A Lie algebraic map, factored according to Dragt and Finn. More...

#include <DragtFinnMap.h>

Collaboration diagram for DragtFinnMap< N >:

Public Member Functions
	DragtFinnMap (const DragtFinnMap &)

	~DragtFinnMap ()

const DragtFinnMap &	operator= (const DragtFinnMap &)

	DragtFinnMap ()
	Construct identity map. More...

	DragtFinnMap (int)
	Construct identity map with space for given order. More...

	DragtFinnMap (const FVps< double, 2 *N > &map)
	Build factored representation from a Taylor series map. More...

	DragtFinnMap (const FTps< double, 2 *N > &map)
	Build factored representation from a pseudo-Hamiltonian. More...

	DragtFinnMap (const LinearMap< double, 2 *N > &map)
	Build factored representation from a linear map. More...

	operator FVps< double, 2 *N > () const
	Convert to Taylor series map. More...

	operator LinearMap< double, 2 *N > () const
	Convert to Taylor series map. More...

void	assign (const FMatrix< double, 2 N, 2 N > &)
	Assign the matrix representing the linear transform. More...

void	assign (const FTps< double, 2 *N > &)
	Assign the complete set of generators. More...

void	assign (const FLieGenerator< double, N > &)
	Assign the generator for a selected order. More...

const FMatrix< double, 2 N, 2 N > &	getMatrix () const
	Return the matrix representing the linear transform. More...

FMatrix< double, 2 N, 2 N > &	getMatrix ()
	Return the matrix representing the linear transform. More...

const FTps< double, 2 *N > &	getGenerators () const
	Return the complete set of generators. More...

FTps< double, 2 *N > &	getGenerators ()
	Return the complete set of generators. More...

const FLieGenerator< double, N >	getGenerator (int) const
	Return the generator for a selected order. More...

int	getOrder () const
	Return the order of the generators. More...

DragtFinnMap	inverse () const
	Compute inverse map. More...

DragtFinnMap	reverse () const
	Compute inverse factorisation of map. More...

void	operator+= (const FTps< double, 2 *N > &)
	Add to set of generators. More...

void	operator-= (const FTps< double, 2 *N > &)
	Subtract from set of generators. More...

void	operator+= (const FLieGenerator< double, N > &)
	Add to generator of given order. More...

void	operator-= (const FLieGenerator< double, N > &)
	Subtract from generator of given order. More...

DragtFinnMap	catenate (const DragtFinnMap &) const
	Substitute (concatenate) with another map in beam order. More...

DragtFinnMap	conjugate (const DragtFinnMap &) const
	Conjugate with another map. More...

void	dynamicFixedPoint (FVector< double, 2 *N > &fp, DragtFinnMap &map)
	Compute dynamic fixed point. More...

void	staticFixedPoint (FVector< double, 2 *N > &fp, DragtFinnMap &map)
	Compute static fixed point. More...

void	removeDispersion (DragtFinnMap &dm, DragtFinnMap &map)
	Split map into dispersion map and non-dispersive part. More...

void	trackOrbit (FVector< double, 2 *N > &orbit, DragtFinnMap &map)
	Track an orbit through the map. More...

DragtFinnMap	transform (const FLieGenerator< double, N > &g, int topOrder)
	Build the terminating exponential series. More...

Static Public Member Functions
static DragtFinnMap	factorBerzForestIrwin (const FTps< double, 2 *N > &H)

static DragtFinnMap	factorDouglas (const FTps< double, 2 *N > &H)

static DragtFinnMap	factorSimple (const FTps< double, 2 *N > &H)

Private Member Functions
const double *	begin (int) const

double *	begin (int)

const double *	end (int) const

double *	end (int)

DragtFinnMap	catenateZero (const DragtFinnMap &) const

Static Private Member Functions
static FMatrix< double, 2 N, 2 N >	exponentiate (const FMatrix< double, 2 N, 2 N > &)

static DragtFinnMap	factorize (const FTps< double, 2 *N > &H)

static FMatrix< double, 2 N, 2 N >	makeMatrix (const FLieGenerator< double, N > &f_2)

static void	move_g_1 (DragtFinnMap &f, DragtFinnMap &g)

static int	orderModes (FMatrix< double, 2 N, 2 N > &, FVector< std::complex< double >, 2 *N > &)

Private Attributes
FMatrix< double, 2 N, 2 N >	itsMatrix

FTps< double, 2 *N >	itsGenerators

Detailed Description

template<int N>
class DragtFinnMap< N >

A Lie algebraic map, factored according to Dragt and Finn.

