healpix-analyse

A Python toolkit for analysing signals defined on HEALPix spherical grids, with a focus on Earth Observation data. All operators are implemented in PyTorch and are fully differentiable through torch.autograd.

Read the full documentation

Features

• Spherical harmonic transforms — local ALM coefficients, ring-based full-sky SHT (spin-0, 1, 2), power spectra
• Gauge-equivariant convolution — HealPixConv with configurable kernel size, gauge types, and number of gauges
• Multi-resolution operators — HealPixDown (smooth / max-pool) and HealPixUp (adjoint upsampling), NESTED ordering
• Differentiable by default — all hot-path operations are autograd-compatible
• NumPy and Torch interoperability — accepts both array types, returns the same type

Package map

healpix_analyse/
├── alm.py               # Local complex spherical harmonic coefficients
├── alm_latlon.py         # SHT for arbitrary iso-latitude grids
├── healpix_sht.py        # Ring-based full-sky SHT for HEALPix
├── convol.py             # Gauge-equivariant spherical convolution (HealPixConv)
├── down.py               # Resolution reduction (HealPixDown)
├── up.py                 # Resolution increase (HealPixUp)
├── powerspectra.py        # Isotropic power spectrum on HEALPix patches
├── powerspectra_lonlat.py # Power spectrum on irregular lon/lat grids
├── healpix_interp.py      # Bilinear interpolation on HEALPix (NESTED)
├── make_rectangle.py      # Rectangular HEALPix patches from bounding boxes
├── resample.py            # Resample HEALPix onto regular lat/lon grids
└── ps.py                  # Power spectrum utilities

Quick start

import numpy as np
import healpy as hp
from healpix_analyse.alm_latlon import build_rings_from_latlon, anafast_latlon

nside = 64
npix  = 12 * nside**2
lmax  = 3 * nside

# Random test map
im = np.random.randn(npix)

# Build ring structure from HEALPix coordinates
theta, phi = hp.pix2ang(nside, np.arange(npix))
ring_theta, ring_phi_list, ring_counts, sort_idx = build_rings_from_latlon(
    theta, phi, convention="colatitude_rad"
)

# Compute angular power spectrum
cl = anafast_latlon(
    im[sort_idx], ring_theta, ring_phi_list, ring_counts,
    lmax=lmax, quadrature="equal_area",
)
print(cl.shape)   # torch.Size([193])

Installation

pip install git+https://github.com/EOPF-DGGS/healpix-analyse.git

From source (development)

git clone git@github.com:EOPF-DGGS/healpix-analyse.git
cd healpix-analyse
pip install -e .

Documentation

Full documentation is available at eopf-dggs.github.io/healpix-analyse.

To build locally:

pip install -e ".[docs]"
cd docs
make html

Relationship to healpix-geo and healpix-ai

• healpix-geo — HEALPix geometry: pixel coordinates, ellipsoids, coverage queries
• healpix-analyse — signal analysis: SHT, convolutions, power spectra, multi-resolution operators
• healpix-ai — deep learning: autoencoders, U-Nets, forecasters built on top of healpix-analyse

License

Apache 2.0 — see LICENSE.