functions in fitrat.i - f

    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.  
Interpreted function, defined at i/fitrat.i   line 10  

    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.  
Interpreted function, defined at i/fitrat.i   line 72