def kappa(f, bins=100):
"""Estimate the epicyclic frequency from velocity
Parameters
----------
f : TipsySnap
`f` is a Simulation snapshot
bins : int or array-like
Either the number of bins to use or the bin edges
Returns
-------
kappa : SimArray
epicyclic frequency
r_edges : SimArray
binedges used
"""
# Require regular spacing of bins
if not isinstance(bins, int):
dr = bins[[1]] - bins[[0]]
eps = np.finfo(bins.dtype).eps
if not np.all(bins[1:] - bins[0:-1] <= dr + 1000*eps):
warnings.warn('Bins not uniformly spaced')
r = f.g['rxy']
v = f.g['vt']
r_edges, v_mean, dummy = binned_mean(r, v, bins=bins, ret_bin_edges=True)
dummy, rv_mean, dummy2 = binned_mean(r, r*v, bins=r_edges)
r_cent = (r_edges[1:] + r_edges[0:-1])/2
dr = r_edges[[1]] - r_edges[[0]]
drv_dr = np.gradient(rv_mean, float(dr))
if pb.units.has_units(dr):
drv_dr /= dr.units
kappa = np.sqrt(2*v_mean*drv_dr)/r_cent
return kappa, r_edges
def kappa(f, bins=100):
"""Estimate the epicyclic frequency from velocity
Parameters
----------
f : TipsySnap
`f` is a Simulation snapshot
bins : int or array-like
Either the number of bins to use or the bin edges
Returns
-------
kappa : SimArray
epicyclic frequency
r_edges : SimArray
binedges used
"""
# Require regular spacing of bins
if not isinstance(bins, int):
dr = bins[[1]] - bins[[0]]
eps = np.finfo(bins.dtype).eps
if not np.all(bins[1:] - bins[0:-1] <= dr + 1000*eps):
warnings.warn('Bins not uniformly spaced')
r = f.g['rxy']
v = f.g['vt']
r_edges, v_mean, dummy = binned_mean(r, v, bins=bins, ret_bin_edges=True)
dummy, rv_mean, dummy2 = binned_mean(r, r*v, bins=r_edges)
r_cent = (r_edges[1:] + r_edges[0:-1])/2
dr = r_edges[[1]] - r_edges[[0]]
drv_dr = np.gradient(rv_mean, dr)
kappa = np.sqrt(2*v_mean*drv_dr)/r_cent
return kappa, r_edges
def height(snapshot, bins=100, center_on_star=True):
"""
Calculates the characteristic height (h) of a flared disk as a function
of cylindrical radius (r).
Parameters
----------
snapshot : TipsySnap
Simulation snapshot for a flared disk
bins : int or array_like
Specifies the bins to use. If int, specifies the number of bins. If
array_like, specifies the bin edges
center_on_star : bool
If true (DEFAULT), cylindrical r is calculated relative to the star
Returns
-------
r_edges : SimArray
Radial bin edges used for calculating h. Length N+1
h : SimArray
Height as a function of r, calculated as the RMS of z over a bin.
Length N
"""
# Center on star
if center_on_star:
star_pos = snapshot.s['pos'].copy()
snapshot['pos'] -= star_pos
else:
star_pos = 0.0*snapshot.s['pos']
# Calculate height
r = snapshot.g['rxy']
z2 = snapshot.g['z']**2
r_edges, z2_mean, err = binned_mean(r, z2, bins=bins, ret_bin_edges=True)
h = np.sqrt(z2_mean)
# Add star_pos back to snapshot
snapshot['pos'] += star_pos
return r_edges, h
def height(snapshot, bins=100, center_on_star=True):
"""
Calculates the characteristic height (h) of a flared disk as a function
of cylindrical radius (r).
Parameters
----------
snapshot : TipsySnap
Simulation snapshot for a flared disk
bins : int or array_like
Specifies the bins to use. If int, specifies the number of bins. If
array_like, specifies the bin edges
center_on_star : bool
If true (DEFAULT), cylindrical r is calculated relative to the star
Returns
-------
r_edges : SimArray
Radial bin edges used for calculating h. Length N+1
h : SimArray
Height as a function of r, calculated as the RMS of z over a bin.
