The Radial Basis Function Toolbox

The Radial Basis Function Toolbox (RBFT) is a collection of functions for implementing RBF interpolation methods and RBF methods for the numerical solution of PDEs on scattered centers located in complexly shaped domains. The toolbox is currently available in Matlab (MRBFT). A Python (PRBFT) version will be released in the future. The Matlab version uses the Multiprecision Computing Toolbox to seamlessly implement extended precision floating point arithmetic in all RBFT routines.

Comments, questions, bug reports, code requests, etc. can be sent to sarra@marshall.edu

Functionality

The functionality of the toolbox is organized via object oriented programming into several classes.

Classes:

rbfX - basic RBF method functionality

gax - Gaussian RBF
iqx - Inverse Quadratic RBF
imqx - inverse multiquadric RBF class (new in version 1.1)

rbfCenters - center locations
rbfCentro - reduced flop count and storage algorithms for RBF methods in symmetric domains.
Functions - test functions and derivatives.
rbfRational - (new in version 1.1) a rational RBF method
rbfMisc - (new in version 1.1) miscellaneous functions used in examples such as a 4th order Runge-Kutta method

Scripts: The toolbox comes with a collection of scripts that demonstrate its usage, benchmark its performance, and verify that its algorithms produce the correct results. The scripts are located in the following folders.

\examples
\tests
\benchmarks

MRBFT Downloads

version 1.0 (May 27, 2016): can be downloaded from GitHub or MRBFTv1p0.zip
version 1.1: (April 20, 2017): MRBFTv1p1.zip

References

The MRBFT is described in the manuscript

The Matlab Radial Basis Function Toolbox. Journal of Open Research Software, vol. 5, 2017.

All the numerical results in the following manuscript were produced with the MRBFT (in particular the rbfCentro class was used)

Radial Basis Function Methods - the case of symmetric domains. Numerical Methods for Partial Differential Equations, 2018. DOI:10.1002/num.22272

The double and extended precision "standard basis" RBF results in the following used the

An examination of evaluation algorithms for the RBF methods. Engineering Analysis with Boundary Elements, volume 75, p. 36-45, February 2017. DOI: 10.1016/j.enganabound.2016.11.006.

The rbfRational class that is new in version 1.1 was used in

A rational radial basis function method for accurately resolving discontinuities and steep gradients (with Y. Bai). Applied Numerical Mathematics 130, p. 131-142, 2018. DOI: 10.1016/j.apnum.2018.04.001

Future plans

development of new classes for local RBF methods
add Mercer's method to the GA class
expansion of the rbfCenters class

Change logs

MRBFT

Citing the MRBFT

If the RBFT has been significant to a project that leads to an academic publication, please acknowledge that fact by citing the project. The academic reference for the MRBFT is this paper. The BibTex entry for the paper is

@article{Sarra2017,
doi = {10.5334/jors.131},
year = {2017},
month = {March},
volume = {5},
author = {S. A. Sarra},
title = {The {M}atlab Radial Basis Function Toolbox},
journal = {Journal of Open Research Software}
}

or in plain text:

S. A. Sarra. The Matlab Radial Basis Function Toolbox. Journal of Open Research Software, vol. 5, 2017.

Thank you!