def compute_next_point(self, location, direction):
#lam = int(dist / self.clumpNH)
# generate random number of clumps to encounter
(xi, yi, zi) = location
(dist, beta, alpha) = direction
k = numpy.random.poisson(self.nclumps)
NHfull = k * self.clumpNH
#d = dist / self.NH
if dist > NHfull:
# we land outside
d = 10
elif dist < NHfull:
# we go as far as we get
j = int(dist / self.clumpNH)
NHremainder = numpy.fmod(dist, self.clumpNH)
d = NHfull / self.NH
# how deep do we go into the k-th cloud
d = (NHfull + NHremainder) / self.NH
if self.verbose: print(' .. .. mean in nH units: ', d.mean())
# compute relative vector traveled
xv, yv, zv = to_cartesian((d, beta, alpha))
# compute new position
xf, yf, zf = xi + xv, yi + yv, zi + zv
# compute spherical coordinates
rad, phi, theta = to_spherical((xf, yf, zf))
# are we inside the cone?
inside = rad < 1.
return inside, (xf,yf,zf), (rad, phi, theta)
def compute_los_nh(self, beta, alpha):
a, b, c = to_cartesian((1, beta, alpha))
x = a * 0 + self.center[0]
y = b * 0 + self.center[1]
z = c * 0 + self.center[2]
NH = grid_raytrace_flat(self.rho_flat, self.rho.shape[0], x, y, z, a,
b, c)
return NH
def compute_next_point(self, location, direction):
(xi, yi, zi) = location
(dist, beta, alpha) = direction
a, b, c = to_cartesian((1, beta, alpha))
t = sphere_raytrace_finite(self.x, self.y, self.z, self.r, self.rho,
xi, yi, zi, a, b, c, dist)
# are we still inside?
inside = t >= 0
# compute new position
xf, yf, zf = xi + a * t, yi + b * t, zi + c * t
# compute spherical coordinates
rad, phi, theta = to_spherical((xf, yf, zf))
return inside, (xf, yf, zf), (rad, phi, theta)
def compute_next_point(self, location, direction):
(xi, yi, zi) = location
(dist, beta, alpha) = direction
d = dist / self.NH # distance in units of nH
if self.verbose: print(' .. .. mean in nH units: ', d.mean())
# compute relative vector traveled
xv, yv, zv = to_cartesian((d, beta, alpha))
# compute new position
xf, yf, zf = xi + xv, yi + yv, zi + zv
# compute spherical coordinates
rad, phi, theta = to_spherical((xf, yf, zf))
# are we inside the disk
inside = zf <= 0
return inside, (xf, yf, zf), (rad, phi, theta)
def compute_next_point(self, location, direction):
(xi, yi, zi) = location
(dist, beta, alpha) = direction
a, b, c = to_cartesian((1, beta, alpha))
t = cone_raytrace_finite(self.Theta_tors, self.NHs, xi, yi, zi, a, b,
c, dist)
# are we still inside?
inside = t >= 0
t = numpy.where(t < 0, dist, t)
# compute new position
xf, yf, zf = xi + a * t, yi + b * t, zi + c * t
# compute spherical coordinates
rad, theta, phi = to_spherical((xf, yf, zf))
return inside, (xf, yf, zf), (rad, theta, phi)
def compute_next_point(self, location, direction):
(xi, yi, zi) = location
(dist, beta, alpha) = direction
a, b, c = to_cartesian((1, beta, alpha))
x = xi + self.center[0]
y = yi + self.center[1]
z = zi + self.center[2]
t = grid_raytrace_finite_flat(self.rho_flat, self.rho.shape[0], x, y,
z, a, b, c, dist)
