Truncated power series in N variables of type T. More...

#include <TransportMapper.h>

Public Member Functions
	FTps ()
	Default constructor. More...

	FTps (const FTps &x)
	Copy constructor. More...

	FTps (int minOrder, int maxOrder, int trcOrder)
	Constructor. More...

	FTps (const T &)
	Conversion. More...

	FTps (int)
	Conversion. More...

	~FTps ()
	Destructor. More...

FTps &	operator= (const FTps &y)
	Assign. More...

FTps &	operator= (const T &y)
	Convert and assign. More...

const T	getCoefficient (int index) const
	Get coefficient. More...

void	setCoefficient (int index, const T &value)
	Set coefficient. More...

const T	getCoefficient (const FMonomial< N > &monomial) const
	Get coefficient. More...

void	setCoefficient (const FMonomial< N > &monomial, const T &value)
	Set coefficient. More...

const T	operator[] (int index) const
	Get coefficient. More...

T &	operator[] (int index)
	Get (Set) coefficient. More...

const T	operator[] (const FMonomial< N > &monomial) const
	Get coefficient. More...

T &	operator[] (const FMonomial< N > &monomial)
	Get (Set) coefficient. More...

T *	begin () const
	Return beginning of monomial array. More...

T *	end () const
	Return end of monomial array. More...

T *	begin (int order) const
	Return beginning of coefficient storage for given order. More...

T *	end (int order) const
	Return end of coefficient storage for given order. More...

int	getSize () const
	Get total number of coefficients. More...

int	getMinOrder () const
	Get minimum order. More...

void	setMinOrder (int order)
	Set minimum order. More...

int	getMaxOrder () const
	Get maximum order. More...

void	setMaxOrder (int order)
	Set maximum order. More...

int	getTruncOrder () const
	Get truncation order. More...

void	setTruncOrder (int order)
	Set truncation order. More...

FTps	filter (int minOrder, int maxOrder, int trcOrder=EXACT) const
	Extract given range of orders, with truncation. More...

FTps	truncate (int trunc)
	Truncate. More...

FTps	operator+ () const
	Unary plus. More...

FTps	operator- () const
	Unary minus. More...

FTps &	operator+= (const FTps &y)
	Add and assign. More...

FTps &	operator-= (const FTps &y)
	Subtract and assign. More...

FTps &	operator*= (const FTps &y)
	Multiply and assign. More...

FTps &	operator/= (const FTps &y)
	Divide and assign. More...

FTps &	operator+= (const T &y)
	Add constant and assign. More...

FTps &	operator-= (const T &y)
	Subtract constant and assign. More...

FTps &	operator*= (const T &y)
	Multiply by constant and assign. More...

FTps &	operator/= (const T &y)
	Divide by constant and assign. More...

FTps	scaleMonomials (const FTps &y) const
	Scale monomial coefficients by coefficients in [b]y[/b]. More...

FTps	multiplyVariable (int var, int trunc=EXACT) const
	Multiply by variable [b]var[/b]. More...

FTps	multiply (const FTps &y, int trunc=EXACT) const
	Multiplication. More...

FTps	inverse (int trunc=EXACT) const
	Reciprocal, 1/(*this). More...

FTps	divide (const FTps &y, int trunc=EXACT) const
	Division. More...

bool	operator== (const FTps &y) const
	Equality operator. More...

bool	operator== (const T &y) const
	Equality with constant. More...

bool	operator!= (const FTps &y) const
	Inequality operator. More...

bool	operator!= (const T &y) const
	Inequality with constant. More...

T	evaluate (const FVector< T, N > &) const
	Evaluate FTps at point. More...

Array1D< int >	getSubstOrders (const FVps< T, N > &rhs, int trunc=EXACT) const
	Return orders {min, max, trc} of f(rhs(z)). More...

FTps	substitute (const FMatrix< T, N, N > &M, int n) const
	Substitute. More...

FTps	substitute (const FMatrix< T, N, N > &M, int nl, int nh) const
	Substitute. More...

FTps	substitute (const FMatrix< T, N, N > &M) const
	Substitute. More...

FTps	substitute (const FVps< T, N > &m, int trunc=EXACT) const
	Substitute. More...

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

FVps< T, N >	gradient () const
	Gradient. More...

FTps	integral (int var, int trunc=EXACT) const
	Partial integral. More...

FTps	taylor (const Array1D< T > &series, int order) const
	Taylor series. More...

void	unique ()
	Make representation unique. More...

std::list< int >	getListOfNonzeroCoefficients () const
	Get a list containing the indexes of non-zero coefficients of a FTps. More...

FArray1D< int, N >	extractExponents (int index) const
	Extract exponents of coefficient. More...

FTps< T, N >	makePower (int power) const
	Multiply FTps with itself. More...

std::istream &	get (std::istream &is)
	Read FTps on the stream [b]is[/b]. More...

std::ostream &	put (std::ostream &os) const
	Write FTps on the stream [b]os[/b]. More...

Static Public Member Functions
static int	getVariables ()
	Get number of variables. More...

static int	getSize (int order)
	Get number of coefficients of degree [b]order[/b] or less. More...

static int	orderStart (int order)
	Get index at which [b]order[/b] starts. More...

static int	orderEnd (int order)
	Get one plus index at which [b]order[/b] ends. More...

static int	orderLength (int order)

static int	orderLength (int orderL, int orderH)

static const FMonomial< N > &	getExponents (int index)
	Get exponents for given index. More...

static int	getIndex (const FMonomial< N > &mono)
	Get Giorgilli index for monomial. More...

static int	getGlobalTruncOrder ()
	Return the global truncation order. More...

static void	setGlobalTruncOrder (int order)
	Set the global truncation order. More...

static const Array1D< int > &	getProductArray (int index)
	Index array for products of monomial "index". More...

static const Array1D< int > &	getVariableList (int index)
	List of variables contained in monomial "index". More...

static const Array1D < TpsSubstitution > &	getSubTable ()
	Return the substitution table. More...

static FTps	makeVariable (int var)
	Make variable. More...

static FTps	makeVarPower (int var, int power)
	Make power. More...

static FTps	makeMonomial (int index, const T &t)
	Make monomial. More...

static FTps	makeMonomial (const FMonomial< N > &m, const T &t)
	Make monomial. More...

static Array1D< T >	evalMonoms (const FVector< T, N > &, int)
	Evaluate monomials at point. More...

static Array1D< int >	getSubstOrders (Array1D< int > &ordersL, Array1D< int > &ordersR, int trunc=EXACT)
	Return orders {min, max, trc} of f(rhs(z)),. More...

Static Public Attributes
static const int	EXACT = INT_MAX
	Representation of infinite precision. More...

Private Member Functions
void	grow (int maxOrder, int trcOrder)

Array1D< int >	getRepOrders () const

Static Private Member Functions
static FTpsRep< T, N > *	allocate (int minOrder, int maxOrder, int trcOrder)

static void	deallocate (FTpsRep< T, N > *)

static void	checkOrders (const std::string &method, int minOrder, int maxOrder, int &trcOrder)

Private Attributes
FTpsRep< T, N > *	itsRep

Static Private Attributes
static FTpsRep< T, N > *	freeList [100]

static int	globalTruncOrder

Detailed Description

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

Truncated power series in N variables of type T.

Definition at line 29 of file TransportMapper.h.

Constructor & Destructor Documentation

template<class T , int N>

FTps< T, N >::FTps ( )

Default constructor.

Definition at line 159 of file FTps.hpp.

References T.

template<class T , int N>

FTps< T, N >::FTps ( const FTps< T, N > & x )

Copy constructor.

Definition at line 166 of file FTps.hpp.

References FTps< T, N >::itsRep.

template<class T , int N>

FTps< T, N >::FTps	(	int	minOrder,
		int	maxOrder,
		int	trcOrder
	)

Constructor.

Definition at line 173 of file FTps.hpp.

template<class T, int N>

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

Conversion.

Definition at line 180 of file FTps.hpp.

template<class T, int N>

FTps< T, N >::FTps ( int rhs )

Conversion.

Definition at line 187 of file FTps.hpp.

References T.

template<class T , int N>

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

Destructor.

Definition at line 194 of file FTps.hpp.

Member Function Documentation

template<class T , int N>

FTpsRep< T, N > * FTps< T, N >::allocate	(	int	minOrder,
		int	maxOrder,
		int	trcOrder
	)

inlinestaticprivate

Definition at line 1692 of file FTps.hpp.

References FTpsRep< T, N >::allocOrd, endl(), FTpsRep< T, N >::maxOrd, FTpsRep< T, N >::minOrd, FTpsRep< T, N >::next, FTpsRep< T, N >::ref, and FTpsRep< T, N >::trcOrd.

Referenced by FTps< T, N >::unique().

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template<class T, int N>

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

inline

Return beginning of monomial array.

Definition at line 118 of file FTps.h.

