Source code for beast.physicsmodel.grid_and_prior_weights
"""
Grid and Prior Weights
======================
The use of a non-uniformly spaced grid complicates the marginalization
step as the trick of summation instead of integration is used. But this
trick only works when the grid is uniformaly spaced in all dimensions.
If the grid is not uniformally spaced, weights can be used to correct
for the non-uniform spacing.
Basically, we want the maginalization using these grid weights to provide
flat priors on all the fit parameters. Non-flat priors will be implemented
with prior weights.
"""
import numpy as np
from beast.physicsmodel.grid_weights_stars import compute_distance_grid_weights
from beast.physicsmodel.grid_weights_stars import compute_age_grid_weights
from beast.physicsmodel.grid_weights_stars import compute_mass_grid_weights
from beast.physicsmodel.grid_weights_stars import compute_metallicity_grid_weights
from beast.physicsmodel.priormodel import (
PriorAgeModel,
PriorMassModel,
PriorMetallicityModel,
PriorDistanceModel,
)
__all__ = [
"compute_age_mass_metallicity_weights",
"compute_distance_age_mass_metallicity_weights",
]
[docs]def compute_distance_age_mass_metallicity_weights(
_tgrid,
distance_prior_model={"name": "flat"},
age_prior_model={"name": "flat"},
mass_prior_model={"name": "kroupa"},
met_prior_model={"name": "flat"},
):
"""
Computes the distance and age-mass-metallicity grid
and prior weights on the BEAST model spectra grid
Parameters
----------
_tgrid : BEAST model spectra grid.
distance_prior_model,
age_prior_model,
mass_prior_model,
met_prior_model: dict
dict including prior model name and parameters
Returns
-------
Grid and prior weight columns updated by multiplying by the
the distance and age-mass-metallicity weight.
"""
# get the unique distances
uniq_dists = np.unique(_tgrid["distance"])
# setup the vector to hold the distance weight vectors
n_dist = len(uniq_dists)
total_dist_grid_weight = np.zeros((n_dist))
total_dist_prior_weight = np.zeros((n_dist))
total_dist_weight = np.zeros((n_dist))
for dz, dist_val in enumerate(uniq_dists):
print("computing the distance plus weights for dist = ", dist_val)
(dindxs,) = np.where(_tgrid["distance"] == dist_val)
compute_age_mass_metallicity_weights(
_tgrid,
dindxs,
age_prior_model=age_prior_model,
mass_prior_model=mass_prior_model,
met_prior_model=met_prior_model,
)
total_dist_grid_weight[dz] = np.sum(_tgrid[dindxs]["grid_weight"])
total_dist_prior_weight[dz] = np.sum(_tgrid[dindxs]["prior_weight"])
total_dist_weight[dz] = np.sum(_tgrid[dindxs]["weight"])
# ensure that the distance prior is uniform
if n_dist > 1:
# get the distance weights
dist_grid_weights = compute_distance_grid_weights(uniq_dists)
dist_grid_weights /= np.sum(dist_grid_weights)
dist_prior = PriorDistanceModel(distance_prior_model)
dist_prior_weights = dist_prior(uniq_dists)
dist_prior_weights /= np.sum(dist_prior_weights)
dist_weights = dist_grid_weights * dist_prior_weights
# correct for any non-unformity in the number size of the
# age-mass grids between metallicity points
total_dist_grid_weight /= np.sum(total_dist_grid_weight)
total_dist_prior_weight /= np.sum(total_dist_prior_weight)
total_dist_weight /= np.sum(total_dist_weight)
for i, dist_val in enumerate(uniq_dists):
# get the grid for this distance
(dindxs,) = np.where(_tgrid["distance"] == dist_val)
_tgrid[dindxs]["grid_weight"] *= (
dist_grid_weights[i] * total_dist_grid_weight[i]
)
_tgrid[dindxs]["prior_weight"] *= (
dist_prior_weights[i] * total_dist_prior_weight[i]
)
_tgrid[dindxs]["weight"] *= dist_weights[i] * total_dist_weight[i]
[docs]def compute_age_mass_metallicity_weights(
_tgrid,
indxs,
age_prior_model={"name": "flat"},
mass_prior_model={"name": "kroupa"},
met_prior_model={"name": "flat"},
**kwargs
):
"""
Computes the age-mass-metallicity grid and prior weights
on the BEAST model spectra grid
Grid and prior weight columns updated by multiplying by the
age-mass-metallicity weight.
