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<HTML><HEAD><META NAME="Author" CONTENT="Yves Gratton"><TITLE>MATLAB Kriging Toolbox</TITLE></HEAD><BODY><P ALIGN="CENTER"><FONT FACE="Helvetica"SIZE="+2"><STRONG></STRONG></FONT><FONT FACE="Helvetica"SIZE="+2"><STRONG>MATLAB Kriging Toolbox</STRONG></FONT></P><P ALIGN="CENTER"><FONT FACE="Helvetica" SIZE="-1"><STRONG>(version3.0: février 1998)</STRONG></FONT></P><P ALIGN="CENTER"><FONT FACE="Helvetica" SIZE="-1"><STRONG>Note:During conversion from a Word document to html, the figures wereeither lost or only partially converted. Please use the <ahref="english.doc">original Word document</a> in order to see allequations and other figures.</STRONG></FONT></P><P ALIGN="CENTER"><FONT FACE="Helvetica" SIZE="-1"><STRONG>CarolineLafleur</STRONG></FONT></P><P ALIGN="CENTER"><FONT FACE="Helvetica"SIZE="-1">INRS-Océanologie, 310 Allée des Ursulines,Rimouski, Qc., Canada, G5L 3A1</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">The Matlab Kringing Toolbox isfree and hence no support or warranty are provided.</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Specifications</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">The Kriging Toolbox version 3.0is matlab 5.1 and 5.2 compatible under Windows 95. It is an upgradeof version 2.0 which has been compiled under matlab 4.2. Pleasenote that this upgrade only uses 2-D matrices even though the newmatlab version supports greater matrix dimensions.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">This toolbox can be used "as itis" without other matlab toolbox except the probability functions(chi). However, it may also use the leastsq.m function fromMatlab's Opimization toolbox (see fitvario.m). The mex files havebeen compiled with Microsoft Fortran Power station V4.0 for Matlab5.1. As far as we have been able to test, they also work withMatlab 5.2. </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">The Chi Toolbox is necessary fornormality study. It is provided with the KrigingToolbox.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">The development of this toolboxis based on the necessity of using objective analysis of scalars in2 or 3 dimensions in physical oceanography. This type ofinterpolation usually gives better results than standardinterpolation methods. Furthermore, it has the non-negligibleadvantage of giving estimates of interpolation errors.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">This toolbox is almost entirelymade up of functions from the book by Deutsch and Journel (1992) andfrom the paper by Marcotte (1991). The variogram functions areMEX-files compiled from the former while the cokriging functionswere published, in Matlab format, in Marcotte's 1991 paper. All theparameters and examples can be found, in English, in the twopublications. The book by Journel and Huijbregts (1992) is the bestbook on semivariograms. A complete example of optimal estimation inphysical oceanography can be found in the paper by Denman andFreeland (1985). As well, kridemo shows outlines of a 2-D objectiveanalysis.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Denman, K.L. and H.J.Freeland, 1985. Correlation Scales, Objective Mapping and aStatistical Test of Geostrophy over the Continental Shelf. J. Mar.Res., 43: 517-539.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Deutsch, C. V and A. G.Journel, 1992. <EM>GSLIB: Geostatistical Software Library andUser's Guide</EM>. Oxford University Press, Oxford, 340p.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Journel, A.G. and C.J.Huijbregts, 1992. <EM>Mining Geostatistics</EM>. Academic Press,New York, 600 p.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Marcotte, D. 1991. Cokrigeagewith MATLAB. Computers & Geosciences. 17(9):1265-1280.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Comments, suggestions orquestions?</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Many functions are still notcompletely tested. Please report any bugs or problems to</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Caroline Lafleur,INRS-Océanologie, Tél: (418) 724 1650 poste1296</FONT></P><P><FONT FACE="Helvetica"SIZE="-1">caroline_lafleur@uqar.uquebec.ca</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Yves Gratton,INRS-Océanologie, Tél: (418) 724 1741</FONT></P><P><FONT FACE="Helvetica"SIZE="-1">yves_gratton@uqar.uquebec.ca</FONT></P><P><FONT FACE="Helvetica"><STRONG>Kriging ToolboxContents</STRONG></FONT><FONT FACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"> <STRONG>Variogramfunctions</STRONG></FONT><FONT FACE="Helvetica"SIZE="-1"><STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> confint Confidenceintervals.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> fitvario Optimization ofvariogr.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> fitvari2 Optimization ofvariogr2 (without the Optimization Toolbox).</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> fun Called from fitvario toestimate variograms. </FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> gam2 MEX-file called fromvario2dr. </FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> gam3 MEX-file called fromvario3dr.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> gamv2 MEX-file called fromvario2di.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> gamv2uv MEX-file called fromvar2diuv.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> gamv3 MEX-file called fromvario3di.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> mrqmin Least-square fitting:Levenberg-Marquardt method.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> outvario Output of variogramfunctions. </FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> variogr Models of semivariogramand correlogram.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> variogr2 variogr for fittingprocedures not using the Optimization Toolbox.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> vario2di Variogram ofirregularly spaced 2-D data.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> vario2dr Variogram of regularlyspaced 2-D data.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> vario3di Variogram ofirregularly spaced 3-D data.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> vario3dr Variogram of regularlyspaced 3-D data.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> var2diuv Variogram ofirregularly spaced 2-D vectors.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG> </STRONG></FONT><FONTFACE="Helvetica"><STRONG>Kriging functions</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> barnes 2-D spatial filter forkriged data.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> cokri Point or block cokrigingin D dimensions.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> cokri2 Cokriging functioncalled from cokri.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> davis Point kriging usingDavis' set of equations.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> filresp Barnes' filter responsein the wavelength domain.