Rechercher une page de manuel
QuantLib_BSpline
Langue: en
Version: 380612 (fedora - 01/12/10)
Section: 3 (Bibliothèques de fonctions)
NAME
QuantLib::BSpline -B-spline basis functions.
SYNOPSIS
#include <ql/math/bspline.hpp>
Public Member Functions
BSpline (Natural p, Natural n, const std::vector< Real > &knots)
Real operator() (Natural i, Real x) const
Detailed Description
B-spline basis functions.
Follows treatment and notation from:
Weisstein, Eric W. 'B-Spline.' From MathWorld--A Wolfram Web Resource. <http://mathworld.wolfram.com/B-Spline.html>
$ (p+1) $-th order B-spline (or p degree polynomial) basis functions $ N_{i,p}(x), i = 0,1,2
knot vector of size $ p+n+2 $ defined at the increasingly sorted points $ (x_0, x_1
ratic B-spline has $ p=2 $, a cubic B-spline has $ p=3 $, etc.
The B-spline basis functions are defined recursively as follows:
[ xtrm{ if } x_{i}
xtrm{ otherwise} \ N_{i,p}(x) &=& N_{i,p-1}(x) ac{(x - x_{i})}{ (x_{i+p-1} - x_{i})} + N_{i+1,p-1}(x) ac{(x_{i+p} - x)}{(x_{i+p} - x_{i+1})} \nd{array} ]
Author
Generated automatically by Doxygen for QuantLib from the source code.
Contenus ©2006-2024 Benjamin Poulain
Design ©2006-2024 Maxime Vantorre