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

       To use CSA2XS, load the NCAR Graphics library ngmath.

       Copyright (C) 2000
       University Corporation for Atmospheric Research

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

UNIX                                              January 1999                                    CSA2XS(3NCARG)

       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.

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

       csagrid, csa2s, csa2ls, csa2lxs

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

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

       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.