def _velocity(field, data, idir, prefix=None):
"""Velocity = linear momentum / density"""
# This is meant to be used with functools.partial to produce
# functions with only 2 arguments (field, data)
# idir : int
# the direction index (1, 2 or 3)
# prefix : str
# used to generalize to dust fields
if prefix is None:
prefix = ""
moment = data["gas", "%smoment_%d" % (prefix, idir)]
rho = data["gas", f"{prefix}density"]
mask1 = rho == 0
if mask1.any():
mylog.info(
"zeros found in %sdensity, "
"patching them to compute corresponding velocity field.",
prefix,
)
mask2 = moment == 0
if not ((mask1 & mask2) == mask1).all():
raise RuntimeError
rho[mask1] = 1
return moment / rho
def check_model(self):
n = len(self.ee)
rho = np.zeros(n)
rho_int = lambda e, psi: self.f(e)*np.sqrt(2*(psi-e))
for i, e in enumerate(self.ee[::-1]):
rho[i] = 4.*np.pi*quad(rho_int, 0., e, args=(e))[0]
chk = np.abs(rho-self.pden)/self.pden
mylog.info("The maximum relative deviation of this profile from "
"virial equilibrium is %g" % np.abs(chk).max())
return rho, chk
def from_scratch(cls, num_particles, rmin, rmax, profile,
num_points=1000):
rr = np.logspace(np.log10(rmin), np.log10(rmax), num_points, endpoint=True)
pden = profile(rr)
mylog.info("Integrating dark matter mass profile.")
mdm = integrate_mass(profile, rr)
mylog.info("Integrating gravitational potential profile.")
gpot_profile = lambda r: profile(r)*r
gpot = G.v*(mdm/rr + 4.*np.pi*integrate_toinf(gpot_profile, rr))
return cls(num_particles, rr, gpot, pden, mdm)
def check_model(self):
r"""
Determine the deviation of the model from hydrostatic equilibrium. Returns
an array containing the relative deviation at each radius or height.
"""
xx = self.fields[self.x_field].v
pressure_spline = InterpolatedUnivariateSpline(xx, self.fields["pressure"].v)
dPdx = YTArray(pressure_spline(xx, 1), "Msun/(Myr**2*kpc**2)")
rhog = self.fields["density"] * self.fields["gravitational_field"]
chk = dPdx - rhog
chk /= rhog
mylog.info(
"The maximum relative deviation of this profile from " "hydrostatic equilibrium is %g" % np.abs(chk).max()
)
return chk
def setup_fluid_fields(self):
setup_magnetic_field_aliases(self, "amrvac",
[f"mag{ax}" for ax in "xyz"])
self._setup_velocity_fields() # gas velocities
self._setup_dust_fields() # dust derived fields (including velocities)
# fields with nested dependencies are defined thereafter
# by increasing level of complexity
us = self.ds.unit_system
def _kinetic_energy_density(field, data):
# devnote : have a look at issue 1301
return 0.5 * data["gas", "density"] * data["gas",
"velocity_magnitude"]**2
self.add_field(
("gas", "kinetic_energy_density"),
function=_kinetic_energy_density,
units=us["density"] * us["velocity"]**2,
dimensions=dimensions.density * dimensions.velocity**2,
sampling_type="cell",
)
# magnetic energy density
if ("amrvac", "b1") in self.field_list:
def _magnetic_energy_density(field, data):
emag = 0.5 * data["gas", "magnetic_1"]**2
for idim in "23":
if not ("amrvac", f"b{idim}") in self.field_list:
break
emag += 0.5 * data["gas", f"magnetic_{idim}"]**2
# in AMRVAC the magnetic field is defined in units where mu0 = 1,
# such that
# Emag = 0.5*B**2 instead of Emag = 0.5*B**2 / mu0
# To correctly transform the dimensionality from gauss**2 -> rho*v**2,
# we have to take mu0 into account. If we divide here, units when adding
# the field should be us["density"]*us["velocity"]**2.
# If not, they should be us["magnetic_field"]**2 and division should
# happen elsewhere.
emag /= 4 * np.pi
# divided by mu0 = 4pi in cgs,
# yt handles 'mks' and 'code' unit systems internally.
return emag
self.add_field(
("gas", "magnetic_energy_density"),
function=_magnetic_energy_density,
units=us["density"] * us["velocity"]**2,
dimensions=dimensions.density * dimensions.velocity**2,
sampling_type="cell",
)
# Adding the thermal pressure field.
# In AMRVAC we have multiple physics possibilities:
# - if HD/MHD + energy equation P = (gamma-1)*(e - ekin (- emag)) for (M)HD
# - if HD/MHD but solve_internal_e is true in parfile, P = (gamma-1)*e for both
# - if (m)hd_energy is false in parfile (isothermal), P = c_adiab * rho**gamma
def _full_thermal_pressure_HD(field, data):
# energy density and pressure are actually expressed in the same unit
pthermal = (data.ds.gamma -
1) * (data["gas", "energy_density"] -
data["gas", "kinetic_energy_density"])
return pthermal
def _full_thermal_pressure_MHD(field, data):
pthermal = (
_full_thermal_pressure_HD(field, data) -
(data.ds.gamma - 1) * data["gas", "magnetic_energy_density"])
return pthermal
def _polytropic_thermal_pressure(field, data):
return (data.ds.gamma - 1) * data["gas", "energy_density"]
def _adiabatic_thermal_pressure(field, data):
return data.ds._c_adiab * data["gas", "density"]**data.ds.gamma
pressure_recipe = None
if ("amrvac", "e") in self.field_list:
if self.ds._e_is_internal:
pressure_recipe = _polytropic_thermal_pressure
mylog.info("Using polytropic EoS for thermal pressure.")
elif ("amrvac", "b1") in self.field_list:
pressure_recipe = _full_thermal_pressure_MHD
mylog.info("Using full MHD energy for thermal pressure.")
else:
pressure_recipe = _full_thermal_pressure_HD
mylog.info("Using full HD energy for thermal pressure.")
elif self.ds._c_adiab is not None:
pressure_recipe = _adiabatic_thermal_pressure
mylog.info(
"Using adiabatic EoS for thermal pressure (isothermal).")
mylog.warning("If you used usr_set_pthermal you should "
"redefine the thermal_pressure field.")
if pressure_recipe is not None:
self.add_field(
("gas", "thermal_pressure"),
function=pressure_recipe,
units=us["density"] * us["velocity"]**2,
dimensions=dimensions.density * dimensions.velocity**2,
sampling_type="cell",
)
# sound speed and temperature depend on thermal pressure
def _sound_speed(field, data):
return np.sqrt(data.ds.gamma *
data["gas", "thermal_pressure"] /
data["gas", "density"])
self.add_field(
("gas", "sound_speed"),
function=_sound_speed,
units=us["velocity"],
dimensions=dimensions.velocity,
sampling_type="cell",
)
else:
mylog.warning(
"e not found and no parfile passed, can not set thermal_pressure."
)
def save(obj, filename='test.hdf5'):
"""Function to save a CAESAR file to disk.
Parameters
----------
obj : :class:`main.CAESAR`
Main caesar object to save.
filename : str, optional
Filename of the output file.