Length N
"""
# Center on star
if center_on_star:
star_pos = snapshot.s['pos'].copy()
snapshot['pos'] -= star_pos
else:
star_pos = 0.0*snapshot.s['pos']
# Calculate height
r = snapshot.g['rxy']
z2 = snapshot.g['z']**2
r_edges, z2_mean, err = binned_mean(r, z2, bins=bins, ret_bin_edges=True)
h = np.sqrt(z2_mean)
# Add star_pos back to snapshot
snapshot['pos'] += star_pos
return r_edges, h
def Qeff(ICobj, bins=None):
if bins is None:
bins = ICobj.sigma.r_bins
# Constants
G = SimArray([1.0],'G')
kB = SimArray([1.0], 'k')
if not hasattr(ICobj, 'snapshot'):
raise ValueError('Could not find snapshot. Must generate ICs first')
snap = ICobj.snapshot
T = snap.g['temp']
r = snap.g['rxy']
M = snap.s['mass']
m = ICobj.settings.physical.m
cs = np.sqrt(kB*T/m)
omega = snap.g['vt']/r
sigma = ICobj.sigma(r)
r_edges, h_binned = height(snap, bins=bins)
r_cent = (r_edges[1:] + r_edges[0:-1])/2
h_spl = extrap1d(r_cent, h_binned)
h = SimArray(h_spl(r), h_binned.units)
Q = (cs*omega/(np.pi*G*sigma)).in_units('1')
Q1 = Q * ((h/r).in_units('1'))**0.192
dummy, Q1_binned, dummy2 = binned_mean(r, Q1, bins=r_edges)
return r_edges, Q1_binned
def Qeff(ICobj, bins=None):
if bins is None:
bins = ICobj.sigma.r_bins
# Constants
G = SimArray([1.0],'G')
kB = SimArray([1.0], 'k')
if not hasattr(ICobj, 'snapshot'):
raise ValueError('Could not find snapshot. Must generate ICs first')
snap = ICobj.snapshot
T = snap.g['temp']
r = snap.g['rxy']
M = snap.s['mass']
m = ICobj.settings.physical.m
cs = np.sqrt(kB*T/m)
omega = snap.g['vt']/r
sigma = ICobj.sigma(r)
r_edges, h_binned = height(snap, bins=bins)
r_cent = (r_edges[1:] + r_edges[0:-1])/2
h_spl = extrap1d(r_cent, h_binned)
h = SimArray(h_spl(r), h_binned.units)
Q = (cs*omega/(np.pi*G*sigma)).in_units('1')
Q1 = Q * ((h/r).in_units('1'))**0.192
dummy, Q1_binned, dummy2 = binned_mean(r, Q1, bins=r_edges)
return r_edges, Q1_binned
def v_xy(f, param, changbin=None, nr=50, min_per_bin=100, changa_preset=None, max_particles=None, est_eps=True):
"""
Attempts to calculate the circular velocities for particles in a thin
(not flat) keplerian disk. Also estimates gravitational softening (eps)
for the gas particles
Requires ChaNGa
Note that this will change the velocities IN f
**ARGUMENTS**
f : tipsy snapshot
For a gaseous disk
param : dict
a dictionary containing params for changa. (see configparser)
changbin : str (OPTIONAL)
If set, should be the full path to the ChaNGa executable. If None,
an attempt to find ChaNGa is made
nr : int (optional)
number of radial bins to use when averaging over accelerations
min_per_bin : int (optional)
The minimum number of particles to be in each bin. If there are too
few particles in a bin, it is merged with an adjacent bin. Thus,
actual number of radial bins may be less than nr.
changa_preset : str
Which ChaNGa execution preset to use (ie 'mpi', 'local', ...). See
ICgen_utils.changa_command
max_particles : int or None
Specifies the maximum number of particles to use for calculating
accelerations and velocities. Setting a smaller number can speed up
computation and save on memory but can yield noisier results.
If None, max is unlimited.
est_eps : bool
Estimate eps (gravitational softening length). Default is True.
