STK: a Small (Matlab/Octave) Toolbox for Kriging

This README file is part of

STK: a Small (Matlab/Octave) Toolbox for Kriging

STK is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

STK is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with STK. If not, see

General information

Version: See stk_version.m

Authors: See AUTHORS file

Maintainers: Julien Bect and Emmanuel Vazquez

Description: The STK is a (not so) Small Toolbox for Kriging. Its primary focus is on the interpolation/regression technique known as kriging, which is very closely related to Splines and Radial Basis Functions, and can be interpreted as a non-parametric Bayesian method using a Gaussian Process (GP) prior. The STK also provides tools for the sequential and non-sequential design of experiments. Even though it is, currently, mostly geared towards the Design and Analysis of Computer Experiments (DACE), the STK can be useful for other applications areas (such as Geostatistics, Machine Learning, Non-parametric Regression, etc.).

Copyright: Large portions are Copyright (C) 2011-2014 SUPELEC and Copyright (C) 2015-2023 CentraleSupelec. See individual copyright notices for more details.

License: GNU General Public License, version 3 (GPLv3). See COPYING for the full license.


One toolbox, two flavours

The STK toolbox comes in two flavours:

Hint: if you’re not sure about the version that you have…

Quick Start

Quick start with the “all purpose” release (Matlab/Octave)

Download and unpack an archive of the “all purpose” release.

Run stk_init in either Octave or Matlab. One way to do so is to navigate to the root directory of STK and then simply type:


Alternatively, if you don’t want to change the current directory, you can use:

run /path/to/stk/stk_init.m

Note that this second approach is suitable for inclusion in your startup script.

After that, you should be able to run the examples located in the examples directory. All of them are scripts, the file name of which starts with the stk_example_ prefix.

For instance, type


to run the third example in the “kriging basics” series.

Remark: when using STK with Mathworks’ Parallel Computing Toolbox, it is important to run stk_init within each worker. This can be achieved using:

pctRunOnAll run /path/to/stk/stk_init.m

Quick start with the Octave package release (Octave only)

Assuming that you have a working Internet connection, typing

pkg install -forge stk

(from within Octave) will automatically download the latest STK package tarball from the Octave Forge file release system on SourceForge and install it for you.

Alternatively, if you want to install an older (or beta) release, you can download the tarball from either the STK project FRS or the Octave Forge FRS, and install it with

pkg install FILENAME.tar.gz

After that, you can load STK using

pkg load stk

To check that STK is properly loaded, try for instance


to run the third example in the “kriging basics” series.

Requirements and recommendations

Common requirement

Your installation must be able to compile C mex files.

Requirements and recommendations for use with GNU Octave

The STK is tested to work with GNU Octave 4.0.1 or newer.

Requirements and recommendations for use with Matlab

The STK is tested to work with Matlab R2014a or newer.

The Optimization Toolbox is recommended.

The Parallel Computing Toolbox is optional.


By publishing this toolbox, the idea is to provide a convenient and flexible research tool for working with kriging-based methods. The code of the toolbox is meant to be easily understandable, modular, and reusable. By way of illustration, it is very easy to use this toolbox for implementing the EGO algorithm [1]. Besides, this toolbox can serve as a basis for the implementation of advanced algorithms such as Stepwise Uncertainty Reduction (SUR) algorithms [2].

The toolbox consists of three parts:

  1. The first part is the implementation of a number of covariance functions, and tools to compute covariance vectors and matrices. The structure of the STK makes it possible to use any kind of covariances: stationary or non-stationary covariances, aniso- tropic covariances, generalized covariances, etc.

  2. The second part is the implementation of a REMAP procedure to estimate the parameters of the covariance. This makes it possible to deal with generalized covariances and to take into account prior knowledge about the parameters of the covariance.

  3. The third part consists of prediction procedures. In its current form, the STK has been optimized to deal with moderately large data sets.


[1] D. R. Jones, M. Schonlau, and William J. Welch. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13(4):455-492, 1998.

[2] J. Bect, D. Ginsbourger, L. Li, V. Picheny, and E. Vazquez. Sequential design of computer experiments for the estimation of a probability of failure. Statistics and Computing, pages 1-21, 2011. DOI: 10.1007/s11222-011-9241-4.

Ways to get help, report bugs, ask for new features…

Use the “help” mailing-list: (register/browse the archives: here)

to ask for help on STK, and the ticket manager:

to report bugs or ask for new features (do not hesitate to do so!).

If you use STK in Octave, you can also have a look there:

How to contribute

The contribution process is explained in