Referenced by DragtFinnMap< N >::assign(), FTps< T, N >::derivative(), FTps< T, N >::divide(), FTps< T, N >::filter(), FLieGenerator< T, N >::FLieGenerator(), FTps< T, N >::integral(), FVps< T, N >::linearTerms(), FTps< T, N >::multiply(), FTps< T, N >::multiplyVariable(), operator+(), DragtFinnMap< N >::operator+=(), FTps< T, N >::operator-(), operator-(), DragtFinnMap< N >::operator-=(), FTps< T, N >::operator==(), FTps< T, N >::scaleMonomials(), and FTps< T, N >::substitute().

template<class T, int N>

T* FTps< T, N >::begin ( int order ) const

inline

Return beginning of coefficient storage for given order.

Definition at line 124 of file FTps.h.

template<class T , int N>

void FTps< T, N >::checkOrders	(	const std::string &	method,
		int	minOrder,
		int	maxOrder,
		int &	trcOrder
	)

staticprivate

Definition at line 1767 of file FTps.hpp.

References endl().

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template<class T, int N>

void FTps< T, N >::deallocate ( FTpsRep< T, N > * rep )

inlinestaticprivate

Definition at line 1726 of file FTps.hpp.

References FTpsRep< T, N >::allocOrd, and FTpsRep< T, N >::next.

template<class T , int N>

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

Partial derivative.

Definition at line 1396 of file FTps.hpp.

References Array1D< T >::begin(), FTps< T, N >::begin(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTpsData< N >::getProductArray(), FVps< T, N >::getTruncOrder(), and T.

Referenced by ThickMapper::applyDrift(), OrbitTracker::applySBendBody(), LinearMapper::applySBendBody(), TransportMapper::applySBendBody(), Mapper::applyThinSBend(), Tracker::applyThinSBend(), TransportMapper::applyThinSBend(), AbstractMapper::buildSBendVectorPotential(), Tracker::buildSBendVectorPotential(), OrbitTracker::buildSBendVectorPotential(), LinearMapper::buildSBendVectorPotential(), TransportMapper::buildSBendVectorPotential(), Tracker::buildSBendVectorPotential2D(), ExpMap(), FVps< T, N >::linearTerms(), PoissonBracket(), ThickMapper::visitMultipole(), ThickMapper::visitRBend(), and ThickMapper::visitSBend().

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template<class T , int N>

FTps< T, N > FTps< T, N >::divide	(	const FTps< T, N > &	y,
		int	trunc = `EXACT`
	)		const

Division.

Definition at line 761 of file FTps.hpp.

References FTps< T, N >::begin(), Physics::c, endl(), FVps< T, N >::getMaxOrder(), FTps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTpsData< N >::getProductArray(), FVps< T, N >::getTruncOrder(), FTps< T, N >::getTruncOrder(), FTps< T, N >::itsRep, max(), min(), prod(), and T.

Referenced by operator/().

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template<class T, int N>

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

inline

Return end of monomial array.

Definition at line 121 of file FTps.h.

Referenced by FTps< T, N >::substitute().

template<class T, int N>

T* FTps< T, N >::end ( int order ) const

inline

Return end of coefficient storage for given order.

Definition at line 128 of file FTps.h.

template<class T, int N>

Array1D< T > FTps< T, N >::evalMonoms	(	const FVector< T, N > &	rhs,
		int	maxOrder
	)

static

Evaluate monomials at point.

Definition at line 898 of file FTps.hpp.

References Array1D< T >::begin(), FArray1D< T, N >::begin(), FTpsData< N >::orderStart(), and T.

Referenced by FVps< T, N >::linearTerms().

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template<class T, int N>

T FTps< T, N >::evaluate ( const FVector< T, N > & rhs ) const

Evaluate FTps at point.

Definition at line 934 of file FTps.hpp.

References FArray1D< T, N >::begin(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTpsData< N >::orderStart(), and T.

Referenced by Tracker::applyThinSBend(), and operator*().

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template<class T , int N>

FArray1D< int, N > FTps< T, N >::extractExponents ( int index ) const

Extract exponents of coefficient.

Definition at line 1535 of file FTps.hpp.

References FTps< T, N >::getExponents().

Referenced by FVps< T, N >::operator*().

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template<class T , int N>

FTps< T, N > FTps< T, N >::filter	(	int	minOrder,
		int	maxOrder,
		int	trcOrder = `EXACT`
	)		const

Extract given range of orders, with truncation.

Definition at line 451 of file FTps.hpp.

References FTps< T, N >::begin(), max(), and min().

Referenced by LieMapper::applyDrift(), DragtFinnMap< N >::catenate(), DragtFinnMap< N >::catenateZero(), DragtFinnMap< N >::DragtFinnMap(), DragtFinnMap< N >::factorBerzForestIrwin(), DragtFinnMap< N >::factorSimple(), Period::fill(), DragtFinnMap< N >::move_g_1(), DragtFinnMap< N >::operator FVps< double, 2 *N >(), and DragtFinnMap< N >::trackOrbit().