Definition at line 43 of file DragtFinnMap.h.

Constructor & Destructor Documentation

template<int N>

DragtFinnMap< N >::DragtFinnMap ( const DragtFinnMap< N > & rhs )

Definition at line 250 of file DragtFinnMap.h.

template<int N>

DragtFinnMap< N >::~DragtFinnMap ( )

Definition at line 273 of file DragtFinnMap.h.

template<int N>

DragtFinnMap< N >::DragtFinnMap ( )

Construct identity map.

Definition at line 257 of file DragtFinnMap.h.

References DragtFinnMap< N >::itsMatrix.

template<int N>

DragtFinnMap< N >::DragtFinnMap ( int order )

explicit

Construct identity map with space for given order.

Definition at line 265 of file DragtFinnMap.h.

References DragtFinnMap< N >::itsMatrix.

template<int N>

DragtFinnMap< N >::DragtFinnMap ( const FVps< double, 2 *N > & map )

explicit

Build factored representation from a Taylor series map.

Definition at line 288 of file DragtFinnMap.h.

References DragtFinnMap< N >::itsGenerators.

template<int N>

DragtFinnMap< N >::DragtFinnMap ( const FTps< double, 2 *N > & map )

explicit

Build factored representation from a pseudo-Hamiltonian.

Definition at line 352 of file DragtFinnMap.h.

References assign(), DragtFinnMap< N >::assign(), DragtFinnMap< N >::catenateZero(), FTps< T, N >::filter(), DragtFinnMap< N >::getGenerator(), DragtFinnMap< N >::getGenerators(), DragtFinnMap< N >::getMatrix(), FTps< T, N >::getMaxOrder(), FTps< T, N >::substitute(), and DragtFinnMap< N >::transform().

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template<int N>

DragtFinnMap< N >::DragtFinnMap ( const LinearMap< double, 2 *N > & map )

explicit

Build factored representation from a linear map.

Definition at line 300 of file DragtFinnMap.h.

References DragtFinnMap< N >::itsGenerators.

Member Function Documentation

template<int N>

void DragtFinnMap< N >::assign ( const FMatrix< double, 2 *N, 2 *N > & mat )

Assign the matrix representing the linear transform.

Definition at line 395 of file DragtFinnMap.h.

template<int N>

void DragtFinnMap< N >::assign ( const FTps< double, 2 *N > & gen )

Assign the complete set of generators.

Definition at line 402 of file DragtFinnMap.h.

template<int N>

void DragtFinnMap< N >::assign ( const FLieGenerator< double, N > & gen )

Assign the generator for a selected order.

Definition at line 409 of file DragtFinnMap.h.

References FLieGenerator< T, N >::begin(), FTps< T, N >::begin(), FLieGenerator< T, N >::end(), FLieGenerator< T, N >::getOrder(), and FTps< T, N >::unique().

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template<int N>

const double * DragtFinnMap< N >::begin ( int order ) const

inlineprivate

Definition at line 1058 of file DragtFinnMap.h.

References FTpsData< N >::getSize().

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template<int N>

double * DragtFinnMap< N >::begin ( int order )

inlineprivate

Definition at line 1051 of file DragtFinnMap.h.

References FTpsData< N >::getSize().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::catenate ( const DragtFinnMap< N > & rhs ) const

Substitute (concatenate) with another map in beam order.

Definition at line 813 of file DragtFinnMap.h.

