pywiggle 0.1.15

Fast angular power spectrum estimator

wiggle stands for the WIGner Gauss-Legendre Estimator. This Python package provides a fast implementation of unbiased angular power spectrum estimation of spin-0 and spin-2 fields on the sphere, most commonly encountered in the context of cosmological data analysis.

Typically, estimates of the power spectrum of masked fields involve products of Wigner-3j symbols, which can be factorized into products of Wigner-d matrices and integrated exactly using Gauss-Legendre quadrature. This code provides efficient implementations of this approach to mode decoupling for exact power spectrum estimation, which in the case of binned spectra can be orders of magnitude faster than other approaches (often around a second of compute-time at most).

• Free software: BSD license

• Documentation: https://wiggle.readthedocs.io.

Installing

Make sure your pip tool is up-to-date. To install wiggle, run:

$ pip install pywiggle --user

This will install a pre-compiled binary suitable for your system (only Linux and Mac OS X with Python>=3.9 are supported). After installation, make sure to run a test with:

$ pytest --pyargs pywiggle.tests

If you require more control over your installation, e.g. using Intel compilers, please see the section below on compiling from source.

Compiling from source (advanced / development workflow)

The easiest way to install from source is to use the pip tool, with the --no-binary flag. This will download the source distribution and compile it for you. Don’t forget to make sure you have CXX set if you have any problems.

For all other cases, below are general instructions.

First, download the source distribution or git clone this repository. You can work from master or checkout one of the released version tags (see the Releases section on Github). Then change into the cloned/source directory.

Once downloaded, you can install using pip install . inside the project directory. We use the meson build system, which should be understood by pip (it will build in an isolated environment).

We suggest you then test the installation by running the unit tests. You can do this by running pytest.

To run an editable install, you will need to do so in a way that does not have build isolation (as the backend build system, meson and ninja, actually perform micro-builds on usage in this case):

$ pip install --upgrade pip meson ninja meson-python cython numpy pybind11
$ pip install  --no-build-isolation --editable .

After installation, make sure to run a test with:

$ pytest

Quick Usage

Accurate power spectrum estimation requires you to first convert a pixelated and masked map to its spherical harmonic coefficients. wiggle does not provide tools for SHTs and expects you to have the alm coefficients both for the masked fields and the mask itself already in hand. These can be obtained using a code like healpy in the case of HEALPix maps or a code like pixell in the case of rectangular pixelization maps.

If you are interested in accurate power spectra out to some maximum multipole lmax, we recommend you evaluate SHTs out to lmax for the masked fields, but out to 2 lmax for the mask itself. With these in hand, you can obtain unbiased power spectra as follows, in the case of a spin-0 field for example:

> import pywiggle
> import numpy as np

> lmax = 4000
> bin_edges = np.arange(40,lmax,40)

> dcls, th_filt = pywiggle.alm2auto_power_spin0(lmax,alm,mask_alm,bin_edges = bin_edges)

Here dcls is the mode-decoupled unbiased power spectrum and th_filt is a matrix that can be dotted with a theory spectrum to obtain the binned theory to compare the power spectrum to (e.g. for inference):

> chisquare = get_chisquare(dcls,th_filt @ theory_cls,cinv)

While the above function alm2auto_power_spin0 is intended for the auto-spectra of a spin-0 field, many additional convenience functions are provided:

• alm2cross_power_spin0: Cross-power of spin-0 fields (\(T_1\) x \(T_2\))

• alm2auto_power_spin2: Auto-power of E/B decomposition of spin-2 fields (EE and BB)

• alm2auto_power_spin02: Auto-power of scalar,E,B fields along with the scalar-E power (TT, EE, BB, TE)

• alm2cross_power_spin2: Cross-power of E/B decomposition of spin-2 fields (\(E_1\) x \(E_2\) and \(B_1\) x \(B_2\))

• alm2cross_power_spin02: Cross-power of scalar,E/B fields along with the scalar-E power (\(T_1\) x \(T_2\), \(E_1\) x \(E_2\) and \(B_1\) x \(B_2\), \(T_1\) x \(E_2\), \(T_2\) x \(E_1\))

Cached workflow

The above functions are convenience wrappers around the core class Wiggle, which can be used directly if speed and efficient re-use of cached mode-coupling matrices is important. For example,

> w = Wiggle(lmax, bin_edges=bin_edges)
# Register the SHT of a mask and identify it with a key
> w.add_mask('mt1', mask_alm_t1)
# Register another mask
> w.add_mask('mt2', mask_alm_p2)
# Register a beam to deconvolve from both fields
> g.add_beam('b1', beam_fl)
# Get the decoupled cross-Cls from the masked field SHTs
> ret_TT = g.decoupled_cl(alm_t1, alm_t2, 'mt1', 'mt2', spectype='TT',
                          return_theory_filter=False,
                          beam_id1='b1', beam_id2='b1')

This object can then be reused if the same masks are being re-used, which avoids re-calculation of mode-coupling matrices. The interface to decoupled_cl is flexible enough to allow all auto- and cross- spectra of spin-0 and spin-2 fields.

Coming soon

TB and EB spectra as well as mode-decoupling for purified E/B fiels have not been implemented yet, but are planned to in a future release.

Contributions

If you have write access to this repository, please:

1. create a new branch

2. push your changes to that branch

3. merge or rebase to get in sync with master

4. submit a pull request on github

If you do not have write access, create a fork of this repository and proceed as described above.