ler.lens_galaxy_population.sampler_functions

Module for lens galaxy parameter sampling functions.

This module provides probability density functions (PDFs) and random variable samplers (RVS) for lens galaxy parameters including redshift, velocity dispersion, and axis ratio. It also includes rejection and importance sampling algorithms for sampling lens parameters weighted by gravitational lensing cross sections.

Key Components:

• Lens redshift samplers (SIS model from Haris et al. 2018)

• Velocity dispersion samplers (generalized gamma distribution)

• Axis ratio samplers (Rayleigh and Padilla-Strauss distributions)

• Rejection and importance sampling for cross-section weighted parameters

Copyright (C) 2026 Hemantakumar Phurailatpam. Distributed under MIT License.

Module Contents

Functions

available_sampler_list()	Return list of available lens parameter samplers.
lens_redshift_strongly_lensed_sis_haris_pdf(zl, zs[, ...])	Compute lens redshift PDF for SIS model (Haris et al. 2018).
lens_redshift_strongly_lensed_sis_haris_rvs(size, zs)	Sample lens redshifts for SIS model (Haris et al. 2018).
velocity_dispersion_ewoud_denisty_function(sigma, z[, ...])	Calculate the lens galaxy velocity dispersion function at redshift z (Oguri et al. (2018b) + Wempe et al. (2022)).
velocity_dispersion_bernardi_denisty_function(sigma, ...)	Calculate the local universe velocity dispersion function.
velocity_dispersion_gengamma_density_function(sigma[, ...])	Compute unnormalized velocity dispersion function using generalized gamma.
velocity_dispersion_gengamma_pdf(sigma[, sigma_min, ...])	Compute normalized velocity dispersion PDF using generalized gamma.
velocity_dispersion_gengamma_rvs(size[, sigma_min, ...])	Sample velocity dispersions from generalized gamma distribution.
axis_ratio_rayleigh_rvs(size, sigma[, q_min, q_max])	Sample axis ratios from velocity-dependent Rayleigh distribution.
axis_ratio_rayleigh_pdf(q, sigma[, q_min, q_max])	Compute truncated Rayleigh PDF for axis ratio.
axis_ratio_padilla_strauss_rvs(size)	Sample axis ratios from Padilla & Strauss (2008) distribution.
axis_ratio_padilla_strauss_pdf(q)	Compute axis ratio PDF from Padilla & Strauss (2008).
bounded_normal_sample(size, mean, std, low, high)	Sample from truncated normal distribution via rejection.
rejection_sampler(zs, zl, sigma_max, sigma_rvs, q_rvs, ...)	Core rejection sampling algorithm for lens parameters.
create_rejection_sampler(sigma_max, sigma_rvs, q_rvs, ...)	Create a rejection sampler for cross-section weighted lens parameters.
importance_sampler(zs, zl, sigma_min, sigma_max, ...)	Core importance sampling algorithm for lens parameters.
importance_sampler_mp(zs, zl, sigma_min, sigma_max, ...)	Multiprocessing version of importance sampling for lens parameters.
create_importance_sampler(sigma_min, sigma_max, q_rvs, ...)	Create an importance sampler for cross-section weighted lens parameters.

ler.lens_galaxy_population.sampler_functions.available_sampler_list()

Return list of available lens parameter samplers.

Returns:

sampler_listlist

List of available sampler function names.

Examples

>>> samplers = available_sampler_list()
>>> print(samplers)
['lens_redshift_strongly_lensed_sis_haris', 'velocity_dispersion_gengamma', 'axis_ratio_rayleigh', 'axis_ratio_padilla_strauss']

ler.lens_galaxy_population.sampler_functions.lens_redshift_strongly_lensed_sis_haris_pdf(zl, zs, cosmo=LambdaCDM(H0=70, Om0=0.3, Ode0=0.7, Tcmb0=0.0, Neff=3.04, m_nu=None, Ob0=0.0))

Compute lens redshift PDF for SIS model (Haris et al. 2018).

