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

[Toyin A. <toy...@ho...>]

Hi,

I think this would be a great addition to quantlib.

Any chance of sending me a copy of the library (source code) with some test 
code so that I can play with it a bit?

This should be great, for example, for the extrapolation of volatility data 
from a 2D grid (maturity/strike) or (maturity/underlying length).

Toy out.


>From: Rom...@ao...
>To: qua...@li...
>Subject: [Quantlib-dev] Re: N-dimensional interpolation template library
>Date: Thu, 16 Mar 2006 13:33:47 EST
>
>
>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
>