# rainwoodman/fastpm

fastPM - A N-body Particle Mesh solver that scales
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# FastPM

CI-Status

## Introduction

FastPM solves the gravity Possion equation with a boosted particle mesh. Arbitrary time steps can be used. The code is indented to study the formation of large scale structure.

Serious attempts are made to ensure the source code of FastPM is relatively clear to read (mirroring the complicity of the algorithms). FastPM provides a library and a C-API (still unstable) to be reused at binary level in another application.

FastPM supports plain PM and Comoving-Lagranian (COLA) solvers. A broadband correction enforces the linear theory model growth factor at large scale. See the code paper [FastPMPaper]

Thanks to the PFFT Fourier Transform library, FastPM scales extremely well, to hundred thousand MPI ranks.

The size of mesh in FastPM can vary with time, allowing one to use coarse force mesh at high redshift with increase temporal resolution for accurate large scale modes.

FastPM supports a huge varieties of Greens function and differentiation kernels, though for most practical simulations the choice of kernels does not make a difference.

A parameter file interpreter is provided to validate and execute the configuration files without running the simulation, allowing creative usages of the configuration files.

## IO and Compatibility

The snapshot container format of FastPM is [bigfile]. The format can be easily accessed by python, C, or Fortran.

The snapshots can be read by nbodykit via the BigFileCatalog, or via the DataSet interface of bigfile python package, or directly accessed as binary files from Fortran, C, or with the unix command od.

Position is stored in the unit of Mpc/h as double precision 3 vectors. Velocity is stored in peculiar velocity km/s as single precision 3 vectors. ID is stored as 8 bit unsigned integers.

The attributes of the Header column/dataset stores the meta data about the simulation, including the fully evaluated parameter file.

A rarely used feature is to store the snapshot in the TPM container format by Martin White, which can be subtly accessed by Python, C, or Fortran.

The FastPM container can be converted to a legacy Gadget-1/2 container format with the supplied python script in python directory.

The nbody post-analysis package [NBODYKIT] natively supports bigfile and TPM formats via the BigFileCatalog class and TPMBinaryCatalog interfaces. Refer to nbodykit documentation (search for the class name) for examples.

[NBODYKIT] provides tools for calculating two point functions, generating QPM mocks, and identifying Friends-of-Friends (also know as DBSCAN) halos and calculating spherical overdensity properties of subhalos.

In addition to the snapshots, FastPM calculates and writes the power-spectrum at each time step. These power spectrum files are compatible with k, p = numpy.loadtxt(filename, unpack=True) Note that these are the power spectrum of the density field that goes into the force calculation, thus contain the mass assignment window effects.

FastPM can also write the Linear Density field, white noise, or non-linear density. Use write_lineark, write_whitenoise, white_nonlineark in the parameter file. The output is also stored as columns in a bigfile container. Read these via the BigFileMesh class from [NBBODYKIT]_, or directly access the bigfile container via the bigfile module.

## Units

FastPM format

• Position is in units of Mpc/h.
• Velocity is in peculiar Km/s, v_p = \frac{a}\dot{x}

To convert velocity to RSD, use \delta x_{rsd} = \frac{1}{aH} v_p This number is saved in the header.

RunPB format

• Position is between 0 and 1.
• Velocity is in RSD units, between 0 and 1.

Interanal Units

• Position is in units of Mpc/h.
• Velocity is v_i = \frac{a^2}{H_0}\dot{x}

## Acknowledgement

FastPM uses or references publicly avaiable codes ([PFFT] [2LPT], [COLAHALO], [LUA], [NBODYKIT], [MP-GADGET]) and private codes (mpipm and ic_2lpt by Martin White).

The Particle Mesh solver and 2LPT initial condition generator in FastPM are written from scratch to properly support pencil / stencil domain decomposition schemes.

The following files distributed in FastPM are originally from other projects:

FastPM shared a majority of the particle mesh code with the pmesh python package.

 [2LPT] (1, 2, 3) http://cosmo.nyu.edu/roman/2LPT/
 [NBODYKIT] (1, 2, 3) http://github.com/bccp/nbodykit/
 [COLAHALO] (1, 2, 3, 4) http://github.com/junkoda/cola_halo
 [LUA] (1, 2) http://lua.org/
 [bigfile] (1, 2) https://github.com/rainwoodman/bigfile

## Source Code Installation

FastPM works out-of-the-box on many GNU/Linux and compatible systems. Notably the development is performed on a Cray system, a Fedora Workstation, and the integrated continuous integration tests are performed on a Ubuntu based Linux distribution.

The recommended compiler is gcc. FastPM is built with the GNU make tool.

Set up the compilers and location of files in Makefile.local. An example is provided in Makefile.local.example which shall work on a recent version of Fedora .

• gsl : Most super-computing facility have these already installed. Locate the path. Point GSL_DIR to the installation dir. (parent directory of lib and include)
• pfft : bundled and built statically in depends directory Makefile.pfft. Some minor tweaks to Makefile.pfft on the configure scripts may be needed. Especially the --enable-avx and --enable-sse / --enable-sse2 flags if compliation fails with strange errors about invalid instructions.

The automatical dependency requires a working version of gcc, so its the best to compile with the gnu compilers.

The make process requires a Makefile.local file, which sets the variables like compiler (MPICC). A few examples are provided, but you shall customize it based on the example for your site.

