The N-way toolbox for MATLAB


Rasmus Bro & Claus A. Andersson


The N-way toolbox provides means for


Fitting multi-way PARAFAC models
Fitting multi-way PLS regression models
Fitting multi-way Tucker models
Fitting the generalized rank annihilation method
Fitting the direct trilinear decomposition
Fitting models subject to constraints on the parameters such as e.g. nonnegativity, unimodality, orthogonality
Fitting models with missing values (using expectation maximization)
Fitting models with a weighted least squares loss function (including MILES)
Predicting scores for new samples using a given model
Predicting the dependent variable(s) of PLS models
Performing multi-way scaling and centering
Performing cross-validation of models
Calculating core consistency of PARAFAC models
Using additional diagnostic tools to evaluate the appropriate number of components
Perform rotations of core and models in Tucker models
Plus additional utility functions

In addition to the N-way toolbox, you can find a number of other multi-way tools on this site including PARAFAC2, Slicing (for exponential data such as low-res NMR), GEMANOVA for generalized multiplicative ANOVA, MILES for maximum likelihood fitting, conload for congruence and correlation loadings, eemscat for scatter handling of EEM data, clustering for multi-way clustering, CuBatch for batch data analysis, indafac for PARAFAC, PARALIND for constrained PARAFAC models, jackknifing for PARAFAC.

The N-way toolbox for MATLAB is freely available


Read the information on this page and download the files to your own computer.

The older version of N-way toolbox for MATLAB (version 1.xx) has been developed for MATLAB version 4.2 and 5.x and 6.x. Version 2 will function under MATLAB version 5.x and 6.x. Version 3 works under MATLAB version 7.x

If you use the N-way toolbox for MATLAB we would appreciate a reference to the toolbox. This may for example be

C. A. Andersson and R. Bro

The N-way Toolbox for MATLAB

Chemometrics & Intelligent Laboratory Systems. 52 (1):1-4, 2000.

You can download a PDF-file of the paper here.

If you have any questions, suggestions or comments please feel free to mail us.

Download the N-way Toolbox


All versions of The N-way Toolbox for MATLAB (most recent version 3.30 for MATLAB 7.3)

Learn to use the N-way Toolbox


You can learn to use the toolbox from the WWW-based interactive courses: Internet-based MATLAB courses in multi-way analysis

Extend to the N-way Toolbox


Tamara Kolda & Brett Bader have made a very nice toolbox for basic tensor operations. With this you can do all sorts of basic manipulations and products. This toolbox makes handling of multi-way arrays much simpler. Have a look at a report and download the toolbox here.

Why doesn't it work!


See the N-way toolbox faq: FAQ



The success of the N-way Toolbox relies on feedback from many users. In this regard we wish to acknowledge Christian Zacchariassen, Jostein Risa and Thomas Cullen for their elaborate and precise comments.