Welcome to parafields

parafields is a Python package that provides Gaussian random fields based on circulant embedding. Core features are:

• Large variety of covariance functions: exponential, Gaussian, Matérn, spherical and cubic covariance functions, among others
• Generation of distributed fields using domain decomposition and MPI through mpi4py
• Uses numpy data structures to ease integration with the Python ecosystem of scientific software
• Optional caching of matrix-vector products
• Easy integration into FEniCSx-based PDE solvers (Example)

parafields implements these features through Python bindings to the parafields-core C++ library. The following options are supported in the backend but not yet in the Python bindings:

• axiparallel and full geometric anisotropy
• value transforms like log-normal, folded normal, or sign function (excursion set)
• Coarsening and refinement of random fields for multigrid/-scale methods

Usage

This is a minimal usage example of the parafields package:

For more examples, check out the parafields documentation.

Installation

parafields is available from PyPI and can be installed using pip:

python -m pip install parafields

This will install a sequential, pre-compiled version of parafields. In order to use parafields in an MPI-parallel context, you need to instead build the package from source:

python -m pip install --no-binary parafields -v parafields

This will build the package from source and link against your system MPI.

Additionally, parafields defines the following optional dependency sets:

• jupyter: All requirements for an interactive Jupyter interface to parafields
• tests: All requirements for running parafields's unit tests
• docs: All requirements for buildings parafields's Sphinx documentation

These optional dependencies can be installed by installing e.g. parafields[jupyter].

Acknowledgments

The parafields-core C++ library is work by Ole Klein whichis supported by the federal ministry of education and research of Germany (Bundesministerium für Bildung und Forschung) and the ministry of science, research and arts of the federal state of Baden-Württemberg (Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg).

The Python bindings are realized by the Scientific Software Center of Heidelberg University. The Scientific Software Center is funded as part of the Excellence Strategy of the German Federal and State Governments.