# the following example works at NERSC
# this will set GSL_DIR automatically

# copy the edison example file to Makefile.local

cp Makefile.local.example Makefile.local

# the rest is just make. It may take a while.
make


## Binary installation via Anaconda

Anaconda is a popular Python distribution that provides portable binary distributions of software on most x86-64 and Linux platforms. FastPM compiles cleanly under the MPI provided by Anaconda.

Binaries for Linux-64 and OSX-64 are provides. Sorry we do not have enough expertise on Windows builds.

The following command will install FastPM and nbodykit to the cfastpm environment.

conda create -n cfastpm
conda activate cfastpm

conda install -c bccp cfastpm nbodykit


Notice that there is a package called fastpm from Python, which is a Python rewrite of FastPM that provides a playground for different ParticleMesh based Poisson solvers.

For now, openmp does not seem to work with Anaconda, unless the anaconda compiler is used (installed via gcc_linux-64), but this currently interferes with the MPI compiler provided by the mpich2 package. Most problems we solve with FastPM are small enough that hybrid with threads is not necessary; for real large problems we likely will need to recompiler from source code on the super-computer anyways.

## Docker

There is a basic docker configuration file to set up a container for FastPM.

To build it, run:

# first remove all prebuilt binary files

make deep-clean

sudo docker build -t fastpm .


To start the docker container in interactive mode, with port 8888 exposed and linking /my/file/directory to /worksapce, run

sudo docker run -it -v /my/file/directory:/workspace -p 8888:8888 fastpm


We install a jupyter notebook service in the docker image, which listens on the forwarded port of 8888.

jupyter notebook --ip=* --allow-root


As of now, proper set up of docker needs root access. It may be necesssary to prepend su -c or sudo in docker command line, see [docker-root].

## Examples

• refer to tests/nbodykit.lua for a basic parameter file.
• refer to python/make-pklin.py for generation a linear power spectrum to start the simulation.
• refer to python/fof.py for halo finding. It is a MPI capable script that we frequently use on a few thousand cores!
• refer to python/convert-to-gadget-1.py for conversion from FastPM's bigfile to Gadget container format. The result can be used as an 2LPT or non-linear intial condition for Gadget. The script is currently sequential and takes about 6 hours to convert a 4096**3 simulation.

Feel free to copy and modify these files to fit your own need, especially if you have strong opinions on the choice data containers.

## Commandline Interface

The CLI consists of two main executable files:

• fastpm is the main executable file of FastPM.
• fastpm-lua is an interpreter that executes the main function defined in a parameter file.

A parameter file instructs the run of FastPM. The parameter file is written in the LUA programming language. We refer the readers to the Lua Reference manual for syntax and run-time libraries of the LUA programming language. In a parameter file, the command-line arguments to fastpm can be accessed by the args variable, allowing dynamic generation of parameters during run-time. The interpreter fastpm-lua can be used to process the parameter file and generate job script files. The example parameter file standard.lua is distributed with the software in the code repository.

FastPM use the initial condition from a 3-dimensional white-noise, a linear density field read_lineark, or initial position and velocity of particles read_runpbic.

• The white noise field requires a linear theory power spectrum input. The white noise can be retrieved from

a Fourier space dump from FastPM (read_whitenoisek), or a configuration space dump from GRAFIC. The GRAFIC file contains a set of FORTRAN 77 unformatted data blocks, one per each slab in z-y plane. The size of the GRAFIC mesh must match with the number of particles in FastPM. It is important to be aware that the coordinates in FastPM is transposed from GRAFIC, with the transformation x \to z, y \to y, z \to x. (read_grafic), or generated from a random seed (random_seed) based on the scale invariant Gadget N-GenIC sequence.

• A linear density field in Fourier space (read_lineark). The field shall have the correct linear theory power at z=0.
• Particle position and velocity evolved with 2LPT initial condition generator. (read_runpbic). The Lagrangian position of the particles are assumed to be on a regular grid, and the s_1, s_2 terms are recovered from velocity and displacement according to the cosmology specified in the parameter file. This type of input is used for the comparison with RunPB TreePM simulations.

An arbitrary list of time steps can be specified in the parameter file(time_steps). We provide functions the create three commonly used time stepping:

• linspace(a_0, a_1, N): N + 1 steps linear in scaling factor a \in [a_0, a_1].
• logspace(log a_0, log a_1, N): N + 1 steps linear in \log a \in [\lg a_0, \lg a_1].

The names are inspired from similar functions to generate sequences in numpy, but be aware of the subtle differences. Functions here always includes an additional end point, while those in numpy do not.

FastPM measures and stores the dark matter power spectrum at each Kick step to a path specified in the parameter file(write_powerspectrum). The measurement is performed on the density field that produces the gravitational force; no correction for aliasing or shot noise is applied.

At selected redshifts (output_redshift), FastPM writes snapshot in [bigfile] format to a path (write_snapshot). The bigfile format stores data in a sequence of plain binary files and meta data in plain text files.

## C Application Programming Interface

The FastPM CLI is built on top of libfastpm. The core functionality of libfastpm is to evolve a linear theory over-density field to a non-linear density field and a list of particle displacement and velocities. There are also tools for measurement of power spectrum and generating Gaussian realizations of initial linear density field.

The library is built as libfastpm/libfastpm.a. To use the library, include fastpm/libfastpm.h from the api directory. Two solver classes are provided,

• FastPM : for multi-step particle mesh simulations)
• FastPM2LPT : for 1/2LPT particle mesh simulations).

We refer interested users to src/test2lpt.c and src/testpm.c for example uses of the C-API. We make the best effort to ensure the API is compatible with C++. If not, please report an issue.