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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.