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> tintore Application of Barnes'filter with the Tintoré's parameters (1991).</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> </FONT><FONTFACE="Helvetica"><STRONG>Related functions</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> </FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> covsrt Transform the covariancematrix of mrqmin.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> déplie Vector to matrixtransformation.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> gaussj Linear equation solutionby Gauss-Jordan elimination.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> kregrid Matrix (m x 2) of 2-Dgrid coordinates.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> kregrid3 Matrix (m x 3) of 3-Dgrid coordinates.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> kridemo Kriging Toolboxdemo.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> ksone MEX-file called fromkstest.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> kstest Kolmogorov-Smirnovnormality test.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> mat3dp Get a value out of apseudo 3-D matrix.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> mat4dp Get a value out of apseudo 4-D matrix.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> means Mean function called fromcokri2.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> mrqcof M-file called frommrqmin.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> trans Translation functioncalled from cokri2.</FONT></P><P><FONT FACE="Helvetica"><STRONG>VariogramOptions</STRONG></FONT><FONT FACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Available variograms are:</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">1. Semivariogram: <imgsrc="engli0{image0}.gif" width="167" height="52" align=bottom></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">2. Cross semivariogram: <imgsrc="engli0{image1}.gif" width="217" height="52" align=bottom></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">3. Covariance: <imgsrc="engli0{image2}.gif" width="249" height="52" align=bottom ></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">4. Correlogram: <imgsrc="engli0{image3}.gif" width="91" height="54" align=bottom></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">5. General relativesemivariogram: <img src="engli0{image4}.gif" width="226"height="83" align=bottom ></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">6. Pairwise relativesemivariogram: <img src="engli0{image5}.gif" width="191"height="54" align=bottom ></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">7. Semivariogram of logarithms:<img src="engli0{image6}.gif" width="219" height="52" align=bottom></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">8. Semirodogram: <imgsrc="engli0{image7}.gif" width="176" height="52" align=bottom></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">9. Semimadogram: <imgsrc="engli0{image8}.gif" width="165" height="52" align=bottom></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">10. Semivariogramme indicator:<img src="engli0{image9}.gif" width="154" height="55" align=bottom></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Variabledescriptions:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">C(h) = covariance as a functionof distance h; C(0) gives the variance.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">g(h) = semivariance = [ C(0) -C(h) ].</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">h = separationvector.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">N(h) = number of samplepairs</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">xi,yi = value of the sample pairseparated by vector h: xi is the value at the start (or tail) andyi is the value at the end (or head) of interval h.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">zi,zi' et yi,yi' = same as(xi,yi) in the cross semivariogram: yi and zi are the values at thestart and yi' and zi' are the values at the end of intervalh.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">For more information, pleaseconsult Deutsch and Journel (1992).</FONT></P><P><FONT FACE="Helvetica"><STRONG>KrigingOptions</STRONG></FONT><FONT FACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Available kriging options are:</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> simple cokriging </FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> ordinary cokriging with onenonbias condition (Isaaks and Srivastava)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> ordinary cokriging with pnonbias condition</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> universal cokriging with driftof order 1</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> universal cokriging with driftof order 2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">99. cokriging is not performed,only sample variance sv is computed</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Cokriging means kriging withmore than one variable. When the cokriging program is called withonly one variable at a time, the results will be those of simplekriging, ordinary kriging, universal kriging, point kriging or blockkriging. More details can be found in the paper of Marcotte(1991).</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG> </STRONG></FONT></P><P><FONT FACE="Helvetica"><STRONG>Chi ToolboxContents</STRONG></FONT><FONT FACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">This toolbox is used by thenormality test. The included functions compute the Chi-squaredprobability function and the percentage points of the probabilityfunction. The m-files were downloaded from the matlab public site:</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><EM>http://www.mathworks.com/ftp/statv4/shtml</EM></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Probability functionc<SUP>2</SUP></STRONG></FONT><FONT FACE="Helvetica"SIZE="-1"><SUP></SUP></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> chiprob Probability ofobserving a given c<SUP>2</SUP>value.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> chitable c<SUP>2</SUP> valuefor a given probability.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> chiaux Function called fromchitable.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Toolboxauthor:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Peter R. Shaw</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Woods Hole OceanographicInstitution, Woods Hole, MA 02543</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">(508) 457-2000 ext.2473</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">pshaw@whoi.edu</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Note</U>: OptimizationToolbox needed</FONT></P><P><FONT FACE="Helvetica"><STRONG>barnes</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"?? 快捷鍵說明
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