Vector truncated power series in n variables. More...

#include <FVps.h>

Inheritance diagram for FVps< T, N >:

Collaboration diagram for FVps< T, N >:

Public Member Functions
	FVps (int minOrder, int maxOrder, int trcOrder)
	Constructor.
	FVps (const FMatrix< T, N, N > &M)
	Convert from matrix.
	FVps (const FVector< T, N > &V)
	Convert from vector.
	FVps (const LinearMap< T, N > &rhs)
	Convert from linear map.
	FVps (const TransportMap< T, N > &rhs)
	Convert from second-order map.
	FVps ()
	FVps (const FVps &)
	~FVps ()
const FVps &	operator= (const FVps &)
void	identity ()
	Set to identity.
void	zero ()
	Set to zero.
const FTps< T, N > &	getComponent (int n) const
	Get component.
void	setComponent (int, const FTps< T, N > &)
	Set component.
const FTps< T, N > &	operator[] (int) const
	Get Component.
FTps< T, N > &	operator[] (int)
	Get (Set) component.
int	getDimension () const
	Get dimension.
int	getVariables () const
	Get number of variables.
int	getMinOrder () const
	Get lowest order contained in any component.
void	setMinOrder (int order)
	Set minimum order.
int	getMaxOrder () const
	Get highest order contained in any component.
void	setMaxOrder (int order)
	Set maximum order.
int	getTopOrder () const
	Get highest order contained in any component.
int	getTruncOrder () const
	Get lowest truncation order in any component.
void	setTruncOrder (int order)
	Set truncation order for all components.
FVps	filter (int minOrder, int maxOrder, int trcOrder=(FTps< T, N >::EXACT)) const
	Extract given range of orders, with truncation.
FVps	truncate (int trunc)
	Truncate.
FVps	operator+ () const
	Unary plus.
FVps	operator- () const
	Unary minus.
FVps &	operator+= (const FVps &rhs)
	Add and assign.
FVps &	operator-= (const FVps &rhs)
	Subtract and assign.
FVps &	operator+= (const FVector< T, N > &)
	Add and assign.
FVps &	operator-= (const FVector< T, N > &)
	Subtract and assign.
FVps &	operator*= (const FTps< T, N > &rhs)
	Multiply and assign.
FVps	operator* (const FVps< T, N > &rhs) const
	Multiply.
FVps &	operator/= (const FTps< T, N > &rhs)
	Divide and assign.
FVps &	operator*= (const T &rhs)
	Multiply and assign.
FVps &	operator/= (const T &rhs)
	Divide and assign.
FVps	inverse (int trunc=(FTps< T, N >::EXACT)) const
	Inverse.
FVps	myInverse (int trunc=(FTps< T, N >::EXACT)) const
	Inverse.
FVps	derivative (int var) const
	Partial derivative.
FVps	integral (int var) const
	Partial integral.
FVector< T, N >	constantTerm () const
	Extract the constant part of the map.
FVector< T, N >	constantTerm (const FVector< T, N > &P) const
	Extract the constant part of the map expanded about point [b]P[/b].
FMatrix< T, N, N >	linearTerms () const
	Extract the linear part of the map.
FMatrix< T, N, N >	linearTerms (const FVector< T, N > &P) const
	Extract the linear part of the map expanded about point [b]P[/b].
Array1D< int >	getSubstOrders (const FVps< T, N > &rhs, int trunc=(FTps< T, N >::EXACT)) const
	Return orders {min, max, trc} of f(rhs(z)).
FVps	substitute (const FMatrix< T, N, N > &M, int n) const
	Substitute.
FVps	substitute (const FMatrix< T, N, N > &M, int nl, int nh) const
	Substitute.
FVps	substitute (const FMatrix< T, N, N > &M) const
	Substitute.
FVps	substitute (const FVps< T, N > &m, int trunc=(FTps< T, N >::EXACT)) const
	Substitute.
FVps	substituteInto (const FMatrix< T, N, N > &lhs) const
	Substitute map into matrix.
FTps< T, N >	getFTps (const FArray1D< int, N > &power) const
	Get a FTps that is a combination of the polynomials of FVps.
std::istream &	get (std::istream &is)
	Get a FVps from stream [b]is[/b].
std::ostream &	put (std::ostream &os) const
	Put a FVps to stream [b]os[/b].