Computes the probability density function for lens redshift between zl=0 and zl=zs using the analytical form from Haris et al. (2018) equation A7, based on the SIS (Singular Isothermal Sphere) lens model.

Parameters:

zlfloat

Redshift of the lens galaxy.

zsfloat

Redshift of the source.

cosmoastropy.cosmology

Cosmology object for distance calculations.

default: LambdaCDM(H0=70, Om0=0.3, Ode0=0.7, Tcmb0=0.0, Neff=3.04, m_nu=None, Ob0=0.0)

Returns:

pdffloat

Probability density at the given lens redshift.

Examples

>>> from astropy.cosmology import LambdaCDM
>>> cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7, Tcmb0=0.0, Neff=3.04, m_nu=None, Ob0=0.0)
>>> pdf = lens_redshift_strongly_lensed_sis_haris_pdf(zl=0.5, zs=1.0, cosmo=cosmo)
>>> print(f"PDF at zl=0.5: {pdf:.4f}")
PDF at zl=0.5: 1.8750

ler.lens_galaxy_population.sampler_functions.lens_redshift_strongly_lensed_sis_haris_rvs(size, zs, z_min=0.001, z_max=10.0, cosmo=LambdaCDM(H0=70, Om0=0.3, Ode0=0.7, Tcmb0=0.0, Neff=3.04, m_nu=None, Ob0=0.0))

Sample lens redshifts for SIS model (Haris et al. 2018).

Uses inverse transform sampling with the analytical CDF of the Haris et al. (2018) lens redshift distribution to efficiently generate samples.

Parameters:

sizeint

Number of samples to draw.

zsfloat

Redshift of the source.

z_minfloat

Minimum redshift for interpolation grid.

default: 0.001

z_maxfloat

Maximum redshift for interpolation grid.

default: 10.0

cosmoastropy.cosmology

Cosmology object for distance calculations.

default: LambdaCDM(H0=70, Om0=0.3, Ode0=0.7, Tcmb0=0.0, Neff=3.04, m_nu=None, Ob0=0.0)

Returns:

zlnumpy.ndarray

Array of sampled lens redshifts with shape (size,).

Examples

>>> from astropy.cosmology import LambdaCDM
>>> cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7, Tcmb0=0.0, Neff=3.04, m_nu=None, Ob0=0.0)
>>> zl_samples = lens_redshift_strongly_lensed_sis_haris_rvs(
...     size=1000,
...     zs=1.5,
...     z_min=0.001,
...     z_max=10.0,
...     cosmo=cosmo,
... )
>>> print(f"Mean lens redshift: {zl_samples.mean():.2f}")
>>> print(f"Redshift range: [{zl_samples.min():.3f}, {zl_samples.max():.3f}]")

ler.lens_galaxy_population.sampler_functions.velocity_dispersion_ewoud_denisty_function(sigma, z, alpha=0.94, beta=1.85, phistar=0.02099, sigmastar=113.78)

Calculate the lens galaxy velocity dispersion function at redshift z (Oguri et al. (2018b) + Wempe et al. (2022)).

Parameters:

sigmanumpy.ndarray

Velocity dispersion of the lens galaxy (km/s).

zfloat

Redshift of the lens galaxy.

alphafloat

Shape parameter of the velocity dispersion function.

default: 0.94

betafloat

Slope parameter of the velocity dispersion function.

default: 1.85

phistarfloat

Normalization of the velocity dispersion function (Mpc^-3).

default: 2.099e-2

sigmastarfloat

Characteristic velocity dispersion (km/s).

default: 113.78

Returns:

resultnumpy.ndarray

Velocity dispersion function values.

Negative values are clipped to 0.

ler.lens_galaxy_population.sampler_functions.velocity_dispersion_bernardi_denisty_function(sigma, alpha, beta, phistar, sigmastar)

Calculate the local universe velocity dispersion function.