# are we still inside?
inside = t >= 0
# compute new position
t = numpy.where(t < 0, dist, t)
xf, yf, zf = xi + a * t, yi + b * t, zi + c * t
# compute spherical coordinates
rad, phi, theta = to_spherical((xf, yf, zf))
return inside, (xf, yf, zf), (rad, phi, theta)
def compute_los_nh(self, beta, alpha):
a, b, c = to_cartesian((1, beta, alpha))
mindistances = numpy.zeros(1)
NH = sphere_raytrace(self.x, self.y, self.z, self.r, self.rho, a, b, c,
mindistances)[0, :]
return NH
def compute_next_point(self, location, direction):
(xi, yi, zi) = location
(dist, beta, alpha) = direction
d = dist / self.NH # distance in units of nH
if self.verbose: print(' .. .. mean in nH units: ', d.mean())
# compute relative vector traveled
xv, yv, zv = to_cartesian((d, beta, alpha))
# compute new position
xf, yf, zf = xi + xv, yi + yv, zi + zv
# compute intersection with cone border
a = zv**2 - (xv**2 + yv**2) * tan(0.5 * pi - self.Theta_tor)**2
b = 2. * zi * zv - (2. * xi * xv +
2. * yi * yv) * tan(0.5 * pi - self.Theta_tor)**2
c = zi**2 - (xi**2 + yi**2) * tan(0.5 * pi - self.Theta_tor)**2
quad = b**2 - 4. * a * c
# compute the two solutions
e1 = (-b - quad**0.5) / (2. * a)
e2 = (-b + quad**0.5) / (2. * a)
# if both are positive and e1<1
twosolmask = logical_and(logical_and(quad > 0., e1 > 0.),
logical_and(e1 < 1., e2 > 0.))
#if self.verbose: print ' .. %d of %d have 2 solutions' % (twosolmask.sum(), len(twosolmask))
# compute the two possible new positions
#print 'twosol:', twosolmask
x1 = xi[twosolmask] + e1[twosolmask] * xv[twosolmask]
x2 = xi[twosolmask] + e2[twosolmask] * xv[twosolmask]
y1 = yi[twosolmask] + e1[twosolmask] * yv[twosolmask]
y2 = yi[twosolmask] + e2[twosolmask] * yv[twosolmask]
z1 = zi[twosolmask] + e1[twosolmask] * zv[twosolmask]
z2 = zi[twosolmask] + e2[twosolmask] * zv[twosolmask]
#print 'e2', e2
ltsol = e2[twosolmask] < 1.
gtsol = ~ltsol
asol = twosolmask.copy()
asol[twosolmask] = ltsol
bsol = twosolmask.copy()
bsol[twosolmask] = gtsol
xf[asol] = x2[ltsol] + xv[asol] - (x1[ltsol] - xi[asol])
yf[asol] = y2[ltsol] + yv[asol] - (y1[ltsol] - yi[asol])
zf[asol] = z2[ltsol] + zv[asol] - (z1[ltsol] - zi[asol])
xf[bsol] += (x2[gtsol] - x1[gtsol])
yf[bsol] += (y2[gtsol] - y1[gtsol])
zf[bsol] += (z2[gtsol] - z1[gtsol])
#print ' .. using symmetries'
# use symmetries
# bring to upper side of torus
zf = numpy.abs(zf)
# compute spherical coordinates
rad, theta, phi = to_spherical((xf, yf, zf))
assert not numpy.isnan(rad).any()
assert not numpy.isnan(theta).any()
assert not numpy.isnan(phi).any()
#if self.verbose: print ' .. checking if left cone'
