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 and a Julia version (JRBFT) may 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
Installation
Add all folders to the Matlab path variable.
References
The MRBFT is described in the manuscript
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. Under review, Numerical Methods for Partial
Differential Equations, 2017.
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 RBF method for accurately resolving discontinuities
and steep gradients. Under review, Applied Numerical
Mathematics, 2017.
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
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!