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 useful to many
of Quntlib Users and can be incorporated into the Quntlib.
Any feedback will be
greatly appreciated..
Roman
Gitlin