# are we inside the cone?
inside = numpy.logical_and(rad < 1., theta > self.Theta_tor)
return inside, (xf, yf, zf), (rad, phi, theta)
def pump(self):
if self.verbose:
print('photon iteration: %d free photons, %d scattering %s' %
((~self.stuck).sum(), self.stuck.sum(), '_' * 20))
phi, theta, rad, alpha, beta, energy, bin = self.get_free()
# first half deals with free photons
if len(energy) > 0:
if self.verbose: print(' .. distance travelled')
nphot = len(energy)
r1 = rng.uniform(size=nphot)
taur = -log(1. - r1) # effective tau
dist = taur / xboth[bin] # distance travelled
#if self.verbose: print ' .. .. tau min: %f mean: %f max: %f ' % (taur.min(), taur.mean(), taur.max())
if self.verbose:
print(' .. .. dist min: %f mean: %f max: %f ' %
(dist.min(), dist.mean(), dist.max()))
phi0 = phi
theta0 = theta
rad0 = rad
xi, yi, zi = to_cartesian((rad0, theta0, phi0))
#if self.verbose: print ' .. computing position'
# compute position
inside, (xf, yf, zf), (rad, phi,
theta) = self.geometry.compute_next_point(
(xi, yi, zi), (dist, beta, alpha))
outside = ~inside
# emit
if self.verbose:
print(' .. emitting %d to outside, %d inside material' %
((~inside).sum(), inside.sum()))
self.update_free(phi, theta, rad, alpha, beta, energy, bin)
mask = ~self.stuck
mask[mask] = outside
self.cut_free(inside)
emit = dict(phi=phi0[outside],
theta=theta0[outside],
rad=rad0[outside],
beta=beta[outside],
alpha=alpha[outside],
energy=energy[outside],
bin=bin[outside],
x=xi[outside],
y=yi[outside],
z=zi[outside],
mask=mask)
#print ' ', rad.shape, theta.shape, len(inside)
xf, yf, zf = xf[inside], yf[inside], zf[inside]
phi, theta, rad, alpha, beta, energy, bin = self.get_free()
nphot = len(energy)
assert nphot == inside.sum()
if self.verbose: print(' .. checking if absorbed')
# what effect are we dealing with
r2 = rng.uniform(size=nphot)
# Photon-absorbed
q = absorption_ratio[bin]
photabsorbed = r2 < q
#if self.verbose: print ' .. .. photon-abs prob min: %f mean: %f max: %f ' % (q.min(), q.mean(), q.max())
# Iron to photon-absorption effectiveness
omega = xlines_cumulative[bin[
photabsorbed]] # Importance of lines compared to photon-absorption
# omega *= 0 # disable fluorescent lines
#print ' .. .. omega:', omega
r3 = rng.uniform(size=photabsorbed.sum())
# Are we coming out as a line
# This handles all lines (lines loaded in xsects)
line_mask = omega > r3[:, None]
iline = numpy.where(line_mask.any(axis=1),
line_mask.argmax(axis=1), -1)
is_line = iline >= 0
photabsorbed_line = photabsorbed.copy()
photabsorbed_notline = photabsorbed.copy()
# set the absorbed ones (where we have true) to the criterion
photabsorbed_line[photabsorbed] = is_line
photabsorbed_notline[photabsorbed] = ~is_line
r4 = rng.uniform(size=photabsorbed_line.sum())
if is_line.any():
e2 = xlines_energies[iline[is_line]]
e = energy2bin(e2)
energy[photabsorbed_line] = e2
bin[photabsorbed_line] = e
del e2, e
# emit line in random direction
if photabsorbed_line.any():
nline = photabsorbed_line.sum()
alpha_random = rng.uniform(0, 2 * pi, size=nline)
beta_random = acos(rng.uniform(-1, 1, size=nline))
alpha[photabsorbed_line] = alpha_random
beta[photabsorbed_line] = beta_random
self.update_free(phi, theta, rad, alpha, beta, energy, bin)
# no, we are just being swallowed (photon-absorption).
# photabsorbed & ~is_line
# remove photabsorbed_line
absorbed = photabsorbed_notline
if self.verbose:
print(' .. .. line emission: %3d' % (is_line.sum()))
if self.verbose:
print(' .. .. absorbed: %d (%d lost)' %
(photabsorbed.sum(), absorbed.sum()))
if self.verbose: print(' .. checking if scattered')
