A representation for a homogeneous polynomial, used as a Lie generator. More...

#include <DragtFinnMap.h>

Public Member Functions
	FLieGenerator (int)
	Construct a zero generator of given order. More...

	FLieGenerator (const FTps< T, 2 *N > &, int)
	Construct a zero generator of given order by extraction. More...

	FLieGenerator ()

	FLieGenerator (const FLieGenerator &)

	~FLieGenerator ()

const FLieGenerator &	operator= (const FLieGenerator &)

bool	operator== (const FLieGenerator &) const

T *	begin ()
	Get pointer to beginning of generator. More...

T *	end ()
	Get pointer past end of generator. More...

const T *	begin () const
	Get pointer to beginning of generator. More...

const T *	end () const
	Get pointer past end of generator. More...

T &	operator[] (int n)
	Get element. More...

const T &	operator[] (int n) const
	Get element. More...

FLieGenerator	operator- () const
	Change sign of generator. More...

FLieGenerator &	operator*= (const T &)
	Multiply by scalar and assign. More...

FLieGenerator &	operator/= (const T &)
	Divide by scalar and assign. More...

FLieGenerator &	operator+= (const FLieGenerator &)
	Add vector and assign. More...

FLieGenerator &	operator-= (const FLieGenerator &)
	Subtract vector and assign. More...

void	clear ()
	Clear all coefficients. More...

FLieGenerator	derivative (int var) const
	Partial derivative. More...

bool	isZero () const
	Test for zero. More...

FLieGenerator	scale (const FLieGenerator &) const
	Scale monomial-wise. More...

template<class U >
FLieGenerator< U, N >	transform (const FMatrix< U, 2 N, 2 N > &) const
	Substitute matrix in Lie generator. More...

int	getOrder () const
	Return order of this generator. More...

int	getBottomIndex () const
	Return bottom index of this generator. More...

int	getTopIndex () const
	Return top index of this generator. More...

Static Private Member Functions
static int	getSize (int order)

static int	getBottomIndex (int order)

static int	getTopIndex (int order)

Private Attributes
int	itsOrder

int	bottomIndex

int	topIndex

Array1D< T >	itsCoeffs

Detailed Description

template<class T, int N>
class FLieGenerator< T, N >

A representation for a homogeneous polynomial, used as a Lie generator.

Definition at line 29 of file DragtFinnMap.h.

Constructor & Destructor Documentation

template<class T , int N>

FLieGenerator< T, N >::FLieGenerator ( int order )

explicit

Construct a zero generator of given order.

Definition at line 38 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::itsCoeffs, and T.

template<class T , int N>

FLieGenerator< T, N >::FLieGenerator	(	const FTps< T, 2 *N > &	tps,
		int	order
	)

Construct a zero generator of given order by extraction.

Definition at line 49 of file FLieGenerator.hpp.

References FTps< T, N >::begin(), FLieGenerator< T, N >::bottomIndex, FTps< T, N >::getMaxOrder(), FLieGenerator< T, N >::itsCoeffs, T, and FLieGenerator< T, N >::topIndex.

Here is the call graph for this function:

template<class T , int N>

FLieGenerator< T, N >::FLieGenerator ( )

Definition at line 64 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::itsCoeffs, and T.

template<class T , int N>

FLieGenerator< T, N >::FLieGenerator ( const FLieGenerator< T, N > & rhs )

Definition at line 75 of file FLieGenerator.hpp.

template<class T , int N>

FLieGenerator< T, N >::~FLieGenerator ( )

Definition at line 85 of file FLieGenerator.hpp.

Member Function Documentation

template<class T , int N>

T * FLieGenerator< T, N >::begin ( )

inline

Get pointer to beginning of generator.

Definition at line 102 of file FLieGenerator.hpp.

Referenced by DragtFinnMap< N >::assign(), DragtFinnMap< N >::getGenerator(), DragtFinnMap< N >::operator+=(), DragtFinnMap< N >::operator-=(), PoissonBracket(), and toComplex().

template<class T , int N>

const T * FLieGenerator< T, N >::begin ( ) const

inline

Get pointer to beginning of generator.