This implements the velocity dispersion function from Bernardi et al. (2010).

Parameters:

sigmanumpy.ndarray

Velocity dispersion of the lens galaxy (km/s).

alphafloat

Shape parameter (alpha/beta is used in the gamma function).

For Oguri et al. (2018b): alpha=0.94

For Choi et al. (2008): alpha=2.32/2.67

betafloat

Slope parameter of the velocity dispersion function.

For Oguri et al. (2018b): beta=1.85

For Choi et al. (2008): beta=2.67

phistarfloat

Normalization of the velocity dispersion function (Mpc^-3).

For Oguri et al. (2018b): phistar=2.099e-2*(h/0.7)^3

For Choi et al. (2008): phistar=8.0e-3*h^3

sigmastarfloat

Characteristic velocity dispersion (km/s).

For Oguri et al. (2018b): sigmastar=113.78

For Choi et al. (2008): sigmastar=161.0

Returns:

philocnumpy.ndarray

Local velocity dispersion function values.

ler.lens_galaxy_population.sampler_functions.velocity_dispersion_gengamma_density_function(sigma, alpha=0.94, beta=1.85, phistar=0.02099, sigmastar=113.78, **kwargs)

Compute unnormalized velocity dispersion function using generalized gamma.

Computes the galaxy velocity dispersion function (VDF) using the generalized gamma distribution formulation from Choi et al. (2007).

Parameters:

sigmafloat or numpy.ndarray

Velocity dispersion in km/s.

alphafloat

Power-law index governing the low-velocity slope.

default: 0.94

betafloat

Exponential parameter for high-velocity cutoff sharpness.

default: 1.85

phistarfloat

Normalization constant (comoving number density, Mpc^-3).

default: 8.0e-3

sigmastarfloat

Characteristic velocity scale in km/s.

default: 113.78

Returns:

densityfloat or numpy.ndarray

Unnormalized velocity dispersion function value.

Examples

>>> import numpy as np
>>> sigma = np.array([150.0, 200.0, 250.0])
>>> density = velocity_dispersion_gengamma_density_function(sigma)
>>> print(f"Density at sigma=200 km/s: {density[1]:.6f}")

ler.lens_galaxy_population.sampler_functions.velocity_dispersion_gengamma_pdf(sigma, sigma_min=100.0, sigma_max=400.0, alpha=0.94, beta=1.85, sigmastar=113.78)

Compute normalized velocity dispersion PDF using generalized gamma.

Computes the probability density function for velocity dispersion using the generalized gamma distribution, normalized over the specified range.

Parameters:

sigmafloat or numpy.ndarray

Velocity dispersion in km/s.

sigma_minfloat

Minimum velocity dispersion for normalization (km/s).

default: 100.0

sigma_maxfloat

Maximum velocity dispersion for normalization (km/s).

default: 400.0

alphafloat

Power-law index governing the low-velocity slope.

default: 0.94

betafloat

Exponential parameter for high-velocity cutoff sharpness.

default: 1.85

sigmastarfloat

Characteristic velocity scale in km/s.

default: 113.78

Returns:

pdffloat or numpy.ndarray

Normalized probability density at the given velocity dispersion.

Examples

>>> pdf = velocity_dispersion_gengamma_pdf(
...     sigma=200.0,
...     sigma_min=100.0,
...     sigma_max=400.0,
... )
>>> print(f"PDF at sigma=200 km/s: {pdf:.6f}")

ler.lens_galaxy_population.sampler_functions.velocity_dispersion_gengamma_rvs(size, sigma_min=100.0, sigma_max=400.0, alpha=0.94, beta=1.85, sigmastar=113.78)

Sample velocity dispersions from generalized gamma distribution.

Uses truncated generalized gamma sampling via rejection to generate velocity dispersion samples within the specified bounds.

