"""
Module with functionalities for fitting atmospheric model spectra.
"""
import os
import math
import warnings
from multiprocessing import Pool, cpu_count
import emcee
import numpy as np
try:
import pymultinest
except:
warnings.warn('PyMultiNest could not be imported.')
from species.core import constants
from species.data import database
from species.read import read_model, read_object
from species.util import read_util
[docs]def lnprior(param,
bounds,
modelpar,
prior=None):
"""
Internal function for the prior probability.
Parameters
----------
param : numpy.ndarray
Parameter values.
bounds : dict
Parameter boundaries.
modelpar : list(str, )
Parameter names.
prior : tuple(str, float, float), None
Gaussian prior on one of the parameters. Currently only possible for the mass, e.g.
('mass', 13., 3.) for an expected mass of 13 Mjup with an uncertainty of 3 Mjup. Not
used if set to None.
Returns
-------
float
Log prior probability.
"""
if prior is not None:
modeldict = {}
for i, item in enumerate(modelpar):
modeldict[item] = param[i]
ln_prior = 0
for i, item in enumerate(modelpar):
if bounds[item][0] <= param[i] <= bounds[item][1]:
if prior is not None and prior[0] == 'mass' and item == 'logg':
mass = read_util.get_mass(modeldict)
ln_prior += -0.5*(mass-prior[1])**2/prior[2]**2
else:
ln_prior += 0.
else:
ln_prior = -np.inf
break
return ln_prior
[docs]def lnlike(param,
modelpar,
objphot,
distance,
spectrum,
modelphot,
modelspec):
"""
Internal function for the likelihood function.
Parameters
----------
param : numpy.ndarray
Parameter values.
modelpar : list(str, )
Parameter names.
objphot : list(tuple(float, float), )
List with the fluxes and uncertainties of the object.
distance : tuple(float, float)
Distance and uncertainty (pc).
spectrum : dict
Dictionary with the spectrum stored as wavelength (um), flux (W m-2 um-1),
and error (W m-2 um-1), and optionally the covariance matrix and the inverse of
the covariance matrix.
modelphot : list(species.read.read_model.ReadModel, )
List with the interpolated synthetic photometry.
modelspec : list(species.read.read_model.ReadModel, )
List with the interpolated synthetic spectra.
Returns
-------
float
Log likelihood probability.
"""
paramdict = {}
spec_scaling = {}
for i, item in enumerate(modelpar):
if item == 'radius':
radius = param[i]
elif item[:8] == 'scaling_' and item[8:] in spectrum:
spec_scaling[item[8:]] = param[i]
else:
paramdict[item] = param[i]
scaling = (radius*constants.R_JUP)**2 / (distance[0]*constants.PARSEC)**2
chisq = 0.
if objphot is not None:
for i, item in enumerate(objphot):
flux = scaling * modelphot[i].spectrum_interp(list(paramdict.values()))
chisq += (item[0]-flux)**2 / item[1]**2
if spectrum is not None:
for i, item in enumerate(spectrum.keys()):
flux = scaling * modelspec[i].spectrum_interp(list(paramdict.values()))[0, :]
if item in spec_scaling:
flux_obs = spec_scaling[item]*spectrum[item][0][:, 1]
else:
flux_obs = spectrum[item][0][:, 1]
if spectrum[item][2] is not None:
spec_diff = flux_obs - flux
chisq += np.dot(spec_diff, np.dot(spectrum[item][2], spec_diff))
else:
chisq += np.nansum((flux_obs-flux)**2 / spectrum[item][0][:, 2]**2)
return -0.5*chisq
[docs]def lnprob(param,
bounds,
modelpar,
objphot,
distance,
prior,
spectrum,
modelphot,
modelspec):
"""
Internal function for the posterior probability.
Parameters
----------
param : numpy.ndarray
Parameter values.
bounds : dict
Parameter boundaries.
modelpar : list(str, )
Parameter names.
objphot : list(tuple(float, float), )
List with the fluxes and uncertainties of the object.
distance : tuple(float, float)
Distance and uncertainty (pc).
prior : tuple(str, float, float)
Gaussian prior on one of the parameters. Currently only possible for the mass, e.g.
