# OoDACE:ooDACE toolbox

## Contents |

## Introduction

The ooDACE toolbox is a versatile Matlab toolbox that implements the popular Gaussian Process based kriging surrogate models. Kriging is in particular popular for approximating (and optimizing) deterministic computer experiments. Given a dataset the toolbox automatically fits a kriging surrogate model to it. Afterwards the kriging surrogate can be fully exploited instead of the (probably more expensive) simulation code.

The toolbox is aimed for solving complex applications (expensive simulation codes, physical experiments, ...) and for researching new kriging extensions and techniques.

## Download

See: download page

## Quick start guide

**IMPORTANT**: Before the toolbox can be used you have to include the toolbox in Matlab's search path. You can do this manually by running startup, or, if Matlab is started in the root toolbox directory, then startup will be run automatically.

startup

Now the toolbox is ready to be used. The ooDACE toolbox is designed in an object oriented (OO) fashion. It is strongly recommended to exploit the OO design directly, i.e., use the Kriging and Optimizer matlab classes. However, for convenience wrapper scripts (dacefit, predictor) are provided that emulate the DACE toolbox interface (see wrapper scripts for more information).

Assume you want to fit a dataset of n samples in d dimensions.

**samples** holds the input parameters n-by-d array (each row is one observation) and **values** is the corresponding n-by-1 array containing the output values.
**lb** and **ub** are 1-by-d arrays defining the lower bounds and upper bounds, respectively, needed to optimize the hyperparameters (**theta**). In addition, a set of starting values for **theta** has to be specified (i.e., **theta0** is also an 1-by-d array)

As of version 0.2 of the ooDACE toolbox a script is provided, oodacefit, that just takes your dataset (a **samples** and **values** matrix) and returns a fitted kriging object, all other parameters (**theta0**, etc.) are set to some sensible defaults.

For more flexibility the full example code to fit the dataset is:

... % Generate kriging options structure opts = getDefaultOptions(); opts.hpBounds = [lb ; ub]; % hyperparameter optimization bounds % configure the optimization algorithm (only one optimizer is included) % the Matlab Optimization toolbox is REQUIRED optimopts.GradObj = 'on'; optimopts.DerivativeCheck = 'off'; optimopts.Diagnostics = 'off'; optimopts.Algorithm = 'active-set'; opts.hpOptimizer = MatlabOptimizer( dim, 1, optimopts ); % build and fit Kriging object k = Kriging( opts, theta0, 'regpoly0', @corrgauss ); k = k.fit( samples, values ); % k represents the approximation and can now be used, e.g., [y mse] = k.predict( [1 2] ) ...

See the included demo.m script for more example code on how to use the ooDACE toolbox (including more advanced features such as using blind kriging or how to use regression instead of interpolation). For more information on the classes and their methods please refer to the source files.

## DACE toolbox interface

The ooDACE toolbox provides two scripts dacefit.m and predictor.m that emulate the behavior of the DACE toolbox ([1]). Note, that full compatibility between ooDACE and the DACE toolbox is not provided. The scripts merely aim to ease the transition from the DACE toolbox to the ooDACE toolbox.

Example code:

krige = dacefit(samples, values, 'regpoly0', 'corrgauss', theta0, lb, ub ) y = predictor([1 2], krige)

Obviously, a lot less code is used to copy the setup described above. However, less code means less flexibility (e.g., blind kriging and regression kriging are not available using the wrapper scripts). Hence, it is suggested to learn the object oriented interface of ooDACE and use it instead.

## Contribute

Suggestions on how to improve the ooDACE toolbox are always welcome. For more information please see the feedback page.