---
title: "`PyAutoLens`: Open-Source Lens Modeling"
tags:
  - astronomy
  - galaxy formation and evolution
  - galaxies
  - interferometry
  - Python
authors:
  - name: James. W. Nightingale
    orcid: 0000-0002-8987-7401
    affiliation: 1
  - name: Richard G. Hayes
    affiliation: 1
  - name: Aristeidis Amvrosiadis
    orcid: 0000-0002-4465-1564
    affiliation: 1  
  - name: Ashley Kelly
    orcid: 0000-0003-3850-4469
    affiliation: 1  
  - name: Amy Etherington
    affiliation: 1
  - name: Qiuhan He
    orcid: 0000-0003-3672-9365
    affiliation: 1       
  - name: Nan Li
    orcid: 0000-0001-6800-7389
    affiliation: 2
  - name: XiaoYue Cao
    affiliation: 3
  - name: Jonathan Frawley
    orcid: 0000-0002-9437-7399
    affiliation: 4
  - name: Shaun Cole
    orcid: 0000-0002-5954-7903
    affiliation: 1
  - name: Andrea Enia
    orcid: 0000-0002-0200-2857
    affiliation: 5
  - name: Carlos S. Frenk
    orcid: 0000-0002-2338-716X
    affiliation: 1
  - name: David R. Harvey
    orcid: 0000-0002-6066-6707
    affiliation: 6
  - name: Ran Li
    orcid: 0000-0003-3899-0612
    affiliation: 3
  - name: Richard J. Massey
    orcid:  0000-0002-6085-3780
    affiliation: 1
  - name: Mattia Negrello
    orcid: 0000-0002-7925-7663
    affiliation: 7
  - name: Andrew Robertson
    orcid: 0000-0002-0086-0524
    affiliation: 1
affiliations:
  - name: Institute for Computational Cosmology, Stockton Rd, Durham DH1 3LE
    index: 1
  - name: Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
    index: 2
  - name: National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, China
    index: 3
  - name: Advanced Research Computing, Durham University, Durham DH1 3LE
    index: 4
  - name: Dipartimento di Fisica e Astronomia, Università degli Studi di Bologna, Via Berti Pichat 6/2, I-40127 Bologna, Italy
    index: 5
  - name: Lorentz Institute, Leiden University, Niels Bohrweg 2, Leiden, NL-2333 CA, The Netherlands
    index: 6
  - name: School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, UK
    index: 7

date: 25 January 2022
codeRepository: https://github.com/Jammy2211/PyAutoLens
license: MIT
bibliography: paper.bib
---

# Summary

Strong gravitational lensing, which can make a background source galaxy appears multiple times due to its light rays being 
deflected by the mass of one or more foreground lens galaxies, provides astronomers with a powerful tool to study dark 
matter, cosmology and the most distant Universe. `PyAutoLens` is an open-source Python 3.8 - 3.11 package for strong 
gravitational lensing, with core features including fully automated strong lens modeling of galaxies and galaxy 
clusters, support for direct imaging and interferometer datasets and comprehensive tools for simulating samples of 
strong lenses. The API allows users to perform ray-tracing by using analytic light and mass profiles to build strong 
lens systems. Accompanying `PyAutoLens` is the [autolens workspace](https://github.com/Jammy2211/autolens_workspace), which 
includes example scripts, lens datasets and the `HowToLens`
lectures in Jupyter notebook format which introduce non-experts to strong lensing using `PyAutoLens`. Readers can 
try `PyAutoLens` right now by going to [the introduction Jupyter notebook on Binder](https://mybinder.org/v2/gh/Jammy2211/autolens_workspace/release) 
or checkout the [readthedocs](https://pyautolens.readthedocs.io/en/latest/) for a complete overview of `PyAutoLens`'s features.

# Background

When two galaxies are aligned down the line-of-sight to Earth, light rays from the background galaxy are deflected by the 
intervening mass of one or more foreground galaxies. Sometimes its light is fully bent around the foreground galaxies, 
traversing multiple paths to the Earth, meaning that the background galaxy is observed multiple times. This alignment 
of galaxies is called a strong gravitational lens, an example of which, SLACS1430+4105, is shown in the image 
below. The massive elliptical lens galaxy can be seen in the centre of the left panel, surrounded by a multiply 
imaged source galaxy whose light has been distorted into an Einstein ring. The central panel shows a `PyAutoLens`
reconstruction of the lensed source's light, where the foreground lens's light was simultaneously fitted for and 
subtracted to reveal the source. The right panel shows a pixelized reconstruction of the source's unlensed light 
distribution performed by `PyAutoLens`, which is created using a model of the lens galaxy's mass to trace backwards 
how the source's light is gravitationally lensed.