Parameters:

sizeint

Number of samples to draw.

sigma_minfloat

Minimum velocity dispersion (km/s).

default: 100.0

sigma_maxfloat

Maximum velocity dispersion (km/s).

default: 400.0

alphafloat

Power-law index governing the low-velocity slope.

default: 0.94

betafloat

Exponential parameter for high-velocity cutoff sharpness.

default: 1.85

sigmastarfloat

Characteristic velocity scale in km/s.

default: 113.78

Returns:

sigmanumpy.ndarray

Sampled velocity dispersions in km/s with shape (size,).

Examples

>>> sigma_samples = velocity_dispersion_gengamma(
...     size=1000,
...     sigma_min=100.0,
...     sigma_max=400.0,
... )
>>> print(f"Mean sigma: {sigma_samples.mean():.2f} km/s")
>>> print(f"Range: [{sigma_samples.min():.1f}, {sigma_samples.max():.1f}] km/s")

ler.lens_galaxy_population.sampler_functions.axis_ratio_rayleigh_rvs(size, sigma, q_min=0.2, q_max=1.0)

Sample axis ratios from velocity-dependent Rayleigh distribution.

Generates axis ratio samples using the Rayleigh distribution with scale parameter dependent on velocity dispersion, as described in Wierda et al. (2021) Appendix C.

Parameters:

sizeint

Number of samples to draw.

sigmanumpy.ndarray

Velocity dispersions in km/s with shape (size,).

q_minfloat

Minimum allowed axis ratio.

default: 0.2

q_maxfloat

Maximum allowed axis ratio.

default: 1.0

Returns:

qnumpy.ndarray

Sampled axis ratios with shape (size,).

Examples

>>> import numpy as np
>>> sigma = np.random.uniform(100, 300, 1000)
>>> q_samples = axis_ratio_rayleigh_rvs(size=1000, sigma=sigma, q_min=0.2, q_max=1.0)
>>> print(f"Mean axis ratio: {q_samples.mean():.2f}")
>>> print(f"Range: [{q_samples.min():.2f}, {q_samples.max():.2f}]")

ler.lens_galaxy_population.sampler_functions.axis_ratio_rayleigh_pdf(q, sigma, q_min=0.2, q_max=1.0)

Compute truncated Rayleigh PDF for axis ratio.

Computes the probability density function for axis ratio using the truncated Rayleigh distribution with velocity-dependent scale parameter (Wierda et al. 2021 equation C16).

Parameters:

qnumpy.ndarray

Axis ratios at which to evaluate PDF.

sigmanumpy.ndarray

Velocity dispersions in km/s (same shape as q).

q_minfloat

Minimum axis ratio for truncation.

default: 0.2

q_maxfloat

Maximum axis ratio for truncation.

default: 1.0

Returns:

pdfnumpy.ndarray

Probability density values with same shape as q.

Examples

>>> import numpy as np
>>> q = np.array([0.5, 0.7, 0.9])
>>> sigma = np.array([150.0, 200.0, 250.0])
>>> pdf = axis_ratio_rayleigh_pdf(q, sigma)
>>> print(f"PDF values: {pdf}")

ler.lens_galaxy_population.sampler_functions.axis_ratio_padilla_strauss_rvs(size)

Sample axis ratios from Padilla & Strauss (2008) distribution.

Uses inverse transform sampling with the empirical PDF from Padilla & Strauss (2008) for early-type galaxy axis ratios.

Parameters:

sizeint

Number of samples to draw.

Returns:

qnumpy.ndarray

Sampled axis ratios with shape (size,).

Examples

>>> q_samples = axis_ratio_padilla_strauss_rvs(size=1000)
>>> print(f"Mean axis ratio: {q_samples.mean():.2f}")
>>> print(f"Range: [{q_samples.min():.2f}, {q_samples.max():.2f}]")

ler.lens_galaxy_population.sampler_functions.axis_ratio_padilla_strauss_pdf(q)

Compute axis ratio PDF from Padilla & Strauss (2008).

Evaluates the probability density function for axis ratio using cubic spline interpolation of the Padilla & Strauss (2008) data.