# Were we compton-scattered?
photscattered = (~photabsorbed)
nphotscattered = photscattered.sum()
#assert nphotscattered.shape == energy.shape
if nphotscattered > 0:
if self.verbose:
print(' .. .. scattered: %d' % nphotscattered)
#self.energy[free] = energy
#self.bin[free] = bin
if self.verbose: print(' .. checking if outside of energy range')
# if in relevant energy range, find right bin
#energy = self.energy
# for unstuck and photabsorbed_line we have to check the energy
# just do it for all
energy_outside = bin <= 0
dropouts = numpy.logical_or(energy_outside, absorbed)
remainders = ~dropouts
if self.verbose:
print(' .. .. outside of energy range: %d' %
(energy_outside.sum()))
if self.verbose: print(' .. .. %d left' % (remainders.sum()))
# cut to remainders (so that we only have to compute new positions for few)
#self.set(phi, theta, rad, alpha, beta, energy, bin)
self.cut_free(remainders)
phi, theta, rad, alpha, beta, energy, bin = self.get_free()
# compute new positions for remainder
xf, yf, zf = xf[remainders], yf[remainders], zf[remainders]
rad, theta, phi = to_spherical((xf, yf, zf))
#rad = (xf**2+yf**2+zf**2)**0.5
#phi = atan2(yf, xf)
#theta = numpy.where(rad == 0, 0., acos(zf / rad))
self.update_free(phi, theta, rad, alpha, beta, energy, bin)
self.stuck[~self.stuck] = photscattered[remainders]
if self.verbose:
print(' .. .. %d stuck in scattering' % (self.stuck.sum()))
else:
emit = None
# now deal with stuck photons, i.e. those undergoing compton
# scattering
alpha, beta, energy, bin = self.get_stuck()
nphotscattered = len(energy)
if nphotscattered > 0:
if self.verbose: print(' scattering: %d' % nphotscattered)
a = rng.uniform(size=nphotscattered)
# compute new direction:
alpha_new = a * 2. * pi # left-right angle uniform randomly
# compute up-down angle
beta0 = beta
r5 = rng.uniform(size=nphotscattered)
r5a = rng.uniform(size=nphotscattered)
x = 2. * r5a - 1
mus = numpy.where(r5 > 0.75,
numpy.sign(x) * numpy.abs(x)**(1 / 3.), x)
betas = acos(mus)
mu = cos(beta0) * cos(betas) + sin(beta0) * sin(betas) * cos(
alpha_new - alpha)
beta_new = acos(mu)
# new energy
#if self.verbose: print ' .. .. mus: %.2f' % (mus.mean())
loss = (1. + (1. - mus) * energy / electmass)
if self.verbose:
print(' .. .. energy loss: %.3f, %.3f, %.3f' %
(loss.min(), loss.mean(), loss.max()))
E = energy / loss
if self.verbose:
print(' .. .. new energy: %.3f, %.3f, %.3f' %
(E.min(), E.mean(), E.max()))
processed = E >= 0
self.update_and_free_stuck(alpha_new, beta_new, E, energy2bin(E),
processed)
if self.verbose:
print(' .. finally checking all, if outside of energy range')
phi, theta, rad, alpha, beta, energy, bin = self.get()
energy_outside = numpy.logical_or(energy < 0.1, energy > 1800)
dropouts = energy_outside
remainders = ~dropouts
if self.verbose:
print(' .. .. outside of energy range: %d' %
(energy_outside.sum()))
if self.verbose: print(' .. .. %d left' % (remainders.sum()))
# cut out
if dropouts.any():
self.cut(remainders)
# next round
return emit, len(self.energy) > 0
def compute_next_point(self, location, direction):
(xi, yi, zi) = location
(dist, beta, alpha) = direction
d = dist / self.NH # distance in units of nH
if self.verbose: print(' .. .. mean in nH units: ', d.mean())
# compute relative vector traveled
xv, yv, zv = to_cartesian((1, beta, alpha))
#print xv, yv, zv
# compute intersection with cone border
a = zv**2 - (xv**2 + yv**2) * tan(0.5 * pi - self.Theta_tor)**2
b = 2. * zi * zv - (2. * xi * xv +
2. * yi * yv) * tan(0.5 * pi - self.Theta_tor)**2
c = zi**2 - (xi**2 + yi**2) * tan(0.5 * pi - self.Theta_tor)**2
quad = b**2 - 4. * a * c
# compute the two solutions
with numpy.errstate(invalid='ignore'):
e1 = (-b - quad**0.5) / (2. * a)
e2 = (-b + quad**0.5) / (2. * a)
# if both are positive and e1<1
#assert (quad >= 0).all()
x1 = xi + e1 * xv
x2 = xi + e2 * xv
y1 = yi + e1 * yv
y2 = yi + e2 * yv
z1 = zi + e1 * zv
z2 = zi + e2 * zv
# check if those points are outside the sphere
with numpy.errstate(invalid='ignore'):