('mass', 13., 3.) for an expected mass of 13 Mjup with an uncertainty of 3 Mjup. Not
used if set to None.
spectrum : dict
Wavelength (um), apparent flux (W m-2 um-1), and flux error (W m-2 um-1).
modelphot : list(species.read.read_model.ReadModel, )
List with the interpolated synthetic fluxes.
modelspec : list(species.read.read_model.ReadModel, )
List with the interpolated synthetic spectra.
Returns
-------
float
Log posterior probability.
"""
ln_prior = lnprior(param, bounds, modelpar, prior)
if math.isinf(ln_prior):
ln_prob = -np.inf
else:
ln_prob = ln_prior + lnlike(param,
modelpar,
objphot,
distance,
spectrum,
modelphot,
modelspec)
if np.isnan(ln_prob):
ln_prob = -np.inf
return ln_prob
[docs]class FitModel:
"""
Class for fitting atmospheric model spectra to photometric and/or spectroscopic data.
"""
def __init__(self,
object_name,
filters,
model,
bounds=None,
inc_phot=True,
inc_spec=True):
"""
For each photometric point and spectrum, the model grid is linearly interpolated at the
required synthetic photometry and wavelength sampling before running the MCMC. Therefore,
the computation time of this initial interpolation depends on the wavelength range and
spectral resolution of the spectra that are stored in the database, and the prior
boundaries that are chosen with ``bounds``.
Parameters
----------
object_name : str
Object name in the database as created with
:func:`~species.data.database.Database.add_object` or
:func:`~species.data.database.Database.add_companion`.
filters : tuple(str, )
Filter names for which the photometry is selected. All available photometry of the
object is selected if set to None.
model : str
Atmospheric model (e.g. 'drift-phoenix', 'petitcode-cool-cloudy', or 'bt-settl').
bounds : dict, None
Parameter boundaries. The full range is used for each parameter if set to None. In that
case, the radius range is set to 0.8-1.5 Rjup. It is also possible to specify the bounds
for a subset of the parameters, for example, ``{'radius': (0.5, 10.)}``. Restricting
the boundaries will decrease the computation time with the interpolation prior to the
MCMC sampling. An additional scaling parameter can be fitted for each spectrum in which
case, the boundaries have to be provided with the database tag of the spectrum.
For example, ``{'sphere_ifs': (0.5, 2.)}`` if the spectrum is stored as ``sphere_ifs``
with :func:`~species.data.database.Database.add_object`.
inc_phot : bool
Include photometric data in the fit.
inc_spec : bool
Include spectroscopic data in the fit.
Returns
-------
NoneType
None
"""
self.object = read_object.ReadObject(object_name)
self.distance = self.object.get_distance()
self.model = model
self.bounds = bounds
if not inc_phot and not inc_spec:
raise ValueError('No photometric or spectral data has been selected.')
if self.bounds is not None:
readmodel = read_model.ReadModel(self.model)
bounds_grid = readmodel.get_bounds()
for item in bounds_grid:
if item not in self.bounds:
self.bounds[item] = bounds_grid[item]
else:
readmodel = read_model.ReadModel(self.model, None, None)
self.bounds = readmodel.get_bounds()
if 'radius' not in self.bounds:
self.bounds['radius'] = (0.8, 1.5)
print('Prior and interpolation boundaries:')
for key, value in self.bounds.items():
print(f' - {key} = {value}')
if inc_phot:
self.objphot = []
self.modelphot = []
if filters is None:
species_db = database.Database()
objectbox = species_db.get_object(object_name, None)
filters = objectbox.filters
for item in filters:
print(f'Interpolating {item}...', end='', flush=True)
readmodel = read_model.ReadModel(self.model, filter_name=item)
readmodel.interpolate_grid(self.bounds)
self.modelphot.append(readmodel)
print(f' [DONE]')
obj_phot = self.object.get_photometry(item)
self.objphot.append((obj_phot[2], obj_phot[3]))
else:
self.objphot = None
self.modelphot = None
if inc_spec:
self.spectrum = self.object.get_spectrum()
self.modelspec = []
for key, value in self.spectrum.items():
print(f'\rInterpolating {key}...', end='', flush=True)
wavel_range = (0.9*value[0][0, 0], 1.1*value[0][-1, 0])
readmodel = read_model.ReadModel(self.model, wavel_range=wavel_range)
readmodel.interpolate_grid(self.bounds,
wavel_resample=self.spectrum[key][0][:, 0],
smooth=True,
spec_res=self.spectrum[key][3])
self.modelspec.append(readmodel)
print(f' [DONE]')
else:
self.spectrum = None
self.modelspec = None
self.modelpar = readmodel.get_parameters()
self.modelpar.append('radius')
if self.spectrum is not None:
for item in self.spectrum:
if item in bounds:
self.modelpar.append(f'scaling_{item}')
self.bounds[f'scaling_{item}'] = (bounds[item][0], bounds[item][1])
del self.bounds[item]
[docs] def run_mcmc(self,
tag,
guess,
nwalkers=200,
nsteps=1000,
prior=None):
"""
Function to run the MCMC sampler of ``emcee``.
