wale.CommonUtils module

wale.CommonUtils.apply_pixel_window(ells, theta_deg=10.0, npix=1200)[source]

Compute the pixel window function for a square map and apply it to multipoles.

Parameters:

  • ells (array_like) – Multipole values (ℓ) at which the window function is evaluated.

  • theta_deg (float, optional) – Total angular size of the map in degrees (default is 10.0).

  • npix (int, optional) – Number of pixels per side of the square map (default is 1200).

Returns:

W_ell – The pixel window function evaluated at each ℓ.

Return type:

ndarray

wale.CommonUtils.compute_sigma_kappa_squared(theta_arcmin, chis, lensingweights, redshifts, k, pnl, filter_type, h)[source]

Compute the smoothed convergence variance σ²_κ(θ) at a given angular scale using a filter.

This function computes the convergence power spectrum P_κ(ℓ) from a 3D P(k, z) and integrates over ℓ using a top-hat or starlet filter.

Parameters:

  • theta_arcmin (float) – Angular smoothing scale θ in arcminutes.

  • chis (ndarray) – Comoving distances χ (in Mpc) corresponding to redshifts.

  • lensingweights (ndarray) – Lensing kernel W(χ) evaluated at each χ.

  • redshifts (ndarray) – Redshifts corresponding to chis.

  • k (ndarray) – Wavenumber grid (in h/Mpc).

  • pnl (2D ndarray) – Nonlinear power spectrum P(k, z), shape (n_z, len(k)).

  • filter_type (str) – Type of filter to apply (“tophat” or “starlet”).

  • h (float) – Reduced Hubble constant (H0 / 100).

Returns:

sigma2 – Smoothed convergence variance σ²_κ(θ).

Return type:

float

wale.CommonUtils.fourier_coordinate(x, y, map_size)[source]

Return the 1D Fourier coordinate index corresponding to 2D (x, y) on a square map.

Parameters:

  • x (int) – X-coordinate (horizontal index).

  • y (int) – Y-coordinate (vertical index).

  • map_size (int) – Size of one side of the square map.

Returns:

idx – Flattened Fourier-space index.

Return type:

int

wale.CommonUtils.get_l1_from_pdf(counts, bins)[source]

Compute the L1 norm (∫|x|P(x)dx) from a histogram representation of a PDF.

Parameters:

  • counts (ndarray) – Histogram bin counts or PDF values (P(x)).

  • bins (ndarray) – Bin centers or values corresponding to the counts.

Returns:

l1_norm – L1 norm approximation (P(x) * |x| per bin).

Return type:

ndarray

wale.CommonUtils.get_moments(kappa_values, pdf_values)[source]

Compute the first four moments of a given 1D probability distribution.

Parameters:

  • kappa_values (ndarray) – Bin centers or sample points along the kappa (x-axis).

  • pdf_values (ndarray) – Corresponding PDF values at each kappa.

Returns:

  • mean_kappa (float) – Mean of the distribution.

  • variance (float) – Variance of the distribution.

  • S_3 (float) – Skewness (third standardized moment).

  • K (float) – Kurtosis minus 3 (excess kurtosis).

  • norm (float) – Normalization constant of the input PDF.