Radial Basis Function (RBF) applications are addressed by the treverhines/RBF Python package, offering tools for interpolating scattered N-dimensional data and solving partial differential equations (PDEs) over irregular domains. It targets researchers and engineers needing accurate, meshfree approximation methods, drawing from established RBF literature to simplify complex numerical tasks and enable precise data reconstruction and PDE solutions.

How It Works

The package's core functionality lies in RBF interpolation and its application to PDEs. For PDE solving, it supports both a spectral RBF method, suitable for small-scale problems, and the more scalable Radial Basis Function Finite Difference (RBF-FD) method. The RBF-FD approach is emphasized for its ability to handle large-scale problems without manual shape parameter tuning (when using polyharmonic splines) and for achieving higher accuracy via increased stencil sizes or polynomial orders. A GaussianProcess class is also integrated for Bayesian statistical regression.

Quick Start & Requirements

• Installation: Install via pip: pip install treverhines-rbf.
• Prerequisites: Python environment. Examples utilize numpy, matplotlib, and scipy.
• Documentation: Comprehensive documentation is available at http://rbf.readthedocs.io.
• Verification: Test installation with python -m unittest discover from the test directory.

Highlighted Details

• RBF class: Evaluates RBFs and their exact derivatives.
• RBFInterpolant: Interpolates scattered N-dimensional data, supporting exact derivative evaluation.
• weight_matrix: Generates RBF-FD weights for PDE discretization.
• Node Generation: Functions like poisson_disc_nodes for creating node distributions.
• Computational Geometry: Tools for 2D/3D point-in-polygon testing.
• GaussianProcess: Implements Gaussian Process Regression (GPR).

Maintenance & Community

The provided README content does not detail specific maintenance practices, community channels (e.g., Discord, Slack), or a public roadmap.

Licensing & Compatibility

The license type and any restrictions for commercial use or integration with closed-source projects are not specified in the README.

Limitations & Caveats

The spectral RBF method for PDE solving is limited to small-scale problems and requires careful shape parameter selection. The RBF-FD method is generally recommended for its scalability and robustness.