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template<class T , int N>

std::istream & FTps< T, N >::get ( std::istream & is )

Read FTps on the stream [b]is[/b].

Definition at line 1571 of file FTps.hpp.

References FTpsData< N >::getIndex(), FTps< T, N >::getMaxOrder(), FTps< T, N >::getMinOrder(), FTps< T, N >::itsRep, and T.

Referenced by operator>>().

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template<class T , int N>

const T FTps< T, N >::getCoefficient ( int index ) const

Get coefficient.

Definition at line 223 of file FTps.hpp.

References endl(), and T.

Referenced by FVps< T, N >::operator*().

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template<class T , int N>

const T FTps< T, N >::getCoefficient ( const FMonomial< N > & monomial ) const

Get coefficient.

Definition at line 261 of file FTps.hpp.

References FTpsData< N >::getIndex().

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template<class T , int N>

const FMonomial< N > & FTps< T, N >::getExponents ( int index )

static

Get exponents for given index.

Definition at line 309 of file FTps.hpp.

References FTpsData< N >::getExponents().

Referenced by FTps< T, N >::extractExponents().

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template<class T, int N>

static int FTps< T, N >::getGlobalTruncOrder ( )

inlinestatic

Return the global truncation order.

Definition at line 191 of file FTps.h.

Referenced by FVps< T, N >::operator*().

template<class T , int N>

int FTps< T, N >::getIndex ( const FMonomial< N > & mono )

static

Get Giorgilli index for monomial.

Definition at line 315 of file FTps.hpp.

References FTpsData< N >::getIndex().

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template<class T , int N>

std::list< int > FTps< T, N >::getListOfNonzeroCoefficients ( ) const

Get a list containing the indexes of non-zero coefficients of a FTps.

Definition at line 1515 of file FTps.hpp.

Referenced by FVps< T, N >::operator*().

template<class T, int N>

int FTps< T, N >::getMaxOrder ( ) const

inline

Get maximum order.

Definition at line 174 of file FTps.h.

Referenced by OrbitTracker::applyMultipoleBody(), LinearMapper::applyMultipoleBody(), AbstractMapper::buildMultipoleVectorPotential(), Tracker::buildMultipoleVectorPotential(), Tracker::buildMultipoleVectorPotential2D(), AbstractMapper::buildSBendVectorPotential(), Tracker::buildSBendVectorPotential(), OrbitTracker::buildSBendVectorPotential(), LinearMapper::buildSBendVectorPotential(), Tracker::buildSBendVectorPotential2D(), FTps< T, N >::divide(), DragtFinnMap< N >::DragtFinnMap(), DragtFinnMap< N >::factorBerzForestIrwin(), DragtFinnMap< N >::factorDouglas(), DragtFinnMap< N >::factorSimple(), FLieGenerator< T, N >::FLieGenerator(), FTps< T, N >::get(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getTopOrder(), FVps< T, N >::linearTerms(), operator+(), operator-(), FTps< T, N >::operator==(), PoissonBracket(), and FTps< T, N >::scaleMonomials().

template<class T, int N>

int FTps< T, N >::getMinOrder ( ) const

inline

Get minimum order.

Definition at line 165 of file FTps.h.

Referenced by cos(), cosh(), cot(), coth(), csc(), csch(), erf(), exp(), ExpMap(), FTps< T, N >::get(), FVps< T, N >::getMinOrder(), FVps< T, N >::linearTerms(), log(), FVps< T, N >::operator*(), operator+(), operator-(), FTps< T, N >::operator==(), PoissonBracket(), pow(), FTps< T, N >::scaleMonomials(), sin(), sinh(), and sqrt().

template<class T , int N>

const Array1D< int > & FTps< T, N >::getProductArray ( int index )

inlinestatic

Index array for products of monomial "index".

Definition at line 433 of file FTps.hpp.

References FTpsData< N >::getProductArray().

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template<class T , int N>

Array1D< int > FTps< T, N >::getRepOrders ( ) const

private

Definition at line 1756 of file FTps.hpp.

template<class T, int N>

int FTps< T, N >::getSize ( ) const

inline

Get total number of coefficients.

Definition at line 136 of file FTps.h.

Referenced by FVps< T, N >::substitute().

template<class T , int N>

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

static

Get number of coefficients of degree [b]order[/b] or less.

Definition at line 303 of file FTps.hpp.

References FTpsData< N >::getSize().

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template<class T, int N>

Array1D< int > FTps< T, N >::getSubstOrders	(	const FVps< T, N > &	rhs,
		int	trunc = `EXACT`
	)		const

Return orders {min, max, trc} of f(rhs(z)).

Definition at line 1008 of file FTps.hpp.

References FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FVps< T, N >::getSubstOrders(), and FVps< T, N >::getTruncOrder().

Referenced by FVps< T, N >::getSubstOrders().

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template<class T, int N>

Array1D< int > FTps< T, N >::getSubstOrders	(	Array1D< int > &	ordersL,
		Array1D< int > &	ordersR,
		int	trunc = `EXACT`
	)

static

Return orders {min, max, trc} of f(rhs(z)),.

Definition at line 1022 of file FTps.hpp.

References endl(), and min().

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template<class T , int N>

const Array1D< TpsSubstitution > & FTps< T, N >::getSubTable ( )

inlinestatic

Return the substitution table.

Definition at line 445 of file FTps.hpp.

References FTpsData< N >::getSubTable().

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template<class T, int N>

int FTps< T, N >::getTruncOrder ( ) const

inline

Get truncation order.

Definition at line 183 of file FTps.h.

Referenced by cos(), cosh(), FTps< T, N >::divide(), erf(), exp(), ExpMap(), FVps< T, N >::getTruncOrder(), log(), operator+(), operator-(), FTps< T, N >::operator==(), PoissonBracket(), FTps< T, N >::scaleMonomials(), sin(), sinh(), and sqrt().

template<class T , int N>

const Array1D< int > & FTps< T, N >::getVariableList ( int index )

inlinestatic

List of variables contained in monomial "index".

Definition at line 439 of file FTps.hpp.

References FTpsData< N >::getVariableList().

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template<class T, int N>

static int FTps< T, N >::getVariables ( )

inlinestatic

Get number of variables.

Definition at line 132 of file FTps.h.

template<class T , int N>

FVps< T, N > FTps< T, N >::gradient ( ) const

Gradient.

Definition at line 1433 of file FTps.hpp.

References FVps< T, N >::derivative().

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template<class T , int N>

void FTps< T, N >::grow	(	int	maxOrder,
		int	trcOrder
	)

private

Definition at line 1734 of file FTps.hpp.

References FTpsRep< T, N >::begin(), FTpsRep< T, N >::end(), ge(), min(), and T.

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template<class T , int N>

FTps< T, N > FTps< T, N >::integral	(	int	var,
		int	trunc = `EXACT`
	)		const

Partial integral.

Definition at line 1441 of file FTps.hpp.

References FTps< T, N >::begin(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTpsData< N >::getProductArray(), FVps< T, N >::getTruncOrder(), min(), and T.

Referenced by TransportMapper::buildSBendVectorPotential().

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template<class T , int N>

FTps< T, N > FTps< T, N >::inverse ( int trunc = EXACT ) const

Reciprocal, 1/(*this).

Definition at line 707 of file FTps.hpp.

References Physics::c, endl(), FTpsData< N >::getProductArray(), FTps< T, N >::itsRep, min(), prod(), and T.

Referenced by operator/(), FVps< T, N >::operator/=(), and pow().

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template<class T, int N>

FTps< T, N > FTps< T, N >::makeMonomial	(	int	index,
		const T &	t
	)

static

Make monomial.

Definition at line 499 of file FTps.hpp.

References FTpsData< N >::getOrder().

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template<class T, int N>

FTps< T, N > FTps< T, N >::makeMonomial	(	const FMonomial< N > &	m,
		const T &	t
	)

static

Make monomial.

Definition at line 508 of file FTps.hpp.

References FMonomial< N >::getOrder().

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template<class T , int N>

FTps< T, N > FTps< T, N >::makePower ( int power ) const

Multiply FTps with itself.

Definition at line 1555 of file FTps.hpp.

References FTps< T, N >::multiply().

Referenced by FVps< T, N >::operator*().

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template<class T , int N>

FTps< T, N > FTps< T, N >::makeVariable ( int var )

static

Make variable.

Definition at line 481 of file FTps.hpp.

References T.

Referenced by OrbitTracker::applyMultipoleBody(), LinearMapper::applyMultipoleBody(), TransportMapper::applyMultipoleBody(), Tracker::buildMultipoleVectorPotential2D(), OrbitTracker::buildSBendVectorPotential(), LinearMapper::buildSBendVectorPotential(), TransportMapper::buildSBendVectorPotential(), Tracker::buildSBendVectorPotential2D(), and FStaticFP< N >::FStaticFP().

template<class T , int N>

FTps< T, N > FTps< T, N >::makeVarPower	(	int	var,
		int	power
	)

static

Make power.

Definition at line 489 of file FTps.hpp.

