 c_ftcurvps(3) 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.