Protected Attributes
FTps< T, N >	data [N]

Detailed Description

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

Vector truncated power series in n variables.

Definition at line 39 of file FVps.h.

Constructor & Destructor Documentation

◆ FVps() [1/7]

template<class T, int N>

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

explicit

Constructor.

Definition at line 78 of file FVps.hpp.

References data.

Referenced by derivative(), filter(), FVps(), get(), getSubstOrders(), integral(), inverse(), myInverse(), operator*(), operator*=(), operator*=(), operator+(), operator+=(), operator+=(), operator-(), operator-=(), operator-=(), operator/=(), operator/=(), operator=(), substitute(), substitute(), substitute(), substitute(), substituteInto(), and truncate().

◆ FVps() [2/7]

template<class T, int N>

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

explicit

Convert from matrix.

Definition at line 85 of file FVps.hpp.

References data, and identity().

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◆ FVps() [3/7]

template<class T, int N>

FVps< T, N >::FVps ( const FVector< T, N > & V )

explicit

Convert from vector.

Definition at line 93 of file FVps.hpp.

◆ FVps() [4/7]

template<class T, int N>

FVps< T, N >::FVps ( const LinearMap< T, N > & rhs )

explicit

Convert from linear map.

Definition at line 58 of file FVps.hpp.

References data, and identity().

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◆ FVps() [5/7]

template<class T, int N>

FVps< T, N >::FVps ( const TransportMap< T, N > & rhs )

explicit

Convert from second-order map.

Definition at line 68 of file FVps.hpp.

References data, FTpsData< N >::getSize(), and SIZE.

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◆ FVps() [6/7]

template<class T, int N>

FVps< T, N >::FVps ( )

Definition at line 46 of file FVps.hpp.

References identity().

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◆ FVps() [7/7]

template<class T, int N>

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

Definition at line 52 of file FVps.hpp.

References data, and FVps().

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◆ ~FVps()

template<class T, int N>

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

Definition at line 99 of file FVps.hpp.

Member Function Documentation

◆ constantTerm() [1/2]

template<class T, int N>

FVector< T, N > FVps< T, N >::constantTerm ( ) const

Extract the constant part of the map.

Definition at line 540 of file FVps.hpp.

References data, and getMinOrder().

Referenced by inverse(), and myInverse().

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◆ constantTerm() [2/2]

template<class T, int N>

FVector< T, N > FVps< T, N >::constantTerm ( const FVector< T, N > & P ) const

Extract the constant part of the map expanded about point [b]P[/b].

Definition at line 551 of file FVps.hpp.

◆ derivative()

template<class T, int N>

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

Partial derivative.

Definition at line 524 of file FVps.hpp.

References data, derivative(), and FVps().

Referenced by derivative(), and FTps< T, N >::gradient().

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◆ filter()

template<class T, int N>

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

Extract given range of orders, with truncation.

Definition at line 223 of file FVps.hpp.

References data, filter(), and FVps().

Referenced by filter(), inverse(), myInverse(), FTps< T, N >::truncate(), and truncate().

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◆ get()

template<class T, int N>

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

Get a FVps from stream [b]is[/b].

Definition at line 1057 of file FVps.hpp.

References data, FVps(), and get().

Referenced by get(), and operator>>().

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◆ getComponent()

template<class T, int N>

const FTps< T, N > & FVps< T, N >::getComponent ( int n ) const

Get component.

Definition at line 123 of file FVps.hpp.

References data.

Referenced by getFTps(), operator*(), and operator*().

◆ getDimension()

template<class T, int N>

int FVps< T, N >::getDimension ( ) const

inline

Get dimension.

Definition at line 153 of file FVps.hpp.

◆ getFTps()

template<class T, int N>

FTps< T, N > FVps< T, N >::getFTps ( const FArray1D< int, N > & power ) const

Get a FTps that is a combination of the polynomials of FVps.

Definition at line 1034 of file FVps.hpp.

References FArray1D< T, N >::begin(), FArray1D< T, N >::end(), getComponent(), FTps< T, N >::getGlobalTruncOrder(), and FTps< T, N >::multiply().

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◆ getMaxOrder()

template<class T, int N>

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

Get highest order contained in any component.

Definition at line 181 of file FVps.hpp.

References data, and FTps< T, N >::getMaxOrder().

