<P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[covari, alpha, chisq, alamda,a] = mrqmin (x ,y ,sig ,ndata, a, ia, ma, nca, funcs, alamda,model)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[alpha, beta, chisq] = mrqcof(x, y, sig, ndata, a, ia, ma, nalp, funcs, model)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">covari = covsrt (npc, ma, ia,mfit, covari)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[a, b] = gaussj (a, n, np, b, m,mp)</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">Levenberg-Marquardt method,attempting to reduce the value <EM>c</EM> of a fit between a set ofdata points x(ndata), y(ndata) with standard deviations sig(ndata),and a nonlinear function dependent on ma coefficientsa(1:ma).</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, p680.<STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvario2</FONT></P><P><FONT FACE="Helvetica"><STRONG>outvario</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">Output of variogramfunctions.</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[np, gam, hm, tm, hv, tv] =outvario (nlg, in7, ndir, nvarg, in1, in2, in3, in4, in5,...  in6,ivtype)</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">This function is only used toreorganize the outputs of gam2, gamv2, gam3 and gamv3.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">vario2di, vario2dr, var2diuv,vario3di, vario3dr</FONT></P><P><FONT FACE="Helvetica"><STRONG>tintore</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Application of Barnes' filterwith the Tintor&eacute;'s parameters (1991).</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">[F2, Fb] = tintore (xi, yi,zi)</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">This function is an example ofBarnes' filter to separate mesoscale from macroscale features inphysical oceanography.  The filter parameters are those establishedby Tintor&eacute; et al.  (1991).</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">xi:  vector of the x gridcoordinates (positions of the columns of zi)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">yi:  vector of the y gridcoordinates (positions of the rows of zi)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">zi:  grid data (size(zi) =[length(yi), length(xi)])</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">F2:  macroscalestructure</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Fb:  mesoscalestructure</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Reference</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Tintor&eacute; et al., 1991.Mesoscale Dynamics and Vertical Motion in the Alboran Sea, J.  Phys.Oceanogr., 21:811-823.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">barnes, filresp</FONT></P><P><FONT FACE="Helvetica"><STRONG>trans</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">Translation 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">cx = trans (cx, model,im)</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">This function takes as inputoriginal coordinates and returns the rotated and reduced coordinatesfollowing specifications described in the semivariogrammodel.</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" SIZE="-1"><STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">cokri2</FONT></P><P><FONT FACE="Helvetica"><STRONG>variogr /variogr2</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">variogr:  Models ofsemivariogram and 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"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = variogr (type, r, a, C, b)for semivariograms</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = variogr (-type, r, a, C, b)for correlograms</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = variogr2 (type, r, a, C, b)for semivariograms</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = variogr2 (-type, r, a, C, b)for correlograms</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">This function is used to obtainthe theoretical curve of the variance of a sample as a function ofthe sample pair distance.  </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Available model optionsare:</FONT></P><MULTICOL COLS="2" WIDTH="507" GUTTER="46"><P><FONT FACE="Helvetica" SIZE="-1"><U></U><EM>With asill</EM></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">1.  spherical</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">2.  exponential</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">3.  gaussian</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">4.  quadratic (inpreparation)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U></U></FONT><FONTFACE="Helvetica" SIZE="-1"><EM>Without a sill</EM><U></U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">5.  linear<U></U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">10.  logarithmic (inpreparation)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">11.  power of r (in preparation)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><EM>Hole effects</EM></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">20.  C * ( 1 - sin(b*r) / r)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">21.  C * ( 1 - exp(-r/a) *cos(b*r) )</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">22.  C * ( 1 + exp(-r/a) *cos(b*r) )</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">23.  C * ( 1 - exp(-r/a) *cos(r*b) )</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">24.  C * (1 -exp(-(r/a)<SUP>2</SUP>) * cos(b*r) )</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">25.  C * ( 1 - J<SUB> 0</SUB>(b*r) )</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">26.  C * ( 1 - J<SUB>0</SUB>(b*r) * exp(-r/a) )</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">27.  C * ( 1 -exp(-(r/a)<SUP>2</SUP>) * J<SUB>0</SUB> (b*r) )</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">28.  C * ( 1 -exp(-(r/a)<SUP>2</SUP>) * (1 - br<SUP>2</SUP>)</FONT></P><BR WP="BR1"><BR WP="BR2"></MULTICOL><P><FONT FACE="Helvetica" SIZE="-1">Any new types can be easilyadded to the list.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">r:  distance vector</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">a:  range</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">C:  amplitude</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">b:  coefficient used in themodels 20</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">type:  variogram type</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y:  variance as a function of r</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Reference</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Journel, A.G.  and C.J.Huijbregts, 1992.  <EM>Mining Geostatistics</EM>.  AcademicPress,</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">New York, 600 p.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> <STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvario</FONT></P><P><FONT FACE="Helvetica"><STRONG>vario2di</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Variogram of irregularly spaced2-D data.</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">[np, gam, hm, tm, hv, tv] =vario2di (nd, x, y, vr, nlag, xlag, xltol, ndir, azm, atol, bandw,nvarg, ivtail, ivhead, ivtype, nvar)</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">This function is used tocalculate the variograms of a sample which is irregularlydistributed on a plane.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">nd:  number of data (no missingvalues)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">x(nd):  x coordinates of thedata set</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y(nd):  y coordinates of thedata set</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">vr(nd,nvar):  datavalues</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">nlag:  number of lags tocalculate</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">xlag:  length of the unitlag</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">xltol:  distance tolerance (if&lt;0 then set to xlag/2)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ndir:  number of directions toconsider</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">azm(ndir):  azimuth angle ofdirection (measured positive degrees clockwise from NS).</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">atol(ndir):  azimuth (halfwindow) tolerances</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">bandw(ndir):  maximumbandwidth</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">nvarg:  number of variograms tocompute</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ivtail(nvarg):  variable for thetail of each variogram</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ivhead(nvarg):  variable for thehead of each variogram</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ivtype(nvarg):  type ofvariogram to compute</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">nvar:  number ofvariables</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">np:  number of pairs</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">gam:  semivariogram, covariance,correlogram,...  values</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">hm:  mean of the taildata</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">tm:  mean of the headdata</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">hv:  variance of the taildata</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">tv:  variance of the headdata</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">The first column of each outputvariable is the vector of the corresponding distances.  The firstrow of each output variable is the vector of the correspondingvariogram numbers.  If more than one direction is calculated, thevalues of the output variables for the other directions are added atthe end of the outputs of the first one.  More details can be foundin Deutsch et Journel (1992).<STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG