Spherical Harmonic Transforms Module

Spherical Harmonic Transforms Module

This module provides fast spherical harmonic transforms using the DUCC0 library for HEALPix maps. It offers significant performance improvements over healpy’s default implementation, especially for high-resolution maps.

The module supports: - Forward transforms (map2alm) for spin-0 and spin-2 fields - Adjoint/inverse transforms (alm2map) - Automatic pixel weighting for accurate transforms - Beam smoothing operations - Multi-threaded execution

Classes

HealpixDUCC

Main class for performing spherical harmonic transforms on HEALPix maps using the DUCC0 library.

Example

from cobi.sht import HealpixDUCC import numpy as np

# Initialize for nside=512 hp_ducc = HealpixDUCC(nside=512)

# Transform Q/U polarization maps to E/B alms qu_maps = np.array([q_map, u_map]) eb_alms = hp_ducc.map2alm(qu_maps, lmax=1500, nthreads=4)

# Smooth and transform back smoothed_maps = hp_ducc.smoothing(qu_maps, lmax=1500, fwhm=5.0, nthreads=4)

Notes

This module is imported from https://github.com/antolonappan/PyNILC/blob/main/pynilc/sht.py and provides a high-performance alternative to healpy for spherical harmonic transforms.

class HealpixDUCC(nside)

Bases: object

A class to handle HEALPix geometry and perform spherical harmonic transforms. Attributes: ———- nside : int

The HEALPix nside parameter.

__init__(nside)

getsize(lmax, mmax)

Get size of the alm array for a given lmax and mmax. Parameters: ———– lmax : int

Maximum l.

mmaxint

Maximum m.

__tomap__(alm, spin, lmax, mmax, nthreads, map=None, **kwargs)

A helper function to perform the forward spherical harmonic transform. Parameters: ———– alm : np.ndarray

The input alm array.

spinint

The spin of the field.

lmaxint

Maximum l.

mmaxint

Maximum m.

nthreadsint

Number of threads to use.

mapnp.ndarray

The output map array.

Parameters:

• alm (numpy.ndarray)

• spin (int)

• lmax (int)

• mmax (int)

• nthreads (int)

• map (numpy.ndarray | None)

__toalm__(m, spin, lmax, mmax, nthreads, alm=None, apply_weights=True, **kwargs)

A helper function to perform the adjoint spherical harmonic transform. Parameters: ———– m : np.ndarray

The input map array.

spinint

The spin of the field.

lmaxint

Maximum l.

mmaxint

Maximum m.

nthreadsint

Number of threads to use.

almnp.ndarray

The output alm array.

apply_weightsbool

Whether to apply the weights.

Parameters:

• m (numpy.ndarray)

• spin (int)

• lmax (int)

• mmax (int)

• nthreads (int)

__alm2map_spin2__(alm, lmax, nthreads, **kwargs)

A helper function to perform the forward spherical harmonic transform for spin-2 fields. Parameters: ———– alm : np.ndarray

The input alm array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• alm (numpy.ndarray)

• lmax (int)

• nthreads (int)

__map2alm_spin2__(m, lmax, nthreads, **kwargs)

A helper function to perform the adjoint spherical harmonic transform for spin-2 fields. Parameters: ———– m : np.ndarray

The input map array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• m (numpy.ndarray)

• lmax (int)

• nthreads (int)

__alm2map_spin0__(alm, lmax, nthreads, **kwargs)

A helper function to perform the forward spherical harmonic transform for spin-0 fields. Parameters: ———– alm : np.ndarray

The input alm array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use

Parameters:

• alm (numpy.ndarray)

• lmax (int)

• nthreads (int)

__map2alm_spin0__(m, lmax, nthreads, **kwargs)

A helper function to perform the adjoint spherical harmonic transform for spin-0 fields. Parameters: ———– m : np.ndarray

The input map array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• m (numpy.ndarray)

• lmax (int)

• nthreads (int)

alm2map(alm, lmax, nthreads, **kwargs)

Perform the forward spherical harmonic transform. Parameters: ———– alm : np.ndarray

The input alm array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• alm (numpy.ndarray)

• lmax (int)

• nthreads (int)

map2alm(m, lmax, nthreads, **kwargs)

Perform the adjoint spherical harmonic transform. Parameters: ———– m : np.ndarray

The input map array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• m (numpy.ndarray)

• lmax (int)

• nthreads (int)

smoothing_alms(alms, lmax, fwhm, nthreads, **kwargs)

Smooth the alm array. Parameters: ———– alms : np.ndarray

The input alm array.

lmaxint

Maximum l.

fwhmfloat

The full width at half maximum of the beam.

nthreadsint

Number of threads to use.

Parameters:

• alms (numpy.ndarray)

• lmax (int)

• fwhm (float)

• nthreads (int)

smoothing_maps(map, lmax, fwhm, nthreads, **kwargs)

Smooth the map array. Parameters: ———– map : np.ndarray

The input map array.

lmaxint

Maximum l.

fwhmfloat

The full width at half maximum of the beam.

nthreadsint

Number of threads to use.

