NAME

       c_ftcurvps - compute a smoothing spline for periodic functions.

FUNCTION PROTOTYPE

       int c_ftcurvps (int, float [], float [], float, int, float [], int,
                         float [], float []);

SYNOPSIS

       int c_ftcurvps (n, xi, yi, p, dflg, d, m, xo, yo);

DESCRIPTION

       n           The number of input data points. (n > 1)

       xi          An array containing the abscissae for the input function.

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

       p           The period of the function.

       dflg        A switch for interpreting the value of d (as  described  below).   If  dflg=0,
                   then  d is an array of length n (an error estimate for each input data value);
                   if dflg=1, then d is a scalar that serves  as  an  error  estimate  for  every
                   single data item.

       d           A  user-specified  value  containing  the observed weights. d may either be an
                   array or a scalar, depending on the value of dflg.

       m           The number of output values.

       xo          Contains the abscissae for the output values.

       yo          Contains the functional  values  for  the  smoothing  spline  ((yo[k]  is  the
                   functional value at xo[k] for k=0,n-1).

RETURN VALUE

       c_ftcurvps returns an error value as per:

       = 1 if n is less than 2.
       = 2 if smt is negative.
       = 3 if eps is negative or greater than 1.
       = 4 if x values are not strictly increasing.
       = 5 if d is negative.
       = 6 if p is less than or equal to X(N)-X(1).

USAGE

       This  function computes an interpolatory smoothing spline under tension through a sequence
       of functional values of a periodic function.

       Two parameters and one function argument used to control the degree of smoothness  --  the
       parameters are smt, and eps and the function argument is d.

       The argument d is a value indicating the degree of confidence in the accuracy of the input
       function values -- it should be an approximation  of  the  standard  deviation  of  error.
       Effectively  the  value of d controls how close the smoothed curve comes to the input data
       points.  If d is small, then the interpolated curve will pass close to the input data. The
       larger  the value of d, the more freedom the smooth curve has in how close it comes to the
       input data values.

       The parameter smt is a more subtle global smoothing parameter; smt must  be  non-negative.
       For  small  values of smt, the curve approximates the tension spline and for larger values
       of smt, the curve is smoother. A reasonable value for smt is (float) n.

       The parameter eps controls the precision to which smt is interpreted; eps must be  between
       0. and 1. inclusive. A reasonable value for eps sqrt( 2./(float) n ).

       c_ftcurvps  is called after all of the desired values for control parameters have been set
       using the procedures c_ftseti,  c_ftsetr,  c_ftsetc.  Control  parameters  that  apply  to
       c_ftcurvps are: sig, smt, eps, sf2.

       The  value for the parameter sig specifies the tension factor.  Values near zero result in
       a cubic spline; large values (e.g. 50) result in nearly a polygonal line. A typical  value
       is 1. (the default).

ACCESS

       To use c_ftcurvps, load the NCAR Graphics library ngmath.

SEE ALSO

       fitgrid_params, c_ftseti, c_ftsetr, c_ftsetc.

       Complete documentation for Fitgrid is available at URL
       http://ngwww.ucar.edu/ngdoc/ng/ngmath/fitgrid/fithome.html

COPYRIGHT

       Copyright (C) 2000
       University Corporation for Atmospheric Research

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