ri1 = x1**2 + y1**2 + z1**2 <= 1
ri2 = x2**2 + y2**2 + z2**2 <= 1
#print 'cone points radius', ri1, ri2
# compute intersection with sphere
# a=xD2+yD2-zD2, b=2xExD+2yEyD-2zEzD, and c=xE2+yE2-zE2.
# a=xD2+yD2+zD2, b=2xExD+2yEyD+2zEzD, and c=xE2+yE2+zE2-1
sa = 1
sb = 2. * zi * zv + 2. * xi * xv + 2. * yi * yv
sc = zi**2 + xi**2 + yi**2 - 1
squad = sb**2 - 4. * sa * sc
# compute the two solutions
se1 = (-sb - squad**0.5) / (2. * sa)
se2 = (-sb + squad**0.5) / (2. * sa)
sx1 = xi + se1 * xv
sx2 = xi + se2 * xv
sy1 = yi + se1 * yv
sy2 = yi + se2 * yv
sz1 = zi + se1 * zv
sz2 = zi + se2 * zv
# check if inside cone
with numpy.errstate(invalid='ignore'):
r1 = sx1**2 + sy1**2 + sz1**2
r2 = sx2**2 + sy2**2 + sz2**2
theta1 = numpy.where(r1 == 0, 0., arccos(sz1 / r1))
theta2 = numpy.where(r2 == 0, 0., arccos(sz2 / r2))
theta1[theta1 > pi / 2] = pi - theta1[theta1 > pi / 2]
theta2[theta2 > pi / 2] = pi - theta2[theta2 > pi / 2]
si1 = theta1 >= self.Theta_tor
si2 = theta2 >= self.Theta_tor
#print 'circle points theta', theta1, theta2, si1, si2 #, (sx1, sy1, sz1), (sx2, sy2, sz2)
# now we should go through them
es = numpy.transpose([e1, e2, se1, se2])
#print es, 'es'
good = numpy.transpose([ri1, ri2, si1, si2])
# they will be ignored, because we go in the pos direction
with numpy.errstate(invalid='ignore'):
good[~(es > 0)] = False
es[~good] = -1
nsol = good.sum(axis=1)
#assert nsol.shape == xi.shape, (nsol.shape, xi.shape)
es.sort(axis=1)
# now handle the different cases
#print nsol, good
#assert (nsol >= 0).all(), nsol.min()
#assert (nsol <= 3).all(), nsol.min()
#assert ((nsol == 0) + (nsol == 1) + (nsol == 3)).all(), nsol
# default:
xf, yf, zf = xi + d * xv, yi + d * yv, zi + d * zv
# no solution, we are on the brink of stepping out
# set to False
inside = numpy.zeros(xf.shape, dtype=bool)
es_1 = nsol == 1
t = es[es_1, -1]
# go from where we are to there
inside[es_1] = d[es_1] < t # if true we never left
#print 't:', t, d[es_1], es_1
# 3 solutions
es_2 = nsol == 3
if es_2.any():
#print 'BRANCH2'
t1 = es[es_2, -3]
t2 = es[es_2, -2]
t3 = es[es_2, -1]
# two cases: either we never make it to t1
inside_2 = d[es_2] < t1 # if true we are still inside
#print inside.shape, inside_2.shape
inside[es_2] = inside_2
#print 'es_2', es_2
#print 'inside_2', inside_2
if not inside_2.all():
#print 'BRANCH3'
# alternatively, we make it to t1:
# have to add to the distance we are allowed to travel
# the distance between t1 and t2
es_3 = es_2
es_3[es_3] = ~inside_2 # select those cases
#print 'd', d, es_3, d[es_3].shape, t2.shape, t1.shape, inside_2.shape
#print 't:', t1, t2, t3
#assert es_3.shape == (len(xi),)
#assert es_3.sum() == (~inside_2).sum(), (es_3, ~inside_2)
#assert d[es_3].size == (~inside_2).sum(), (es_3, ~inside_2)
dmod = d[es_3] + t2[~inside_2] - t1[~inside_2]
xf[es_3] = xi[es_3] + dmod * xv[es_3]
yf[es_3] = yi[es_3] + dmod * yv[es_3]
zf[es_3] = zi[es_3] + dmod * zv[es_3]
inside[es_3] = dmod < t3[~inside_2]
# bring to upper side of torus
#zf = numpy.abs(zf)
# compute spherical coordinates
rad, theta, phi = to_spherical((xf, yf, zf))
return inside, (xf, yf, zf), (rad, phi, theta)