dsf.hankel.hankel_transform_fftlog module

FFTLog-basedHankel transforms for 1D radial statistics.

This module provides the HankelTransformFFTLog class, which converts Fourier-space spectra into radial-space quantities using the FFTLog algorithm. It implements 1D projected and spherical Hankel transforms as a HankelTransform backend. It also includes two public functions that perform the FFTLog-based Hankel transforms directly, without requiring a HankelTransform class instance.

class dsf.hankel.hankel_transform_fftlog.HankelTransformFFTLog

Bases: HankelTransformBase

Hankel transform using the FFTLog algorithm.

This class provides methods for performing 1D Hankel transforms using the scipy FFTLog algorithm.

projected_correlation(radial_input=None, spectrum=None, order=2, taper=False, taper_kwargs=None, use_offset=False, **kwargs)

Compute a projected radial statistic from one spectrum.

Parameters:

• radial_input (NDArray[float64] | list[float] | tuple[float, ...] | None) – Radial input grid for tabulated spectra.

• spectrum (NDArray[float64] | list[float] | tuple[float, ...] | Callable[[...], NDArray[float64]] | None) – Spectrum values or callable spectrum.

• order (float | int) – Bessel order to use (default is 2 for tangential shear).

• taper (bool) – Whether to suppress low-k and high-k edge power.

• taper_kwargs (Mapping[str, Any] | None) – Optional settings for the spectrum taper.

• use_offset (bool) – Apply automatic offset to FFTLog to reduce ringing.

• **kwargs – Extra arguments passed to callable spectra.

Returns:

Radial grid, in inverse units of radial_input, and the projected radial statistic.

Return type:

tuple[NDArray[float64], NDArray[float64]]

spherical_correlation(k_pk=None, pk=None, order=0, taper=False, taper_kwargs=None, use_offset=False, **kwargs)

Compute a spherical radial statistic from one spectrum.

Parameters:

• k_pk (NDArray[float64] | list[float] | tuple[float, ...] | None) – Wavenumber grid for tabulated spectra (units of inverse distance).

• pk (NDArray[float64] | list[float] | tuple[float, ...] | Callable[[...], NDArray[float64]] | None) – Spectrum values or callable spectrum.

• order (float | int) – Bessel order to use (default is 0 for Delta Sigma).

• taper (bool) – Whether to suppress low-k and high-k edge power.

• taper_kwargs (Mapping[str, Any] | None) – Optional settings for the spectrum taper.

• use_offset (bool) – Apply automatic offset to FFTLog to reduce ringing.

• **kwargs – Extra arguments passed to callable spectra.

Returns:

Radial grid and spherical radial statistic. The units of the radial grid are the inverse of the units of k.

Return type:

tuple[NDArray[float64], NDArray[float64]]

dsf.hankel.hankel_transform_fftlog.hankel_projected(radial_input, spectrum, order=2, use_offset=False)

Convert an angular power spectrum to a projected correlation using FFTLog.

\(\gamma_t(\theta) = \int \frac{\ell d\ell}{2\pi} C(\ell )J_\mu(\ell \theta)\).

Parameters:

• radial_input (NDArray[float64]) – Radial input array (must be uniform in logspace).

• spectrum (NDArray[float64]) – Spectrum to transform.

• order (float | int) – Bessel order to use (default is 2 for tangential shear).

• use_offset (bool) – Apply automatic offset to FFTLog to reduce ringing.

• Returns – Radial grid, in inverse units of radial_input, and the projected radial statistic.

Return type:

tuple[NDArray[float64], NDArray[float64]]

dsf.hankel.hankel_transform_fftlog.hankel_spherical(k, pk, order=0, use_offset=False)

Convert power spectrum to 3D correlation function using FFTLog:

\(\xi(r) = \int \frac{k^2 dk}{2\pi^2} P(k) j_\ell(kr)\).

Currently, only order 0 is implemented.

Parameters:

• k (NDArray[float64]) – Wavenumber array (must be uniform in logspace).

• pk (NDArray[float64]) – Power spectrum to transform.

• order (float | int) – Bessel order to use (default is 0 for Delta Sigma).

• use_offset (bool) – Apply automatic offset to FFTLog to reduce ringing.

Returns:

Radial grid and 3D correlation function.

Return type:

tuple[NDArray[float64], NDArray[float64]]