Referenced by FTps< T, N >::derivative(), FTps< T, N >::divide(), FTps< T, N >::evaluate(), FTps< T, N >::getSubstOrders(), getSubstOrders(), FTps< T, N >::integral(), inverse(), linearTerms(), FTps< T, N >::multiplyVariable(), myInverse(), FTps< T, N >::operator*=(), FTps< T, N >::operator-(), FTps< T, N >::operator==(), FTps< T, N >::operator==(), FTps< T, N >::put(), FTps< T, N >::scaleMonomials(), FTps< T, N >::substitute(), FTps< T, N >::substitute(), FTps< T, N >::substitute(), FTps< T, N >::substitute(), substitute(), substitute(), substitute(), and substitute().

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◆ getMinOrder()

template<class T, int N>

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

Get lowest order contained in any component.

Definition at line 165 of file FVps.hpp.

References data, and FTps< T, N >::getMinOrder().

Referenced by constantTerm(), FTps< T, N >::derivative(), FTps< T, N >::divide(), FTps< T, N >::evaluate(), FTps< T, N >::getSubstOrders(), getSubstOrders(), FTps< T, N >::integral(), inverse(), FTps< T, N >::multiplyVariable(), myInverse(), FTps< T, N >::operator*=(), FTps< T, N >::operator-(), FTps< T, N >::operator==(), FTps< T, N >::operator==(), FTps< T, N >::put(), FTps< T, N >::scaleMonomials(), FTps< T, N >::substitute(), FTps< T, N >::substitute(), FTps< T, N >::substitute(), FTps< T, N >::substitute(), substitute(), substitute(), substitute(), and substitute().

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◆ getSubstOrders()

template<class T, int N>

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

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

Definition at line 594 of file FVps.hpp.

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

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

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◆ getTopOrder()

template<class T, int N>

int FVps< T, N >::getTopOrder ( ) const

Get highest order contained in any component.

Definition at line 197 of file FVps.hpp.

References data, FTpsData< N >::topOrder, and FTps< T, N >::getMaxOrder().

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◆ getTruncOrder()

template<class T, int N>

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

Get lowest truncation order in any component.

Definition at line 207 of file FVps.hpp.

References data, and FTps< T, N >::getTruncOrder().

Referenced by FTps< T, N >::derivative(), FTps< T, N >::divide(), ExpMap(), FTps< T, N >::getSubstOrders(), getSubstOrders(), FTps< T, N >::integral(), inverse(), FTps< T, N >::multiplyVariable(), myInverse(), FTps< T, N >::operator-(), FTps< T, N >::operator==(), FTps< T, N >::scaleMonomials(), FTps< T, N >::substitute(), FTps< T, N >::substitute(), substitute(), substitute(), and substitute().

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◆ getVariables()

template<class T, int N>

int FVps< T, N >::getVariables ( ) const

inline

Get number of variables.

Definition at line 159 of file FVps.hpp.

◆ identity()

template<class T, int N>

void FVps< T, N >::identity ( )

Set to identity.

Definition at line 111 of file FVps.hpp.

Referenced by FVps(), FVps(), and FVps().

◆ integral()

template<class T, int N>

FVps< T, N > FVps< T, N >::integral ( int var ) const

Partial integral.

Definition at line 532 of file FVps.hpp.

References data, FVps(), and integral().

Referenced by integral().

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◆ inverse()

template<class T, int N>

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

Inverse.

Definition at line 360 of file FVps.hpp.

References constantTerm(), FTps< T, N >::EXACT, filter(), FVps(), getMaxOrder(), getMinOrder(), getTruncOrder(), FLUMatrix< T, N >::inverse(), linearTerms(), setTruncOrder(), and substitute().

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◆ linearTerms() [1/2]

template<class T, int N>

FMatrix< T, N, N > FVps< T, N >::linearTerms ( ) const

Extract the linear part of the map.

Definition at line 561 of file FVps.hpp.

References data.

Referenced by inverse(), myInverse(), and ThickTracker::track_m().

◆ linearTerms() [2/2]

template<class T, int N>

FMatrix< T, N, N > FVps< T, N >::linearTerms ( const FVector< T, N > & P ) const

Extract the linear part of the map expanded about point [b]P[/b].

Definition at line 570 of file FVps.hpp.

