ESTER: diff_leg Class Reference

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The diff_leg class implements Legendre numerical differentiation. More...

#include <numdiff.h>

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Public Member Functions
	diff_leg ()

	~diff_leg ()

	diff_leg (const diff_leg &)

diff_leg &	operator= (const diff_leg &)

void	init ()

matrix	eval_00 (const matrix &y, const matrix &thi, matrix &T) const

matrix	eval_00 (const matrix &y, const matrix &thi) const

matrix	eval_00 (const matrix &y, double thi) const

matrix	eval_00 (const matrix &y, double thi, matrix &T) const

matrix	eval_01 (const matrix &y, const matrix &thi, matrix &T) const

matrix	eval_01 (const matrix &y, const matrix &thi) const

matrix	eval_01 (const matrix &y, double thi) const

matrix	eval_01 (const matrix &y, double thi, matrix &T) const

matrix	eval_10 (const matrix &y, const matrix &thi, matrix &T) const

matrix	eval_10 (const matrix &y, const matrix &thi) const

matrix	eval_10 (const matrix &y, double thi) const

matrix	eval_10 (const matrix &y, double thi, matrix &T) const

matrix	eval_11 (const matrix &y, const matrix &thi, matrix &T) const

matrix	eval_11 (const matrix &y, const matrix &thi) const

matrix	eval_11 (const matrix &y, double thi) const

matrix	eval_11 (const matrix &y, double thi, matrix &T) const

matrix	eval (const matrix &y, const matrix &thi, matrix &T, int par_pol, int par_eq) const

matrix	eval (const matrix &y, double thi, matrix &T, int par_pol, int par_eq) const

matrix	l_00 () const

matrix	l_01 () const

matrix	l_10 () const

matrix	l_11 () const

Public Attributes
int	npts

matrix	th

matrix	P_00

matrix	P_01

matrix	P_10

matrix	P_11

matrix	P1_00

matrix	P1_01

matrix	P1_10

matrix	P1_11

matrix	dP1_00

matrix	dP1_01

matrix	dP1_10

matrix	dP1_11

matrix	D_00

matrix	D_01

matrix	D_10

matrix	D_11

matrix	D2_00

matrix	D2_01

matrix	D2_10

matrix	D2_11

matrix	I_00

matrix	lap_00

matrix	lap_01

matrix	lap_10

matrix	lap_11

Private Member Functions
matrix	Pn (int n, matrix x)

matrix	dPn (int n, matrix x, matrix p)

matrix	nodes (int n, matrix &w)

Detailed Description

The diff_leg class implements Legendre numerical differentiation.

The basis function are Legendre polynomials \( P_l(x) \), and, for \( n \) points, collocation points are defined as the roots of \( P_n(x) \).

\[ P_n(x)= \frac{1}{2^n n!} \frac{d^n}{dx^n}[(x^2-1)] \]

Constructor & Destructor Documentation

diff_leg::diff_leg ( )

diff_leg::~diff_leg ( )

diff_leg::diff_leg ( const diff_leg & leg )

Member Function Documentation

matrix diff_leg::dPn	(	int	n,
		matrix	x,
		matrix	p
	)

private

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matrix diff_leg::eval	(	const matrix &	y,
		const matrix &	thi,
		matrix &	T,
		int	par_pol,
		int	par_eq
	)		const

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matrix diff_leg::eval	(	const matrix &	y,
		double	thi,
		matrix &	T,
		int	par_pol,
		int	par_eq
	)		const

inline

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matrix diff_leg::eval_00	(	const matrix &	y,
		const matrix &	thi,
		matrix &	T
	)		const

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matrix diff_leg::eval_00	(	const matrix &	y,
		const matrix &	thi
	)		const

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matrix diff_leg::eval_00	(	const matrix &	y,
		double	thi
	)		const

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matrix diff_leg::eval_00	(	const matrix &	y,
		double	thi,
		matrix &	T
	)		const

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matrix diff_leg::eval_01	(	const matrix &	y,
		const matrix &	thi,
		matrix &	T
	)		const

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matrix diff_leg::eval_01	(	const matrix &	y,
		const matrix &	thi
	)		const

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matrix diff_leg::eval_01	(	const matrix &	y,
		double	thi
	)		const

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matrix diff_leg::eval_01	(	const matrix &	y,
		double	thi,
		matrix &	T
	)		const

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matrix diff_leg::eval_10	(	const matrix &	y,
		const matrix &	thi,
		matrix &	T
	)		const

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matrix diff_leg::eval_10	(	const matrix &	y,
		const matrix &	thi
	)		const

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matrix diff_leg::eval_10	(	const matrix &	y,
		double	thi
	)		const

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matrix diff_leg::eval_10	(	const matrix &	y,
		double	thi,
		matrix &	T
	)		const

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matrix diff_leg::eval_11	(	const matrix &	y,
		const matrix &	thi,
		matrix &	T
	)		const

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matrix diff_leg::eval_11	(	const matrix &	y,
		const matrix &	thi
	)		const

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matrix diff_leg::eval_11	(	const matrix &	y,
		double	thi
	)		const

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matrix diff_leg::eval_11	(	const matrix &	y,
		double	thi,
		matrix &	T
	)		const

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void diff_leg::init ( )

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matrix diff_leg::l_00 ( ) const

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matrix diff_leg::l_01 ( ) const

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matrix diff_leg::l_10 ( ) const

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matrix diff_leg::l_11 ( ) const

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matrix diff_leg::nodes	(	int	n,
		matrix &	w
	)

private

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diff_leg & diff_leg::operator= ( const diff_leg & leg )

matrix diff_leg::Pn	(	int	n,
		matrix	x
	)

private

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Member Data Documentation

matrix diff_leg::D2_00

matrix diff_leg::D2_01

matrix diff_leg::D2_10

matrix diff_leg::D2_11

matrix diff_leg::D_00

matrix diff_leg::D_01

matrix diff_leg::D_10

matrix diff_leg::D_11

matrix diff_leg::dP1_00

matrix diff_leg::dP1_01

matrix diff_leg::dP1_10

matrix diff_leg::dP1_11

matrix diff_leg::I_00

matrix diff_leg::lap_00

matrix diff_leg::lap_01

matrix diff_leg::lap_10

matrix diff_leg::lap_11

int diff_leg::npts

matrix diff_leg::P1_00

matrix diff_leg::P1_01

matrix diff_leg::P1_10

matrix diff_leg::P1_11

matrix diff_leg::P_00

matrix diff_leg::P_01

matrix diff_leg::P_10

matrix diff_leg::P_11

matrix diff_leg::th

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

src/include/numdiff.h
src/numdiff/diff_leg.cpp