Examples
--------
>>> obj.save('output.hdf5')
"""
from yt.funcs import mylog
if os.path.isfile(filename):
mylog.warning('%s already present, overwriting!' % filename)
os.remove(filename)
mylog.info('Writing %s' % filename)
outfile = h5py.File(filename, 'w')
outfile.attrs.create('caesar', 315)
unit_registry = obj.yt_dataset.unit_registry.to_json()
outfile.attrs.create('unit_registry_json', unit_registry.encode('utf8'))
serialize_global_attribs(obj, outfile)
obj.simulation._serialize(obj, outfile)
if hasattr(obj, 'halos') and obj.nhalos > 0:
hd = outfile.create_group('halo_data')
hdd = hd.create_group('lists')
hddd = hd.create_group('dicts')
# gather
index_lists = ['dmlist']
if 'gas' in obj.data_manager.ptypes: index_lists.append('glist')
if 'star' in obj.data_manager.ptypes:
index_lists.extend(['slist', 'galaxy_index_list'])
if 'dm2' in obj.data_manager.ptypes: index_lists.append('dm2list')
if 'dm3' in obj.data_manager.ptypes: index_lists.append('dm3list')
if obj.data_manager.blackholes:
index_lists.append('bhlist')
if obj.data_manager.dust:
index_lists.append('dlist')
#write
for vals in index_lists:
serialize_list(obj.halos, vals, hdd)
serialize_attributes(obj.halos, hd, hddd)
if hasattr(obj, 'galaxies') and obj.ngalaxies > 0:
hd = outfile.create_group('galaxy_data')
hdd = hd.create_group('lists')
hddd = hd.create_group('dicts')
# gather
index_lists = ['glist', 'slist', 'cloud_index_list']
if obj.data_manager.blackholes:
index_lists.append('bhlist')
if obj.data_manager.dust:
index_lists.append('dlist')
# write
for vals in index_lists:
serialize_list(obj.galaxies, vals, hdd)
serialize_attributes(obj.galaxies, hd, hddd)
if hasattr(obj, 'clouds') and obj.nclouds > 0:
hd = outfile.create_group('cloud_data')
hdd = hd.create_group('lists')
hddd = hd.create_group('dicts')
# gather
index_lists = ['glist']
# write
for vals in index_lists:
serialize_list(obj.clouds, vals, hdd)
serialize_attributes(obj.clouds, hd, hddd)
if hasattr(obj, 'global_particle_lists'):
hd = outfile.create_group('global_lists')
# gather
global_index_lists = [
'halo_dmlist', 'halo_glist', 'halo_slist', 'galaxy_glist',
'galaxy_slist', 'cloud_glist'
]
if obj.data_manager.blackholes:
global_index_lists.extend(['halo_bhlist', 'galaxy_bhlist'])
if obj.data_manager.dust:
global_index_lists.extend(['halo_dlist', 'galaxy_dlist'])
# write
for vals in global_index_lists:
check_and_write_dataset(obj.global_particle_lists, vals, hd)
outfile.close()
def __init__(self, num_particles, rr, gpot, pden, mdm):
fields = OrderedDict()
ee = gpot[::-1]
density_spline = InterpolatedUnivariateSpline(ee, pden[::-1])
energy_spline = InterpolatedUnivariateSpline(rr, gpot)
num_points = gpot.shape[0]
g = np.zeros(num_points)
dgdp = lambda t, e: 2*density_spline(e-t*t, 1)
pbar = get_pbar("Computing particle DF.", num_points)
for i in range(num_points):
g[i] = quad(dgdp, 0., np.sqrt(ee[i]), args=(ee[i]))[0]
pbar.update(i)
pbar.finish()
g_spline = InterpolatedUnivariateSpline(ee, g)
f = lambda e: g_spline(e, 1)/(np.sqrt(8.)*np.pi**2)
self.ee = ee
self.f = f
self.rr = rr
self.pden = pden
mylog.info("We will be assigning %d particles." % num_particles)
mylog.info("Compute particle positions.")
u = np.random.uniform(size=num_particles)
P_r = np.insert(mdm, 0, 0.0)
P_r /= P_r[-1]
radius = np.interp(u, P_r, np.insert(rr, 0, 0.0), left=0.0, right=1.0)
theta = np.arccos(np.random.uniform(low=-1.,high=1.,size=num_particles))
phi = 2.*np.pi*np.random.uniform(size=num_particles)
fields["particle_radius"] = YTArray(radius, "kpc")
fields["particle_position_x"] = YTArray(radius*np.sin(theta)*np.cos(phi), "kpc")
fields["particle_position_y"] = YTArray(radius*np.sin(theta)*np.sin(phi), "kpc")
fields["particle_position_z"] = YTArray(radius*np.cos(theta), "kpc")
mylog.info("Compute particle velocities.")
psi = energy_spline(radius)
vesc = 2.*psi
fv2esc = vesc*f(psi)
vesc = np.sqrt(vesc)
velocity = generate_velocities(psi, vesc, fv2esc, f)
theta = np.arccos(np.random.uniform(low=-1.,high=1.,size=num_particles))
phi = 2.*np.pi*np.random.uniform(size=num_particles)
fields["particle_velocity"] = YTArray(velocity, "kpc/Myr")
fields["particle_velocity_x"] = YTArray(velocity*np.sin(theta)*np.cos(phi), "kpc/Myr")
fields["particle_velocity_y"] = YTArray(velocity*np.sin(theta)*np.sin(phi), "kpc/Myr")
fields["particle_velocity_z"] = YTArray(velocity*np.cos(theta), "kpc/Myr")
fields["particle_mass"] = YTArray([mdm.max()/num_particles], "Msun")
fields["particle_potential"] = YTArray(psi, "kpc**2/Myr**2")
fields["particle_energy"] = fields["particle_potential"]-0.5*fields["particle_velocity"]**2
super(VirialEquilibrium, self).__init__(num_particles, fields, "spherical")
def from_scratch(
cls, mode, xmin, xmax, profiles, input_units=None, num_points=1000, geometry="spherical", P_amb=0.0
):
r"""
Generate a set of profiles of physical quantities based on the assumption
of hydrostatic equilibrium. Currently assumes an ideal gas with a gamma-law
equation of state.
Parameters
----------
mode : string
The method to generate the profiles from an initial set. Can be
one of the following:
"dens_temp": Generate the profiles given a gas density and
gas temperature profile.
"dens_tden": Generate the profiles given a gas density and
total density profile.
"dens_grav": Generate the profiles given a gas density and
gravitational acceleration profile.
"dm_only": Generate profiles of gravitational potential
and acceleration assuming an initial DM density profile.
xmin : float
The minimum radius or height for the profiles, assumed to be in kpc.
xmax : float
The maximum radius or height for the profiles, assumed to be in kpc.
profiles : dict of functions
A dictionary of callable functions of radius or height which return
quantities such as density, total density, and so on. The functions
are not unit-aware for speed purposes, but they assume that the base
units are:
"length": "kpc"
"time": "Myr"
"mass": "Msun"
"temperature": "keV"
parameters : dict of floats
A dictionary of parameters needed for the calculation, which include:
"mu": The mean molecular weight of the gas. Default is to assume a
primordial H/He gas.
"gamma": The ratio of specific heats. Default: 5/3.
num_points : integer
The number of points at which to evaluate the profile.
geometry : string
The geometry of the model. Can be "cartesian" or "spherical", which will
determine whether or not the profiles are of "radius" or "height".
"""
if not isinstance(P_amb, YTQuantity):
P_amb = YTQuantity(P_amb, "erg/cm**3")
P_amb.convert_to_units("Msun/(Myr**2*kpc)")
for p in modes[mode]:
if p not in profiles:
raise RequiredProfilesError(mode)
if mode in ["dens_tden", "dm_only"] and geometry != "spherical":
raise NotImplemented(
"Constructing a HydrostaticEquilibrium from gas density and/or "
"total density profiles is only allowed in spherical geometry!"
)
extra_fields = [field for field in profiles if field not in cls.default_fields]
if geometry == "cartesian":
x_field = "height"
elif geometry == "spherical":
x_field = "radius"
fields = OrderedDict()
xx = np.logspace(np.log10(xmin), np.log10(xmax), num_points, endpoint=True)
fields[x_field] = YTArray(xx, "kpc")
if mode == "dm_only":
fields["density"] = YTArray(np.zeros(num_points), "Msun/kpc**3")
fields["pressure"] = YTArray(np.zeros(num_points), "Msun/kpc/Myr**2")
fields["temperature"] = YTArray(np.zeros(num_points), "keV")
else:
fields["density"] = YTArray(profiles["density"](xx), "Msun/kpc**3")
if mode == "dens_temp":
mylog.info("Computing the profiles from density and temperature.")
fields["temperature"] = YTArray(profiles["temperature"](xx), "keV")
fields["pressure"] = fields["density"] * fields["temperature"]
fields["pressure"] *= muinv / mp
fields["pressure"].convert_to_units("Msun/(Myr**2*kpc)")
pressure_spline = InterpolatedUnivariateSpline(xx, fields["pressure"].v)
dPdx = YTArray(pressure_spline(xx, 1), "Msun/(Myr**2*kpc**2)")
fields["gravitational_field"] = dPdx / fields["density"]
fields["gravitational_field"].convert_to_units("kpc/Myr**2")
else:
if mode == "dens_tden" or mode == "dm_only":
mylog.info("Computing the profiles from density and total density.")