If False, it is assumed eps has already been estimated
**RETURNS**
Nothing. Velocities are updated within f as is eps
"""
# If the snapshot has too many particles, randomly select gas particles
# To use for calculating velocity and make a view of the snapshot
n_gas = len(f) - 1
subview = (n_gas > max_particles) and (max_particles is not None)
if subview:
max_particles = int(max_particles)
mask = np.zeros(n_gas + 1, dtype=bool)
mask[-1] = True # Use the star particle always
# randomly select particles to use
m = np.random.rand(n_gas)
ind = m.argsort()[0:max_particles]
mask[ind] = True
# Make a subview and create a reference to the complete snapshot
complete_snapshot = f
f = complete_snapshot[mask]
# Scale gas mass
m_scale = float(n_gas) / float(max_particles)
f.g["mass"] *= m_scale
if not est_eps:
f.g["eps"] *= m_scale ** (1.0 / 3)
# Load stuff from the snapshot
r = f.g["rxy"].astype(np.float32)
cosine = (f.g["x"] / r).in_units("1").astype(np.float32)
sine = (f.g["y"] / r).in_units("1").astype(np.float32)
z = f.g["z"]
vel = f.g["vel"]
a = None # arbitrary initialization
# Temporary filenames for running ChaNGa
f_prefix = str(np.random.randint(0, 2 ** 32))
f_name = f_prefix + ".std"
p_name = f_prefix + ".param"
# Update parameters
p_temp = param.copy()
p_temp["achInFile"] = f_name
p_temp["achOutName"] = f_prefix
p_temp["dDelta"] = 1e-10
if "dDumpFrameTime" in p_temp:
p_temp.pop("dDumpFrameTime")
if "dDumpFrameStep" in p_temp:
p_temp.pop("dDumpFrameStep")
# --------------------------------------------
# Estimate velocity from gravity only
# --------------------------------------------
for iGrav in range(2):
# Save files
f.write(filename=f_name, fmt=pynbody.tipsy.TipsySnap)
configsave(p_temp, p_name, ftype="param")
if iGrav == 0:
# Run ChaNGa calculating all forces (for initial run)
command = ICgen_utils.changa_command(p_name, changa_preset, changbin, "+gas +n 0")
else:
# Run ChaNGa, only calculating gravity (on second run)
command = ICgen_utils.changa_command(p_name, changa_preset, changbin, "-gas +n 0")
print command
p = ICgen_utils.changa_run(command)
p.wait()
if (iGrav == 0) and est_eps:
# Estimate the gravitational softening length on the first iteration
smoothlength_file = f_prefix + ".000000.smoothlength"
eps = ICgen_utils.est_eps(smoothlength_file)
f.g["eps"] = eps
# Load accelerations
acc_name = f_prefix + ".000000.acc2"
del a
gc.collect()
a = load_acc(acc_name, low_mem=True)
gc.collect()
# Clean-up
for fname in glob.glob(f_prefix + "*"):
os.remove(fname)
# Calculate cos(theta) where theta is angle above x-y plane
cos = (r / np.sqrt(r ** 2 + z ** 2)).in_units("1").astype(np.float32)
# Calculate radial acceleration times r^2
ar2 = (a[:, 0] * cosine + a[:, 1] * sine) * r ** 2
# Bin the data
r_edges = np.linspace(r.min(), (1 + np.spacing(2)) * r.max(), nr + 1)
ind, r_edges = digitize_threshold(r, min_per_bin, r_edges)
ind -= 1
nr = len(r_edges) - 1
r_bins, ar2_mean, err = binned_mean(r, ar2, binedges=r_edges, weighted_bins=True)
gc.collect()
# Fit lines to ar2 vs cos for each radial bin
m = np.zeros(nr)
b = np.zeros(nr)
for i in range(nr):
mask = ind == i
p = np.polyfit(cos[mask], ar2[mask], 1)
m[i] = p[0]
b[i] = p[1]
# Interpolate the line fits
m_spline = extrap1d(r_bins, m)
b_spline = extrap1d(r_bins, b)
# Calculate circular velocity
ar2 = SimArray(m_spline(r) * cos + b_spline(r), ar2.units)
gc.collect()
v_calc = (np.sqrt(abs(ar2) / r)).in_units(vel.units)
gc.collect()
vel[:, 0] = -v_calc * sine
vel[:, 1] = v_calc * cosine
del v_calc
gc.collect()
# --------------------------------------------
# Estimate pressure/gas dynamics accelerations
# --------------------------------------------
# Save files
f.write(filename=f_name, fmt=pynbody.tipsy.TipsySnap)
configsave(p_temp, p_name, ftype="param")
# Run ChaNGa, including SPH
command = ICgen_utils.changa_command(p_name, changa_preset, changbin, "+gas -n 0")
p = ICgen_utils.changa_run(command)
p.wait()
# Load accelerations
acc_name = f_prefix + ".000000.acc2"
a_total = load_acc(acc_name, low_mem=True)
gc.collect()
# Clean-up
for fname in glob.glob(f_prefix + "*"):
os.remove(fname)
# Estimate the accelerations due to pressure gradients/gas dynamics
a_gas = a_total - a
