NAME

       c_csa3xs - cubic spline approximation, expanded entry for three-dimensional input, gridded
       output

FUNCTION PROTOTYPE

       loat *c_csa3xs(int, float [], float [], float [], float [], float [],
                       int [], float, int [], int, int, int, float [],
                       float [], float [], int *);

SYNOPSIS

       float *c_csa3xs (int n, float xi[], float yi[], float zi[],
                       float ui[], float wts[], int knots[3], float smth,
                       int nderiv[3], int nxo, int nyo,
                       int nzo, float xo[], float yo[], float zo[],
                       int *ier);

DESCRIPTION

       n           (integer,input) The number of input data points. It must be that n is  greater
                   than 3 and, depending on the size of knots below, n may have to be larger.

       xi          (real,  input)  An  array dimensioned for n containing the X coordinate values
                   for the input function.

       yi          (real, input) An array dimensioned for n containing the  Y  coordinate  values
                   for the input function.

       zi          (real,  input)  An  array dimensioned for n containing the Z coordinate values
                   for the input function.

       ui          (real, input) An array containing the functional values of the input  function
                   -- ui[k] is the functional value at (xi[k], yi[k], zi[k]) for k=0,n-1.

       wts         (real,  input)  An  array  containing  weights  for the ui values at the input
                   values, that is, wts[l] is a weight for the value of ui[l] for l=0,n-1. If you
                   do  not  desire  to  weight  the  input  ui values, then set wts[0] to -1. The
                   weights in the wts array are relative and  may  be  set  to  any  non-negative
                   value.  When  c_csa3xs  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[0], knots[1] and knots[2] must each be at least 4.
                   The larger the value 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)  For each of the two coordinate direction, specifies whether
                   you want functional values (nderiv=0), first derivative values (nderiv=1),  or
                   second   derivative   values  (nderiv=2).  For  example,  if  nderiv[0]=1  and
                   nderiv[1]=1, then the second order mixed partial would be computed.

       nxo         (integer, input) The number of X coordinate values to be  calculated  for  the
                   output spline.

       nyo         (integer,  input)  The  number of Y coordinate values to be calculated for the
                   output spline.

       nzo         (integer, input) The number of Z coordinate values to be  calculated  for  the
                   output spline.

       xo          (real, input) An array dimensioned for nxo containing the X coordinates of the
                   output spline.

       yo          (real, output) An array dimensioned for nyo containing the  Y  coordinates  of
                   the output spline.

       zo          (real,  output)  An  array dimensioned for nzo containing the Z coordinates of
                   the output spline.

       ier         (pointer to 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 error
                   list in the error table for details.

USAGE

       c_csa3xs is called to find an approximating cubic spline for three-dimensional input data.
       c_csa3xs  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 c_csa3s.

       c_csa3xs  returns  a  pointer  to  a linear array of data that is the approximation spline
       stored in row-major order. That is, if out is declared as
         float *out;

       and we set:

       out = c_csa3xs(ni, xi, yi, zi, ui, wts, knots, smth, nderiv,
                      nx, ny, nz, xo, yo, zo, &ier)
       then out[nz*ny*i + nz*j + k] is the  approximation  function  value  at  coordinate  point
       (xo[i],  yo[j], zo[k]) for 0 <= i < nx, 0 <= j < ny, and 0 <= k < nz. The space for out is
       allocated internal to c_csa3xs and is nx*ny*nz floats in size.

ACCESS

       To use c_csa3xs, load the NCAR Graphics library ngmath.

SEE ALSO

       csagrid, c_csa3s, c_csa3ls, c_csa3lxs

       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.