wale.ComputePDF module

class wale.ComputePDF.computePDF(variables, variance, plot_scgf=False)[source]

Bases: object

Compute the Probability Distribution Function (PDF) of the convergence field (kappa) using Large Deviation Theory (LDT) and the scaled cumulant generating function (SCGF).

This class takes a VariablesGenerator instance that encapsulates cosmological inputs, angular scales, redshift distributions, and lensing weights, along with a smoothed variance value.

The PDF is computed using the Legendre transform of the SCGF and the Bromwich integral.

variables

Contains all required parameters like angles, redshifts, chi, weights, and lambda grid.

Type:: VariablesGenerator

variance

Smoothed variance σ²_κ(θ) for the angular scale and filter used.

Type:: float

plot_scgf

Whether to plot the SCGF during PDF computation.

Type:: bool

pdf_values

Computed PDF values over the kappa grid.

Type:: list of float

kappa_values

Grid of kappa values over which the PDF is evaluated.

Type:: ndarray

Methods

`compute_pdf_for_kappa`(kappa, lambda_new, ...)	Evaluate the PDF at a given kappa using the inverse Laplace (Bromwich) integral.
`compute_pdf_values`()	Compute the PDF across a grid of kappa values using the Bromwich integral.
`compute_phi_values`()	Compute the Legendre-transformed function φ(λ) from the SCGF.
`get_scgf`()	Compute the scaled cumulant generating function (SCGF) for the given inputs.

compute_pdf_for_kappa(kappa, lambda_new, phi_values)[source]

Evaluate the PDF at a given kappa using the inverse Laplace (Bromwich) integral.

Parameters:

kappa (float) – Value of the convergence (κ) for which the PDF is evaluated.
lambda_new (ndarray) – Array of complex λ values.
phi_values (ndarray) – Corresponding φ(λ) values.

Returns:

pdf_kappa – Estimated value of the PDF at the given kappa.

Return type:

float

compute_pdf_values()[source]

Compute the PDF across a grid of kappa values using the Bromwich integral.

Returns:

pdf_values (list of float) – Evaluated PDF values.
kappa_values (ndarray) – Grid of kappa values over which the PDF is computed.

compute_phi_values()[source]

Compute the Legendre-transformed function φ(λ) from the SCGF.

Returns:

lambda_new (ndarray) – Imaginary grid of lambda values used for the inverse Laplace transform (Bromwich integral).
phi_values (ndarray) – Corresponding φ(λ) values used to compute the PDF.

get_scgf()[source]

Compute the scaled cumulant generating function (SCGF) for the given inputs.

Returns:: scgf – Array of SCGF values evaluated on the lambda grid.
Return type:: ndarray