def createModel(iniFileName):
"""
parse the ini file and construct the initial data for the entire model:
all density, potentials, and Schwarzschild model components,
with initial conditions for the orbit library and relevant density/kinematic targets.
"""
model = type('Model', (), {})
ini = RawConfigParser()
ini.read(iniFileName)
sec = ini.sections()
sec_den = dict() # list of density components
sec_pot = dict() # same for potential
sec_comp = dict(
) # list of model components (each one may include several density objects)
Omega = None
for s in sec:
if s.lower().startswith('density'):
sec_den[s.lower()] = dict(ini.items(s))
if s.lower().startswith('potential'):
sec_pot[s.lower()] = dict(ini.items(s))
if s.lower().startswith('component'):
sec_comp[s.lower()] = dict(ini.items(s))
if s.lower() == 'global': # pattern speed
for name, value in ini.items(s):
if name.lower() == 'omega':
Omega = float(value)
# construct all density and potential objects
den = dict()
pot = dict()
for name, value in sec_den.items():
den[name] = agama.Density(**value)
for name, value in sec_pot.items():
if 'density' in value:
listdens = list()
for den_str in filter(None,
re.split('[,\s]', value['density'].lower())):
if den_str in sec_den:
listdens.append(den[den_str])
if len(listdens) == 1:
value['density'] = listdens[0]
elif len(listdens) > 1:
value['density'] = agama.Density(*listdens)
# else there are no user-defined density sections
print("Creating " + name)
pot[name] = agama.Potential(**value)
pot[name].export("model_" + name)
model.density = den
if len(pot) == 0:
raise ValueError("No potential components defined")
if len(pot) == 1:
model.potential = pot.values()[0]
else:
model.potential = agama.Potential(*pot.values())
# determine corotation radius in case of nonzero pattern speed
if Omega != 0:
try:
from scipy.optimize import brentq
print("Omega=%.3g => corotation radius: %.3g" % (
Omega,
brentq(
lambda r: model.potential.force(r, 0, 0)[0] / r + Omega**2,
1e-10,
1e10,
rtol=1e-4)))
except Exception as e:
print("Omega=%.3g, corotation radius unknown: %s" %
(Omega, str(e)))
# construct all model components
if len(sec_comp) == 0:
raise ValueError("No model components defined")
model.components = dict()
for name, value in sec_comp.items():
targets = list()
if not 'density' in value:
raise ValueError("Component " + name +
" does not have an associated density")
listdens = list()
for den_str in filter(None, re.split('[,\s]',
value['density'].lower())):
if den_str in sec_den:
listdens.append(den[den_str])
elif den_str in sec_pot:
listdens.append(pot[den_str])
else:
raise ValueError("Unknown density component: " + den_str +
" in " + name)
if len(listdens) == 1:
density = listdens[0]
elif len(listdens) > 1:
density = agama.Density(*listdens)
else:
raise ValueError("No density components in " + name)
print("Creating density target for " + name)
targets.append(agama.Target(**value))
if 'kinemgrid' in value:
options = { "type": 'KinemShell', \
"gridr": value['kinemgrid'], \
"degree": int(value['kinemdegree']) }
print("Creating kinematic target for " + name)
targets.append(agama.Target(**options))
if 'numorbits' in value:
icoptions = {
'n': int(value['numorbits']),
'potential': model.potential
}
if 'icbeta' in value: icoptions['beta'] = float(value['icbeta'])
if 'ickappa' in value: icoptions['kappa'] = float(value['ickappa'])
print("Creating initial conditions for %i orbits in %s" %
(icoptions['n'], name))
ic, weightprior = density.sample(**icoptions)
else:
raise ValueError("No orbits defined in " + name)
if 'inttime' in value:
inttime = float(value['inttime']) * model.potential.Tcirc(ic)
else:
raise ValueError("No integration time defined in " + name)
comp = type('Component', (), \
