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.

UNIX                                              January 1999                                  c_csa3xs(3NCARG)