References T.

template<class T , int N>

FTps< T, N > FTps< T, N >::multiply	(	const FTps< T, N > &	y,
		int	trunc = `EXACT`
	)		const

Multiplication.

Definition at line 650 of file FTps.hpp.

References FTps< T, N >::begin(), endl(), FTpsData< N >::getProductArray(), FTps< T, N >::itsRep, min(), prod(), and T.

Referenced by ExpMap(), FVps< T, N >::getFTps(), FTps< T, N >::makePower(), FVps< T, N >::operator*(), operator*(), PoissonBracket(), pow(), and FTps< T, N >::taylor().

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template<class T , int N>

FTps< T, N > FTps< T, N >::multiplyVariable	(	int	var,
		int	trunc = `EXACT`
	)		const

Multiply by variable [b]var[/b].

Definition at line 610 of file FTps.hpp.

References FTps< T, N >::begin(), endl(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTpsData< N >::getProductArray(), FVps< T, N >::getTruncOrder(), min(), and T.

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template<class T , int N>

bool FTps< T, N >::operator!= ( const FTps< T, N > & y ) const

Inequality operator.

Definition at line 886 of file FTps.hpp.

template<class T, int N>

bool FTps< T, N >::operator!= ( const T & y ) const

Inequality with constant.

Definition at line 892 of file FTps.hpp.

template<class T , int N>

FTps< T, N > & FTps< T, N >::operator*= ( const FTps< T, N > & y )

Multiply and assign.

Definition at line 545 of file FTps.hpp.

template<class T, int N>

FTps< T, N > & FTps< T, N >::operator*= ( const T & y )

Multiply by constant and assign.

Definition at line 575 of file FTps.hpp.

References FVps< T, N >::getMaxOrder(), and FVps< T, N >::getMinOrder().

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template<class T , int N>

FTps< T, N > FTps< T, N >::operator+ ( ) const

Unary plus.

Definition at line 517 of file FTps.hpp.

template<class T , int N>

FTps< T, N > & FTps< T, N >::operator+= ( const FTps< T, N > & y )

Add and assign.

Definition at line 533 of file FTps.hpp.

template<class T, int N>

FTps< T, N > & FTps< T, N >::operator+= ( const T & y )

Add constant and assign.

Definition at line 557 of file FTps.hpp.

References FVps< T, N >::setMinOrder().

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template<class T , int N>

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

Unary minus.

Definition at line 523 of file FTps.hpp.

References FTps< T, N >::begin(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), and FVps< T, N >::getTruncOrder().

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template<class T , int N>

FTps< T, N > & FTps< T, N >::operator-= ( const FTps< T, N > & y )

Subtract and assign.

Definition at line 539 of file FTps.hpp.

template<class T, int N>

FTps< T, N > & FTps< T, N >::operator-= ( const T & y )

Subtract constant and assign.

Definition at line 566 of file FTps.hpp.

References FVps< T, N >::setMinOrder().

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template<class T , int N>

FTps< T, N > & FTps< T, N >::operator/= ( const FTps< T, N > & y )

Divide and assign.

Definition at line 551 of file FTps.hpp.

template<class T, int N>

FTps< T, N > & FTps< T, N >::operator/= ( const T & y )

Divide by constant and assign.

Definition at line 583 of file FTps.hpp.

References T.

template<class T , int N>

FTps< T, N > & FTps< T, N >::operator= ( const FTps< T, N > & y )

Assign.

Definition at line 201 of file FTps.hpp.

References FTps< T, N >::itsRep.

template<class T, int N>

FTps< T, N > & FTps< T, N >::operator= ( const T & y )

Convert and assign.

Definition at line 213 of file FTps.hpp.

References T.

template<class T , int N>

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

Equality operator.

Definition at line 831 of file FTps.hpp.

References FTps< T, N >::begin(), FVps< T, N >::getMaxOrder(), FTps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTps< T, N >::getMinOrder(), FVps< T, N >::getTruncOrder(), FTps< T, N >::getTruncOrder(), FTps< T, N >::itsRep, max(), min(), and T.

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template<class T, int N>

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

Equality with constant.

Definition at line 867 of file FTps.hpp.

References FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), and T.

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template<class T , int N>

const T FTps< T, N >::operator[] ( int index ) const

inline

Get coefficient.

Definition at line 275 of file FTps.hpp.

template<class T , int N>

T & FTps< T, N >::operator[] ( int index )

inline

Get (Set) coefficient.

Definition at line 281 of file FTps.hpp.

template<class T , int N>

const T FTps< T, N >::operator[] ( const FMonomial< N > & monomial ) const

Get coefficient.

Definition at line 288 of file FTps.hpp.

References FTpsData< N >::getIndex().

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template<class T , int N>

T & FTps< T, N >::operator[] ( const FMonomial< N > & monomial )

Get (Set) coefficient.

Definition at line 295 of file FTps.hpp.

References FTpsData< N >::getIndex().

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template<class T, int N>

static int FTps< T, N >::orderEnd ( int order )

inlinestatic

Get one plus index at which [b]order[/b] ends.

Definition at line 147 of file FTps.h.

Referenced by FVps< T, N >::linearTerms(), operator+(), operator-(), and FVps< T, N >::substitute().

template<class T, int N>

static int FTps< T, N >::orderLength ( int order )

inlinestatic

Definition at line 151 of file FTps.h.

template<class T, int N>

static int FTps< T, N >::orderLength	(	int	orderL,
		int	orderH
	)

inlinestatic

Definition at line 155 of file FTps.h.

template<class T, int N>

static int FTps< T, N >::orderStart ( int order )

inlinestatic

Get index at which [b]order[/b] starts.

Definition at line 143 of file FTps.h.

Referenced by FVps< T, N >::linearTerms(), operator+(), operator-(), and FVps< T, N >::substitute().

template<class T , int N>

std::ostream & FTps< T, N >::put ( std::ostream & os ) const

Write FTps on the stream [b]os[/b].

Definition at line 1648 of file FTps.hpp.

References endl(), FTpsData< N >::getExponents(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), Inform::precision(), and T.

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template<class T , int N>

FTps< T, N > FTps< T, N >::scaleMonomials ( const FTps< T, N > & y ) const

Scale monomial coefficients by coefficients in [b]y[/b].

Definition at line 589 of file FTps.hpp.

References FTps< T, N >::begin(), FVps< T, N >::getMaxOrder(), FTps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTps< T, N >::getMinOrder(), FVps< T, N >::getTruncOrder(), FTps< T, N >::getTruncOrder(), max(), and min().

Referenced by FNormalForm< N >::FNormalForm().

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template<class T, int N>

void FTps< T, N >::setCoefficient	(	int	index,
		const T &	value
	)

Set coefficient.

Definition at line 236 of file FTps.hpp.

References endl(), FTpsData< N >::getOrder(), FVps< T, N >::setMaxOrder(), and FVps< T, N >::setMinOrder().

Referenced by TransportMapper::applyMultipoleBody(), TransportMapper::buildSBendVectorPotential(), FNormalForm< N >::FNormalForm(), and FNormalForm< N >::invariant().

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template<class T, int N>

void FTps< T, N >::setCoefficient	(	const FMonomial< N > &	monomial,
		const T &	value
	)

Set coefficient.

Definition at line 268 of file FTps.hpp.

References FTpsData< N >::getIndex().

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template<class T , int N>

void FTps< T, N >::setGlobalTruncOrder ( int order )

static

Set the global truncation order.

Definition at line 419 of file FTps.hpp.

References FTpsData< N >::setup().

Referenced by TransportMapper::applyMultipoleBody(), TransportMapper::buildSBendVectorPotential(), Dynamic::execute(), Static::execute(), Micado::execute(), Insertion::fill(), and main().

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template<class T , int N>

void FTps< T, N >::setMaxOrder ( int order )

Set maximum order.

Definition at line 357 of file FTps.hpp.

References endl().

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template<class T , int N>

void FTps< T, N >::setMinOrder ( int order )

Set minimum order.

Definition at line 321 of file FTps.hpp.

References endl().

Referenced by ThickMapper::applyDrift(), FVps< T, N >::operator*(), FTps< T, N >::taylor(), ThickMapper::visitMultipole(), ThickMapper::visitRBend(), and ThickMapper::visitSBend().

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template<class T , int N>

void FTps< T, N >::setTruncOrder ( int order )

Set truncation order.

Definition at line 393 of file FTps.hpp.

Referenced by OrbitTracker::applyMultipoleBody(), LinearMapper::applyMultipoleBody(), AbstractMapper::buildMultipoleVectorPotential(), Tracker::buildMultipoleVectorPotential(), Tracker::buildMultipoleVectorPotential2D(), AbstractMapper::buildSBendVectorPotential(), Tracker::buildSBendVectorPotential(), OrbitTracker::buildSBendVectorPotential(), LinearMapper::buildSBendVectorPotential(), Tracker::buildSBendVectorPotential2D(), ExpMap(), FTps< T, N >::taylor(), ThickMapper::visitMultipole(), ThickMapper::visitRBend(), and ThickMapper::visitSBend().

template<class T, int N>

FTps< T, N > FTps< T, N >::substitute	(	const FMatrix< T, N, N > &	M,
		int	n
	)		const

Substitute.