del a_total, a
gc.collect()
ar2_gas = (a_gas[:, 0] * cosine + a_gas[:, 1] * sine) * r ** 2
del a_gas
gc.collect()
logr_bins, ratio, err = binned_mean(np.log(r), ar2_gas / ar2, nbins=nr, weighted_bins=True)
r_bins = np.exp(logr_bins)
del ar2_gas
gc.collect()
ratio_spline = extrap1d(r_bins, ratio)
# If not all the particles were used for calculating velocity,
# Make sure to use them now
if subview:
# Re-scale mass back to normal
f.g["mass"] /= m_scale
# Scale eps appropriately
f.g["eps"] /= m_scale ** (1.0 / 3)
complete_snapshot.g["eps"] = f.g["eps"][[0]]
# Rename complete snapshot
f = complete_snapshot
# Calculate stuff for all particles
r = f.g["rxy"]
z = f.g["z"]
cos = (r / np.sqrt(r ** 2 + z ** 2)).in_units("1").astype(np.float32)
ar2 = SimArray(m_spline(r) * cos + b_spline(r), ar2.units)
cosine = (f.g["x"] / r).in_units("1").astype(np.float32)
sine = (f.g["y"] / r).in_units("1").astype(np.float32)
vel = f.g["vel"]
ar2_calc = ar2 * (1 + ratio_spline(r))
del ar2
gc.collect()
# Calculate velocity
v = (np.sqrt(abs(ar2_calc) / r)).in_units(f.g["vel"].units)
del ar2_calc
gc.collect()
vel[:, 0] = -v * sine
vel[:, 1] = v * cosine
return
def v_xy(f, param, changbin=None, nr=50, min_per_bin=100, changa_preset=None, \
max_particles=None, est_eps=True, changa_args=''):
"""
Attempts to calculate the circular velocities for particles in a thin
(not flat) keplerian disk. Also estimates gravitational softening (eps)
for the gas particles and a reasonable time step (dDelta)
Requires ChaNGa
Note that this will change the velocities IN f
Parameters
----------
f : tipsy snapshot
For a gaseous disk
param : dict
a dictionary containing params for changa. (see configparser)
changbin : str (OPTIONAL)
If set, should be the full path to the ChaNGa executable. If None,
an attempt to find ChaNGa is made
nr : int (optional)
number of radial bins to use when averaging over accelerations
min_per_bin : int (optional)
The minimum number of particles to be in each bin. If there are too
few particles in a bin, it is merged with an adjacent bin. Thus,
actual number of radial bins may be less than nr.
changa_preset : str
Which ChaNGa execution preset to use (ie 'mpi', 'local', ...). See
ICgen_utils.changa_command
max_particles : int or None
Specifies the maximum number of particles to use for calculating
accelerations and velocities. Setting a smaller number can speed up
computation and save on memory but can yield noisier results.
If None, max is unlimited.
est_eps : bool
Estimate eps (gravitational softening length). Default is True.
If False, it is assumed eps has already been estimated
changa_args : str
Additional command line arguments to pass to changa
Returns
-------
dDelta : float
A reasonable time step for the simulation (in code units). Velocties
and eps are updated in the snapshot.
"""
# If the snapshot has too many particles, randomly select gas particles
# To use for calculating velocity and make a view of the snapshot
n_gas = len(f) - 1
subview = (n_gas > max_particles) and (max_particles is not None)
if subview:
max_particles = int(max_particles)
mask = np.zeros(n_gas + 1, dtype=bool)
mask[-1] = True # Use the star particle always
# randomly select particles to use
m = np.random.rand(n_gas)
ind = m.argsort()[0:max_particles]
mask[ind] = True
# Make a subview and create a reference to the complete snapshot
complete_snapshot = f
f = complete_snapshot[mask]
# Scale gas mass
m_scale = float(n_gas)/float(max_particles)
f.g['mass'] *= m_scale
if not est_eps:
f.g['eps'] *= m_scale**(1.0/3)
# Load stuff from the snapshot
r = f.g['rxy'].astype(np.float32)
cosine = (f.g['x']/r).in_units('1').astype(np.float32)
sine = (f.g['y']/r).in_units('1').astype(np.float32)
z = f.g['z']
vel = f.g['vel']
a = None # arbitrary initialization
# Temporary filenames for running ChaNGa
f_prefix = str(np.random.randint(0, 2**32))
f_name = f_prefix + '.std'
p_name = f_prefix + '.param'
# Update parameters
p_temp = param.copy()
p_temp['achInFile'] = f_name
p_temp['achOutName'] = f_prefix
p_temp['dDelta'] = 1e-10
if 'dDumpFrameTime' in p_temp: p_temp.pop('dDumpFrameTime')
if 'dDumpFrameStep' in p_temp: p_temp.pop('dDumpFrameStep')
