rpenl=([numpy.inf], numpy.ones_like(rhs1), numpy.ones_like(rhs2)), \
xpenq=numpy.ones(len(initcond))*0.1 )
# check if all constraints were satisfied
delta1 = data1.T.dot(weights) - rhs1
for i, d in enumerate(delta1):
if abs(d) > 1e-8:
print("DensityConstraint %i not satisfied: %s, val=%.4g, rel.err=%.4g" % \
(i, target1[i], rhs1[i], d / rhs1[i]))
delta2 = datak.T.dot(weights)
for i, d in enumerate(delta2):
if abs(d) > 1e-8: print("KinemConstraint %i not satisfied: %.4g" % (i, d))
# export an N-body model
nbody = 100000
status, result = agama.sampleOrbitLibrary(nbody, trajs, weights)
if not status:
# this may occur if there was not enough recorded trajectory points for some high-weight orbits:
# in this case their indices and the required numbers of points are returned in the result tuple
indices, trajsizes = result
print("reintegrating %i orbits; max # of sampling points is %i" %
(len(indices), max(trajsizes)))
trajs[indices] = agama.orbit(potential=pot, ic=initcond[indices], time=inttimes[indices], \
trajsize=trajsizes)
status, result = agama.sampleOrbitLibrary(nbody, trajs[:, 1], weights)
if not status: print("Failed to produce output N-body model")
agama.writeSnapshot("schwarzschild_model_nbody.txt", result,
't') # one could also use numpy.savetxt
# also store the entire Schwarzschild model in a numpy binary archive
numpy.savez_compressed("schwarzschild_model_data", ic=initcond, inttime=inttimes, weight=weights, \
def runComponent(comp, pot):
"""
run the orbit integration, optimization, and construction of an N-body model
for a given component of the Schwarzschild model
"""
if hasattr(comp, 'trajsize'):
result = agama.orbit(potential=pot,
ic=comp.ic,
time=comp.inttime,
Omega=comp.Omega,
targets=comp.targets,
trajsize=comp.trajsize)
traj = result[-1]
else:
result = agama.orbit(potential=pot,
ic=comp.ic,
time=comp.inttime,
Omega=comp.Omega,
targets=comp.targets)
traj = None
if type(result) == numpy.array: result = (result, )
# targets[0] is density, targets[1], if provided, is kinematics
matrix = list()
rhs = list()
rpenl = list()
mass = comp.density.totalMass()
# density constraints
matrix.append(result[0].T)
rhs.append(comp.targets[0](comp.density))
avgrhs = mass / len(rhs[0]) # typical magnitude of density constraints
rpenl.append(numpy.ones_like(rhs[0]) / avgrhs)
# kinematic constraints
if len(comp.targets) == 2 and hasattr(comp, 'beta'):
numrow = len(comp.targets[1]) // 2
matrix.append(result[1].T[0:numrow] * 2 * (1 - comp.beta) -
result[1].T[numrow:2 * numrow])
rhs.append(numpy.zeros(numrow))
rpenl.append(numpy.ones(numrow))
# total mass constraint
matrix.append(numpy.ones((len(comp.ic), 1)).T)
rhs.append(numpy.array([mass]))
rpenl.append(numpy.array([numpy.inf]))
# regularization (penalty for unequal weights)
avgweight = mass / len(comp.ic)
xpenq = numpy.ones(len(comp.ic)) / avgweight**2 / len(comp.ic) * 0.1
# solve the linear equation for weights
weights = agama.solveOpt(matrix=matrix, rhs=rhs, rpenl=rpenl, xpenq=xpenq)
# check for any outstanding constraints
for t in range(len(matrix)):
delta = matrix[t].dot(weights) - rhs[t]
norm = 1e-4 * abs(rhs[t]) + 1e-8
for c, d in enumerate(delta):
if abs(d) > norm[c]:
print("Constraint %i:%i not satisfied: %s, val=%.4g, dif=%.4g" % \
(t, c, comp.targets[t][c], rhs[t][c], d))
print("Entropy: %f, # of useful orbits: %i / %i" %\