![Hubble Space Telescope imaging of the strong lens SLACSJ1430+1405 (left column), a fit to its lensed source galaxy (middle column) and unlensed source reconstruction (right column) using `PyAutoLens`.\label{figure:example}](imageaxis.png)

Strong lensing provides astronomers with an invaluable tool to study a diverse range of topics. Mass modeling of 
strong lenses has quantified the distribution of stars [@Koopmans2009] [@Sonnenfeld2015] [@Treu2009] [@Nightingale2019] 
and invisible dark matter [@Vegetti2014] of galaxies. The source galaxy is highly magnified and reconstruction of 
its light allows a view of fainter or more distant objects than would otherwise be possible [@Dye2014] [@Enia2018]. 
Strong lensing is a competitive test of cosmological models, for example the expansion rate of the Universe can 
be inferred from the 'time-delay' between different image paths to the same distant quasar [@Suyu2016]. Strong lensing
of galaxy clusters has also made many contributions to all these topics [@Jullo2010] [@Richard2014] [@Atek2015]. 

# Statement of Need

The past decade has seen the discovery of many hundreds of galaxy-scale and cluster-scale lenses, with high quality 
imaging [@Bolton2012], interferometer [@Negrello2014] [@Enia2018] and spectroscopy [@Czoske2012] datasets now available. 
Historically, the modeling of a strong lens is a time-intensive process that requires significant human intervention 
to perform, restricting the scope and size of the scientific analysis. In the next decade of 
order of _one hundred thousand_ strong lenses will be discovered by surveys such as Euclid, LSST and 
SKA [@Collett2015], demanding a widely available and automated approach for strong lens analysis. `PyAutoLens` aims to 
meet this need, by making strong lens analysis accessible to the wider Astronomy community and enabling the automated 
analysis of large samples of strong lenses.

# Software API and Features

A gravitational lens system can be quickly assembled from Python objects which provide abstract data representations 
of the different components of a strong lens. A `Galaxy` object contains one or more `LightProfile`'s and `MassProfile`'s, 
which represent its two dimensional distribution of starlight and mass. `Galaxy`’s lie at a particular distance 
(redshift) from the observer, and are grouped into `Plane`'s. Raytracing through multiple `Plane`s is achieved by 
passing them to a `Tracer` with an `astropy` Cosmology. By passing any of these objects a `Grid2D` object strong lens 
quantities can be computed, including multi-plane ray-tracing sightlines [@McCully2014]. All of these objects are 
extensible, making it straightforward to compose highly customized lensing system. Ray-tracing calculations are 
optimized using the packages `NumPy` [@numpy], `numba` [@numba] and `pyquad` [@pyquad].

To perform lens modeling, `PyAutoLens` adopts the probabilistic programming 
language `PyAutoFit` (https://github.com/rhayes777/PyAutoFit). `PyAutoFit` allows users to compose a 
lens model from `LightProfile`, `MassProfile` and `Galaxy` objects, customize the model parameterization and fit it to 
data via a non-linear search (e.g., `dynesty` [@dynesty], `emcee` [@emcee], `PySwarms` [@pyswarms]). By composing a 
lens model with a `Pixelization`  object, the background source's light is reconstructed using a 
rectangular grid or Voronoi mesh that accounts for irregular galaxy morphologies. Lensed quasar and supernovae datasets 
can be fitted using a `Point`, which uses their observed positions, flux-ratios and time-delays to fit the lens 
model. Strong lensing clusters consisting of any number of lens galaxies can also be analysed with `PyAutoLens` using these objects.

Automated lens modeling uses `PyAutoFit`'s non-linear search chaining feature, which breaks the model-fit into 
a chained sequence of non-linear searches. These fits pass information gained about simpler lens models fitted by earlier 
searches to subsequent searches, which fit progressively more complex models. By granularizing the model-fitting 
procedure, automated pipelines that fit complex lens models without human intervention can be carefully crafted, with 
example pipelines found on the [autolens workspace](https://github.com/Jammy2211/autolens_workspace). To ensure the 
analysis and interpretation of fits to large lens datasets is feasible, `PyAutoFit`'s database tools write lens modeling 
results to a relational database which can be queried from hard-disk to a Python script or Jupyter notebook. This uses 
memory-light `Python` generators, ensuring it is practical for thousands of lenses.

