ftcurvs

ftcurvs calculates a smoothing spline. ftcurvs is in the Fitgrid package -- a package containing 1D and 2D interpolators using cubic splines under tension.

Synopsis

    function ftcurvs(
        xi[*] : float,
        yi[*] : float,
        d[*]  : float,
        xo[*] : float
    )

Arguments

xi
A 1D array of any size (npts) containing the abscissae for the input function.
yi
A 1D array containing the npts functional values of the input function -- yi(k) is the functional value at xi(k) for k=0,npts-1.
d
A user-specified value containing the observed weights. d may either be a 1D array (of length npts) or a scalar.
xo
A 1D array containing the abscissae for the interpolated values.

Return value

ftcurvs returns a 1D array that contains the interpolated functional values of the smooting spline at the points specified in xo.

Description

There are some parameters that can alter the behavior of ftcurvs. These parameters all have reasonable default values. However, users may change any of these parameters by invoking ftsetp prior to calling ftcurvs. ftcurvs is called after all of the desired values for control parameters have been set.

Control parameters that apply to ftcurvs are: sig, smt, eps, sf2.

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 is sqrt( 2./(float) n ).

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).

You can extrapolate values with ftcurvs (that is calculate interpolated values for abscissae outside of the domain of the input), but these values are, in general, unreliable.

Example

begin
  xi = (/  0.00,   2.00,   5.00,   8.00,  10.00,  13.00,     \
          15.00,  18.00,  21.00,  23.00,  30.00         /)
  yi = (/  1.00,   0.81,   0.00,  -0.81,  -1.00,  -0.84,     \
          -0.56,   0.04,   0.73,   1.18,   2.0          /)

  npts = 201
  xo   = fspan(0.,30.,npts)

  yo = ftcurvs(xi, yi, 0.1, xo)
end

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$Revision: 1.7 $ $Date: 1998/11/11 23:32:18 $