[Quantlib-dev] Re: N-dimensional interpolation template library

[<Rom...@ao...>]

 
Hi everyone
 
Since I  wrote an N-dimensional cubic spline class back in 2003,  I have 
developed a framework for N-dimensional algoriths that allows  incorporation of a 
widely divergent set of 1-dimensional algorithms.into it. For  example within 
the library I have developed so far such entirely diffferent  algoriths as 
quintic_hermite interpolation and rational polinomial interpolation  can be 
chosen by the user to interpolate the same set of tabulated  data.  ...
    Tthis programatic framework is implemented as a template  class 
instantiated using  1-dimensional algorithms along with number of  dimensions as its  
template parameters. The library features a  uniform user friendly interface. 
Thus the user, instead of going through the  tedium of plugging the same set of 
data into different algorithms for can choose  and run any algorithm 
implemented within the framework by choosing  between a  few typedefs. The choice of 
an algorithb becomes a  matte of a few clics of the mouth.
      Among the algorithsI have implemented  so far within this framework are 
the following:
multi-linear interpolation, natural cubic spline interpolation;  clamped  
cubic spline interpolation, monotonicity preserving clamped   cubic spline 
interpolation, polinomial interpolation, rational polinomial  interpolation, 
cubic-hermite  and quintic-hermite spline.
   Also, since quintic-hermite spline implementation takes cubic  spline as 
its template parameter that means that the user have a choice of 3  flavors of 
quintic-hermite spline.
     Besides , every algorithm that uses second  detivatives is implemented 
in two ways: one that calculates second derivatives  globally when memory is 
not an issue, and locally when memory is at  premium.
    Though it may sound counterintuitive, this united  approach to 
implementation of different algorithms within united  framework, besides being user 
friendly, also made each of the library's  implementations more efficient.
   For example N-dimensional cubic spline as  implemented within this 
framework runs few times faster than the  one currewntly  implemented in the Quantlib 
library, and on top  of that the library as a whole and this the library's 
cubic spline  implementation's in particular features vastly improved memory 
management.
    I hope this library can be incorporated  into the Quntlib. 
         Any feedback is  welcome..
 
         Roman  Gitlin