Rythmos::HermiteInterpolator< Scalar > Class Template Reference

#include <Rythmos_HermiteInterpolator.hpp>

Inheritance diagram for Rythmos::HermiteInterpolator< Scalar >:


Public Member Functions
	~HermiteInterpolator ()
	Destructor.
	HermiteInterpolator ()
	Constructor.
void	interpolate (const typename DataStore< Scalar >::DataStoreVector_t &data_in, const Array< Scalar > &t_values, typename DataStore< Scalar >::DataStoreVector_t *data_out) const
	Interpolation: Hermite interpolation function.
int	order () const
	Order of interpolation:.
std::string	description () const
	Inherited from Teuchos::Describable .
void	describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const

void	setParameterList (Teuchos::RCP< Teuchos::ParameterList > const &paramList)
	Redefined from Teuchos::ParameterListAcceptor .
Teuchos::RCP< Teuchos::ParameterList >	getParameterList ()

Teuchos::RCP< Teuchos::ParameterList >	unsetParameterList ()

void	assertInterpolatePreconditions (const typename DataStore< Scalar >::DataStoreVector_t &data_in, const Array< Scalar > &t_values, typename DataStore< Scalar >::DataStoreVector_t *data_out) const

Detailed Description

template<class Scalar>
class Rythmos::HermiteInterpolator< Scalar >

This class implements piecewise Hermite interpolation on each interval where the data is: (x0,f(x0)), (x1,f(x1)), (x0,f'(x0)), (x1,f'(x1)) The Hermite Interpolation polynomial is: H_3(x) = f[z0] + f[z0,z1](x-x0) + f[z0,z1,z2](x-x0)^2 + f[z0,z1,z2,z3](x-x0)^2(x-x1) where z0 = z1 = x0 and z2 = z3 = x1 and f[z0,z1] = f'(x0) and f[z2,z3] = f'(x1) This reduces to: H_3(x) = f(x0) + f'(x0)(x-x0) + ((f(x1)-f(x0))/(x1-x0) - f'(x0))(x-x0)^2/(x1-x0) +(f'(x1) - 2(f(x1)-f(x0))/(x1-x0) + f'(x0))(x-x0)^2(x-x1)/(x1-x0)^2 With derivative: H_3'(x) = f'(x0) + 2*((f(x1)-f(x0))/(x1-x0) - f'(x0))(x-x0)/(x1-x0) +(f'(x1) - 2(f(x1)-f(x0))/(x1-x0) + f'(x0))[2*(x-x0)(x-x1) + (x-x0)^2]/(x1-x0)^2 With the error expression: f(x) - H_3(x) = (f^{(3)}((x))/(4!))(x-x0)^2(x-x1)^2 Which is 2nd order in f(x) and 1st order in f'(x)

Definition at line 53 of file Rythmos_HermiteInterpolator.hpp.

Constructor & Destructor Documentation

template<class Scalar>

Rythmos::HermiteInterpolator< Scalar >::~HermiteInterpolator ( ) [inline]

Destructor.

Definition at line 58 of file Rythmos_HermiteInterpolator.hpp.

template<class Scalar>

Rythmos::HermiteInterpolator< Scalar >::HermiteInterpolator ( )

Constructor.

Definition at line 113 of file Rythmos_HermiteInterpolator.hpp.

Member Function Documentation

template<class Scalar>

void Rythmos::HermiteInterpolator< Scalar >::interpolate	(	const typename DataStore< Scalar >::DataStoreVector_t &	data_in,
		const Array< Scalar > &	t_values,
		typename DataStore< Scalar >::DataStoreVector_t *	data_out
	)			const `[virtual]`