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photon_1d.py
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photon_1d.py
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import numpy as np
from simulation import *
from model import *
from common import *
from numba import jit, prange
@jit(nopython=True)
def vfunc(v, s, rpos, phi, vphot):
# Get direction and position at location s along l.o.s.
psis = np.arctan2(s*np.sin(phi), rpos + s*np.cos(phi))
phis = phi - psis
r = np.sqrt(rpos**2. + s**2. + 2.*rpos*s*np.cos(phi))
# vfunc is velocity difference between between photon and gas
# projected on l.o.s.
vfunc = vphot - np.cos(phis)*v[0]
return vfunc
@jit(nopython=True)
def calcLineAmp(b, vel_grid, rpos, ds, phi, deltav, idx):
v1 = vfunc(vel_grid[:, idx], 0., rpos, phi, deltav)
v2 = vfunc(vel_grid[:, idx], ds, rpos, phi, deltav)
nspline = np.maximum(1, int(np.abs(v1 - v2)/b))
vfac = 0.
for ispline in range(nspline):
s1 = ds*(ispline)/nspline
s2 = ds*(ispline+1.)/nspline
v1 = vfunc(vel_grid[:, idx], s1, rpos, phi, deltav)
v2 = vfunc(vel_grid[:, idx], s2, rpos, phi, deltav)
naver = np.maximum(1, int(np.abs(v1 - v2)/b))
for iaver in range(naver):
s = s1 + (s2-s1)*(iaver + 0.5)/naver
v = vfunc(vel_grid[:, idx], s, rpos, phi, deltav)
vfacsub = np.exp(-(v/b)**2)
vfac += vfacsub/naver
vfac /= nspline
return vfac
@jit(nopython=True)
def photon(fixseed, stage, ra, rb, nmol, doppb, vel_grid, lau, lal, aeinst, beinstu, beinstl, blending, blends, tcmb, ncell, nline, pops, dust, knu, norm, cmb, nphot, idx):
phot = np.zeros((nline+2, nphot))
if stage ==1:
np.random.seed(fixseed)
for iphot in range(nphot):
tau = np.zeros(nline)
posn = idx
firststep = True
# Assign random position within cell id, direction and velocity, and
# determine distance ds to edge of cell. Choose position so that the
# cell volume is equally sampled in volume, the direction so that
# all solid angles are equally sampled, and the velocity offset
# homogeneously distributed over +/-2.15 * local Doppler b from
# local velocity.
dummy = np.random.random()
if (ra[idx] > 0.):
rpos = ra[idx]*(1. + dummy*((rb[idx]/ra[idx])**3 - 1.))**(1./3.)
else:
rpos = rb[idx]*dummy**(1./3.)
dummy = 2.*np.random.random() - 1.
phi = np.arcsin(dummy) + np.pi/2.
vel = vel_grid[:, idx]
deltav = (np.random.random() - 0.5)*4.3*doppb[idx] + np.cos(phi)*vel[0]
# Propagate to edge of cloud by moving from cell edge to cell edge.
# After the first step (i.e., after moving to the edge of cell id),
# store ds and vfac in phot(1,iphot) and phot(2,iphot). After
# leaving the source, add CMB and store intensities in
# phot(iline+2,iphot)
in_cloud = True
while in_cloud:
cosphi = np.cos(phi)
sinphi = np.sin(phi)
# Find distance to nearest cell edge
if (np.abs(phi) < np.pi/2.) or (posn == 0):
dpos = 1
rnext = rb[posn]*(1 + delta)
bac = 4.*((rpos*cosphi)**2. - rpos**2. + rnext**2.)
else:
dpos = -1
rnext = ra[posn]*(1 - delta)
bac = 4.*((rpos*cosphi)**2. - rpos**2. + rnext**2.)
if (bac < 0.):
dpos = 1
rnext = rb[posn]*(1 + delta)
bac = 4.*((rpos*cosphi)**2. - rpos**2. + rnext**2.)
dsplus = -0.5*(2.*rpos*cosphi + np.sqrt(bac))
dsminn = -0.5*(2.*rpos*cosphi - np.sqrt(bac))
if (dsminn*dsplus == 0.):
ds = 0.
else:
if (dsplus < 0.): ds = dsminn
if (dsminn < 0.): ds = dsplus
if (dsminn*dsplus > 0.): ds = np.min(np.array([dsplus, dsminn]))
# Find "vfac", the velocity line profile factor
# Number of splines nspline=los_delta_v/local_line_width
# Number of averaging steps naver=local_delta_v/local_line_width
if (nmol[posn] > eps):
b = doppb[posn]
vfac = calcLineAmp(b, vel_grid, rpos, ds, phi, deltav, idx)
# backwards integrate dI/ds
jnu = dust[:,posn]*knu[:,posn] + vfac*hpip/b*nmol[posn]*pops[lau,posn]*aeinst
alpha = knu[:,posn] + vfac*hpip/b*nmol[posn]*(pops[lal,posn]*beinstl - pops[lau,posn]*beinstu)
snu = jnu/alpha/norm
snu[np.abs(alpha) < eps] = 0.
dtau = alpha*ds
dtau[dtau < negtaulim] = negtaulim
if not firststep:
phot[2:, iphot] += np.exp(-tau)*(1. - np.exp(-dtau))*snu
tau += dtau
tau[tau < negtaulim] = negtaulim
# Line blending step - note that this is not vectorized as the previous calculations have been
if blending:
for iblend in range(blends.shape[0]):
bjnu = 0.
balpha = 0.
iline = int(blends[iblend,0])
jline = int(blends[iblend,1])
bdeltav = blends[iblend,2]
velproj = deltav - bdeltav
bvfac = calcLineAmp(b, vel_grid, rpos, ds, phi, velproj, idx)
bjnu = bvfac*hpip/b*nmol[posn]*pops[lau,posn][jline]*aeinst[jline]
balpha = bvfac*hpip/b*nmol[posn]*(pops[lal,posn][jline]*beinstl[jline] - pops[lau,posn][jline]*beinstu[jline])
if np.abs(balpha) < eps:
bsnu = 0.
else:
bsnu = bjnu/balpha/norm[jline]
bdtau = balpha*ds
if bdtau < negtaulim: bdtau = negtaulim
if not firststep:
#if (np.exp(-tau[iline])*(1. - np.exp(-bdtau))*bsnu > 0.) :
# print(phot[2 + iline, iphot], np.exp(-tau[iline])*(1. - np.exp(-bdtau))*bsnu)
phot[2 + iline, iphot] += np.exp(-tau[iline])*(1. - np.exp(-bdtau))*bsnu
tau[iline] += bdtau
tau[tau < negtaulim] = negtaulim
if firststep:
phot[0, iphot] = ds
phot[1, iphot] = vfac
firststep = False
# Update photon position, direction; check if escaped
posn = posn + dpos
if (posn >= ncell):
break # reached edge of cloud, break
psi = np.arctan2(ds*sinphi, rpos + ds*cosphi)
phif = phi - psi
phi = np.mod(phif, np.pi)
rpos = rnext
# Finally, add cmb to memorized i0 incident on cell id
if (tcmb > 0.):
for iline in range(nline):
phot[iline+2, iphot] += np.exp(-tau[iline])*cmb[iline]
return phot