Parameters
----------
tag : str
Database tag where the samples will be stored.
guess : dict, None
Guess for the parameter values. Random values between the boundary values are used
if set to None.
nwalkers : int
Number of walkers.
nsteps : int
Number of steps per walker.
prior : tuple(str, float, float), None
Gaussian prior on one of the parameters. Currently only possible for the mass, e.g.
('mass', 13., 3.) for an expected mass of 13 Mjup with an uncertainty of 3 Mjup. Not
used if set to None.
Returns
-------
NoneType
None
"""
sigma = {'teff': 5., 'logg': 0.01, 'feh': 0.01, 'fsed': 0.01, 'co': 0.01, 'radius': 0.01}
if self.spectrum is not None:
for item in self.spectrum:
if f'scaling_{item}' in self.bounds:
sigma[f'scaling_{item}'] = 0.01
guess[f'scaling_{item}'] = guess[item]
del guess[item]
print('Running MCMC...')
ndim = len(self.bounds)
initial = np.zeros((nwalkers, ndim))
for i, item in enumerate(self.modelpar):
if guess[item] is not None:
initial[:, i] = guess[item] + np.random.normal(0, sigma[item], nwalkers)
else:
initial[:, i] = np.random.uniform(low=self.bounds[item][0],
high=self.bounds[item][1],
size=nwalkers)
with Pool(processes=cpu_count()):
ens_sampler = emcee.EnsembleSampler(nwalkers,
ndim,
lnprob,
args=([self.bounds,
self.modelpar,
self.objphot,
self.distance,
prior,
self.spectrum,
self.modelphot,
self.modelspec]))
ens_sampler.run_mcmc(initial, nsteps, progress=True)
species_db = database.Database()
spec_labels = []
if self.spectrum is not None:
for item in self.spectrum:
if f'scaling_{item}' in self.bounds:
spec_labels.append(f'scaling_{item}')
else:
spec_labels = None
species_db.add_samples(sampler='emcee',
samples=ens_sampler.chain,
ln_prob=ens_sampler.lnprobability,
mean_accept=np.mean(ens_sampler.acceptance_fraction),
spectrum=('model', self.model),
tag=tag,
modelpar=self.modelpar,
distance=self.distance[0],
spec_labels=spec_labels)
[docs] def run_multinest(self,
tag,
n_live_points=4000,
output='multinest/'):
"""
Function to run the ``PyMultiNest`` wrapper of the ``MultiNest`` sampler. While
``PyMultiNest`` can be installed with ``pip`` from the PyPI repository, ``MultiNest``
has to to be build manually. See the ``PyMultiNest`` documentation for details:
http://johannesbuchner.github.io/PyMultiNest/install.html. Note that the library path
of ``MultiNest`` should be set to the environmental variable ``LD_LIBRARY_PATH`` on a
Linux machine and ``DYLD_LIBRARY_PATH`` on a Mac. Alternatively, the variable can be
set before importing the ``species`` package, for example:
.. code-block:: python
>>> import os
>>> os.environ['DYLD_LIBRARY_PATH'] = '/path/to/MultiNest/lib'
>>> import species
Parameters
----------
tag : str
Database tag where the samples will be stored.
n_live_points : int
Number of live points.
output : str
Path that is used for the output files from MultiNest.
Returns
-------
NoneType
None
"""
print('Running nested sampling...')
# create the output folder if required
if not os.path.exists(output):
os.mkdir(output)
# create a dictionary with the cube indices of the parameters
cube_index = {}
for i, item in enumerate(self.modelpar):
cube_index[item] = i
def lnprior_multinest(cube, n_dim, n_param):
"""
Function to transform the unit cube into the parameter cube. It is not clear how to
pass additional arguments to the function, therefore it is placed here.
