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import numpy as np
from astropy.cosmology import FlatLambdaCDM
from ..density_estimation import FunctionDistribution
from sklearn.utils import check_random_state
def redshift_distribution(z, z0):
return (z / z0) ** 2 * np.exp(-1.5 * (z / z0))
def generate_mu_z(size=1000, z0=0.3, dmu_0=0.1, dmu_1=0.02,
random_state=None, cosmo=None):
"""Generate a dataset of distance modulus vs redshift.
Parameters
----------
size : int or tuple
size of generated data
z0 : float
parameter in redshift distribution:
p(z) ~ (z / z0)^2 exp[-1.5 (z / z0)]
dmu_0, dmu_1 : float
specify the error in mu, dmu = dmu_0 + dmu_1 * mu
random_state : None, int, or np.random.RandomState instance
random seed or random number generator
cosmo : astropy.cosmology instance specifying cosmology
to use when generating the sample. If not provided,
a Flat Lambda CDM model with H0=71, Om0=0.27, Tcmb=0 is used.
Returns
-------
z, mu, dmu : ndarrays
arrays of shape ``size``
"""
if cosmo is None:
cosmo = FlatLambdaCDM(H0=71, Om0=0.27, Tcmb0=0)
random_state = check_random_state(random_state)
zdist = FunctionDistribution(redshift_distribution, func_args=dict(z0=z0),
xmin=0.1 * z0, xmax=10 * z0,
random_state=random_state)
z_sample = zdist.rvs(size)
mu_sample = cosmo.distmod(z_sample).value
dmu = dmu_0 + dmu_1 * mu_sample
mu_sample = random_state.normal(mu_sample, dmu)
return z_sample, mu_sample, dmu
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