{"density": density, "ic": ic, "weightprior": weightprior, \
"inttime": inttime, "targets": targets, "Omega": Omega} )
if 'trajsize' in value: comp.trajsize = int(value['trajsize'])
if 'beta' in value: comp.beta = float(value['beta'])
if 'nbody' in value:
comp.nbody = int(value['nbody'])
if not 'trajsize' in value:
raise ValueError("No trajectory will be stored in " + name +
", cannot create Nbody model")
model.components[name] = comp
return model
posvel,
gridx = numpy.linspace(-30.0, 30.0, 61), # [REQ] X-axis pixel boundaries for the 1st (LR) dataset
gridy = numpy.linspace(-30.0, 30.0, 61), # [REQ] same for Y axis
nbins = 150, # [REQ] desired number of Voronoi bins (the result may differ somewhat)
alpha = alpha, # orientation angles - same as in kinemParams1
beta = beta,
gamma = gamma1
)
# save the binning scheme to text file
numpy.savetxt(filenameVorBin1, numpy.column_stack((xc, yc, bintags)), fmt='%7.3f %7.3f %7d')
# 2st step: construct the LOSVD target and apply it to the N-body snapshot
print('Computing LOSVDs of input snapshot')
apertures = agama.schwarzlib.getBinnedApertures(xc, yc, bintags) # obtain boundary polygons from Voronoi bins
gridx, gridy = agama.schwarzlib.makeGridForTargetLOSVD(apertures, psf1) # construct a suitable image-plane grid
target = agama.Target(apertures=apertures, gridx=gridx, gridy=gridy, **kinemParams1)
datacube = target((posvel, mass)).reshape(len(apertures), -1)
# assign errors/noise on the computed values from the Poisson noise estimate of B-spline amplitudes
particlemass = numpy.mean(mass)
noisecube = (numpy.maximum(datacube, particlemass) * particlemass)**0.5
# 3rd step: convert the B-spline LOSVDs to GH moments
print('Computing Gauss-Hermite moments and their error estimates')
ghorder = 6 # [OPT] order of GH expansion
ghm_val, ghm_err = agama.schwarzlib.ghMomentsErrors(degree=degree, gridv=gridv, values=datacube, errors=noisecube, ghorder=ghorder)
ind = (1,2,6,7,8,9) # keep only these columns, corresponding to v,sigma,h3,h4,h5,h6
numpy.savetxt(filenameGH1, numpy.dstack((ghm_val, ghm_err))[:,ind,:].reshape(len(apertures), -1), fmt='%8.3f',
header='v v_err sigma sigma_err h3 h3_err h4 h4_err h5 h5_err h6 h6_err')
# 4th step: convert the B-splines to histograms, which are in fact 0th-degree B-splines;
# we might have constructed model LOSVDs in terms of histograms directly, but this would have been less accurate
"""
import agama, numpy
# density profile
den = agama.Density(type='Dehnen',
axisRatioY=0.8,
axisRatioZ=0.6,
scaleRadius=1,
mass=1,
gamma=1)
# potential corresponding to this density
pot = agama.Potential(type='Multipole', lmax=8, mmax=6, density=den)
# target1 is discretized density profile
target1 = agama.Target(type='DensityClassicLinear', gridr=agama.nonuniformGrid(25, 0.1, 20.0), \
axisratioy=0.8, axisratioz=0.6, stripsPerPane=2)
# target2 is discretized kinematic constraint (we will enforce velocity isotropy)
target2 = agama.Target(type='KinemShell',
gridR=agama.nonuniformGrid(15, 0.2, 10.0),
degree=1)
# construct initial conditions for the orbit library
initcond, weightprior = den.sample(5000, potential=pot)
# integration time is 50 orbital periods
inttimes = 50 * pot.Tcirc(initcond)
# integrate all orbits, storing the recorded data corresponding to each target
# in the data1 and data2 arrays, and the trajectories - in trajs
data1, data2, trajs = agama.orbit(potential=pot, ic=initcond, time=inttimes, \
trajsize=101, targets=[target1,target2])
def createModel(iniFileName):
"""
parse the ini file and construct the initial data for the entire model:
all density, potentials, and Schwarzschild model components,
with initial conditions for the orbit library and relevant density/kinematic targets.
