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Package fitrat (in fitrat.i) -

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DOCUMENT yp= fitpol(y, x, xp) or yp= fitpol(y, x, xp, keep=1) is an interpolation routine similar to interp, except that fitpol returns the polynomial of degree numberof(X)-1 which passes through the given points (X,Y), evaluated at the requested points XP. The X must either increase or decrease monotonically. If the KEEP keyword is present and non-zero, the external variable yperr will contain a list of error estimates for the returned values yp on exit. The algorithm is taken from Numerical Recipes (Press, et. al., Cambridge University Press, 1988); it is called Neville's algorithm. The rational function interpolator fitrat is better for "typical" functions. The Yorick implementaion requires numberof(X)*numberof(XP) temporary arrays, so the X and Y arrays should be reasonably small.

DOCUMENT yp= fitrat(y, x, xp) or yp= fitrat(y, x, xp, keep=1) is an interpolation routine similar to interp, except that fitpol returns the diagonal rational function of degree numberof(X)-1 which passes through the given points (X,Y), evaluated at the requested points XP. (The numerator and denominator polynomials have equal degree, or the denominator has one larger degree.) The X must either increase or decrease monotonically. Also, this algorithm works by recursion, fitting successively to consecutive pairs of points, then consecutive triples, and so forth. If there is a pole in any of these fits to subsets, the algorithm fails even though the rational function for the final fit is non- singular. In particular, if any of the Y values is zero, the algorithm fails, and you should be very wary of lists for which Y changes sign. Note that if numberof(X) is even, the rational function is Y-translation invariant, while numberof(X) odd generally results in a non-translatable fit (because it decays to y=0). If the KEEP keyword is present and non-zero, the external variable yperr will contain a list of error estimates for the returned values yp on exit. The algorithm is taken from Numerical Recipes (Press, et. al., Cambridge University Press, 1988); it is called the Bulirsch-Stoer algorithm. The Yorick implementaion requires numberof(X)*numberof(XP) temporary arrays, so the X and Y arrays should be reasonably small.