Parameters:

• map (numpy.ndarray)

• lmax (int)

• fwhm (float)

• nthreads (int)

smoothing(data, lmax, fwhm, nthreads, **kwargs)

Smooth the Map or alm. Parameters: ———– data : np.ndarray

The input data array.

lmaxint

Maximum l.

fwhmfloat

The full width at half maximum of the beam.

nthreadsint

Number of threads to use.

Parameters:

• data (numpy.ndarray)

• lmax (int)

• fwhm (float)

• nthreads (int)

HealpixDUCC Class

class HealpixDUCC(nside)

A class to handle HEALPix geometry and perform spherical harmonic transforms. Attributes: ———- nside : int

The HEALPix nside parameter.

__init__(nside)

getsize(lmax, mmax)

Get size of the alm array for a given lmax and mmax. Parameters: ———– lmax : int

Maximum l.

mmaxint

Maximum m.

__tomap__(alm, spin, lmax, mmax, nthreads, map=None, **kwargs)

A helper function to perform the forward spherical harmonic transform. Parameters: ———– alm : np.ndarray

The input alm array.

spinint

The spin of the field.

lmaxint

Maximum l.

mmaxint

Maximum m.

nthreadsint

Number of threads to use.

mapnp.ndarray

The output map array.

Parameters:

• alm (numpy.ndarray)

• spin (int)

• lmax (int)

• mmax (int)

• nthreads (int)

• map (numpy.ndarray | None)

__toalm__(m, spin, lmax, mmax, nthreads, alm=None, apply_weights=True, **kwargs)

A helper function to perform the adjoint spherical harmonic transform. Parameters: ———– m : np.ndarray

The input map array.

spinint

The spin of the field.

lmaxint

Maximum l.

mmaxint

Maximum m.

nthreadsint

Number of threads to use.

almnp.ndarray

The output alm array.

apply_weightsbool

Whether to apply the weights.

Parameters:

• m (numpy.ndarray)

• spin (int)

• lmax (int)

• mmax (int)

• nthreads (int)

__alm2map_spin2__(alm, lmax, nthreads, **kwargs)

A helper function to perform the forward spherical harmonic transform for spin-2 fields. Parameters: ———– alm : np.ndarray

The input alm array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• alm (numpy.ndarray)

• lmax (int)

• nthreads (int)

__map2alm_spin2__(m, lmax, nthreads, **kwargs)

A helper function to perform the adjoint spherical harmonic transform for spin-2 fields. Parameters: ———– m : np.ndarray

The input map array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• m (numpy.ndarray)

• lmax (int)

• nthreads (int)

__alm2map_spin0__(alm, lmax, nthreads, **kwargs)

A helper function to perform the forward spherical harmonic transform for spin-0 fields. Parameters: ———– alm : np.ndarray

The input alm array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use

Parameters:

• alm (numpy.ndarray)

• lmax (int)

• nthreads (int)

__map2alm_spin0__(m, lmax, nthreads, **kwargs)

A helper function to perform the adjoint spherical harmonic transform for spin-0 fields. Parameters: ———– m : np.ndarray

The input map array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• m (numpy.ndarray)

• lmax (int)

• nthreads (int)

alm2map(alm, lmax, nthreads, **kwargs)

Perform the forward spherical harmonic transform. Parameters: ———– alm : np.ndarray

The input alm array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• alm (numpy.ndarray)

• lmax (int)

• nthreads (int)

map2alm(m, lmax, nthreads, **kwargs)

Perform the adjoint spherical harmonic transform. Parameters: ———– m : np.ndarray

The input map array.

lmaxint

Maximum l.

nthreadsint

Number of threads to use.

Parameters:

• m (numpy.ndarray)

• lmax (int)

• nthreads (int)

smoothing_alms(alms, lmax, fwhm, nthreads, **kwargs)

Smooth the alm array. Parameters: ———– alms : np.ndarray

The input alm array.

lmaxint

Maximum l.

fwhmfloat

The full width at half maximum of the beam.

nthreadsint

Number of threads to use.

Parameters:

• alms (numpy.ndarray)

• lmax (int)

• fwhm (float)

• nthreads (int)

smoothing_maps(map, lmax, fwhm, nthreads, **kwargs)

Smooth the map array. Parameters: ———– map : np.ndarray

The input map array.

lmaxint

Maximum l.

fwhmfloat

The full width at half maximum of the beam.

nthreadsint

Number of threads to use.

Parameters:

• map (numpy.ndarray)

• lmax (int)

• fwhm (float)

• nthreads (int)

smoothing(data, lmax, fwhm, nthreads, **kwargs)

Smooth the Map or alm. Parameters: ———– data : np.ndarray

The input data array.

lmaxint

Maximum l.

fwhmfloat

The full width at half maximum of the beam.

nthreadsint

Number of threads to use.

Parameters:

• data (numpy.ndarray)

• lmax (int)

• fwhm (float)

• nthreads (int)