Definition at line 109 of file FLieGenerator.hpp.

template<class T , int N>

void FLieGenerator< T, N >::clear ( )

Clear all coefficients.

Definition at line 209 of file FLieGenerator.hpp.

References T.

template<class T , int N>

FLieGenerator< T, N > FLieGenerator< T, N >::derivative ( int var ) const

Partial derivative.

Definition at line 215 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::getBottomIndex(), FTpsData< N >::getProductArray(), and FLieGenerator< T, N >::getTopIndex().

Referenced by DragtFinnMap< N >::factorize().

Here is the call graph for this function:

template<class T , int N>

T * FLieGenerator< T, N >::end ( )

inline

Get pointer past end of generator.

Definition at line 115 of file FLieGenerator.hpp.

Referenced by DragtFinnMap< N >::assign(), DragtFinnMap< N >::getGenerator(), imag(), real(), and toComplex().

template<class T , int N>

const T * FLieGenerator< T, N >::end ( ) const

inline

Get pointer past end of generator.

Definition at line 122 of file FLieGenerator.hpp.

template<class T , int N>

int FLieGenerator< T, N >::getBottomIndex ( ) const

inline

Return bottom index of this generator.

Definition at line 314 of file FLieGenerator.hpp.

Referenced by FLieGenerator< T, N >::derivative(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), operator*(), and PoissonBracket().

template<class T , int N>

int FLieGenerator< T, N >::getBottomIndex ( int order )

inlinestaticprivate

Definition at line 335 of file FLieGenerator.hpp.

References FTpsData< N >::getSize().

Here is the call graph for this function:

template<class T , int N>

int FLieGenerator< T, N >::getOrder ( ) const

inline

Return order of this generator.

Definition at line 307 of file FLieGenerator.hpp.

Referenced by DragtFinnMap< N >::assign(), operator*(), DragtFinnMap< N >::operator+=(), DragtFinnMap< N >::operator-=(), operator<<(), PoissonBracket(), toComplex(), and DragtFinnMap< N >::transform().

template<class T , int N>

int FLieGenerator< T, N >::getSize ( int order )

inlinestaticprivate

Definition at line 328 of file FLieGenerator.hpp.

References FTpsData< N >::getSize().

Here is the call graph for this function:

template<class T , int N>

int FLieGenerator< T, N >::getTopIndex ( ) const

inline

Return top index of this generator.

Definition at line 321 of file FLieGenerator.hpp.

Referenced by FLieGenerator< T, N >::derivative(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), and operator*().

template<class T , int N>

int FLieGenerator< T, N >::getTopIndex ( int order )

inlinestaticprivate

Definition at line 342 of file FLieGenerator.hpp.

References FTpsData< N >::getSize().

Here is the call graph for this function:

template<class T , int N>

bool FLieGenerator< T, N >::isZero ( ) const

Test for zero.

Definition at line 234 of file FLieGenerator.hpp.

References T.

Referenced by DragtFinnMap< N >::factorize(), DragtFinnMap< N >::factorSimple(), operator*(), FLieGenerator< T, N >::operator+=(), FLieGenerator< T, N >::operator-=(), and PoissonBracket().

template<class T , int N>

FLieGenerator< T, N > & FLieGenerator< T, N >::operator*= ( const T & val )

Multiply by scalar and assign.

Definition at line 152 of file FLieGenerator.hpp.

template<class T , int N>

FLieGenerator< T, N > & FLieGenerator< T, N >::operator+= ( const FLieGenerator< T, N > & rhs )

Add vector and assign.

Definition at line 177 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::isZero(), FLieGenerator< T, N >::itsCoeffs, and FLieGenerator< T, N >::itsOrder.

Here is the call graph for this function:

template<class T , int N>

FLieGenerator< T, N > FLieGenerator< T, N >::operator- ( ) const

Change sign of generator.

Definition at line 140 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::itsCoeffs.

template<class T , int N>

FLieGenerator< T, N > & FLieGenerator< T, N >::operator-= ( const FLieGenerator< T, N > & rhs )

Subtract vector and assign.

