NAME

       CSA2XS  -  cubic  spline  approximation, expanded entry for two-dimensional input, gridded
       output

SYNOPSIS

       CALL CSA2XS (NI, XI, UI, WTS, KNOTS, SMTH, DERIV, NXO, NYO, XO, YO, UO, NWRK, WORK, IER)

DESCRIPTION

       NI          (integer,input) The number of input data points. It must be  that  NI  .gt.  3
                   and, depending on the size of KNOTS below, NI may have to be larger.

       XI          (real,  input)  An  array  containing  the X - Y coordinates of the input data
                   points. XI is dimensioned for 2 x NI.  XI(1,L) is the X coordinate and XI(2,L)
                   is the Y coordinate for the input domain for L=1,NI.

       UI          (real,  input)  An  array dimensioned for NI containing function values at the
                   input XI values, that is UI(L) is the value  of  the  input  function  at  the
                   coordinate (XI(1,L),XI(2,L)) for L=1,NI.

       WTS         (real, input) An array dimensioned for NI containing weights for the UI values
                   at the input XI values, that is, WTS(L) is a weight for the value of UI(L) for
                   L=1,NI.   If  you do not desire to weight the input UI values, then set WTS(1)
                   to -1.  The weights in the WTS array are relative and may be set to  any  non-
                   negative  value.   When  CSA2XS  is  called,  the  weights  are summed and the
                   individual weights are normalized so that the weight sum is unity.

       KNOTS       (integer,  input)  The  number  of  knots  to  be  used  in  constructing  the
                   approximation  spline.   KNOTS is dimensioned for 2 and provides the number of
                   knots to be used in the X and the Y directions.  Both  KNOTS(1)  and  KNOTS(2)
                   must  be  at  least  4.   The  larger  the  values  for  KNOTS, the closer the
                   approximated curve will come to passing through the input function values.

       SMTH        (real, input)  A  parameter  that  controls  extrapolation  into  data  sparse
                   regions.   If  SMTH  is  zero,  then  nothing  special  is done in data sparse
                   regions.  A good first choice for SMTH is 1.

       NDERIV      (integer,  input)  An  array  dimensioned  for  2  that  specifies,  for  each
                   coordinate,   whether you want functional values (=0), first derivative values
                   (=1), or second derivative values (=2).

       NXO         (integer, input) The number of X coordinate values in the output grid.

       NYO         (integer, input) The number of Y coordinate values in the output grid.

       XO          (real, input) An array dimensioned for NXO containing the X coordinates of the
                   output surface.

       YO          (real, input) An array dimensioned for NYO containing the Y coordinates of the
                   output surface.

       UO          (real, output) An array dimensioned for NXO x NYO  containing  the  calculated
                   function  values for the output surface.  UO(I,J) is the calculated functional
                   value at (XO(I),YO(J)) for I=1,NXO and J=1,NYO.

       NWRK        (integer, input)  The  size  of  the  WORK  array.   NWRK  must  be  at  least
                   KNOTS(1)*KNOTS(2)*(KNOTS(1)*KNOTS(2)+3).

       WORK        (real, input) A work array dimensioned for NWRK.

       IER         (integer,  output)  An  error  return value.  If IER is returned as 0, then no
                   errors were detected. If IER is non-zero, then  refer  to  the  man  page  for
                   csagrid_errors for details.

USAGE

       CSA2XS  is  called  to  find an approximating cubic spline for two-dimensional input data.
       CSA2XS is called if you want to weight the input data values,  calculate  derivatives,  or
       handle  data  sparse areas specially.  If you do not want to do any of these three things,
       then use CSA2S.

ACCESS

       To use CSA2XS, load the NCAR Graphics library ngmath.

SEE ALSO

       csagrid, csa2s, csa2ls, csa2lxs

       Complete documentation for Csagrid is available at URL
       http://ngwww.ucar.edu/ngdoc/ng/ngmath/csagrid/csahome.html

COPYRIGHT

       Copyright (C) 2000
       University Corporation for Atmospheric Research

       The use of this Software is governed by a License Agreement.