Parameters
----------
cube : pymultinest.run.LP_c_double
Unit cube.
Returns
-------
NoneType
None
"""
# Effective temperature (K)
cube[cube_index['teff']] = self.bounds['teff'][0] + \
(self.bounds['teff'][1]-self.bounds['teff'][0])*cube[cube_index['teff']]
# Surface gravity (dex)
cube[cube_index['logg']] = self.bounds['logg'][0] + \
(self.bounds['logg'][1]-self.bounds['logg'][0])*cube[cube_index['logg']]
# Radius (Rjup)
cube[cube_index['radius']] = self.bounds['radius'][0] + \
(self.bounds['radius'][1]-self.bounds['radius'][0])*cube[cube_index['radius']]
# Metallicity [Fe/H]
if 'feh' in self.bounds:
cube[cube_index['feh']] = self.bounds['feh'][0] + \
(self.bounds['feh'][1]-self.bounds['feh'][0])*cube[cube_index['feh']]
# C/O ratio
if 'co' in self.bounds:
cube[cube_index['co']] = self.bounds['co'][0] + \
(self.bounds['co'][1]-self.bounds['co'][0])*cube[cube_index['co']]
# Sedimentation parameter
if 'fsed' in self.bounds:
cube[cube_index['fsed']] = self.bounds['fsed'][0] + \
(self.bounds['fsed'][1]-self.bounds['fsed'][0])*cube[cube_index['fsed']]
# Spectrum scaling
if self.spectrum is not None:
for item in self.spectrum:
if f'scaling_{item}' in self.bounds:
cube[cube_index[f'scaling_{item}']] = self.bounds[f'scaling_{item}'][0] + \
(self.bounds[f'scaling_{item}'][1]-self.bounds[f'scaling_{item}'][0]) \
* cube[cube_index[f'scaling_{item}']]
def lnlike_multinest(cube, n_dim, n_param):
"""
Function for the logarithm of the likelihood, computed from the parameter cube.
Parameters
----------
cube : pymultinest.run.LP_c_double
Unit cube.
Returns
-------
float
The logarithm of the likelihood.
"""
paramdict = {}
spec_scaling = {}
for i, item in enumerate(self.modelpar):
if item == 'radius':
radius = cube[cube_index['radius']]
elif item[:8] == 'scaling_' and item[8:] in self.spectrum:
spec_scaling[item[8:]] = cube[cube_index[item]]
else:
paramdict[item] = cube[cube_index[item]]
scaling = (radius*constants.R_JUP)**2 / (self.distance[0]*constants.PARSEC)**2
chisq = 0.
if self.objphot is not None:
for i, item in enumerate(self.objphot):
flux = scaling * self.modelphot[i].spectrum_interp(list(paramdict.values()))
chisq += (item[0]-flux)**2 / item[1]**2
if self.spectrum is not None:
for i, item in enumerate(self.spectrum.keys()):
flux = scaling * self.modelspec[i].spectrum_interp(list(paramdict.values()))[0, :]
if item in spec_scaling:
flux_obs = spec_scaling[item]*self.spectrum[item][0][:, 1]
else:
flux_obs = self.spectrum[item][0][:, 1]
if self.spectrum[item][2] is not None:
spec_diff = flux_obs - flux
chisq += np.dot(spec_diff, np.dot(self.spectrum[item][2], spec_diff))
else:
chisq += np.nansum((flux_obs-flux)**2 / self.spectrum[item][0][:, 2]**2)
return -0.5*chisq
pymultinest.run(lnlike_multinest,
lnprior_multinest,
len(self.modelpar),
outputfiles_basename=output,
resume=False,
n_live_points=n_live_points)
samples = np.loadtxt(f'{output}/post_equal_weights.dat')
species_db = database.Database()
spec_labels = []
if self.spectrum is not None:
for item in self.spectrum:
if f'scaling_{item}' in self.bounds:
spec_labels.append(f'scaling_{item}')
else:
spec_labels = None
species_db.add_samples(sampler='multinest',
samples=samples[:, :-1],
ln_prob=samples[:, -1],
mean_accept=None,
spectrum=('model', self.model),
tag=tag,
modelpar=self.modelpar,
distance=self.distance[0],
spec_labels=spec_labels)