Definition at line 1075 of file FTps.hpp.

References FTps< T, N >::begin(), endl(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTpsData< N >::getProductArray(), FVps< T, N >::getTruncOrder(), FTpsData< N >::getVariableList(), Hypervolume::n, prod(), and T.

Referenced by ThickMapper::applyEntranceFringe(), ThickMapper::applyExitFringe(), OrbitTracker::applyMultipoleBody(), LinearMapper::applyMultipoleBody(), Mapper::applyThinSBend(), OrbitTracker::buildSBendVectorPotential(), LinearMapper::buildSBendVectorPotential(), DragtFinnMap< N >::DragtFinnMap(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), DragtFinnMap< N >::factorBerzForestIrwin(), FNormalForm< N >::FNormalForm(), DragtFinnMap< N >::reverse(), ThickMapper::visitMultipole(), ThickMapper::visitRBend(), and ThickMapper::visitSBend().

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template<class T, int N>

FTps< T, N > FTps< T, N >::substitute	(	const FMatrix< T, N, N > &	M,
		int	nl,
		int	nh
	)		const

Substitute.

Definition at line 1174 of file FTps.hpp.

References FTps< T, N >::begin(), FTps< T, N >::end(), endl(), FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FTpsData< N >::getProductArray(), FVps< T, N >::getTruncOrder(), FTpsData< N >::getVariableList(), max(), min(), prod(), and T.

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template<class T, int N>

FTps< T, N > FTps< T, N >::substitute ( const FMatrix< T, N, N > & M ) const

Substitute.

Definition at line 1302 of file FTps.hpp.

References FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), and FVps< T, N >::substitute().

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template<class T, int N>

FTps< T, N > FTps< T, N >::substitute	(	const FVps< T, N > &	m,
		int	trunc = `EXACT`
	)		const

Substitute.

Definition at line 1308 of file FTps.hpp.

References FVps< T, N >::getMaxOrder(), FVps< T, N >::getMinOrder(), FVps< T, N >::getSubstOrders(), FTpsData< N >::getVariableList(), max(), and T.

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template<class T, int N>

FTps< T, N > FTps< T, N >::taylor	(	const Array1D< T > &	series,
		int	order
	)		const

Taylor series.

Definition at line 1481 of file FTps.hpp.

References FTps< T, N >::itsRep, FTps< T, N >::multiply(), FTps< T, N >::setMinOrder(), FTps< T, N >::setTruncOrder(), T, and FTps< T, N >::unique().

Referenced by cos(), cosh(), erf(), exp(), log(), sin(), sinh(), and sqrt().

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template<class T , int N>

FTps< T, N > FTps< T, N >::truncate ( int trunc )

inline

Truncate.

Definition at line 475 of file FTps.hpp.

References FVps< T, N >::filter().

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template<class T , int N>

void FTps< T, N >::unique ( )

inline

Make representation unique.

Definition at line 1505 of file FTps.hpp.

References FTps< T, N >::allocate(), FTpsRep< T, N >::begin(), FTpsRep< T, N >::end(), and FTpsRep< T, N >::ref.

Referenced by DragtFinnMap< N >::assign(), DragtFinnMap< N >::operator+=(), DragtFinnMap< N >::operator-=(), and FTps< T, N >::taylor().

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Member Data Documentation

template<class T, int N>

const int FTps< T, N >::EXACT = INT_MAX

static

Representation of infinite precision.

Definition at line 383 of file FTps.h.

template<class T, int N>

FTpsRep< T, N > * FTps< T, N >::freeList

staticprivate

Definition at line 409 of file FTps.h.

template<class T, int N>

int FTps< T, N >::globalTruncOrder

staticprivate

Definition at line 412 of file FTps.h.

Referenced by FTps< double, 6 >::getGlobalTruncOrder().

template<class T, int N>

FTpsRep<T, N>* FTps< T, N >::itsRep

private

Definition at line 405 of file FTps.h.

Referenced by FTps< double, 6 >::begin(), FTps< T, N >::divide(), FTps< double, 6 >::end(), FTps< T, N >::FTps(), FTps< T, N >::get(), FTps< double, 6 >::getMaxOrder(), FTps< double, 6 >::getMinOrder(), FTps< double, 6 >::getSize(), FTps< double, 6 >::getTruncOrder(), FTps< T, N >::inverse(), FTps< T, N >::multiply(), FTps< T, N >::operator=(), FTps< T, N >::operator==(), and FTps< T, N >::taylor().

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

src/Algorithms/TransportMapper.h
src/Classic/FixedAlgebra/FTps.h
src/Classic/FixedAlgebra/FTps.hpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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