# --------------------------------------------
# Estimate velocity from gravity only
# --------------------------------------------
for iGrav in range(2):
# Save files
f.write(filename=f_name, fmt = pynbody.tipsy.TipsySnap)
configsave(p_temp, p_name, ftype='param')
if iGrav == 0:
# Run ChaNGa calculating all forces (for initial run)
command = ICgen_utils.changa_command(p_name, changa_preset, \
changbin, '+gas +n 0 ' + changa_args)
else:
# Run ChaNGa, only calculating gravity (on second run)
command = ICgen_utils.changa_command(p_name, changa_preset, \
changbin, '-gas +n 0 ' + changa_args)
print command
p = ICgen_utils.changa_run(command)
p.wait()
if (iGrav == 0) and est_eps:
# Estimate the gravitational softening length on the first iteration
smoothlength_file = f_prefix + '.000000.smoothlength'
eps = ICgen_utils.est_eps(smoothlength_file)
f.g['eps'] = eps
# Load accelerations
acc_name = f_prefix + '.000000.acc2'
del a
gc.collect()
a = load_acc(acc_name, low_mem=True)
gc.collect()
# Clean-up
for fname in glob.glob(f_prefix + '*'): os.remove(fname)
# Calculate cos(theta) where theta is angle above x-y plane
cos = (r/np.sqrt(r**2 + z**2)).in_units('1').astype(np.float32)
# Calculate radial acceleration times r^2
ar2 = (a[:,0]*cosine + a[:,1]*sine)*r**2
# Bin the data
r_edges = np.linspace(r.min(), (1+np.spacing(2))*r.max(), nr + 1)
ind, r_edges = digitize_threshold(r, min_per_bin, r_edges)
ind -= 1
nr = len(r_edges) - 1
r_bins, ar2_mean, err = binned_mean(r, ar2, binedges=r_edges, \
weighted_bins=True)
gc.collect()
# Fit lines to ar2 vs cos for each radial bin
m = np.zeros(nr)
b = np.zeros(nr)
for i in range(nr):
mask = (ind == i)
p = np.polyfit(cos[mask], ar2[mask], 1)
m[i] = p[0]
b[i] = p[1]
# Interpolate the line fits
m_spline = extrap1d(r_bins, m)
b_spline = extrap1d(r_bins, b)
# Calculate circular velocity
ar2 = SimArray(m_spline(r)*cos + b_spline(r), ar2.units)
gc.collect()
v_calc = (np.sqrt(abs(ar2)/r)).in_units(vel.units)
gc.collect()
vel[:,0] = -v_calc*sine
vel[:,1] = v_calc*cosine
del v_calc
gc.collect()
# --------------------------------------------
# Estimate pressure/gas dynamics accelerations
# --------------------------------------------
# Save files
f.write(filename=f_name, fmt = pynbody.tipsy.TipsySnap)
configsave(p_temp, p_name, ftype='param')
# Run ChaNGa, including SPH
command = ICgen_utils.changa_command(p_name, changa_preset, changbin, \
'+gas -n 0 ' + changa_args)
p = ICgen_utils.changa_run(command)
p.wait()
# Load accelerations
acc_name = f_prefix + '.000000.acc2'
a_total = load_acc(acc_name, low_mem=True)
gc.collect()
# Estimate the accelerations due to pressure gradients/gas dynamics
a_gas = a_total - a
absa = np.sqrt((a_total**2).sum(1)) # magnitude of the acceleration
del a_total, a
gc.collect()
ar2_gas = (a_gas[:,0]*cosine + a_gas[:,1]*sine)*r**2
del a_gas
gc.collect()
logr_bins, ratio, err = binned_mean(np.log(r), ar2_gas/ar2, nbins=nr,\
weighted_bins=True)
r_bins = np.exp(logr_bins)
del ar2_gas
gc.collect()
ratio_spline = extrap1d(r_bins, ratio)
# Calculate time stepping parameters
f0 = pynbody.load(f_prefix + '.000000')
etaGrav = param.get('dEta', 0.2)
dtGrav = etaGrav * np.sqrt(f0.g['eps']/absa)
etaCourant = param.get('dEtaCourant', 0.4)
mumax = f0.g['mumax']
mumax[mumax < 0] = 0
h = f0.g['smoothlength']
dtCourant = etaCourant * h/(1.6*f0.g['c'] + 1.2*mumax)
# If not all the particles were used for calculating velocity,
# Make sure to use them now
if subview:
# Re-scale mass back to normal
f.g['mass'] /= m_scale
# Scale eps appropriately
f.g['eps'] /= m_scale**(1.0/3)
complete_snapshot.g['eps'] = f.g['eps'][[0]]
# Re-scale time steps
dtGrav /= m_scale**(1.0/6)
dtCourant /= m_scale**(1.0/3)
# Rename complete snapshot
f = complete_snapshot
# Calculate stuff for all particles
r = f.g['rxy']
z = f.g['z']
cos = (r/np.sqrt(r**2 + z**2)).in_units('1').astype(np.float32)
ar2 = SimArray(m_spline(r)*cos + b_spline(r), ar2.units)
cosine = (f.g['x']/r).in_units('1').astype(np.float32)
sine = (f.g['y']/r).in_units('1').astype(np.float32)
vel = f.g['vel']
dt = np.array([dtGrav, dtCourant]).min(0)
dDelta = np.median(dt)
ar2_calc = ar2*(1 + ratio_spline(r))
del ar2
gc.collect()
