englis~1.htm

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<P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONT
FACE="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><FONT
FACE="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 of
data points x(ndata), y(ndata) with standard deviations sig(ndata),
and a nonlinear function dependent on ma coefficients
a(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 Scientific
Computing</EM>, second ed., Cambridge University Press, Cambridge, p
680.<STRONG></STRONG></FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><STRONG>See
also</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">fitvario2</FONT></P>


<P><FONT FACE="Helvetica"><STRONG>outvario</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">Output of variogram
functions.</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 to
reorganize the outputs of gam2, gamv2, gam3 and gamv3.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><STRONG>See
also</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">vario2di, vario2dr, var2diuv,
vario3di, vario3dr</FONT></P>



<P><FONT FACE="Helvetica"><STRONG>tintore</STRONG></FONT><FONT
FACE="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' filter
with the Tintor&eacute;'s parameters (1991).</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONT
FACE="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><FONT
FACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">This function is an example of
Barnes' filter to separate mesoscale from macroscale features in
physical oceanography.  The filter parameters are those established
by Tintor&eacute; et al.  (1991).</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><U>Input
variables:</U></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">xi:  vector of the x grid
coordinates (positions of the columns of zi)</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">yi:  vector of the y grid
coordinates (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>Output
variables:</U></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">F2:  macroscale
structure</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">Fb:  mesoscale
structure</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>See
also</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">barnes, filresp</FONT></P>





<P><FONT FACE="Helvetica"><STRONG>trans</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">Translation function called from
cokri2.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONT
FACE="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><FONT
FACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">This function takes as input
original coordinates and returns the rotated and reduced coordinates
following specifications described in the semivariogram
model.</FONT></P>


<P><FONT FACE="Helvetica"
SIZE="-1"><STRONG>Reference</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">Marcotte, D., 1991.  Cokrigeage
with MATLAB.  Computers &amp; Geosciences.  17 (9):
1265-1280.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><STRONG>See
also</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 of
semivariogram and correlogram.</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">variogr2:  variogr for fitting
procedures not using the Optimization Toolbox.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONT
FACE="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><FONT
FACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">This function is used to obtain
the theoretical curve of the variance of a sample as a function of
the sample pair distance.  </FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1">Available model options
are:</FONT></P>


<MULTICOL COLS="2" WIDTH="507" GUTTER="46">

<P><FONT FACE="Helvetica" SIZE="-1"><U></U><EM>With a
sill</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 (in
preparation)</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><U></U></FONT><FONT
FACE="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 (in
preparation)</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 easily
added to the list.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><U>Input
variables:</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 the
models 20</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">type:  variogram type</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><U>Output
variable:</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>.  Academic
Press,</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">New York, 600 p.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"> <STRONG>See
also</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">fitvario</FONT></P>


<P><FONT FACE="Helvetica"><STRONG>vario2di</STRONG></FONT><FONT
FACE="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 spaced
2-D data.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONT
FACE="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><FONT
FACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">This function is used to
calculate the variograms of a sample which is irregularly
distributed on a plane.</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><U>Input
variables:</U></FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">nd:  number of data (no missing
values)</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">x(nd):  x coordinates of the
data set</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">y(nd):  y coordinates of the
data set</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">vr(nd,nvar):  data
values</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">nlag:  number of lags to
calculate</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">xlag:  length of the unit
lag</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 to
consider</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">azm(ndir):  azimuth angle of
direction (measured positive degrees clockwise from NS).</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">atol(ndir):  azimuth (half
window) tolerances</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">bandw(ndir):  maximum
bandwidth</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">nvarg:  number of variograms to
compute</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">ivtail(nvarg):  variable for the
tail of each variogram</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">ivhead(nvarg):  variable for the
head of each variogram</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">ivtype(nvarg):  type of
variogram to compute</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">nvar:  number of
variables</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1"><U>Output
variables:</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 tail
data</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">tm:  mean of the head
data</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">hv:  variance of the tail
data</FONT></P>

<P><FONT FACE="Helvetica" SIZE="-1">tv:  variance of the head
data</FONT></P>


<P><FONT FACE="Helvetica" SIZE="-1">The first column of each output
variable is the vector of the corresponding distances.  The first
row of each output variable is the vector of the corresponding
variogram numbers.  If more than one direction is calculated, the
values of the output variables for the other directions are added at
the end of the outputs of the first one.  More details can be found
in Deutsch et Journel (1992).<STRONG></STRONG></FONT></P>


<P><FONT FACE="Helvetica"
SIZE="-1"><STRONG