FLieGenerator.h File Reference

#include "Algebra/Array1D.h"
#include <complex>
#include "FixedAlgebra/FLieGenerator.hpp"

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Classes
class	FLieGenerator< T, N >
	A representation for a homogeneous polynomial, used as a Lie generator. More...

Functions
template<class T, int N>
FLieGenerator< T, N >	operator+ (const FLieGenerator< T, N > &, const FLieGenerator< T, N > &)
	Add.
template<class T, int N>
FLieGenerator< T, N >	operator- (const FLieGenerator< T, N > &, const FLieGenerator< T, N > &)
	Subtract.
template<class T, int N>
FLieGenerator< T, N >	operator* (const FLieGenerator< T, N > &, const T &)
	Multiply by scalar.
template<class T, int N>
FLieGenerator< T, N >	operator* (const T &, const FLieGenerator< T, N > &)
	Multiply by scalar.
template<class T, int N>
FLieGenerator< T, N >	operator* (const FLieGenerator< T, N > &, const FLieGenerator< T, N > &)
	Multiply by Lie generator.
template<class T, int N>
FLieGenerator< T, N >	operator/ (const FLieGenerator< T, N > &, const T &)
	Divide by scalar.
template<class T, int N>
FLieGenerator< T, N >	real (const FLieGenerator< std::complex< T >, N > &)
	Take real part of a complex generator.
template<class T, int N>
FLieGenerator< T, N >	imag (const FLieGenerator< std::complex< T >, N > &)
	Take imaginary part of a complex generator.
template<class T, int N>
FLieGenerator< std::complex< T >, N >	toComplex (const FLieGenerator< T, N > &)
	Convert real generator to complex.
template<class T, int N>
FLieGenerator< T, N >	PoissonBracket (const FLieGenerator< T, N > &, const FLieGenerator< T, N > &)
	Poisson bracket of two Lie generators.
template<class T, int N>
std::ostream &	operator<< (std::ostream &, const FLieGenerator< T, N > &)
	Output.

Function Documentation

imag()

template<class T, int N>

FLieGenerator< T, N > imag

(

const FLieGenerator< std::complex< T >, N > &

x

)

Take imaginary part of a complex generator.

Definition at line 437 of file FLieGenerator.hpp.

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

Referenced by MapAnalyser::normalizeEigen_m(), and PETE_DefineUnary().

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operator*() [1/3]

template<class T, int N>

FLieGenerator< T, N > operator*	(	const FLieGenerator< T, N > &	x,
		const FLieGenerator< T, N > &	y )

Multiply by Lie generator.

Definition at line 384 of file FLieGenerator.hpp.

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

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operator*() [2/3]

template<class T, int N>

FLieGenerator< T, N > operator*	(	const FLieGenerator< T, N > &	x,
		const T &	y )

Multiply by scalar.

Definition at line 368 of file FLieGenerator.hpp.

operator*() [3/3]

template<class T, int N>

FLieGenerator< T, N > operator*	(	const T &	x,
		const FLieGenerator< T, N > &	y )

Multiply by scalar.

Definition at line 376 of file FLieGenerator.hpp.

operator+()

template<class T, int N>

FLieGenerator< T, N > operator+	(	const FLieGenerator< T, N > &	x,
		const FLieGenerator< T, N > &	y )

Add.

Definition at line 352 of file FLieGenerator.hpp.

operator-()

template<class T, int N>

FLieGenerator< T, N > operator-	(	const FLieGenerator< T, N > &	x,
		const FLieGenerator< T, N > &	y )

Subtract.

Definition at line 360 of file FLieGenerator.hpp.

operator/()

template<class T, int N>

FLieGenerator< T, N > operator/	(	const FLieGenerator< T, N > &	x,
		const T &	y )

Divide by scalar.

Definition at line 414 of file FLieGenerator.hpp.

operator<<()

template<class T, int N>

std::ostream & operator<<	(	std::ostream &	os,
		const FLieGenerator< T, N > &	gen )

Output.

Definition at line 515 of file FLieGenerator.hpp.

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

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PoissonBracket()

template<class T, int N>

FLieGenerator< T, N > PoissonBracket	(	const FLieGenerator< T, N > &	f,
		const FLieGenerator< T, N > &	g )

Poisson bracket of two Lie generators.

Definition at line 466 of file FLieGenerator.hpp.

References FLieGenerator< T, N >::begin(), FLieGenerator< T, N >::getBottomIndex(), FTpsData< N >::getExponents(), FLieGenerator< T, N >::getOrder(), FTpsData< N >::getProductArray(), and FLieGenerator< T, N >::isZero().

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real()

template<class T, int N>

FLieGenerator< T, N > real

(

const FLieGenerator< std::complex< T >, N > &

x

)

Take real part of a complex generator.

Definition at line 422 of file FLieGenerator.hpp.

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

Referenced by FixedFFTLowPassFilter::apply(), RelativeFFTLowPassFilter::apply(), FixedFFTLowPassFilter::calc_derivative(), RelativeFFTLowPassFilter::calc_derivative(), GreenWakeFunction::CalcWakeFFT(), Util::checkInt(), GreenWakeFunction::compEnergy(), GreenWakeFunction::compEnergy(), interpolation::complex(), interpolation::complex(), interpolation::complex(), interpolation::complex(), _Astra1D_fast::computeFourierCoefficients(), convlv(), Attributes::getStringArray(), matheval::detail::grammar< real_t, Iterator >::grammar(), GreenWakeFunction::Wake::operator()(), interpolation::operator-=(), interpolation::operator/(), MapAnalyser::printPhaseShift_m(), _Astra1DDynamic::readMap(), _Astra1DElectroStatic::readMap(), _Astra1DMagnetoStatic::readMap(), real(), and GreenWakeFunction::setWakeFromFile().

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toComplex()

template<class T, int N>

FLieGenerator< std::complex< T >, N > toComplex

(

const FLieGenerator< T, N > &

x

)

Convert real generator to complex.

Definition at line 452 of file FLieGenerator.hpp.

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

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