# Calculate velocity
v = (np.sqrt(abs(ar2_calc)/r)).in_units(f.g['vel'].units)
del ar2_calc
gc.collect()
vel[:,0] = -v*sine
vel[:,1] = v*cosine
# Clean-up
for fname in glob.glob(f_prefix + '*'): os.remove(fname)
return dDelta
def v_xy(f, param, changbin=None, nr=50, min_per_bin=100, changa_preset=None, \
max_particles=None, est_eps=True, changa_args=''):
"""
Attempts to calculate the circular velocities for particles in a thin
(not flat) keplerian disk. Also estimates gravitational softening (eps)
for the gas particles and a reasonable time step (dDelta)
Requires ChaNGa
Note that this will change the velocities IN f
Parameters
----------
f : tipsy snapshot
For a gaseous disk
param : dict
a dictionary containing params for changa. (see configparser)
changbin : str (OPTIONAL)
If set, should be the full path to the ChaNGa executable. If None,
an attempt to find ChaNGa is made
nr : int (optional)
number of radial bins to use when averaging over accelerations
min_per_bin : int (optional)
The minimum number of particles to be in each bin. If there are too
few particles in a bin, it is merged with an adjacent bin. Thus,
actual number of radial bins may be less than nr.
changa_preset : str
Which ChaNGa execution preset to use (ie 'mpi', 'local', ...). See
ICgen_utils.changa_command
max_particles : int or None
Specifies the maximum number of particles to use for calculating
accelerations and velocities. Setting a smaller number can speed up
computation and save on memory but can yield noisier results.
If None, max is unlimited.
est_eps : bool
Estimate eps (gravitational softening length). Default is True.
If False, it is assumed eps has already been estimated
changa_args : str
Additional command line arguments to pass to changa
Returns
-------
dDelta : float
A reasonable time step for the simulation (in code units). Velocties
and eps are updated in the snapshot.
"""
# If the snapshot has too many particles, randomly select gas particles
# To use for calculating velocity and make a view of the snapshot
n_gas = len(f) - 1
subview = (n_gas > max_particles) and (max_particles is not None)
if subview:
max_particles = int(max_particles)
mask = np.zeros(n_gas + 1, dtype=bool)
mask[-1] = True # Use the star particle always
# randomly select particles to use
m = np.random.rand(n_gas)
ind = m.argsort()[0:max_particles]
mask[ind] = True
# Make a subview and create a reference to the complete snapshot
complete_snapshot = f
f = complete_snapshot[mask]
# Scale gas mass
m_scale = float(n_gas) / float(max_particles)
f.g['mass'] *= m_scale
if not est_eps:
f.g['eps'] *= m_scale**(1.0 / 3)
# Load stuff from the snapshot
r = f.g['rxy'].astype(np.float32)
cosine = (f.g['x'] / r).in_units('1').astype(np.float32)
sine = (f.g['y'] / r).in_units('1').astype(np.float32)
z = f.g['z']
vel = f.g['vel']
a = None # arbitrary initialization
# Temporary filenames for running ChaNGa
f_prefix = str(np.random.randint(0, 2**32))
f_name = f_prefix + '.std'
p_name = f_prefix + '.param'
# Update parameters
p_temp = param.copy()
p_temp['achInFile'] = f_name
p_temp['achOutName'] = f_prefix
p_temp['dDelta'] = 1e-10
p_temp['iBinaryOutput'] = 0 # Needed to output smoothlength array
if 'dDumpFrameTime' in p_temp: p_temp.pop('dDumpFrameTime')
if 'dDumpFrameStep' in p_temp: p_temp.pop('dDumpFrameStep')
# --------------------------------------------
# Estimate velocity from gravity only
# --------------------------------------------
for iGrav in range(2):
# Save files
f.write(filename=f_name, fmt=pynbody.tipsy.TipsySnap)
configsave(p_temp, p_name, ftype='param')
if iGrav == 0:
# Run ChaNGa calculating all forces (for initial run)
command = ICgen_utils.changa_command(p_name, changa_preset, \
changbin, '+gas +n 0 ' + changa_args)
else:
# Run ChaNGa, only calculating gravity (on second run)
command = ICgen_utils.changa_command(p_name, changa_preset, \
changbin, '-gas +n 0 ' + changa_args)
print command
p = ICgen_utils.changa_run(command)
p.wait()
if (iGrav == 0) and est_eps:
# Estimate the gravitational softening length on the first iteration
smoothlength_file = f_prefix + '.000000.smoothlength'
eps = ICgen_utils.est_eps(smoothlength_file)
f.g['eps'] = eps