Definition at line 193 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::isZero(), FLieGenerator< T, N >::itsCoeffs, and FLieGenerator< T, N >::itsOrder.

Here is the call graph for this function:

template<class T , int N>

FLieGenerator< T, N > & FLieGenerator< T, N >::operator/= ( const T & val )

Divide by scalar and assign.

Definition at line 164 of file FLieGenerator.hpp.

template<class T , int N>

const FLieGenerator< T, N > & FLieGenerator< T, N >::operator= ( const FLieGenerator< T, N > & rhs )

Definition at line 91 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::bottomIndex, FLieGenerator< T, N >::itsCoeffs, FLieGenerator< T, N >::itsOrder, and FLieGenerator< T, N >::topIndex.

template<class T, int N>

bool FLieGenerator< T, N >::operator== ( const FLieGenerator< T, N > & ) const

template<class T , int N>

T & FLieGenerator< T, N >::operator[] ( int n )

inline

Get element.

Definition at line 128 of file FLieGenerator.hpp.

template<class T , int N>

const T & FLieGenerator< T, N >::operator[] ( int n ) const

inline

Get element.

Definition at line 134 of file FLieGenerator.hpp.

template<class T , int N>

FLieGenerator< T, N > FLieGenerator< T, N >::scale ( const FLieGenerator< T, N > & rhs ) const

Scale monomial-wise.

Definition at line 247 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::itsCoeffs.

Referenced by DragtFinnNormalForm< N >::DragtFinnNormalForm(), and DragtFinnMap< N >::factorBerzForestIrwin().

template<class T , int N>

template<class U >

FLieGenerator< U, N > FLieGenerator< T, N >::transform ( const FMatrix< U, 2 *N, 2 *N > & mat ) const

Substitute matrix in Lie generator.

Definition at line 257 of file FLieGenerator.hpp.

References Array1D< T >::begin(), Physics::c, FTpsData< N >::getProductArray(), FTpsData< N >::getSubTable(), TpsSubstitution::index, TpsSubstitution::order, prod(), Array1D< T >::size(), TpsSubstitution::skip, T, and TpsSubstitution::variable.

Referenced by DragtFinnNormalForm< N >::DragtFinnNormalForm(), DragtFinnMap< N >::factorBerzForestIrwin(), DragtFinnMap< N >::factorSimple(), DragtFinnMap< N >::move_g_1(), DragtFinnMap< N >::operator LinearMap< double, 2 *N >(), and DragtFinnMap< N >::trackOrbit().

Here is the call graph for this function:

Member Data Documentation

template<class T, int N>

int FLieGenerator< T, N >::bottomIndex

private

Definition at line 146 of file FLieGenerator.h.

Referenced by FLieGenerator< T, N >::FLieGenerator(), and FLieGenerator< T, N >::operator=().

template<class T, int N>

Array1D<T> FLieGenerator< T, N >::itsCoeffs

private

Definition at line 152 of file FLieGenerator.h.

Referenced by FLieGenerator< T, N >::FLieGenerator(), FLieGenerator< T, N >::operator+=(), FLieGenerator< T, N >::operator-(), FLieGenerator< T, N >::operator-=(), FLieGenerator< T, N >::operator=(), and FLieGenerator< T, N >::scale().

template<class T, int N>

int FLieGenerator< T, N >::itsOrder

private

Definition at line 143 of file FLieGenerator.h.

Referenced by FLieGenerator< T, N >::operator+=(), FLieGenerator< T, N >::operator-=(), and FLieGenerator< T, N >::operator=().

template<class T, int N>

int FLieGenerator< T, N >::topIndex

private

Definition at line 149 of file FLieGenerator.h.

Referenced by FLieGenerator< T, N >::FLieGenerator(), and FLieGenerator< T, N >::operator=().

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

src/Classic/FixedAlgebra/DragtFinnMap.h
src/Classic/FixedAlgebra/FLieGenerator.h
src/Classic/FixedAlgebra/FLieGenerator.hpp

Public Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

template<class T, int N> class FLieGenerator< T, N >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class T, int N>
class FLieGenerator< T, N >