Parameters:

qnumpy.ndarray

Axis ratios at which to evaluate PDF.

Returns:

pdfnumpy.ndarray

Probability density values with same shape as q.

Examples

>>> import numpy as np
>>> q = np.array([0.3, 0.5, 0.7, 0.9])
>>> pdf = axis_ratio_padilla_strauss_pdf(q)
>>> print(f"PDF at q=0.5: {pdf[1]:.4f}")

ler.lens_galaxy_population.sampler_functions.bounded_normal_sample(size, mean, std, low, high)

Sample from truncated normal distribution via rejection.

Generates samples from a normal distribution with specified mean and standard deviation, rejecting samples outside the specified bounds.

Parameters:

sizeint

Number of samples to draw.

meanfloat

Mean of the normal distribution.

stdfloat

Standard deviation of the normal distribution.

lowfloat

Lower bound for samples.

highfloat

Upper bound for samples.

Returns:

samplesnumpy.ndarray

Bounded normal samples with shape (size,).

Examples

>>> samples = bounded_normal_sample(size=1000, mean=2.0, std=0.2, low=1.5, high=2.5)
>>> print(f"Mean: {samples.mean():.2f}, Std: {samples.std():.2f}")
>>> print(f"Range: [{samples.min():.2f}, {samples.max():.2f}]")

ler.lens_galaxy_population.sampler_functions.rejection_sampler(zs, zl, sigma_max, sigma_rvs, q_rvs, phi_rvs, gamma_rvs, shear_rvs, cross_section, safety_factor=1.2)

Core rejection sampling algorithm for lens parameters.

Parameters:

zsnumpy.ndarray

Source redshifts.

zlnumpy.ndarray

Lens redshifts.

sigma_maxfloat

Maximum velocity dispersion (km/s) for computing upper bound.

sigma_rvscallable

Function to sample velocity dispersion: sigma_rvs(n, zl) -> array.

q_rvscallable

Function to sample axis ratio: q_rvs(n, sigma) -> array.

phi_rvscallable

Function to sample orientation angle: phi_rvs(n) -> array.

gamma_rvscallable

Function to sample power-law index: gamma_rvs(n) -> array.

shear_rvscallable

Function to sample external shear: shear_rvs(n) -> (gamma1, gamma2).

cross_sectioncallable

Function to compute lensing cross section.

safety_factorfloat

Multiplicative safety factor for the upper bound.

default: 1.2

Returns:

sigma_arraynumpy.ndarray

Sampled velocity dispersions (km/s).

q_arraynumpy.ndarray

Sampled axis ratios.

phi_arraynumpy.ndarray

Sampled orientation angles (rad).

gamma_arraynumpy.ndarray

Sampled power-law indices.

gamma1_arraynumpy.ndarray

Sampled external shear component 1.

gamma2_arraynumpy.ndarray

Sampled external shear component 2.

ler.lens_galaxy_population.sampler_functions.create_rejection_sampler(sigma_max, sigma_rvs, q_rvs, phi_rvs, gamma_rvs, shear_rvs, cross_section, safety_factor=1.2, use_njit_sampler=True)

Create a rejection sampler for cross-section weighted lens parameters.

Returns a callable that samples lens parameters using rejection sampling, weighting by the gravitational lensing cross section. Optionally uses Numba JIT compilation for improved performance.

Parameters:

sigma_maxfloat

Maximum velocity dispersion (km/s) for computing upper bound.

sigma_rvscallable

Function to sample velocity dispersion: sigma_rvs(n, zl) -> array.

q_rvscallable

Function to sample axis ratio: q_rvs(n, sigma) -> array.

phi_rvscallable

Function to sample orientation angle: phi_rvs(n) -> array.

gamma_rvscallable

Function to sample power-law index: gamma_rvs(n) -> array.

shear_rvscallable

Function to sample external shear: shear_rvs(n) -> (gamma1, gamma2).

cross_sectioncallable

Function to compute lensing cross section.

safety_factorfloat

Multiplicative safety factor for the upper bound.

default: 1.2

use_njit_samplerbool

If True, uses Numba JIT compilation for faster execution.

default: True

Returns:

rejection_sampler_wrappercallable

Function with signature (zs, zl) -> (sigma, q, phi, gamma, gamma1, gamma2).

