structure-factor 1.0.1

Approximate the structure factor of a stationary point process, test its effective hyperuniformity, and identify its class of hyperuniformity.

structure-factor

Approximate the structure factor of a stationary point process, test its effective hyperuniformity, and identify its class of hyperuniformity.

• structure-factor
  • Introduction
  • Dependencies
  • Installation
    • Install the project as a dependency
    • Install in editable mode and potentially contribute to the project
  • Documentation
    • Build the documentation
  • Getting started

Introduction

Hyperuniformity is the study of stationary point processes with a sub-Poisson variance of the number of points in a large window. To study the hyperuniformity of a given point process, a common practice in statistical physics is to estimate a spectral measure called the structure factor, the behavior of which around zero is a sign of hyperuniformity. The structure factor of a point process is defined via the Fourier transform of its total correlation function, and a point process is hyperuniform if its structure factor vanishes at zero. This Python toolbox gathers many estimators of the structure factor, along with a numerical test of effective hyperuniformity and a test for identifying the possible hyperuniformity class.

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structure-factor is an open-source Python project which currently collects

• Three estimators of the structure factor:

  1. the scattering intensity,
  2. an estimator using Ogata quadrature for approximating the Hankel transform,
  3. an estimator using Baddour and Chouinard Discrete Hankel transform.

• Two ways to qualify hyperuniformity:

  1. effective hyperuniformity,
  2. classes of hyperuniformity.

Dependencies

• R programming language, since we call the spatstat R package to estimate the pair correlation function of point processes using spatstat-interface.

• Python dependencies are listed in the pyproject.toml file. Note that they mostly correspond to the latest version.

  [tool.poetry.dependencies]
  python = ">=3.7.1,<3.10"
  
  numpy = "^1.20.3"
  scipy = "^1.6.3"
  matplotlib = "^3.4.2"
  pandas = "^1.2.4"
  spatstat-interface = "^0.1.0"
  # spatstat-interface https://github.com/For-a-few-DPPs-more/spatstat-interface requires rpy2 https://rpy2.github.io/
  

Installation

structure-factor works with .

Once installed it can be called from

• import structure_factor
• from structure_factor import ...

Install the project as a dependency

• Install the latest version published on

  # activate your virtual environment an run
  poetry add structure-factor
  # pip install structure-factor
  

• Install from source (this may be broken)

  # activate your virtual environment and run
  poetry add git+https://github.com/For-a-few-DPPs-more/structure-factor.git
  # pip install git+https://github.com/For-a-few-DPPs-more/structure-factor.git
  

Install in editable mode and potentially contribute to the project

The package can be installed in editable mode using poetry.

To do this, clone the repository:

• if you considered forking the repository

  git clone https://github.com/your_user_name/structure-factor.git
  

• if you have not forked the repository

  git clone https://github.com/For-a-few-DPPs-more/structure-factor.git
  

and install the package in editable mode

cd structure-factor
poetry shell  # to create/activate local .venv (see poetry.toml)
poetry install
# poetry install --no-dev  # to avoid installing the development dependencies
# poetry add -E docs -E notebook  # to install extra dependencies

Documentation

The documentation is

• generated using Sphinx, and
• published via the GitHub workflow file .github/workflows/docs.yml.

Build the documentation

If you use poetry

• install the documentation dependencies (see [tool.poetry.extras] in pyproject.toml)

  cd structure-factor
  poetry shell  # to create/activate local .venv (see poetry.toml)
  poetry install -E docs  # (see [tool.poetry.extras] in pyproject.toml)
  

• and run

  # cd structure-factor
  # poetry shell  # to create/activate local .venv (see poetry.toml)
  poetry run sphinx-build -b html docs docs/_build/html
  open _build/html/index.html
  

Otherwise, if you don't use poetry

• install the documentation dependencies (listed in [tool.poetry.extras] in pyproject.toml), and

• run

  cd structure-factor
  sphinx-build -b html docs docs/_build/html
  open _build/html/index.html
  

Getting started

• Jupyter notebooks that showcase structure-factor are available in the ./notebooks folder.

  • if you use poetry

    cd structure-factor
    poetry shell  # to create/activate local .venv (see poetry.toml)
    poetry install -E notebook  # (see [tool.poetry.extras] in pyproject.toml)
    # open a notebook within VSCode for example
    

• See the documentation