References DragtFinnMap< N >::catenateZero(), FTps< T, N >::filter(), and DragtFinnMap< N >::itsGenerators.

Referenced by LieMapper::applyDrift(), LieMapper::applyTransform(), DragtFinnMap< N >::conjugate(), LieMapper::visitCorrector(), LieMapper::visitMultipole(), LieMapper::visitRBend(), LieMapper::visitRFCavity(), LieMapper::visitSBend(), LieMapper::visitSeparator(), and LieMapper::visitSolenoid().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::catenateZero ( const DragtFinnMap< N > & g ) const

private

Definition at line 1079 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), FTps< T, N >::filter(), DragtFinnMap< N >::getGenerators(), DragtFinnMap< N >::getMatrix(), DragtFinnMap< N >::getOrder(), max(), and PoissonBracket().

Referenced by DragtFinnMap< N >::catenate(), DragtFinnMap< N >::DragtFinnMap(), and DragtFinnMap< N >::removeDispersion().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::conjugate ( const DragtFinnMap< N > & rhs ) const

Conjugate with another map.

Definition at line 828 of file DragtFinnMap.h.

References DragtFinnMap< N >::catenate(), and DragtFinnMap< N >::inverse().

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

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template<int N>

void DragtFinnMap< N >::dynamicFixedPoint	(	FVector< double, 2 *N > &	fp,
		DragtFinnMap< N > &	map
	)

Compute dynamic fixed point.

Definition at line 835 of file DragtFinnMap.h.

References FLUMatrix< T, N >::backSubstitute(), euclidean_norm(), fp1(), and DragtFinnMap< N >::getMatrix().

Referenced by Dynamic::execute().

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template<int N>

const double * DragtFinnMap< N >::end ( int order ) const

inlineprivate

Definition at line 1072 of file DragtFinnMap.h.

References FTpsData< N >::getSize().

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template<int N>

double * DragtFinnMap< N >::end ( int order )

inlineprivate

Definition at line 1065 of file DragtFinnMap.h.

References FTpsData< N >::getSize().

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template<int N>

FMatrix< double, 2 *N, 2 *N > DragtFinnMap< N >::exponentiate ( const FMatrix< double, 2 *N, 2 *N > & A )

staticprivate

Definition at line 1146 of file DragtFinnMap.h.

References FLUMatrix< T, N >::backSubstitute().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::factorBerzForestIrwin ( const FTps< double, 2 *N > & H )

static

Definition at line 426 of file DragtFinnMap.h.

References abs(), DragtFinnMap< N >::assign(), Physics::c, DragtFinnMap< N >::conjugate(), cos(), cosh(), FDoubleEigen< N >::eigenValues(), FTps< T, N >::filter(), FTpsData< N >::getExponents(), DragtFinnMap< N >::getGenerators(), FTps< T, N >::getMaxOrder(), imag(), FLUMatrix< T, N >::inverse(), FDoubleEigen< N >::packedEigenVectors(), pi, pow(), real(), FLieGenerator< T, N >::scale(), sin(), sinh(), FTps< T, N >::substitute(), FLieGenerator< T, N >::transform(), and DragtFinnMap< N >::transform().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::factorDouglas ( const FTps< double, 2 *N > & H )

static

Definition at line 555 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), FTps< T, N >::getMaxOrder(), PoissonBracket(), and Taylor< T >::sum().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::factorize ( const FTps< double, 2 *N > & H )

staticprivate

Definition at line 1130 of file DragtFinnMap.h.

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

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::factorSimple ( const FTps< double, 2 *N > & H )

static

Definition at line 652 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), FTps< T, N >::filter(), FTps< T, N >::getMaxOrder(), FLieGenerator< T, N >::isZero(), and FLieGenerator< T, N >::transform().

Referenced by LieMapper::applyDrift(), LieMapper::visitMultipole(), LieMapper::visitRBend(), LieMapper::visitRFCavity(), LieMapper::visitSBend(), and LieMapper::visitSolenoid().