Parameters
----------
_tgrid : SpectralGrid
BEAST models spectral grid
age_prior_model : dict
dict including prior model name and parameters
mass_prior_model : dict
dict including prior model name and parameters
met_prior_model : dict
dict including prior model name and parameters
"""
# get the unique metallicities
uniq_Zs = np.unique(_tgrid[indxs]["Z"])
# setup the vector to hold the z weight vector
total_z_grid_weight = np.zeros(len(uniq_Zs))
total_z_prior_weight = np.zeros(len(uniq_Zs))
total_z_weight = np.zeros(len(uniq_Zs))
for az, z_val in enumerate(uniq_Zs):
print("computing the age-mass-metallicity grid weight for Z = ", z_val)
# get the grid for a single metallicity
(zindxs,) = np.where(_tgrid[indxs]["Z"] == z_val)
# get the unique ages for this metallicity
zindxs = indxs[zindxs]
uniq_ages = np.unique(_tgrid[zindxs]["logA"])
# compute the age weights
age_grid_weights = compute_age_grid_weights(uniq_ages)
age_prior = PriorAgeModel(age_prior_model)
age_prior_weights = age_prior(uniq_ages)
for ak, age_val in enumerate(uniq_ages):
# get the grid for a single age
(aindxs,) = np.where(
(_tgrid[indxs]["logA"] == age_val) & (_tgrid[indxs]["Z"] == z_val)
)
aindxs = indxs[aindxs]
_tgrid_single_age = _tgrid[aindxs]
# compute the mass weights
if len(aindxs) > 1:
cur_masses = _tgrid_single_age["M_ini"]
mass_grid_weights = compute_mass_grid_weights(cur_masses)
mass_prior = PriorMassModel(mass_prior_model)
mass_prior_weights = mass_prior(cur_masses)
else:
# must be a single mass for this age,z combination
# set mass weight to zero to remove this point from the grid
mass_grid_weights = np.zeros(1)
mass_prior_weights = np.zeros(1)
# apply both the mass and age weights
for i, k in enumerate(aindxs):
comb_grid_weights = mass_grid_weights[i] * age_grid_weights[ak]
comb_prior_weights = mass_prior_weights[i] * age_prior_weights[ak]
_tgrid[k]["grid_weight"] *= comb_grid_weights
_tgrid[k]["prior_weight"] *= comb_prior_weights
_tgrid[k]["weight"] *= comb_grid_weights * comb_prior_weights
# compute the current total weight at each metallicity
total_z_grid_weight[az] = np.sum(_tgrid[zindxs]["grid_weight"])
total_z_prior_weight[az] = np.sum(_tgrid[zindxs]["prior_weight"])
total_z_weight[az] = np.sum(_tgrid[zindxs]["weight"])
# ensure that the metallicity prior is uniform
if len(uniq_Zs) > 1:
# get the metallicity weights
met_grid_weights = compute_metallicity_grid_weights(uniq_Zs)
met_grid_weights /= np.sum(met_grid_weights)
met_prior = PriorMetallicityModel(met_prior_model)
met_prior_weights = met_prior(uniq_Zs)
met_prior_weights /= np.sum(met_prior_weights)
met_weights = met_grid_weights * met_prior_weights
# correct for any non-unformity in the number size of the
# age-mass grids between metallicity points
total_z_grid_weight /= np.sum(total_z_grid_weight)
total_z_prior_weight /= np.sum(total_z_prior_weight)
total_z_weight /= np.sum(total_z_weight)
for i, z_val in enumerate(uniq_Zs):
# get the grid for this metallicity
(zindxs,) = np.where(_tgrid[indxs]["Z"] == z_val)
zindxs = indxs[zindxs]
_tgrid[zindxs]["grid_weight"] *= (
met_grid_weights[i] * total_z_grid_weight[i]
)
_tgrid[zindxs]["prior_weight"] *= (
met_prior_weights[i] * total_z_prior_weight[i]
)
_tgrid[zindxs]["weight"] *= met_weights[i] * total_z_weight[i]