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