Examples

>>> import numpy as np
>>> from numba import njit
>>> @njit
... def sigma_rvs(n, zl):
...     return 100 + 200 * np.random.random(n)
>>> @njit
... def q_rvs(n, sigma):
...     return 0.5 + 0.5 * np.random.random(n)
>>> @njit
... def phi_rvs(n):
...     return np.pi * np.random.random(n)
>>> @njit
... def gamma_rvs(n):
...     return 2.0 + 0.2 * np.random.randn(n)
>>> @njit
... def shear_rvs(n):
...     return 0.05 * np.random.randn(n), 0.05 * np.random.randn(n)
>>> @njit
... def cross_section(zs, zl, sigma, q, phi, gamma, gamma1, gamma2):
...     return sigma**4
>>> sampler = create_rejection_sampler(
...     sigma_max=400.0,
...     sigma_rvs=sigma_rvs,
...     q_rvs=q_rvs,
...     phi_rvs=phi_rvs,
...     gamma_rvs=gamma_rvs,
...     shear_rvs=shear_rvs,
...     cross_section=cross_section,
... )
>>> zs = np.array([1.0, 1.5, 2.0])
>>> zl = np.array([0.3, 0.5, 0.7])
>>> sigma, q, phi, gamma, gamma1, gamma2 = sampler(zs, zl)

ler.lens_galaxy_population.sampler_functions.importance_sampler(zs, zl, sigma_min, sigma_max, q_rvs, phi_rvs, gamma_rvs, shear_rvs, number_density, cross_section, n_prop)

Core importance sampling algorithm for lens parameters.

This function samples lens galaxy parameters weighted by their lensing cross sections using importance sampling with a uniform proposal distribution for velocity dispersion.

Parameters:

zsnumpy.ndarray

Source redshifts.

zlnumpy.ndarray

Lens redshifts.

sigma_minfloat

Minimum velocity dispersion (km/s) for uniform proposal.

sigma_maxfloat

Maximum velocity dispersion (km/s) for uniform proposal.

q_rvscallable

Function to sample axis ratio: q_rvs(n, sigma) -> array.

phi_rvscallable

Function to sample orientation angle: phi_rvs(n) -> array.

gamma_rvscallable

Function to sample power-law index: gamma_rvs(n) -> array.

shear_rvscallable

Function to sample external shear: shear_rvs(n) -> (gamma1, gamma2).

number_densitycallable

Number density or velocity dispersion function: number_density(sigma, zl) -> array.

cross_sectioncallable

Function to compute lensing cross section.

n_propint

Number of proposal samples per lens.

Returns:

sigma_postnumpy.ndarray

Sampled velocity dispersions (km/s).

q_postnumpy.ndarray

Sampled axis ratios.

phi_postnumpy.ndarray

Sampled orientation angles (rad).

gamma_postnumpy.ndarray

Sampled power-law indices.

gamma1_postnumpy.ndarray

Sampled external shear component 1.

gamma2_postnumpy.ndarray

Sampled external shear component 2.

ler.lens_galaxy_population.sampler_functions.importance_sampler_mp(zs, zl, sigma_min, sigma_max, q_rvs, phi_rvs, gamma_rvs, shear_rvs, number_density, cross_section, n_prop, npool=4)

Multiprocessing version of importance sampling for lens parameters.

