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SIZE="-1"><STRONG>Example</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Let us say that we want togenerate the following grid:</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><img src="engli0{image26}.gif"width="132" height="55" align=bottom > </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = kregrid (1, 1, 3, 0, 5,5)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y =</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">1 0</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">2 0</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">3 0</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">1 5</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">2 5</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">3 5</FONT></P><P><FONT FACE="Helvetica"><STRONG>ksone</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">MEX-file called fromkstest.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[d, prob] = ksone (sample, n,normal)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">MEX-file compiled from thesource Fortran code ksone.for, a Numerical Recipes subroutine.  Acomparison is made between the sample cumulative distribution and anormal cumulative distribution.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables</U>:</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">sample:  standardized sample(mean(sample) = 0 et std(sample) = 1) </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">n:  number of data in the sample</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">normal:  normal cumulativedistribution ranging from 0 to 1</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">d:  K-S statistic</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">prob:  significance level.Small values show that the sample cumulative distribution issignificantly different from normal.</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Reference</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Press, W et al.  1992.<EM>Numerical Recipes in Fortran, The Art of ScientificComputing</EM>, second ed., Cambridge University Press, Cambridge, p619.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>See also</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">kstest</FONT></P><P><FONT FACE="Helvetica"><STRONG>kstest</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Kolmogorov-Smirnov normalitytest.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[d, prob] = kstest(sample)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Normality test with the ksoneMEX-file.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables</U>:</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">sample:  sample </FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">d:  K-S statistic</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">prob:  significance level.Small values show that the sample cumulative distribution issignificantly different from normal.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> </FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Example</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Normality test of a vector ofnormally distributed random numbers:</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">data = randn(100,1);</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[d,prob] =kstest(data)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">d =</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 0.0456</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">prob =</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">0.9854<STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>References</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Kreyszig, E., 1988.<EM>Advanced Engineering Mathematics</EM>, sixth ed., John Wiley&amp; Sons, New York, p.1211.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Legendre, L.  and Legendre, P.(1983) Numerical Ecology.  Developments in Environment Modeling 3.Elsevier, New York, 419p.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ksone</FONT></P><P><FONT FACE="Helvetica"><STRONG>mat3dp</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Get a value out of a pseudo 3-Dmatrix.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">r = mat3d ( mat, d3, i, j, k)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">A pseudo 3-D matrix is a 2-Dmatrix made up of successive 2-D slices.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mat:  pseudo 3-Dmatrix</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">d3:  number of levels in thethird dimension </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">i:  position in the firstdimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">j:  position in the seconddimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">k:  position in the thirddimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">r:  value corresponding tomat(i,j,k)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Example</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">x =</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 1.0 1.2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 1.5 1.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 2.0 2.2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 2.5 2.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 3.0 3.2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 3.5 3.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mat3dp (x, 3, 1, 2, 2) =2.2<STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"><STRONG></STRONG></FONT><FONTFACE="Helvetica"><STRONG>mat4dp</STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Get a value out of a pseudo 4-Dmatrix.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">r = mat4d (mat, d3, d4, ii, jj,kk, ll)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">A pseudo 4-D matrix is a 2-Dmatrix made up of successive pseudo 3-D matrices.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mat:  pseudo 4-Dmatrix</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">d3:  number of levels in thethird dimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">d4:  number of levels in thefourth dimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ii:  position in the firstdimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">jj:  position in the seconddimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">kk:  position in the thirddimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ll:  position in the fourthdimension</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">r:  value corresponding tomat(ii,jj,kk,ll)</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Example</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">x =</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 1.0 1.2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 1.5 1.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 2.0 2.2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 2.5 2.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 3.0 3.2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 3.5 3.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 4.0 4.2</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 4.5 4.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mat4dp (x, 2, 2, 1, 2, 2, 1) =2.2<STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"><STRONG>means</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Mean function called fromcokri2.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = means (x)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Average or mean value.  The onlydifference with matlab function mean is for a row vector.  Meansreturns the same row vector instead of the mean value of theelements of the row.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">x:  a vector or amatrix</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y:  row vector of the mean ofeach column</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Example</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Let us consider the followingmatrix:</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">x = 1.0 1.5 2.0 2.5 3.03.5</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">1.2 1.7 2.2 2.7 3.23.7</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">means (x) = 1.1 1.6 2.1 2.6 3.13.6</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mean (x) = 1.1 1.6 2.1 2.6 3.13.6</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">whereas</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">means (x(1,:)) = 1.0 1.5 2.0 2.53.0 3.5</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mean (x(1,:)) = 2.25</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Reference</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Marcotte, D., 1991.  Cokrigeagewith MATLAB.  Computers &amp; Geosciences.  17(9):1265-1280.</FONT></P><P><FONT FACE="Helvetica"><STRONG>mrqmin / mrqcof / covsrt /gaussj</STRONG></FONT><FONT FACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mrqmin:  Least-square fitting:Levenberg-Marquardt method.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mrqcof:  M-file called frommrqmin.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">covsrt:  Transform thecovariance matrix of mrqmin.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">gaussj:  Linear equationsolution by Gauss-Jordan elimination.</FONT></P>

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