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template<int N>

const FLieGenerator< double, N > DragtFinnMap< N >::getGenerator ( int order ) const

Return the generator for a selected order.

Definition at line 699 of file DragtFinnMap.h.

References FLieGenerator< T, N >::begin(), and FLieGenerator< T, N >::end().

Referenced by DragtFinnMap< N >::DragtFinnMap(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), and DragtFinnMap< N >::move_g_1().

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template<int N>

const FTps< double, 2 *N > & DragtFinnMap< N >::getGenerators ( ) const

Return the complete set of generators.

Definition at line 685 of file DragtFinnMap.h.

Referenced by DragtFinnMap< N >::catenateZero(), DragtFinnMap< N >::DragtFinnMap(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), DragtFinnMap< N >::factorBerzForestIrwin(), DragtFinnMap< N >::inverse(), DragtFinnMap< N >::move_g_1(), DragtFinnMap< N >::removeDispersion(), and DragtFinnMap< N >::trackOrbit().

template<int N>

FTps< double, 2 *N > & DragtFinnMap< N >::getGenerators ( )

Return the complete set of generators.

Definition at line 692 of file DragtFinnMap.h.

template<int N>

const FMatrix< double, 2 *N, 2 *N > & DragtFinnMap< N >::getMatrix ( ) const

Return the matrix representing the linear transform.

Definition at line 671 of file DragtFinnMap.h.

Referenced by DragtFinnMap< N >::catenateZero(), DragtFinnMap< N >::DragtFinnMap(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), DragtFinnMap< N >::dynamicFixedPoint(), DragtFinnMap< N >::move_g_1(), DragtFinnMap< N >::removeDispersion(), DragtFinnMap< N >::staticFixedPoint(), LieMapper::visitCorrector(), and LieMapper::visitSeparator().

template<int N>

FMatrix< double, 2 *N, 2 *N > & DragtFinnMap< N >::getMatrix ( )

Return the matrix representing the linear transform.

Definition at line 678 of file DragtFinnMap.h.

template<int N>

int DragtFinnMap< N >::getOrder ( ) const

Return the order of the generators.

Definition at line 714 of file DragtFinnMap.h.

Referenced by DragtFinnMap< N >::catenateZero(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), and DragtFinnMap< N >::move_g_1().

template<int N>

DragtFinnMap< N > DragtFinnMap< N >::inverse ( ) const

Compute inverse map.

Definition at line 721 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), DragtFinnMap< N >::getGenerators(), and FLUMatrix< T, N >::inverse().

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

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template<int N>

FMatrix< double, 2 *N, 2 *N > DragtFinnMap< N >::makeMatrix ( const FLieGenerator< double, N > & f_2 )

staticprivate

Definition at line 1167 of file DragtFinnMap.h.

template<int N>

void DragtFinnMap< N >::move_g_1	(	DragtFinnMap< N > &	f,
		DragtFinnMap< N > &	g
	)

staticprivate

Definition at line 1196 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), FTps< T, N >::filter(), DragtFinnMap< N >::getGenerator(), DragtFinnMap< N >::getGenerators(), DragtFinnMap< N >::getMatrix(), DragtFinnMap< N >::getOrder(), PoissonBracket(), and FLieGenerator< T, N >::transform().

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template<int N>

DragtFinnMap< N >::operator FVps< double, 2 *N > ( ) const

Convert to Taylor series map.

Definition at line 311 of file DragtFinnMap.h.

References ExpMap(), FVps< T, N >::filter(), FTps< T, N >::filter(), and FVps< T, N >::substitute().

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template<int N>

DragtFinnMap< N >::operator LinearMap< double, 2 *N > ( ) const

Convert to Taylor series map.

Definition at line 336 of file DragtFinnMap.h.

References FLieGenerator< T, N >::transform().

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template<int N>

void DragtFinnMap< N >::operator+= ( const FTps< double, 2 *N > & gen )

Add to set of generators.

