :], x=mu_grid)
inorm_tmp[:, :] = 0
# depth
l = n_depth_pts - 1
for j, each_ray in enumerate(rays):
# at depth, we don't have an "i-1" term on rays with mu > 0 because they start at depth
if (each_ray.mu < 0):
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lim1 = get_grid_index_for_ray_point(
each_ray, ray_idx_l - 1, n_depth_pts)
inorm_tmp[grid_idx_lim1, j] = each_ray.gamma(ray_idx_l - 1)
inorm_tmp[l, j] = each_ray.gamma(ray_idx_l - 1) * exp(
-each_ray.Delta_tau(ray_idx_l - 1)) + each_ray.beta(ray_idx_l)
else:
ray_idx_l = get_ray_index_for_grid_point(each_ray, l, n_depth_pts)
grid_idx_lip1 = get_grid_index_for_ray_point(
each_ray, ray_idx_l + 1, n_depth_pts)
inorm_tmp[l, j] = 0.0
inorm_tmp[grid_idx_lip1, j] = each_ray.alpha(ray_idx_l + 1)
Lambda_star[l - 1, l] = 0.5 * simps(inorm_tmp[l - 1, :], x=mu_grid)
Lambda_star[l, l] = 0.5 * simps(inorm_tmp[l, :], x=mu_grid)
return (Lambda_star)