References Array1D< T >::begin(), FTps< T, N >::begin(), data, FTps< T, N >::evalMonoms(), FTps< T, N >::getMaxOrder(), getMaxOrder(), FTps< T, N >::getMinOrder(), FTps< T, N >::orderEnd(), and FTps< T, N >::orderStart().

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◆ myInverse()

template<class T, int N>

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

Inverse.

Definition at line 441 of file FVps.hpp.

References constantTerm(), FTps< T, N >::EXACT, filter(), FVps(), getMaxOrder(), getMinOrder(), getTruncOrder(), FLUMatrix< T, N >::inverse(), linearTerms(), setTruncOrder(), and substitute().

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◆ operator*()

template<class T, int N>

FVps< T, N > FVps< T, N >::operator* ( const FVps< T, N > & rhs ) const

Multiply.

Definition at line 288 of file FVps.hpp.

References FTps< T, N >::extractExponents(), FVps(), FTps< T, N >::getCoefficient(), getComponent(), FTps< T, N >::getGlobalTruncOrder(), FTps< T, N >::getListOfNonzeroCoefficients(), FTps< T, N >::getMinOrder(), FTps< T, N >::makePower(), FTps< T, N >::multiply(), setComponent(), and FTps< T, N >::setMinOrder().

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◆ operator*=() [1/2]

template<class T, int N>

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

Multiply and assign.

Definition at line 282 of file FVps.hpp.

References data, and FVps().

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◆ operator*=() [2/2]

template<class T, int N>

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

Multiply and assign.

Definition at line 346 of file FVps.hpp.

References data, and FVps().

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◆ operator+()

template<class T, int N>

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

Unary plus.

Definition at line 240 of file FVps.hpp.

References FVps().

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◆ operator+=() [1/2]

template<class T, int N>

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

Add and assign.

Definition at line 268 of file FVps.hpp.

References data, and FVps().

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◆ operator+=() [2/2]

template<class T, int N>

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

Add and assign.

Definition at line 254 of file FVps.hpp.

References data, and FVps().

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◆ operator-()

template<class T, int N>

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

Unary minus.

Definition at line 246 of file FVps.hpp.

References data, and FVps().

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◆ operator-=() [1/2]

template<class T, int N>

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

Subtract and assign.

Definition at line 275 of file FVps.hpp.

References data, and FVps().

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◆ operator-=() [2/2]

template<class T, int N>

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

Subtract and assign.

Definition at line 261 of file FVps.hpp.

References data, and FVps().

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◆ operator/=() [1/2]

template<class T, int N>

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

Divide and assign.

Definition at line 338 of file FVps.hpp.

References data, FVps(), and FTps< T, N >::inverse().

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◆ operator/=() [2/2]

template<class T, int N>

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

Divide and assign.

Definition at line 353 of file FVps.hpp.

References data, and FVps().

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◆ operator=()

template<class T, int N>

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

Definition at line 104 of file FVps.hpp.

References data, and FVps().

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◆ operator[]() [1/2]

template<class T, int N>

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

inline

Get (Set) component.

Definition at line 147 of file FVps.hpp.

References data.

◆ operator[]() [2/2]

template<class T, int N>

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

inline

Get Component.

Definition at line 141 of file FVps.hpp.

References data.

◆ put()

template<class T, int N>

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

Put a FVps to stream [b]os[/b].

Definition at line 1078 of file FVps.hpp.

References data.

Referenced by operator<<().

◆ setComponent()

template<class T, int N>

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

Set component.

Definition at line 132 of file FVps.hpp.

References data.

Referenced by operator*().

◆ setMaxOrder()

template<class T, int N>

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

Set maximum order.

Definition at line 191 of file FVps.hpp.

References data, and setMaxOrder().

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

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◆ setMinOrder()

template<class T, int N>

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

Set minimum order.

Definition at line 175 of file FVps.hpp.

References data, and setMinOrder().

Referenced by FTps< T, N >::operator+=(), FTps< T, N >::operator-=(), FTps< T, N >::setCoefficient(), setMinOrder(), substitute(), substitute(), and substitute().

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◆ setTruncOrder()

template<class T, int N>

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

Set truncation order for all components.

Definition at line 217 of file FVps.hpp.

References data, and setTruncOrder().

Referenced by inverse(), myInverse(), setTruncOrder(), substitute(), substitute(), and substitute().

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◆ substitute() [1/4]

template<class T, int N>

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

Substitute.