"""
ini = ConfigParser.RawConfigParser()
ini.read(iniFileName)
sec = ini.sections()
sec_den = dict() # list of density components
sec_pot = dict() # same for potential
sec_comp = dict(
) # list of model components (each one may include several density objects)
for s in sec:
if s.lower().startswith('density'):
sec_den[s.lower()] = dict(ini.items(s))
if s.lower().startswith('potential'):
sec_pot[s.lower()] = dict(ini.items(s))
if s.lower().startswith('component'):
sec_comp[s.lower()] = dict(ini.items(s))
# construct all density and potential objects
den = dict()
pot = dict()
for name, value in sec_den.items():
den[name] = agama.Density(**value)
for name, value in sec_pot.items():
if value.has_key('density'):
listdens = list()
for den_str in filter(None,
re.split('[,\s]', value['density'].lower())):
if sec_den.has_key(den_str):
listdens.append(den[den_str])
if len(listdens) == 1:
value['density'] = listdens[0]
elif len(listdens) > 1:
value['density'] = agama.Density(*listdens)
# else there are no user-defined density sections
print "Creating", name
pot[name] = agama.Potential(**value)
pot[name].export("model_" + name)
model = {'density': den}
if len(pot) == 0:
raise ValueError("No potential components defined")
if len(pot) == 1:
model['potential'] = pot.values()[0]
else:
model['potential'] = agama.Potential(*pot.values())
# construct all model components
if len(sec_comp) == 0:
raise ValueError("No model components defined")
comp = dict()
model['components'] = comp
for name, value in sec_comp.items():
targets = list()
if not value.has_key('density'):
raise ValueError("Component " + name +
" does not have an associated density")
listdens = list()
for den_str in filter(None, re.split('[,\s]',
value['density'].lower())):
if sec_den.has_key(den_str):
listdens.append(den[den_str])
elif sec_pot.has_key(den_str):
listdens.append(pot[den_str])
else:
raise ValueError("Unknown density component: " + den_str +
" in " + name)
if len(listdens) == 1:
value['density'] = listdens[0]
elif len(listdens) > 1:
value['density'] = agama.Density(*listdens)
else:
raise ValueError("No density components in " + name)
print "Creating density target for", name
targets.append(agama.Target(**value))
if value.has_key('kinemshells'):
options = { "type": 'KinemJeans', "gridSizeR": int(value['kinemshells']), \
"density": value['density'], "potential": model['potential'] }
if value.has_key('kinemdegree'):
options['degree'] = int(value['kinemdegree'])
print "Creating kinematic target for", name
targets.append(agama.Target(**options))
if value.has_key('numorbits'):
icoptions = {
'n': int(value['numorbits']),
'potential': model['potential']
}
if value.has_key('icbeta'):
icoptions['beta'] = float(value['icbeta'])
if value.has_key('ickappa'):
icoptions['kappa'] = float(value['ickappa'])
print "Creating initial conditions for", icoptions[
'n'], "orbits in", name
ic, weightprior = value['density'].sample(**icoptions)
else:
raise ValueError("No orbits defined in " + name)
if value.has_key('inttime'):
inttime = float(value['inttime']) * model['potential'].Tcirc(ic)
else:
raise ValueError("No integration time defined in " + name)
comp[name] = {
"ic": ic,
"weightprior": weightprior,
"inttime": inttime,
"targets": targets
}
if value.has_key('trajsize'):
comp[name]['trajsize'] = int(value['trajsize'])
if value.has_key('beta'): comp[name]['beta'] = float(value['beta'])
if value.has_key('nbody'):
comp[name]['nbody'] = int(value['nbody'])
if not value.has_key('trajsize'):
raise ValueError("No trajectory will be stored in " + name +
", cannot create Nbody model")
return model
sersicIndex=4,
axisRatioZ=0.6,
scaleRadius=1,
mass=1)
# central black hole (slightly softened)
potbh = agama.Potential(type='Plummer', scaleRadius=1e-4, mass=0.1)
# total potential
pot = agama.Potential(potstars, potbh)
# discretized density profile is recorded on a grid of radial points and spherical harmonics up to lmax
gridr = agama.nonuniformGrid(
50, 0.02,
20.0) # !! make sure that the grid covers the range of interest !!