# Load accelerations
acc_name = f_prefix + '.000000.acc2'
del a
gc.collect()
a = load_acc(acc_name, low_mem=True)
a = a[0:-1] # drop the star
gc.collect()
# Clean-up
for fname in glob.glob(f_prefix + '*'):
os.remove(fname)
# Calculate cos(theta) where theta is angle above x-y plane
cos = (r / np.sqrt(r**2 + z**2)).in_units('1').astype(np.float32)
# Calculate radial acceleration times r^2
ar2 = (a[:, 0] * cosine + a[:, 1] * sine) * r**2
# Bin the data
r_edges = np.linspace(r.min(), (1 + np.spacing(2)) * r.max(), nr + 1)
ind, r_edges = digitize_threshold(r, min_per_bin, r_edges)
ind -= 1
nr = len(r_edges) - 1
r_bins, ar2_mean, err = binned_mean(r, ar2, binedges=r_edges, \
weighted_bins=True)
gc.collect()
# Fit lines to ar2 vs cos for each radial bin
m = np.zeros(nr)
b = np.zeros(nr)
for i in range(nr):
mask = (ind == i)
p = np.polyfit(cos[mask], ar2[mask], 1)
m[i] = p[0]
b[i] = p[1]
# Interpolate the line fits
m_spline = extrap1d(r_bins, m)
b_spline = extrap1d(r_bins, b)
# Calculate circular velocity
ar2 = SimArray(m_spline(r) * cos + b_spline(r), ar2.units)
gc.collect()
v_calc = (np.sqrt(abs(ar2) / r)).in_units(vel.units)
gc.collect()
vel[:, 0] = -v_calc * sine
vel[:, 1] = v_calc * cosine
del v_calc
gc.collect()
# --------------------------------------------
# Estimate pressure/gas dynamics accelerations
# --------------------------------------------
# Save files
f.write(filename=f_name, fmt=pynbody.tipsy.TipsySnap)
configsave(p_temp, p_name, ftype='param')
# Run ChaNGa, including SPH
command = ICgen_utils.changa_command(p_name, changa_preset, changbin, \
'+gas -n 0 ' + changa_args)
p = ICgen_utils.changa_run(command)
p.wait()
# Load accelerations
acc_name = f_prefix + '.000000.acc2'
a_total = load_acc(acc_name, low_mem=True)
a_total = a_total[0:-1] # Drop the star
gc.collect()
# Estimate the accelerations due to pressure gradients/gas dynamics
a_gas = a_total - a
absa = np.sqrt((a_total**2).sum(1)) # magnitude of the acceleration
del a_total, a
gc.collect()
ar2_gas = (a_gas[:, 0] * cosine + a_gas[:, 1] * sine) * r**2
del a_gas
gc.collect()
logr_bins, ratio, err = binned_mean(np.log(r), ar2_gas/ar2, nbins=nr,\
weighted_bins=True)
r_bins = np.exp(logr_bins)
del ar2_gas
gc.collect()
ratio_spline = extrap1d(r_bins, ratio)
# Calculate time stepping parameters
f0 = pynbody.load(f_prefix + '.000000')
etaGrav = param.get('dEta', 0.2)
dtGrav = etaGrav * np.sqrt(f0.g['eps'] / absa)
etaCourant = param.get('dEtaCourant', 0.4)
mumax = f0.g['mumax']
mumax[mumax < 0] = 0
h = f0.g['smoothlength']
dtCourant = etaCourant * h / (1.6 * f0.g['c'] + 1.2 * mumax)
# If not all the particles were used for calculating velocity,
# Make sure to use them now
if subview:
# Re-scale mass back to normal
f.g['mass'] /= m_scale
# Scale eps appropriately
f.g['eps'] /= m_scale**(1.0 / 3)
complete_snapshot.g['eps'] = f.g['eps'][[0]]
# Re-scale time steps
dtGrav /= m_scale**(1.0 / 6)
dtCourant /= m_scale**(1.0 / 3)
# Rename complete snapshot
f = complete_snapshot
# Calculate stuff for all particles
r = f.g['rxy']
z = f.g['z']
cos = (r / np.sqrt(r**2 + z**2)).in_units('1').astype(np.float32)
ar2 = SimArray(m_spline(r) * cos + b_spline(r), ar2.units)
cosine = (f.g['x'] / r).in_units('1').astype(np.float32)
sine = (f.g['y'] / r).in_units('1').astype(np.float32)
vel = f.g['vel']
dt = np.array([dtGrav, dtCourant]).min(0)
dDelta = np.median(dt)
ar2_calc = ar2 * (1 + ratio_spline(r))
del ar2
gc.collect()
# Calculate velocity
v = (np.sqrt(abs(ar2_calc) / r)).in_units(f.g['vel'].units)
del ar2_calc
gc.collect()
vel[:, 0] = -v * sine
vel[:, 1] = v * cosine
# Clean-up
for fname in glob.glob(f_prefix + '*'):
os.remove(fname)
return dDelta
def Q(snapshot, molecular_mass = 2.0, bins=100, use_velocity=False, \
use_omega=True):
"""Calculates the Toomre Q as a function of r, assuming radial temperature
profile and kappa ~= omega
Parameters
----------
snapshot : tipsy snapshot
molecular_mass : float
Mean molecular mass (for sound speed). Default = 2.0
bins : int or array
Either the number of bins or the bin edges
use_velocity : Bool
Determines whether to use the particles' velocities to calculate orbital
velocity. Useful if the circular orbital velocities are set in the
snapshot.
