pysco-nbody 0.8.3

A Python library to run N-body simulations with modified gravity

PySCo: Python Simulations for Cosmology

A Python library to run N-body simulations with modified gravity

Table of Contents

1. About The Project
2. Getting Started
   • Prerequisites
   • Installation
   • Testing the installation
3. Usage
   • As command line
   • As package
4. Outputs
   • Power spectra
   • Particle snapshots
5. Library utilities
6. Contributing
7. License
8. Contact

About The Project

PySCo is a multi-threaded Particle-Mesh code (no MPI parallelization) for cosmological simulations with various gravity models such as (currently)

• Newtonian gravity
• $f(R)$ model from Hu & Sawicki (2007).
• MOND gravity (quasi-linear formulation) from Milgrom (2010).
• Parametrized gravity (scale independent)

The goal is to develop a Python-based N-body code that is user-friendly and efficient. Python was chosen for its widespread use and rapid development capabilities, making it well-suited for collaborative open-source projects. To address performance issues in Python, we utilize Numba, a high-performance library that compiles Python functions using LLVM. Additionally, Numba facilitates straightforward loop parallelization.

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Getting Started

Installation

The first method is to pip install pysco using

python -m pip install pysco-nbody

Otherwise, it is possible to install directly from source

git clone https://github.com/mianbreton/pysco.git
cd pysco
python -m pip install -e .

It is then possible to access other branches. If one wants to use the feature/AwesomeNewFeature branch but without having to download the source directory, it is possible to pip install directly from github

python -m pip install git+https://github.com/mianbreton/pysco.git@feature/AwesomeNewFeature

:warning: If the first method does not work because of a dependency issue (for example, PyFFTW and icc-rt might not work for on some mac versions): use the second method, and comment the lines referring to the problematic dependencies in pyproject.toml

Prerequisites

All dependencies will be automatically installed when using pip install (see Installation) so you can skip the remainder of this section.

However, if you prefer to install each of them by hand, then you will need the following libraries (the conda installation is shown, but the same result can be achieved with pip).

• Numba

  conda install numba
  

• Numba Intel SVML (Optional, to improve performances)

  conda install -c numba icc_rt
  

• NumPy

  conda install -c anaconda numpy
  

• Pandas

  conda install -c anaconda pandas
  

• Astropy

  conda install -c conda-forge astropy
  

• Scipy

  conda install -c anaconda scipy
  

• Rich

  conda install -c conda-forge rich
  

• Pyarrow (optional, to read and write Parquet files)

  conda install -c conda-forge pyarrow
  

• H5py (optional, to read and write HDF5 files)

  conda install -c anaconda h5py
  

• PyFFTW (pip install works better than conda)

  python -m pip install pyfftw
  

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Usage

There are two ways to use Pysco, either as command line with parameter file, or as an external package.

Numba uses Just-in-Time and/or Ahead-of-Time compilation, meaning that for the former the function is compiled when it is reached for the first time, while the latter is compiled before running the code (happens when the input/output types are specified in the function decorator). This means that when the code is run (or imported) for the first time, it will spend some time compiling the functions. These are then cached and subsequent runs will not have to compile the functions again.

As command line

To run PySCo with command line it is not necessary to pip install the package. However, one must still at least install the depdendecies (see Prerequisites)

Move to the main Pysco directory

cd pysco/

A example parameter file is available in examples/param.ini. All strings (except paths and filenames) are case insensitive.