target = agama.Target(type='DensitySphHarm', gridr=gridr, lmax=8, mmax=0)
# discretized density profile to be used as the density constraint
rhs = target(potstars)
print("Density constraint values")
for i in range(len(gridr)):
print("%s: mass= %g" % (target[i], rhs[i]))
# construct initial conditions for the orbit library:
# use the anisotropic Jeans eqs to set the (approximate) shape of the velocity ellipsoid and the mean v_phi;
beta = 0.0 # velocity anisotropy in R/z plane: >0 - sigma_R>sigma_z, <0 - reverse.
kappa = 0.8 # sets the amount of rotation v_phi vs. dispersion sigma_phi; 1 is rather fast rotation, 0 - no rot.
initcond, _ = potstars.sample(10000, potential=pot, beta=beta, kappa=kappa)
# integration time is 100 orbital periods
inttimes = 100 * pot.Tcirc(initcond)
0, 2 * numpy.pi,
73) # approximate a circle with a polygon with this many vertices
sa = numpy.sin(ang)
sa[36] = sa[72] = 0
ca = numpy.cos(ang)
ca[18] = ca[54] = 0
circ = [numpy.column_stack((rr * ca, rr * sa)) for rr in gridr[1:]]
poly = [circ[0]] + [
numpy.vstack((p1, p2[::-1])) for p1, p2 in zip(circ[1:], circ[:-1])
]
numaper = len(
poly
) # total number of apertures (all concentric rings except the central one, which is a circle)
# define different types of target objects
tar_dens = agama.Target(type='DensitySphHarm', gridr=gridr)
tar_shell = agama.Target(type='KinemShell', gridr=gridr, degree=1)
degree = 2 # B-spline degree for LOSVD representation (2 or 3 are strongly recommended)
tar_losvd = agama.Target(type='LOSVD',
degree=degree,
apertures=poly,
gridx=gridx,
gridv=gridv,
symmetry='s')
# generate N-body samples from the model,
# and integrate orbits with (some of) these initial conditions
xv, mass = gm.sample(1000000)
ic = xv[:10000] # use only a subset of ICs, to save time
mat_dens, mat_shell, mat_losvd = agama.orbit(
potential=pot,
# density profile
den = agama.Density(type='Dehnen',
axisRatioY=0.8,
axisRatioZ=0.6,
scaleRadius=1,
mass=1,
gamma=1)
# potential corresponding to this density
pot = agama.Potential(type='Multipole',
lmax=8,
mmax=6,
density=den,
gridsizer=30)
# target1 is discretized density profile
target1 = agama.Target(type='DensityClassicLinear', density=den, gridsizer=15, \
axisratioy=0.8, axisratioz=0.6, stripsPerPane=2, innerShellMass=0.04, outerShellMass=0.96)
# target2 is discretized kinematic constraint (we will enforce velocity isotropy)
target2 = agama.Target(type='KinemJeans',
density=den,
potential=pot,
gridSizeR=10,
degree=1)
# construct initial conditions for the orbit library
initcond, weightprior = den.sample(2000, potential=pot)
# integration time is 50 orbital periods
inttimes = 50 * pot.Tcirc(initcond)
# integrate all orbits, storing the recorded data corresponding to each target
# in the data1 and data2 arrays, and the trajectories - in trajs
data1, data2, trajs = agama.orbit(potential=pot, ic=initcond, time=inttimes, \
trajsize=101, targets=[target1,target2])