`PyAutoLens` includes a comprehensive visualization library for the analysis of both direct imaging and submm / radio 
interferometer datasets, tools for preprocessing data to formats suited to lens analysis and options to include 
effects like the telescope optics and background sky subtraction in the model-fit. Interferometer analysis is 
performed directly on the observed visibilities in their native Fourier space, circumventing issues associated with the 
incomplete sampling of the uv-plane that give rise to artefacts that can bias the inferred mass model and source 
reconstruction in real-space. To make feasible the analysis of millions of visibilities, `PyAutoLens` 
uses `PyNUFFT` [@pynufft] to fit the visibilities via a non-uniform fast Fourier transform. Creating 
realistic simulations of imaging and interferometer strong lensing datasets is possible, as performed 
by [@Alexander2019] [@Hermans2019] who used `PyAutoLens` to train neural networks to detect strong lenses.
 
# Performance

The analysis of direct imaging datasets and interferometer datasets (up to of order 1 million visibilities) are both 
feasible on hardware with at least 4GB of RAM. The time it takes to perform lens modeling with `PyAutoLens` is
highly variable and depends on the size of the dataset being analysed and complexity of the model being fitted. They can 
vary from minutes to thousands of CPU hours. The run-times section on [readthedocs](https://pyautolens.readthedocs.io/en/latest/) 
provides graphs showing the performance of the latest release of `PyAutoLens` and a calculator for estimating how long
a lens model fit may take. For large jobs we recommend users install `PyAutoLens` on a HPC cluster and documentation is 
provided on how to set this up.
 
# Workspace and HowToLens Tutorials

`PyAutoLens` is distributed with the [autolens workspace](https://github.com/Jammy2211/autolens_workspace>), which 
contains example scripts for modeling and simulating strong lenses and tutorials on how to preprocess imaging and 
interferometer datasets before a `PyAutoLens` analysis. Also included are the `HowToLens` tutorials, a five chapter 
lecture series composed of over 30 Jupyter notebooks aimed at non-experts, introducing them to strong gravitational 
lensing, Bayesian inference and teaching them how to use `PyAutoLens` for their scientific study. The lectures 
are available on our [Binder](https://mybinder.org/v2/gh/Jammy2211/autolens_workspace/HEAD) and may therefore be 
taken without a local `PyAutoLens` installation.

# Software Citations

`PyAutoLens` is written in Python 3.8 - 3.11 [@python] and uses the following software packages:

- `Astropy` [@astropy1] [@astropy2]
- `COLOSSUS` [@colossus]
- `corner.py` [@corner]
- `dynesty` [@dynesty]
- `emcee` [@emcee]
- `Matplotlib` [@matplotlib]
- `numba` [@numba]
- `NumPy` [@numpy]
- `PyAutoFit` [@pyautofit]
- `PyMultiNest` [@pymultinest] [@multinest]
- `PyNUFFT` [@pynufft]
- `pyprojroot` (https://github.com/chendaniely/pyprojroot)
- `pyquad` [@pyquad]
- `PySwarms` [@pyswarms]
- `scikit-image` [@scikit-image]
- `scikit-learn` [@scikit-learn]
- `Scipy` [@scipy]

# Related Software

- `AutoLens` [@Nightingale2015] [@Nightingale2018]
- `gravlens` http://www.physics.rutgers.edu/~keeton/gravlens/manual.pdf
- `lenstronomy` https://github.com/sibirrer/lenstronomy [@Birrer2018a]
- `visilens` https://github.com/jspilker/visilens [@spilker16a]

# Acknowledgements

JWN and RJM are supported by the UK Space Agency, through grant ST/V001582/1, and by InnovateUK through grant TS/V002856/1. RGH is supported by STFC Opportunities grant ST/T002565/1.
QH, CSF and SMC are supported by ERC Advanced In-vestigator grant, DMIDAS [GA 786910] and also by the STFCConsolidated Grant for Astronomy at Durham [grant numbersST/F001166/1, ST/I00162X/1,ST/P000541/1].
RJM is supported by a Royal Society University Research Fellowship.
DH acknowledges support by the ITP Delta foundation.
AR is supported bythe ERC Horizon2020 project ‘EWC’ (award AMD-776247-6).
MN has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 707601.
This work used the DiRAC@Durham facility managed by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The equipment was funded by BEIS capital funding via STFC capital grants ST/K00042X/1, ST/P002293/1, ST/R002371/1 and ST/S002502/1, Durham University and STFC operations grant ST/R000832/1. DiRAC is part of the National e-Infrastructure.

# References