# examples/param.ini
# Run this test from the pysco directory, as
# python pysco/main.py -c examples/param.ini
# All strings (except paths and filenames) are case insensitive
##################################################
nthreads = 1  # Number of threads to use in the simulation. For nthreads <= 0 use all threads
# Theoretical model
theory= newton # Cosmological theory to use, either "Newton", "fR", "mond" or "parametrized"
## f(R)
fR_logfR0 = 5 # Background value of the scalaron field today -log(fR0)
fR_n = 1 # Exponent on the curvature in the Hu & Sawicki model. Currently n = 1 or 2
## QUMOND
mond_function = simple # "simple", "n", "beta", "gamma" or "delta"
mond_g0 = 1.2 # Acceleration constant (in 1e-10 m/s²)
mond_scale_factor_exponent = 0 # Exponent N so that g0 -> a^N g0
mond_alpha = 1 #  Interpolating function parameter
## Parametrized
parametrized_mu0 = -0.1 # If null, then is equivalent to GR. Model from Abbott et al. (2019)
# Cosmology -- Put more parameters later
H0 = 72  # Hubble constant at redshift z=0 (in km/s/Mpc).
Om_m = 0.25733   # Matter density parameter
T_cmb = 2.726 # CMB temperature parameter
N_eff = 3.044 # Effective number of neutrino species (by default 3.044)
w0 = -1.0 # Equation of state for dark energy
wa = 0.0 # Evolution parameter for dark energy equation of state
# Simulation dimension
boxlen = 100  # Simulation box length (in Mpc/h)
ncoarse = 7 # Coarse level. Total number of cells = 2**(3*ncoarse)
npart = 128**3 # Number of particles in the simulation
# Initial conditions
z_start = 49 # Starting redshift of the simulation
seed = 42 # Seed for random number generation (completely random if negative)
position_ICS = center # Initial particle position on uniform grid. Put "center" or "edge" to start from cell centers or edges.
fixed_ICS = False # Use fixed initial conditions (Gaussian Random Field). If True, fixes the amplitude to match exactly the input P(k)
paired_ICS = False # Use paired initial conditions. If True, add π to the random phases (works only with fixed_ICS = True)
dealiased_ICS = False # Dealiasing 2LPT and 3LPT components using Orszag 3/2 rule
power_spectrum_file = examples/pk_lcdmw7v2.dat # File path to the power spectrum data
initial_conditions = 2LPT # Type of initial conditions. 1LPT, 2LPT, 3LPT or or snapshot number (for restart), or .h5 RayGal file. Else, assumes Gadget format
# Outputs
base = examples/boxlen100_n128_lcdmw7v2_00000/ # Base directory for storing simulation data
output_snapshot_format = HDF5 # Particle snapshot format. "parquet" or "HDF5"
z_out = [10, 5, 2, 1, 0.5, 0]  # List of redshifts for output snapshots
save_power_spectrum = yes # Save power spectra. Either 'no', 'z_out' for specific redshifts given by z_out or 'yes' to compute at every time step. Uses same mass scheme and grid size (ncoarse) as for the PM solver
# Particles
integrator = leapfrog # Integration scheme for time-stepping "Leapfrog" or "Euler"
mass_scheme = TSC # CIC or TSC
n_reorder = 50  # Re-order particles every n_reorder steps
# Time stepping
Courant_factor = 1.0 # Cell fraction for time stepping based on velocity/acceleration (Courant_factor < 1 means more time steps)
max_aexp_stepping = 10 # Maximum percentage [%] of scale factor that cannot be exceeded by a time step
# Newtonian solver
linear_newton_solver = multigrid # Linear solver for Newton's method: "multigrid", "fft", "fft_7pt" or "full_fft"
gradient_stencil_order = 5 # n-point stencil with n = 2, 3, 5 or 7
# Multigrid
Npre = 2  # Number of pre-smoothing Gauss-Seidel iterations
Npost = 1  # Number of post-smoothing Gauss-Seidel iterations
epsrel = 1e-2  # Maximum relative error on the residual norm
# Verbose
verbose = 1 # Verbose level. 0 : silent, 1 : basic infos, 2 : full timings

Run the command line

python pysco/main.py -c examples/param.ini

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As package

To obtain the same as above, one first need to import the pysco module, then build a dictionnary (or Pandas Series) containing the user inputs.

# examples/example.py
from pathlib import Path
import pysco

path = Path(__file__).parent.absolute()

param = {
    "nthreads": 1,
    "theory": "newton",
    # "fR_logfR0": 5,
    # "fR_n": 1,
    # "mond_function": "simple",
    # "mond_g0": 1.2,
    # "mond_scale_factor_exponent": 0,
    # "mond_alpha": 1,
    # "parametrized_mu0": 0.1,
    "H0": 72,
    "Om_m": 0.25733,
    "T_cmb": 2.726,
    "N_eff": 3.044,
    "w0": -1.0,
    "wa": 0.0,
    "boxlen": 100,
    "ncoarse": 7,
    "npart": 128**3,
    "z_start": 49,
    "seed": 42,
    "position_ICS": "center",
    "fixed_ICS": False,
    "paired_ICS": False,
    "dealiased_ICS": False,
    "power_spectrum_file": f"{path}/pk_lcdmw7v2.dat",
    "initial_conditions": "2LPT",
    "base": f"{path}/boxlen100_n128_lcdmw7v2_00000/",
    "z_out": "[10, 5, 2, 1, 0.5, 0]",
    "output_snapshot_format": "HDF5",
    "save_power_spectrum": "yes",
    "integrator": "leapfrog",
    "n_reorder": 50,
    "mass_scheme": "TSC",
    "Courant_factor": 1.0,
    "max_aexp_stepping": 10,
    "linear_newton_solver": "multigrid",
    "gradient_stencil_order": 5,
    "Npre": 2,
    "Npost": 1,
    "epsrel": 1e-2,
    "verbose": 1,
}

# Run simulation
pysco.run(param)

print("Run completed!")

