ftcurvd

ftcurvd calculates the derivatives of an interpolatory spline under tension. ftcurvd is in the Fitgrid package -- a package containing 1D and 2D interpolators using cubic splines under tension.

Synopsis

    function ftcurvd(
        xi[*] : float,
        yi[*] : 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.
xo
A 1D array containing the abscissae for the calculated derivatives.

Return value

ftcurvd returns a 1D array that contains the derivatives of the interpolated curve at the points specified in xo.

Description

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

Control parameters that apply to ftcurvd are: sig, sl1, sln, sf1.

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).

The values for sl1 and sln specify the slope of the curve at the first point and last point, respectively.

The value of sf1 controls whether to use the values for sl1 and sln, or compute those values internally. Specifically, sf1

= 0 if sl1 and sln are user-specified.
= 1 if sl1 is user-specified, but sln is internally calculated.
= 2 if sln is user-specified, but sl1 is internally calculated.
= 3 if sl1 and sln are internally calculated.
By default the slopes at the end points are computed internally.

You can extrapolate values with ftcurvd (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)

yd = ftcurvd(xi, yi, xo)

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$Revision: 1.7 $ $Date: 1998/11/11 23:32:17 $