NAME

       c_ftcurvs1 - calculate values for a smoothing spline for data in the plane.

FUNCTION PROTOTYPE

       int c_ftcurvs1(int, float [], float [], int, float [],
                      int, float, float, float [], float []);

SYNOPSIS

       int c_ftcurvs1(int n, float xi[], float yi[], int dflg,
                      float d[], int m, float xl, float xr,
                      float xo[], float yo[])

DESCRIPTION

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

       xi          An array containing the X-coordinates for the input data.  These need not be increasing.

       yi          An array containing the Y-coordinates for the input data.

       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 be either an array or a scalar,
                   depending on the value of dflg.

       m           The number of output values.

       xl          A  lower  limit  for  an  interval  of  interpolation.   The  interval  between  zero and one
                   interpolates the entire curve, any value outside this range results  in  extrapolation.   The
                   interval [xl,xr] is divided into m equal values to produce the interpolated curve.

       xr          An  upper  limit  for  an  interval  of  interpolation.   The  interval  between zero and one
                   interpolates the entire curve, any value outside this range results  in  extrapolation.   The
                   interval [xl,xr] is divided into m equal values to produce the interpolated curve.

       xo          The interpolated X values.

       yo          The interpolated Y values.

RETURN VALUE

       c_ftcurvs1 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.
       = 5 if d is negative.

USAGE

       This  function computes an interpolatory smoothing spline under tension through a sequence of data values
       in the plane.

       Two parameters and one function argument are 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. smt can be set with the procedure c_ftsetr.

       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 ). eps can be set with the procedure c_ftsetr.

       c_ftcurvs1  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_ftcurvs 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_ftcurvs1, 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                                               August 2002                                c_ftcurvs1(3NCARG)