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# ncl_c_ftcurvs1 - Man Page

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.