Deac kriging

IMM
INFORMATICS AND MATHEMATICAL MODELLING
Technical University of Denmark
DK-2800 Kgs. Lyngby – Denmark

DACE
A M ATLAB Kriging Toolbox
Version 2.0, August 1, 2002
Søren N. Lophaven
Hans Bruun Nielsen
Jacob Søndergaard

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Technical Report IMM-TR-2002-12

Please direct communication to Hans Bruun Nielsen ([e-mail])

Contents
1. Introduction

1

2. Modelling and Prediction

1

2.1. The Kriging Predictor . . . . . . . . . . . . . . . . . . . . . . . . . .

2

2.2. Regression Models . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.3. Correlation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

3. Generalized Least Squares Fit

9

3.1. Computational Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4. Experimental Design

12

4.1. Rectangular Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2. Latin Hypercube Sampling . . . . . . . . . . . . . . . . . . . . . . . . 12
5. Reference Manual

13

5.1. Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2. Evaluate the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.3. Regression Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.4. Correlation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.5. Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.6. Auxiliary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.7. Data Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6. Examples of Usage

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6.1. Work-through Example . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6.2. Adding a Regression Function . . . . . . . . . . . . . . . . . . . . . . 24
7. Notation

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1.

Introduction

This report describes the background for and use of the

References: [1] G. Golub, C. Van Loan, Matrix Computations. Johns Hopkins University Press, Baltimore, USA, 3rd edition, 1996. [2] E.H. Isaaks, R.M. Srivastava, An Introduction to Applied Geostatistics. Oxford University Press, New York, USA, 1989. Elsevier, New York, USA, 1968. DTU. (2002), 44 pages. Available as http://www.imm.dtu.dk/∼hbn/publ/TR0213.ps Random Fields. Physica-Verlag, Heidelberg, Germany, 2001. [7] J. Nocedal, S.J. Wright, Numerical Optimization, Springer, New York, USA, 1999. 5, pp. 479-488, 1998. [9] J. Sacks, W.J. Welch, T.J. Mitchell, H.P. Wynn, Design and Analysis of Computer Experiments, Statistical Science, vol. 4, no. 4, pp. 409-435, 1989.