WALE — Wavelet ℓ₁-norm Estimator
WALE (pronounced WAL-E) is a Python toolkit for predicting and analyzing the one-point statistics of the wavelet ℓ₁-norm in cosmological density fields. It combines theoretical predictions based on one-point PDF expansions with direct measurements on simulations or observational data, enabling robust multi-scale comparisons.
Repository
Source code and issue tracker:
🔗 https://github.com/vilasinits/WALE
Features
Theoretical Predictions
Derive analytical estimates of the wavelet ℓ₁-norm’s mean and variance using one-point PDF expansions rooted in Large Deviation Theory.Wavelet Decomposition
Perform multi-scale analysis with wavelet bases such as top-hat and starlet to extract scale-resolved information.ℓ₁-norm Measurements
Compute the ℓ₁-norm of wavelet coefficients on weak lensing convergence fields efficiently and accurately.Theory vs. Simulation Comparison
Built-in routines to overlay theoretical predictions with simulation results, including visualization tools and diagnostic metrics.Modular API
Clean, extensible architecture with dedicated modules for theory, analysis, I/O, and utility functions.Parallel Processing (Coming Soon)
MPI-based support for handling large cosmological datasets in parallel.JAX Integration (Coming Soon)
Accelerated computation and auto-differentiation via JAX for high-performance workflows.
Installation
Clone and install in editable mode:
git clone https://github.com/vilasinits/WALE.git
cd WALE
pip install -e .
Quickstart
Explore the example notebooks in the notebooks/ directory to see how WALE can be applied to theoretical predictions or real data analysis.
Citation
If you use WALE in your work, please cite:
@ARTICLE{2024A&A...691A..80S,
author = {{Sreekanth}, Vilasini Tinnaneri and {Codis}, Sandrine and {Barthelemy}, Alexandre and {Starck}, Jean-Luc},
title = "{Theoretical wavelet {\ensuremath{\ell}}$_{1}$-norm from one-point probability density function prediction}",
journal = {Astronomy & Astrophysics},
volume = {691},
eid = {A80},
pages = {A80},
year = {2024},
month = nov,
doi = {10.1051/0004-6361/202450061},
archivePrefix = {arXiv},
eprint = {2406.10033},
primaryClass = {astro-ph.CO}
}