"""Lensing filters.
This module computes different filters for the computation of the angular power
spectrum for the lensing potential.
"""
__version__ = '0.1.6'
__author__ = 'Lucia F. de la Bella'
__email__ = 'lucia.fonsecadelabella@manchester.ac.uk'
__license__ = 'MIT'
__copyright__ = '2020, Lucia Fonseca de la Bella'
__all__ = [
'lensing_efficiency',
'lensing_efficiency_cmb',
'filter_shear',
'filter_convergence',
'filter_galaxy_clustering',
]
import numpy as np
THREE_2C2 = 1.669e-11
INVERSE_C = 3.333e-6
mu = np.array([0.929, 1.278, 1.860, 2.473]) * 1000 / 0.7
eta = np.array([1.235, 0.832, 0.551, 0.412]) * 0.7 / 1000
alpha = 1.0 / (mu * eta - 1.0)
beta = eta / (mu * eta - 1.0)
[docs]def lensing_efficiency(x, zx, nz):
"""Lensing efficiency.
This function computes the general form of the lensing efficiency
function given in [1]_.
Parameters
----------
x: (nx,) array_like
Array of comoving distances at which evaluate the lensing
efficiency function.
zx: array_like
Array of redshift as a function of comoving distance.
nz : (nx, ) array_like
Array of redshift distribution of galaxies.
Returns
-------
efficiency: (nx,) array_like
Array of lensing efficiency values.
Examples
--------
>>> import numpy as np
>>> from astropy.cosmology import FlatLambdaCDM
>>> cosmo = FlatLambdaCDM(H0=67.11, Ob0=0.049, Om0= 0.2685)
>>> z_list = np.linspace(0, 1100,num=1000000)
>>> xl = cosmo.comoving_distance(z_list).value
>>> qf = lensing_efficiency(xl, 1)
References
----------
..[1] Lemos, P. and Challinor, A. and Efstathiou, G., 2017,
arXiv: 1704.01054.
"""
TINY = np.finfo(0.).tiny
return np.trapz(np.clip(x - x[:, None], 0, None) / (x + TINY) * nz, zx)
[docs]def lensing_efficiency_cmb(x, xs):
"""Parametric lensing efficiency cmb.
This function computes the cmb lensing efficiency
function given in [1]_.
Parameters
----------
x : (nx,) array_like
Array of comoving distances at which evaluate the lensing
efficiency function.
xs : float
Value of the comoving distance at the last scatering surface.
Returns
-------
efficiency: (nx,) array_like
Array of lensing efficiency values.
Examples
--------
>>> import numpy as np
>>> from astropy.cosmology import FlatLambdaCDM
>>> cosmo = FlatLambdaCDM(H0=67.11, Ob0=0.049, Om0= 0.2685)
>>> z_list = np.linspace(0, 1100,num=1000000)
>>> xs = 14000
>>> xl = cosmo.comoving_distance(z_list).value
>>> qf = lensing_efficiency_cmb(xl, xs)
References
----------
..[1] Hanson, D. and Challinor, A. and Lewis, A., 2010,
doi: 10.1007/s10714-010-1036-y.
"""
return 1.0 - x / xs
[docs]def filter_shear(x, zx, lens_efficiency, cosmology):
"""Filter for shear.
This function computes the filter for the shear power spectra,
described in [1]_.
Parameters
----------
x: (nx,) array_like
Array of comoving distances at which evaluate the lensing
efficiency function.
zx: array_like
Array of redshift as a function of comoving distance.
lens_efficiency: (nx,) array_like
Array of lensing efficiency values.
cosmology : astropy.cosmology.Cosmology
Cosmology object providing methods for the evolution history of
omega_matter and omega_lambda with redshift.
Returns
-------
filter: (nx,) array_like
Array of filter values.
Examples
--------
>>> import numpy as np
>>> from astropy.cosmology import FlatLambdaCDM
>>> cosmo = FlatLambdaCDM(H0=67.11, Ob0=0.049, Om0= 0.2685)
>>> z_list = np.linspace(0, 1100,num=1000000)
>>> xl = cosmo.comoving_distance(z_list).value
>>> q1 = lensing_efficiency(xl, 1)
>>> f1 = filter(xl, z_list, q1, cosmology)
References
----------
..[1] Lemos, P. and Challinor, A. and Efstathiou, G., 2017,
arXiv: 1704.01054.
"""
factor = THREE_2C2 * np.square(cosmology.H0) * cosmology.Om0
return factor.value * (1.0 + zx) * lens_efficiency / x
[docs]def filter_convergence(x, zx, lens_efficiency, cosmology):
"""Filter for convergence.
This function computes the filter for the convergenge power spectra,
described in [1]_.
Parameters
----------
x: (nx,) array_like
Array of comoving distances at which evaluate the lensing
efficiency function.
zx: array_like
Array of redshift as a function of comoving distance.
lens_efficiency: (nx,) array_like
Array of lensing efficiency values.
cosmology : astropy.cosmology.Cosmology
Cosmology object providing methods for the evolution history of
omega_matter and omega_lambda with redshift.
Returns
-------
filter: (nx,) array_like
Array of filter values.
Examples
--------
>>> import numpy as np
>>> from astropy.cosmology import FlatLambdaCDM
>>> cosmo = FlatLambdaCDM(H0=67.11, Ob0=0.049, Om0= 0.2685)
>>> z_list = np.linspace(0, 1100,num=1000000)
>>> xl = cosmo.comoving_distance(z_list).value
>>> q1 = lensing_efficiency(xl, 1)
>>> f1 = filter(xl, z_list, q1, cosmology)
References
----------
..[1] Kilbinger, M., 2014, doi: 10.1088/0034-4885/78/8/086901.
"""
factor = THREE_2C2 * np.square(cosmology.H0) * cosmology.Om0
return factor.value * (1.0 + zx) * lens_efficiency * x
[docs]def filter_galaxy_clustering(x, zx, nz, linear_bias, cosmology):
"""Filter for galaxy clustering.
This function computes filter for the galaxy clustering power spectra,
described in [1]_.
Parameters
----------
x : (nx,) array_like
Array of comoving distances at which evaluate the lensing
efficiency function.
zx : array_like
Array of redshift as a function of comoving distance.
nz: (nx,) array_like
Array of redshift distribution of galaxies.
linear_bias : float
Float for the value of the linear bias parameter.
cosmology : astropy.cosmology.Cosmology
Cosmology object providing methods for the evolution history of
omega_matter and omega_lambda with redshift.
Returns
-------
filter: (nx,) array_like
Array of filter values.
Examples
--------
>>> import numpy as np
>>> from astropy.cosmology import FlatLambdaCDM
>>> cosmo = FlatLambdaCDM(H0=67.11, Ob0=0.049, Om0= 0.2685)
>>> z_list = np.linspace(0, 1100,num=1000000)
>>> xl = cosmo.comoving_distance(z_list).value
>>> n1 = redshift_distribution_galaxies(xl, 1)
>>> f1 = filter(xl, z_list, n1, cosmo)
References
----------
..[1] Kilbinger, M., 2014, doi: 10.1088/0034-4885/78/8/086901.
"""
H = cosmology.H0 * cosmology.efunc(zx)
return H.value * linear_bias * nz * INVERSE_C
