The Radial Basis Function Toolbox

The Radial Basis Function Toolbox (RBFT) is software for implementing RBF interpolation methods and RBF methods for the numerical solution of PDEs on scattered centers located in complexly shaped domains.  The RBFT is under constant development as it is heavily used in my RBF research projects.

The two earlier versions of the toolbox, versions 1.0 and 1.1, were programmed in Matlab.  For a multitude of reasons I no longer use Matlab.  The Matlab versions will remain available for download and may see minor bug fixes and improvements but will not be developed further.  All future versions of the toolbox will be in the Python programming language.

Comments, questions, bug reports, code requests, etc. can be sent to


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


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.

Future plans

MRBFT Downloads - Matlab version

The Matlab version uses the Multiprecision Computing Toolbox to seamlessly implement extended precision floating point arithmetic in all RBFT routines. 

PRBFT Downloads - Python version

Change logs


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

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

Citing the RBFT

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 RBFT is this paper.  The BibTex entry for the paper is

  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!