( -sum(weights * numpy.log(weights+1e-100)) / mass + numpy.log(avgweight), \
len(numpy.where(weights >= avgweight)[0]), len(comp.ic)))
# create an N-body model if needed
if hasattr(comp, 'nbody'):
status, particles = agama.sampleOrbitLibrary(comp.nbody, traj, weights)
if not status:
indices, trajsizes = particles
print("reintegrating %i orbits; max # of sampling points is %i" %
(len(indices), max(trajsizes)))
traj[indices] = agama.orbit(potential=pot, ic=comp.ic[indices], \
time=comp.inttime[indices], trajsize=trajsizes)
status, particles = agama.sampleOrbitLibrary(
comp.nbody, traj, weights)
if not status: print("Failed to produce output N-body model")
comp.nbodymodel = particles
# output
comp.weights = weights
comp.densitydata = result[0]
if len(comp.targets) >= 2: comp.kinemdata = result[1]
if not traj is None: comp.traj = traj
def runComponent(comp, pot):
"""
run the orbit integration, optimization, and construction of an N-body model
for a given component of the Schwarzschild model
"""
if comp.has_key('trajsize'):
result = agama.orbit(potential=pot, ic=comp['ic'], time=comp['inttime'], \
targets=comp['targets'], trajsize=comp['trajsize'])
traj = result[-1]
else:
result = agama.orbit(potential=pot,
ic=comp['ic'],
time=comp['inttime'],
targets=comp['targets'])
if type(result) == numpy.array: result = (result, )
# targets[0] is density, targets[1], if provided, is kinematics
matrix = list()
rhs = list()
rpenl = list()
matrix.append(result[0].T)
rhs.append(comp['targets'][0].values())
mass = rhs[0][-1] # the last constraint is the total mass
avgrhs = mass / len(rhs[0]) # typical constraint magnitude
rpenl.append(numpy.ones_like(rhs[0]) / avgrhs)
if len(comp['targets']) == 2 and comp.has_key('beta'):
numrow = len(comp['targets'][1]) / 2
matrix.append(result[1].T[0:numrow] * 2 * (1 - comp['beta']) -
result[1].T[numrow:2 * numrow])
rhs.append(numpy.zeros(numrow))
rpenl.append(numpy.ones(numrow) * 10.)
avgweight = mass / len(comp['ic'])
xpenq = numpy.ones(len(comp['ic'])) / avgweight**2 / len(comp['ic']) * 0.1
weights = agama.optsolve(matrix=matrix, rhs=rhs, rpenl=rpenl, xpenq=xpenq)
# check for any outstanding constraints
for t in range(len(matrix)):
delta = matrix[t].dot(weights) - rhs[t]
norm = 1e-4 * abs(comp['targets'][t].values()) + 1e-8
for c, d in enumerate(delta):
if abs(d) > norm[c]:
print "Constraint", t, " #", c, "not satisfied:", comp[
'targets'][t][c], d
print "Entropy:", -sum(weights * numpy.log(weights+1e-100)) / mass + numpy.log(avgweight), \
" # of useful orbits:", len(numpy.where(weights >= avgweight)[0]), "/", len(comp['ic'])
# create an N-body model if needed
if comp.has_key('nbody'):
status, particles = agama.sampleOrbitLibrary(comp['nbody'], traj,
weights)
if not status:
indices, trajsizes = particles
print "reintegrating", len(
indices), "orbits; max # of sampling points is", max(trajsizes)
traj[indices] = agama.orbit(potential=pot, ic=comp['ic'][indices], \
time=comp['inttime'][indices], trajsize=trajsizes)
status, particles = agama.sampleOrbitLibrary(
comp['nbody'], traj, weights)
if not status: print "Failed to produce output N-body model"
comp['nbodymodel'] = particles
# output
comp['weights'] = weights
comp['densitydata'] = result[0]
if len(matrix) == 2: comp['kinemdata'] = result[1]
if comp.has_key('trajsize'): comp['traj'] = traj
return comp