Parameters:

zsnumpy.ndarray

Source redshifts.

zlnumpy.ndarray

Lens redshifts.

sigma_minfloat

Minimum velocity dispersion (km/s) for uniform proposal.

sigma_maxfloat

Maximum velocity dispersion (km/s) for uniform proposal.

q_rvscallable

Function to sample axis ratio: q_rvs(n, sigma) -> array.

phi_rvscallable

Function to sample orientation angle: phi_rvs(n) -> array.

gamma_rvscallable

Function to sample power-law index: gamma_rvs(n) -> array.

shear_rvscallable

Function to sample external shear: shear_rvs(n) -> (gamma1, gamma2).

number_densitycallable

Number density or velocity dispersion function: number_density(sigma, zl) -> array.

cross_sectioncallable

Function to compute lensing cross section.

n_propint

Number of proposal samples per lens.

npoolint

Number of parallel processes to use.

default: 4

Returns:

sigma_postnumpy.ndarray

Sampled velocity dispersions (km/s).

q_postnumpy.ndarray

Sampled axis ratios.

phi_postnumpy.ndarray

Sampled orientation angles (rad).

gamma_postnumpy.ndarray

Sampled power-law indices.

gamma1_postnumpy.ndarray

Sampled external shear component 1.

gamma2_postnumpy.ndarray

Sampled external shear component 2.

ler.lens_galaxy_population.sampler_functions.create_importance_sampler(sigma_min, sigma_max, q_rvs, phi_rvs, gamma_rvs, shear_rvs, number_density, cross_section, n_prop, use_njit_sampler=True, npool=4)

Create an importance sampler for cross-section weighted lens parameters.

Returns a callable that samples lens parameters using importance sampling with uniform proposal distribution, optionally JIT-compiled for improved performance.

Parameters:

sigma_minfloat

Minimum velocity dispersion (km/s) for uniform proposal.

sigma_maxfloat

Maximum velocity dispersion (km/s) for uniform proposal.

q_rvscallable

Function to sample axis ratio: q_rvs(n, sigma) -> array.

phi_rvscallable

Function to sample orientation angle: phi_rvs(n) -> array.

gamma_rvscallable

Function to sample power-law index: gamma_rvs(n) -> array.

shear_rvscallable

Function to sample external shear: shear_rvs(n) -> (gamma1, gamma2).

number_densitycallable

Number density or velocity dispersion function: number_density(sigma, zl) -> array.

cross_sectioncallable

Function to compute lensing cross section.

n_propint

Number of proposal samples per lens.

use_njit_samplerbool

If True, uses Numba JIT compilation for faster execution.

default: True

npoolint

Number of parallel processes (only used when use_njit_sampler=False).

default: 4

Returns:

importance_sampler_wrappercallable

Function with signature (zs, zl) -> (sigma, q, phi, gamma, gamma1, gamma2).

Examples

>>> import numpy as np
>>> from numba import njit
>>> @njit
... def q_rvs(n, sigma):
...     return 0.5 + 0.5 * np.random.random(n)
>>> @njit
... def phi_rvs(n):
...     return np.pi * np.random.random(n)
>>> @njit
... def gamma_rvs(n):
...     return 2.0 + 0.2 * np.random.randn(n)
>>> @njit
... def shear_rvs(n):
...     return 0.05 * np.random.randn(n), 0.05 * np.random.randn(n)
>>> @njit
... def number_density(sigma, zl):
...     return np.ones_like(sigma)
>>> @njit
... def cross_section(zs, zl, sigma, q, phi, gamma, gamma1, gamma2):
...     return sigma**4
>>> sampler = create_importance_sampler(
...     sigma_min=100.0,
...     sigma_max=400.0,
...     q_rvs=q_rvs,
...     phi_rvs=phi_rvs,
...     gamma_rvs=gamma_rvs,
...     shear_rvs=shear_rvs,
...     number_density=number_density,
...     cross_section=cross_section,
...     n_prop=100,
... )
>>> zs = np.array([1.0, 1.5, 2.0])
>>> zl = np.array([0.3, 0.5, 0.7])
>>> sigma, q, phi, gamma, gamma1, gamma2 = sampler(zs, zl)