use_omega : Bool
Default=True. Use omega as a proxy for kappa to reduce noise
Returns
-------
Q : array
Toomre Q as a function of r
r_edges : array
Radial bin edges
"""
# Physical constants
kB = SimArray([1.0],'k')
G = SimArray([1.0],'G')
# Calculate surface density
sig, r_edges = sigma(snapshot, bins)
# Calculate sound speed
m = match_units(molecular_mass,'m_p')[0]
c_s_all = np.sqrt(kB*snapshot.g['temp']/m)
# Bin/average sound speed
dummy, c_s, dummy2 = binned_mean(snapshot.g['rxy'], c_s_all, binedges=r_edges)
if use_omega:
# Calculate keplerian angular velocity (as a proxy for the epicyclic
# frequency, which is a noisy calculation)
if use_velocity:
# Calculate directly from particle's velocity
dummy, omega, dummy2 = binned_mean(snapshot.g['rxy'], \
snapshot.g['vt']/snapshot.g['rxy'], binedges=r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
omega = p['omega']
kappa_calc = omega
else:
if use_velocity:
# Calculate directly from particle's velocities
kappa_calc, dummy = kappa(snapshot, r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
kappa_calc = p['kappa']
return (kappa_calc*c_s/(np.pi*G*sig)).in_units('1'), r_edges
def Q(snapshot, molecular_mass = 2.0, bins=100, use_velocity=False, \
use_omega=True, gamma=1.):
"""Calculates the Toomre Q as a function of r, assuming radial temperature
profile and kappa ~= omega
Parameters
----------
snapshot : tipsy snapshot
molecular_mass : float
Mean molecular mass (for sound speed). Default = 2.0
bins : int or array
Either the number of bins or the bin edges
use_velocity : Bool
Determines whether to use the particles' velocities to calculate orbital
velocity. Useful if the circular orbital velocities are set in the
snapshot.
use_omega : Bool
Default=True. Use omega as a proxy for kappa to reduce noise
gamma : float
'Effective' adiabatic index, used to calculate sound speed. Use
gamma = 1 for an isothermal EOS
Returns
-------
Q : array
Toomre Q as a function of r
r_edges : array
Radial bin edges
"""
# Physical constants
kB = SimArray([1.0],'k')
G = SimArray([1.0],'G')
# Calculate surface density
sig, r_edges = sigma(snapshot, bins)
# Calculate sound speed
m = match_units(molecular_mass,'m_p')[0]
c_s_all = np.sqrt(kB*snapshot.g['temp']*gamma/m)
# Bin/average sound speed
dummy, c_s, dummy2 = binned_mean(snapshot.g['rxy'], c_s_all, binedges=r_edges)
if use_omega:
# Calculate keplerian angular velocity (as a proxy for the epicyclic
# frequency, which is a noisy calculation)
if use_velocity:
# Calculate directly from particle's velocity
dummy, omega, dummy2 = binned_mean(snapshot.g['rxy'], \
snapshot.g['vt']/snapshot.g['rxy'], binedges=r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
omega = p['omega']
kappa_calc = omega
else:
if use_velocity:
# Calculate directly from particle's velocities
kappa_calc, dummy = kappa(snapshot, r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
kappa_calc = p['kappa']
return (kappa_calc*c_s/(np.pi*G*sig)).in_units('1'), r_edges