A Python implementation of LU nulling for weak gravitational lensing tomography, following the methodology described in Huterer & White (2005).

LU nulling is a technique for removing systematic effects in weak lensing measurements by constructing linear combinations of tomographic bins that null specific redshift-dependent systematics while preserving cosmological signal. This package provides tools for:

• Computing Limber integrals for angular power spectra
• Performing LU decomposition of the Limber matrix
• Constructing nulling transformations with specified k-space cutoffs
• Multiple integration node sampling strategies (linear, adaptive quadrature, Monte Carlo)

This package requires Python 3.8+ and depends on:

• pyCCL - Core Cosmology Library
• NumPy
• SciPy

Install pyCCL via pip:

pip install pyccl

Or via conda:

conda install -c conda-forge pyccl

Clone this repository and install in development mode:

git clone https://github.com/ahallcosmo/lunul.git
cd lunul
pip install -e .

import lunul
import pyccl as ccl
import numpy as np

# Set up cosmology
cosmo = ccl.Cosmology(Omega_c=0.27, Omega_b=0.045, h=0.67, sigma8=0.8, n_s=0.96)

# Define redshift bins and create tracers
z_edges = np.array([0.2, 0.6, 1.0, 1.4, 2.0])
z_grid = np.linspace(z_edges[0], z_edges[-1], 200)

tracers = []
for i in range(len(z_edges)-1):
    z_min, z_max = z_edges[i], z_edges[i+1]
    # Create top-hat n(z) distribution for each bin
    nz = np.where((z_grid >= z_min) & (z_grid <= z_max), 1.0, 0.0)
    tracer = ccl.WeakLensingTracer(cosmo, dndz=(z_grid, nz))
    tracers.append(tracer)

# Create nodes for integration
limits = lunul.get_global_lklimits(cosmo, tracers, ell=100)
nodes = lunul.LinearNodes(npoints=50, limits=limits)

# Perform LU nulling analysis
trimmer = lunul.Trimmer(cosmo, nodes, tracers, ell=100, kmax=10.0, tol=0.01)

• get_global_lklimits(cosmo, tracers, ell) - Compute global ln(k) limits
• get_limber_matrix(cosmo, nodes, binpairs, ell) - Build Limber matrix
• cl_integrand(lk, cosmo, tr1, tr2, psp, ell) - Limber integrand

• LinearNodes - Linearly spaced integration points
• QuadNodes - Adaptive quadrature-based sampling
• MCNodes - Monte Carlo sampling from integrand

• Trimmer - LU decomposition and mode selection

For detailed API documentation, see the docstrings in the source code.

See the examples/ directory for Jupyter notebooks demonstrating:

• Basic LU nulling workflow
• Comparison of integration strategies
• Systematic removal validation

If you use this software, please cite:

Primary Reference:

@article{HutererWhite2005,
  title={Nulling Tomography with Weak Gravitational Lensing},
  author={Huterer, Dragan and White, Martin},
  journal={Physical Review D},
  volume={72},
  number={4},
  pages={043002},
  year={2005},
  publisher={APS}
}

This Implementation:

@misc{RobertsonHall2025,
  title={lunul: A Python implementation of LU nulling for weak lensing},
  author={Robertson, N. and Hall, A.},
  year={2025},
  url={https://github.com/ahallcosmo/lunul}
}

Core Cosmology Library: Please also cite the Core Cosmology Library (CCL) papers.

This project is licensed under the GNU General Public License v3.0 - see the LICENSE file for details.

• The DESC Core Cosmology Library
• The original LU nulling methodology by Huterer & White (2005)