fields["total_density"] = YTArray(profiles["total_density"](xx), "Msun/kpc**3")
mylog.info("Integrating total mass profile.")
fields["total_mass"] = YTArray(integrate_mass(profiles["total_density"], xx), "Msun")
fields["gravitational_field"] = -G * fields["total_mass"] / (fields["radius"] ** 2)
fields["gravitational_field"].convert_to_units("kpc/Myr**2")
elif mode == "dens_grav":
mylog.info("Computing the profiles from density and gravitational acceleration.")
fields["gravitational_field"] = YTArray(profiles["gravitational_field"](xx), "kpc/Myr**2")
if mode != "dm_only":
g = fields["gravitational_field"].in_units("kpc/Myr**2").v
g_r = InterpolatedUnivariateSpline(xx, g)
dPdr_int = lambda r: profiles["density"](r) * g_r(r)
mylog.info("Integrating pressure profile.")
fields["pressure"] = -YTArray(integrate(dPdr_int, xx), "Msun/kpc/Myr**2")
fields["temperature"] = fields["pressure"] * mp / fields["density"] / muinv
fields["temperature"].convert_to_units("keV")
if geometry == "spherical":
if "total_mass" not in fields:
fields["total_mass"] = -fields["radius"] ** 2 * fields["gravitational_field"] / G
if "total_density" not in fields:
total_mass_spline = InterpolatedUnivariateSpline(xx, fields["total_mass"].v)
dMdr = YTArray(total_mass_spline(xx, 1), "Msun/kpc")
fields["total_density"] = dMdr / (4.0 * np.pi * fields["radius"] ** 2)
mylog.info("Integrating gravitational potential profile.")
if "total_density" in profiles:
tdens_func = profiles["total_density"]
else:
tdens_func = InterpolatedUnivariateSpline(xx, fields["total_density"].d)
gpot_profile = lambda r: tdens_func(r) * r
gpot = YTArray(4.0 * np.pi * integrate(gpot_profile, xx), "Msun/kpc")
fields["gravitational_potential"] = -G * (fields["total_mass"] / fields["radius"] + gpot)
fields["gravitational_potential"].convert_to_units("kpc**2/Myr**2")
if mode != "dm_only":
mylog.info("Integrating gas mass profile.")
fields["gas_mass"] = YTArray(integrate_mass(profiles["density"], xx), "Msun")
mdm = fields["total_mass"].copy()
ddm = fields["total_density"].copy()
if mode != "dm_only":
mdm -= fields["gas_mass"]
ddm -= fields["density"]
mdm[ddm.v < 0.0][:] = mdm.max()
ddm[ddm.v < 0.0][:] = 0.0
fields["dark_matter_density"] = ddm
fields["dark_matter_mass"] = mdm
fields["pressure"] += P_amb
for field in extra_fields:
fields[field] = profiles[field](xx)
return cls(num_points, fields, geometry)
def setup_fluid_fields(self):
def _v1(field, data):
return data["gas", "moment_1"] / data["gas", "density"]
def _v2(field, data):
return data["gas", "moment_2"] / data["gas", "density"]
def _v3(field, data):
return data["gas", "moment_3"] / data["gas", "density"]
us = self.ds.unit_system
aliases = direction_aliases[self.ds.geometry]
for idir, alias, func in zip("123", aliases, (_v1, _v2, _v3)):
if not ("amrvac", "m%s" % idir) in self.field_list:
break
self.add_field(("gas", "velocity_%s" % alias),
function=func,
units=us['velocity'],
dimensions=dimensions.velocity,
sampling_type="cell")
self.alias(("gas", "velocity_%s" % idir),
("gas", "velocity_%s" % alias),
units=us["velocity"])
self.alias(("gas", "moment_%s" % alias),
("gas", "moment_%s" % idir),
units=us["density"] * us["velocity"])
setup_magnetic_field_aliases(self, "amrvac",
["mag%s" % ax for ax in "xyz"])
# fields with nested dependencies are defined thereafter by increasing level of complexity
# kinetic pressure is given by 0.5 * rho * v**2
def _kinetic_energy_density(field, data):
# devnote : have a look at issue 1301
return 0.5 * data['gas', 'density'] * data['gas',
'velocity_magnitude']**2
self.add_field(("gas", "kinetic_energy_density"),
function=_kinetic_energy_density,
units=us["density"] * us["velocity"]**2,
dimensions=dimensions.density * dimensions.velocity**2,
sampling_type="cell")
# magnetic energy density
if ('amrvac', 'b1') in self.field_list:
def _magnetic_energy_density(field, data):
emag = 0.5 * data['gas', 'magnetic_1']**2
for idim in '23':
if not ('amrvac', 'b%s' % idim) in self.field_list:
