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.

UNIX                                               March 1998                                 c_ftcurvps(3NCARG)