Definition at line 759 of file DragtFinnMap.h.

template<int N>

void DragtFinnMap< N >::operator+= ( const FLieGenerator< double, N > & gen )

Add to generator of given order.

Definition at line 773 of file DragtFinnMap.h.

References FLieGenerator< T, N >::begin(), FTps< T, N >::begin(), FLieGenerator< T, N >::getOrder(), and FTps< T, N >::unique().

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template<int N>

void DragtFinnMap< N >::operator-= ( const FTps< double, 2 *N > & gen )

Subtract from set of generators.

Definition at line 766 of file DragtFinnMap.h.

template<int N>

void DragtFinnMap< N >::operator-= ( const FLieGenerator< double, N > & gen )

Subtract from generator of given order.

Definition at line 793 of file DragtFinnMap.h.

References FLieGenerator< T, N >::begin(), FTps< T, N >::begin(), FLieGenerator< T, N >::getOrder(), and FTps< T, N >::unique().

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template<int N>

const DragtFinnMap< N > & DragtFinnMap< N >::operator= ( const DragtFinnMap< N > & rhs )

Definition at line 279 of file DragtFinnMap.h.

References DragtFinnMap< N >::itsGenerators, and DragtFinnMap< N >::itsMatrix.

template<int N>

int DragtFinnMap< N >::orderModes	(	FMatrix< double, 2 N, 2 N > &	V,
		FVector< std::complex< double >, 2 *N > &	mu
	)

staticprivate

Definition at line 1359 of file DragtFinnMap.h.

References abs(), Physics::c, imag(), real(), sqrt(), and FArray2D< T, M, N >::swapColumns().

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template<int N>

void DragtFinnMap< N >::removeDispersion	(	DragtFinnMap< N > &	dm,
		DragtFinnMap< N > &	map
	)

Split map into dispersion map and non-dispersive part.

Definition at line 892 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), DragtFinnMap< N >::catenateZero(), DragtFinnMap< N >::conjugate(), DragtFinnMap< N >::getGenerators(), DragtFinnMap< N >::getMatrix(), and T.

Referenced by Static::execute().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::reverse ( ) const

Compute inverse factorisation of map.

Definition at line 733 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), PoissonBracket(), and FTps< T, N >::substitute().

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template<int N>

void DragtFinnMap< N >::staticFixedPoint	(	FVector< double, 2 *N > &	fp,
		DragtFinnMap< N > &	map
	)

Compute static fixed point.

Definition at line 858 of file DragtFinnMap.h.

References euclidean_norm(), fp1(), DragtFinnMap< N >::getMatrix(), and X.

Referenced by Static::execute().

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template<int N>

void DragtFinnMap< N >::trackOrbit	(	FVector< double, 2 *N > &	orbit,
		DragtFinnMap< N > &	map
	)

Track an orbit through the map.

Definition at line 966 of file DragtFinnMap.h.

References DragtFinnMap< N >::assign(), FTps< T, N >::filter(), DragtFinnMap< N >::getGenerators(), PoissonBracket(), and FLieGenerator< T, N >::transform().

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template<int N>

DragtFinnMap< N > DragtFinnMap< N >::transform	(	const FLieGenerator< double, N > &	g,
		int	topOrder
	)

Build the terminating exponential series.

Definition at line 1029 of file DragtFinnMap.h.

References FLieGenerator< T, N >::getOrder(), and PoissonBracket().

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

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Member Data Documentation

template<int N>

FTps<double, 2 * N> DragtFinnMap< N >::itsGenerators

private

Definition at line 222 of file DragtFinnMap.h.

Referenced by DragtFinnMap< N >::catenate(), DragtFinnMap< N >::DragtFinnMap(), and DragtFinnMap< N >::operator=().

template<int N>

FMatrix<double, 2 * N, 2 * N> DragtFinnMap< N >::itsMatrix

private

Definition at line 219 of file DragtFinnMap.h.

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

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

src/Classic/FixedAlgebra/DragtFinnMap.h

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

template<int N> class DragtFinnMap< N >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<int N>
class DragtFinnMap< N >