break
emag += 0.5 * data['gas', 'magnetic_%s' % idim]**2
# important note: in AMRVAC the magnetic field is defined in units where mu0 = 1, such that
# Emag = 0.5*B**2 instead of Emag = 0.5*B**2 / mu0
# To correctly transform the dimensionality from gauss**2 -> rho*v**2, we have to take mu0 into account.
# If we divide here, units when adding the field should be us["density"]*us["velocity"]**2
# If not, they should be us["magnetic_field"]**2 and division should happen elsewhere.
emag /= 4 * np.pi
# divided by mu0 = 4pi in cgs, yt handles 'mks' and 'code' unit systems internally.
return emag
self.add_field(
('gas', 'magnetic_energy_density'),
function=_magnetic_energy_density,
units=us["density"] * us["velocity"]**2,
dimensions=dimensions.density * dimensions.velocity**2,
sampling_type='cell')
# Adding the thermal pressure field.
# In AMRVAC we have multiple physics possibilities:
# - if HD/MHD + energy equation, pressure is (gamma-1)*(e - ekin (- emag)) for (M)HD
# - if HD/MHD but solve_internal_e is true in parfile, pressure is (gamma-1)*e for both
# - if (m)hd_energy is false in parfile (isothermal), pressure is c_adiab * rho**gamma
def _full_thermal_pressure_HD(field, data):
# important note : energy density and pressure are actually expressed in the same unit
pthermal = (data.ds.gamma -
1) * (data['gas', 'energy_density'] -
data['gas', 'kinetic_energy_density'])
return pthermal
def _full_thermal_pressure_MHD(field, data):
pthermal = _full_thermal_pressure_HD(field, data) \
- (data.ds.gamma - 1) * data["gas", "magnetic_energy_density"]
return pthermal
def _polytropic_thermal_pressure(field, data):
return (data.ds.gamma - 1) * data['gas', 'energy_density']
def _adiabatic_thermal_pressure(field, data):
return data.ds._c_adiab * data["gas", "density"]**data.ds.gamma
pressure_recipe = None
if ("amrvac", "e") in self.field_list:
if self.ds._e_is_internal:
pressure_recipe = _polytropic_thermal_pressure
mylog.info('Using polytropic EoS for thermal pressure.')
elif ('amrvac', 'b1') in self.field_list:
pressure_recipe = _full_thermal_pressure_MHD
mylog.info('Using full MHD energy for thermal pressure.')
else:
pressure_recipe = _full_thermal_pressure_HD
mylog.info('Using full HD energy for thermal pressure.')
elif self.ds._c_adiab is not None:
pressure_recipe = _adiabatic_thermal_pressure
mylog.info(
'Using adiabatic EoS for thermal pressure (isothermal).')
mylog.warning(
'If you used usr_set_pthermal you should redefine the thermal_pressure field.'
)
if pressure_recipe is not None:
self.add_field(
('gas', 'thermal_pressure'),
function=pressure_recipe,
units=us['density'] * us['velocity']**2,
dimensions=dimensions.density * dimensions.velocity**2,
sampling_type='cell')
# sound speed and temperature depend on thermal pressure
def _sound_speed(field, data):
return np.sqrt(data.ds.gamma *
data["gas", "thermal_pressure"] /
data["gas", "density"])
self.add_field(("gas", "sound_speed"),
function=_sound_speed,
units=us["velocity"],
dimensions=dimensions.velocity,
sampling_type="cell")
else:
mylog.warning(
"e not found and no parfile passed, can not set thermal_pressure."
)