Lagrange< Real > Class Template Reference

#include <Lagrange.hpp>

Public Member Functions
	Lagrange (const std::vector< Real > &xin, const std::vector< Real > &xev)
	Interpolation object which interpolates from to the grid xin to xev.
	~Lagrange ()
void	interp (const std::vector< Real > &f, std::vector< Real > &p)
	Given the values of a function on the interpolation points xin, stored in f, evaluate the interpolating polynomial on the evaluation points xev.
void	dinterp (const std::vector< Real > &f, std::vector< Real > &p)
void	interpolant (const int k, std::vector< Real > &l)
	Evaluate the kth interpolant on the evaluation points.
void	derivative (const int k, std::vector< Real > &d)
	Derivative of the \(k\)th interpolant on the interpolation points.
void	bi_sum (const std::vector< Real > &f, std::vector< Real > &y)
	This routine evaluates sums of the form shown in equation (4.2) in the paper by J-P Berrut and L.N. Trefethen.

Private Attributes
const std::vector< Real >	xin_
const std::vector< Real >	xev_
const int	nin_
const int	nev_
std::vector< Real >	w_
std::vector< Real >	ell_
std::vector< Real >	D_

Detailed Description

template<class Real>
class Lagrange< Real >

Definition at line 16 of file Lagrange.hpp.

Constructor & Destructor Documentation

Lagrange()

template<class Real>

Lagrange< Real >::Lagrange	(	const std::vector< Real > &	xin,
		const std::vector< Real > &	xev )

Interpolation object which interpolates from to the grid xin to xev.

Parameters

[in]	xin	vector of interpolation points
[in]	xev	vector of evaluation points

Definition at line 66 of file Lagrange.hpp.

References bi_sum(), D_, ell_, nev_, nin_, w_, xev_, and xin_.

~Lagrange()

template<class Real>

Lagrange< Real >::~Lagrange

(

)

Definition at line 124 of file Lagrange.hpp.

Member Function Documentation

interp()

template<class Real>

void Lagrange< Real >::interp	(	const std::vector< Real > &	f,
		std::vector< Real > &	p )

Given the values of a function on the interpolation points xin, stored in f, evaluate the interpolating polynomial on the evaluation points xev.

Parameters

[in]	f	vector of function values sampled at xin
[out]	y	vector of interpolating polynomial values evaluated ay xev

Definition at line 156 of file Lagrange.hpp.

References bi_sum(), ell_, and nev_.

Referenced by derivative().

dinterp()

template<class Real>

void Lagrange< Real >::dinterp	(	const std::vector< Real > &	f,
		std::vector< Real > &	p )

Definition at line 166 of file Lagrange.hpp.

References bi_sum(), ell_, nev_, and nin_.

interpolant()

template<class Real>

void Lagrange< Real >::interpolant	(	const int	k,
		std::vector< Real > &	l )

Evaluate the kth interpolant on the evaluation points.

Parameters

[in]	k	vector of function values sampled at xin
[out]	y	vector of interpolating polynomial values evaluated ay xev

Definition at line 185 of file Lagrange.hpp.

References bi_sum(), ell_, nev_, nin_, w_, xev_, and xin_.

derivative()

template<class Real>

void Lagrange< Real >::derivative	(	const int	k,
		std::vector< Real > &	d )

Derivative of the \(k\)th interpolant on the interpolation points.

Definition at line 200 of file Lagrange.hpp.

References D_, interp(), and nin_.

bi_sum()

template<class Real>

void Lagrange< Real >::bi_sum	(	const std::vector< Real > &	f,
		std::vector< Real > &	y )

This routine evaluates sums of the form shown in equation (4.2) in the paper by J-P Berrut and L.N. Trefethen.

Parameters

[in]	f	vector of values appearing in the sum
[out]	y	the result

Definition at line 131 of file Lagrange.hpp.

References nev_, nin_, w_, xev_, and xin_.

Referenced by dinterp(), interp(), interpolant(), and Lagrange().

Member Data Documentation

xin_

template<class Real>

const std::vector<Real> Lagrange< Real >::xin_

private

Parameters

xin_	Vector of interpolation points

Definition at line 39 of file Lagrange.hpp.

Referenced by bi_sum(), interpolant(), and Lagrange().

xev_

template<class Real>

const std::vector<Real> Lagrange< Real >::xev_

private

Definition at line 42 of file Lagrange.hpp.

Referenced by bi_sum(), interpolant(), and Lagrange().

nin_

template<class Real>

const int Lagrange< Real >::nin_

private

Definition at line 45 of file Lagrange.hpp.

Referenced by bi_sum(), derivative(), dinterp(), interpolant(), and Lagrange().

nev_

template<class Real>

const int Lagrange< Real >::nev_

private

Definition at line 48 of file Lagrange.hpp.

Referenced by bi_sum(), dinterp(), interp(), interpolant(), and Lagrange().

w_

template<class Real>

std::vector<Real> Lagrange< Real >::w_

private

Definition at line 51 of file Lagrange.hpp.

Referenced by bi_sum(), interpolant(), and Lagrange().

ell_

template<class Real>

std::vector<Real> Lagrange< Real >::ell_

private

Definition at line 54 of file Lagrange.hpp.

Referenced by dinterp(), interp(), interpolant(), and Lagrange().

D_

template<class Real>

std::vector<Real> Lagrange< Real >::D_

private

Definition at line 57 of file Lagrange.hpp.

Referenced by derivative(), and Lagrange().

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The documentation for this class was generated from the following file:

• Lagrange.hpp