KernelInterpolation Class Reference

Kernel interpolation between discrete points. More...

#include <ql/math/interpolations/kernelinterpolation.hpp>

Inheritance diagram for KernelInterpolation:

Public Member Functions
template<class I1 , class I2 , class Kernel >
	KernelInterpolation (const I1 &xBegin, const I1 &xEnd, const I2 &yBegin, const Kernel &kernel, const double epsilon=1.0E-7)
Public Member Functions inherited from Interpolation
bool	empty () const
Real	operator() (Real x, bool allowExtrapolation=false) const
Real	primitive (Real x, bool allowExtrapolation=false) const
Real	derivative (Real x, bool allowExtrapolation=false) const
Real	secondDerivative (Real x, bool allowExtrapolation=false) const
Real	xMin () const
Real	xMax () const
bool	isInRange (Real x) const
void	update ()
Public Member Functions inherited from Extrapolator
void	enableExtrapolation (bool b=true)
	enable extrapolation in subsequent calls
void	disableExtrapolation (bool b=true)
	disable extrapolation in subsequent calls
bool	allowsExtrapolation () const
	tells whether extrapolation is enabled

Additional Inherited Members
Public Types inherited from Interpolation
typedef Real	argument_type
typedef Real	result_type
Protected Member Functions inherited from Interpolation
void	checkRange (Real x, bool extrapolate) const
Protected Attributes inherited from Interpolation
ext::shared_ptr< Impl >	impl_

Detailed Description

Kernel interpolation between discrete points.

Implementation of the kernel interpolation approach, which can be found in "Foreign Exchange Risk" by Hakala, Wystup page 256.

The kernel in the implementation is kept general, although a Gaussian is considered in the cited text.

Warning:

See the Interpolation class for information about the required lifetime of the underlying data.

Constructor & Destructor Documentation

KernelInterpolation()

KernelInterpolation	(	const I1 &	xBegin,
		const I1 &	xEnd,
		const I2 &	yBegin,
		const Kernel &	kernel,
		const double	epsilon = 1.0E-7
	)

Precondition

the \( x \) values must be sorted.

kernel needs a Real operator()(Real x) implementation

The calculation will solve \( y = Ma \) for \(a\). Due to singularity or rounding errors the recalculation \( Ma \) may not give \( y\). Here, a failure will be thrown if

\[ \left\| Ma-y \right\|_\infty \geq \epsilon \]