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Outputs

Pysco produces power spectra, snapshots, and extra information.

Power spectra

Power spectra are written as ascii files in the directory base/power/ where base in given by the user.

The name formatting is pk_theory_ncoarseN_XXXXX_.dat where theory and N are user inputs.

The ascii file contains three columns: k [h/Mpc], P(k) [Mpc/h]^3, N_modes

Additionally, the file header contains the scale factor, the box length and number of particles.

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Background evolution

Background evolution file written as ascii files in base/evolution_table_pysco.txt where base in given by the user.

The ascii file contains three columns: aexp, H/H0, t_supercomoving, dplus1, f1, dplus2, f2, dplus3a, f3a, dplus3b, f3b, dplus3c, f3c

where aexp is the scale factor, H/H0 the dimensionless Hubble parameter, t_supercomoving is the time in dimensionless supercomoving units, while dplusN and fN are the N-th order growth factor and growth rate respectively.

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Particle snapshots

Particles are written as either HDF5 or Parquet format. For the former, additional informations are written as attributes at the file root. For the latter, an extra ascii file is written.

• Positions are given in box units (between 0 and 1).

• Velocities are given in supercomoving units. To recover km/s one need to multiply by unit_l/unit_t, where both quantities are written either in the attributes for HDF5 file or in the associated information file for parquet format.

Note that output_00000/ is used to write the initial conditions. The additional number of directories depend on the length of the input list z_out.

HDF5 format

Particle snapshots are written as HDF5 files in the directory base/output_XXXXX

The name formatting is particles_theory_ncoarseN_XXXXX.h5

The HDF5 file contains two datasets: "position" and "velocity" as well as attributes. These files can be read as

import h5py
with h5py.File('snapshot.h5', 'r') as h5r:
  pos = h5r['position'][:]
  vel = h5r['velocity'][:]
  unit_t = h5r.attrs['unit_t']

Parquet format

Particle snapshots can also be written as parquet files in the directory base/output_XXXXX

The name formatting is particles_theory_ncoarseN_XXXXX.parquet

The parquet file contains six columns: x, y, z, vx, vy, vz. These files can be read as

import pandas as pd
df = pd.read_parquet('snapshot.parquet')
x = df['x']
vx = df['vx']

Alongside every parquet file there is an associated ascii information file.

The name formatting is param_theory_ncoarseN_XXXXX.txt

It contains parameter file informations as well as useful quantities such as the scale factor and unit conversions (unit_l, unit_t, unit_d for length, time and density respectively) from Pysco units to SI.

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Library utilities

As a side-product , PySCo can also be used as a library which contains utilities for particle and mesh computations.

Since PySCo does not use classes (not supported by Numba), we made it straightforward to use its functions on NumPy arrays for various purposes. We give a few examples below.

• Computing a density grid based on particle positions with a Triangular-Shaped Cloud scheme

import numpy as np
from pysco.mesh import TSC
positions = np.random.rand(32**3, 3).astype(np.float32)
density_grid = TSC(positions, ncells_1d=64)

• Interpolating to a finer grid

import numpy as np
from pysco.mesh import prolongation
coarse_field = np.random.rand(32, 32, 32).astype(np.float32)
fine_field = prolongation(coarse_field)

• Re-ordering particles according to Morton indexing (to increase data locality)

import numpy as np
from pysco.utils import reorder_particles
position = np.random.rand(64, 3).astype(np.float32)
velocity = np.random.rand(64, 3).astype(np.float32)
position, velocity = reorder_particles(position, velocity)

• FFT a real-valued grid and compute power spectrum

import numpy as np
from pysco.fourier import fourier_grid_to_Pk, fft_3D_real
nthreads = 2
density = np.random.rand(64, 64, 64).astype(np.float32)
density_k = fft_3D_real(density, nthreads)
MAS = 0 # Mass assignment scheme. # None = 0, NGP = 1, CIC = 2, TSC = 3
k, pk, modes = fourier_grid_to_Pk(density_k, MAS)
# For cosmological densities, need additional conversion factors
boxlen = 100 # Box length, in Mpc/h
pk *= (boxlen / len(density) ** 2) ** 3
k *= 2 * np.pi / boxlen

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Contributing

If you have a suggestion that would make this better, please fork the repo and create a pull request. You can also simply open an issue with the tag "enhancement".

1. Fork the Project
2. Create your Feature Branch (git checkout -b feature/AmazingFeature)
3. Commit your Changes (git commit -m 'Add some AmazingFeature')
4. Push to the Branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

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License

Distributed under the MIT License. See LICENSE for more information.

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Contact

Michel-Andrès Breton - [e-mail]

Project Link: https://github.com/mianbreton/pysco

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