The Python Radial Basis Function Toolbox

The Python 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 PRBFT is under constant development as it is heavily used in 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 Matlab is no longer used.  The Matlab versions will remain available for download (see the bottom of this page) and may see minor bug fixes and improvements but will not be developed further. All future development will be in the Python version.

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.

Classes and modules:

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.

PRBFT Downloads - Python version

new in version 2.0:

Future plans

PRBFT References

version 2.0 is used in

Local Radial Basis Function methods: comparison, improvements, and implementation.  Journal of Applied Mathematics and Physics, 11, p. 3867-3886, 2023. DOI: 10.4236/jamp.2023.1112245.

Older Matlab version

MRBFT Downloads - Matlab version

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

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

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

Citing the MRBFT

The academic reference for the MRBFT 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.