c_csa3ls - cubic spline approximation, simple entry for three-dimensional input, list output

       To use c_csa3ls, 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                                  c_csa3ls(3NCARG)

       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.

       knots       (integer,  input)  The  number  of knots to be used in constructing the approximation spline.
                   knots[0], knots[1], and knots[2] must be at least 4. The larger  the  value  for  knots,  the
                   closer the approximated curve will come to passing through the input function values.

       no          (integer, input) The number of X - Y coordinate values to be calculated for the output array.

       xo          (real, input) An array dimensioned for no containing the X coordinates of the output list.

       yo          (real, output) An array dimensioned for no containing the Y coordinates of the output list.

       zo          (real, output) An array dimensioned for no containing the Z coordinates of the output list.

       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.

       float *c_csa3ls(int, float [], float [], float [], float [],
                       int [], int, float [], float [], float[], int *);

       c_csa3ls - cubic spline approximation, simple entry for three-dimensional input, list output

       csagrid, c_csa3s, c_csa3xs, c_csa3lxs

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

       float *c_csa3ls(int n, float xi[], float yi[], float zi[], float ui[],
                       int knots[3], int no, float xo[], float yo[], float zo[],
                       int *);

       c_csa3ls  is  called  to  find  values  of  an  approximating cubic spline at specified three-dimensional
       coordinates.  If you want to weight the input data values, calculate derivatives, or handle  data  sparse
       areas specially, then you will need to use c_csa3lxs.

       c_csa3ls  returns a pointer to a linear array of data that contains the approximated values calculated at
       the input list of coordinate values. That is, if out is declared as

         float *out;

       and we set:

         out = c_csa3ls(n, x, y, z, u, knots, no, xo, yo, zo, &ier);

       then out[i] is the approximated function value at coordinate point (xo[i], yo[i], zo[i]) for 0 <= i < no.
       The space for out is allocated internal to c_csa3ls and is no floats in size.