Definition at line 889 of file FVps.hpp.

References FVps(), getMaxOrder(), getMinOrder(), and substitute().

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◆ substitute() [2/4]

template<class T, int N>

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

Substitute.

Definition at line 608 of file FVps.hpp.

References begin(), end(), FVps(), FTps< T, N >::getGlobalTruncOrder(), getMaxOrder(), getMinOrder(), FTpsData< N >::getProductArray(), FTps< T, N >::getSize(), getTruncOrder(), FTpsData< N >::getVariableList(), FTps< T, N >::orderEnd(), FTps< T, N >::orderStart(), prod(), setMaxOrder(), setMinOrder(), and setTruncOrder().

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

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◆ substitute() [3/4]

template<class T, int N>

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

Substitute.

Definition at line 728 of file FVps.hpp.

References begin(), end(), FVps(), FTps< T, N >::getGlobalTruncOrder(), getMaxOrder(), getMinOrder(), FTpsData< N >::getProductArray(), FTps< T, N >::getSize(), getTruncOrder(), FTpsData< N >::getVariableList(), FTps< T, N >::orderEnd(), FTps< T, N >::orderStart(), prod(), setMaxOrder(), setMinOrder(), and setTruncOrder().

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◆ substitute() [4/4]

template<class T, int N>

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

Substitute.

Definition at line 895 of file FVps.hpp.

References begin(), FTps< T, N >::EXACT, FVps(), FTps< T, N >::getGlobalTruncOrder(), getMaxOrder(), getMinOrder(), getSubstOrders(), getTruncOrder(), FTpsData< N >::getVariableList(), FTps< T, N >::orderEnd(), FTps< T, N >::orderStart(), setMaxOrder(), setMinOrder(), and setTruncOrder().

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◆ substituteInto()

template<class T, int N>

FVps< T, N > FVps< T, N >::substituteInto ( const FMatrix< T, N, N > & lhs ) const

Substitute map into matrix.

Definition at line 1021 of file FVps.hpp.

References data, FVps(), and sum().

Referenced by operator*().

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◆ truncate()

template<class T, int N>

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

Truncate.

Definition at line 234 of file FVps.hpp.

References filter(), and FVps().

Referenced by ThickTracker::concatenateMaps_m(), and ThickTracker::track_m().

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◆ zero()

template<class T, int N>

void FVps< T, N >::zero ( )

Set to zero.

Definition at line 117 of file FVps.hpp.

References data.

Member Data Documentation

◆ data

template<class T, int N>

FTps<T, N> FVps< T, N >::data[N]

protected

Definition at line 247 of file FVps.h.

Referenced by constantTerm(), derivative(), filter(), FVps(), FVps(), FVps(), FVps(), FVps(), get(), getComponent(), getMaxOrder(), getMinOrder(), getTopOrder(), getTruncOrder(), integral(), linearTerms(), linearTerms(), operator*=(), operator*=(), operator+=(), operator+=(), operator-(), operator-=(), operator-=(), operator/=(), operator/=(), operator=(), operator[](), operator[](), put(), setComponent(), setMaxOrder(), setMinOrder(), setTruncOrder(), substituteInto(), and zero().

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

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FVps() [1/7]

◆ FVps() [2/7]

◆ FVps() [3/7]

◆ FVps() [4/7]

◆ FVps() [5/7]

◆ FVps() [6/7]

◆ FVps() [7/7]

◆ ~FVps()

Member Function Documentation

◆ constantTerm() [1/2]

◆ constantTerm() [2/2]

◆ derivative()

◆ filter()

◆ get()

◆ getComponent()

◆ getDimension()

◆ getFTps()

◆ getMaxOrder()

◆ getMinOrder()

◆ getSubstOrders()

◆ getTopOrder()

◆ getTruncOrder()

◆ getVariables()

◆ identity()

◆ integral()

◆ inverse()

◆ linearTerms() [1/2]

◆ linearTerms() [2/2]

◆ myInverse()

◆ operator*()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ put()

◆ setComponent()

◆ setMaxOrder()

◆ setMinOrder()

◆ setTruncOrder()

◆ substitute() [1/4]

◆ substitute() [2/4]

◆ substitute() [3/4]

◆ substitute() [4/4]

◆ substituteInto()

◆ truncate()

◆ zero()

Member Data Documentation

◆ data