This package contains scripts for computing CMB and lensing covariances as described in Peloton et al. 2016 (https://arxiv.org/abs/1611.01446) It has routines for:

• Spectra
  • computing (analytically) the N0 bias (curve- and flat-sky available)
  • computing (analytically) the N1 bias (only flat-sky available)
  • computing CMB lensed power spectra using series-expansion
  • computing CMB lensed power spectra using correlation functions
• Covariances
  • computing (analytically) the covariance matrix of CMB lensed spectra up to second order in lensing potential power-spectrum
  • computing (analytically) the covariance matrix of lensing potential spectrum
  • computing (analytically) the cross-covariance matrix of CMB lensed spectra and lensing potential spectrum up to second order in lensing potential power-spectrum
• Additional
  • computing derivatives of spectra using correlation functions
  • computing wigner (small) d-matrix efficiently

The code performs computation in the full-sky formalism, except the computation of N1 biases and their derivatives (see the LensingBiases package). The code is fully-parallelized using mpi4py, and some Fortran parts make use of openmp (computation of N1).

This code has the following dependencies:

• numpy, pylab, etc (required)
• scipy (required, for C interfacing)
• f2py (required, for Fortran interfacing)
• mpi4py (optional, to use parallel computing)
• LensingBiases (optional, to compute lensing biases)

Make sure you update your PYTHONPATH to use the code. Just add in your bashrc:

COVPATH=/path/to/the/package
export PYTHONPATH=$PYTHONPATH:$COVPATH:$COVPATH/src

The code is primarily written in Python, although the low-level routines (wigner3-j, nested loops, etc) are implemented in Fortran and C, and interfaced with Python. The compilation of C is done on-the-fly through scipy.weave. The compilation of Fortran is done either using the setup file, by running:

python setup.py build_ext --inplace --fcompiler=gfortran

Depending on system, you may need to specify a different fortran compiler. The compilation has been tested successfully with gfortran (gcc version 5.1.0) and ifort. For the purist, we also provide a Makefile for a direct compilation.

You can find a launcher (run_covariances.sh) to have a quick usage. We also provide a batch file for usage on cluster. You have pre-defined experimental configurations in misc.py.

GNU License (see the LICENSE file for details) covers all files in the lenscov repository unless stated otherwise.