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LimberJack.jl

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<p align="center"> A differentiable cosmological code in Julia. </p>

Design Philosophy

  • Modularity: each main function within LimberJack.jl has its own module. New functions can be added by including extra modules. LimberJack.jl has the following modules:
Modulefunction
boltzmann.jlPerforms the computation of primordial power spectrum
core.jlDefines the structures where the theoretical predictions are stored and computes the background quantities
data_utils.jlManages sacc files for large data vectors
growth.jlComputes the growth factor
halofit.jlComputes the non-linear matter power spectrum as given by the Halofit fitting formula
spectra.jlComputes the power spectra of any two tracers
theory.jlComputes large data vectors that combine many spectra
tracers.jlComputes the kernels associated with each type of kernel
  • Object-oriented: LimberJack.jl mimics CCL.py class structure by using Julia's structures.
  • Transparency: LimberJack.jl is fully written in Julia without needing to interface to any other programming language (C, Python...) to compute thoretical predictions. This allows the user full access to the code from input to output.

Goals

  • Gradients: one order of magnitude faster gradients than finite differences.
  • Precision: sub-percentage error with respect to CCL.
  • Speed: C-like performance.

Installation

In order to run LimberJack.jl you will need Julia-1.7.0 or newer installed in your system. Older versions of Julia might be compatible but haven't been tested. You can find instructions on how to install Julia here: https://julialang.org/downloads/.

Once you have installed Julia you can install LimberJack.jl following these steps:

  1. Clone the git repository
  2. From the repository directory open Julia
  3. In the Julia command line run:
    using Pkg
    Pkg.add("LimberJack")

Installing Sacc.py in Julia

    using Pkg
    Pkg.add("CondaPkg")
    CondaPkg.add("sacc")

Use

    # Import
    using LimberJack
    
    # create LimberJack.jl Cosmology instance
    cosmology = Cosmology(Ωm=0.30, Ωb=0.05, h=0.70, ns=0.96, s8=0.81;
                          tk_mode=:EisHu,
                          Pk_mode=:Halofit)
    
    z = Vector(range(0., stop=2., length=256))
    nz = @. exp(-0.5*((z-0.5)/0.05)^2)
    tracer = NumberCountsTracer(cosmology, zs, nz; b=1.0)
    ls = [10.0, 30.0, 100.0, 300.0]
    cls = angularCℓs(cosmology, tracer, tracer, ls)

Challenges

  1. Parallelization: the current threading parallelization of LimberJack.jl is far away from the optimal one over number of threads scaling. Future works could study alternative parallalization schemes or possible ineficiencies in the code.
  2. GPU's: LimberJack.jl currently cannot run on GPUs which are known to significantly speed-up cosmological inference. Future works could study implementing Julia GPU libraries such as CUDA.jl.
  3. Backwards-AD: currently LimberJack.jl's preferred AD mode is forward-AD. However, the key computation of cosmological inference, obtaining the $\chi^2$, is a map from N parameters to a scalar. For a large number of parameters, backwards-AD is in theory the preferred AD mode and should significantly speed up the computation of the gradient. Future works could look into making LimberJack.jl compatible with the latest Julia AD libraries such as Zygote.jl to implement efficient backwards-AD.