FLieGenerator.h File Reference

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

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Classes
class	FArray1D< T, N >
	A templated representation for one-dimensional arrays. More...
class	FMatrix< T, M, N >
	A templated representation for matrices. More...
class	FTps< T, N >
	Truncated power series in N variables of type T. More...
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. More...
template<class T , int N>
FLieGenerator< T, N >	operator- (const FLieGenerator< T, N > &, const FLieGenerator< T, N > &)
	Subtract. More...
template<class T , int N>
FLieGenerator< T, N >	operator* (const FLieGenerator< T, N > &, const T &)
	Multiply by scalar. More...
template<class T , int N>
FLieGenerator< T, N >	operator* (const T &, const FLieGenerator< T, N > &)
	Multiply by scalar. More...
template<class T , int N>
FLieGenerator< T, N >	operator* (const FLieGenerator< T, N > &, const FLieGenerator< T, N > &)
	Multiply by Lie generator. More...
template<class T , int N>
FLieGenerator< T, N >	operator/ (const FLieGenerator< T, N > &, const T &)
	Divide by scalar. More...
template<class T , int N>
FLieGenerator< T, N >	real (const FLieGenerator< std::complex< T >, N > &)
	Take real part of a complex generator. More...
template<class T , int N>
FLieGenerator< T, N >	imag (const FLieGenerator< std::complex< T >, N > &)
	Take imaginary part of a complex generator. More...
template<class T , int N>
FLieGenerator< std::complex< T > , N >	toComplex (const FLieGenerator< T, N > &)
	Convert real generator to complex. More...
template<class T , int N>
FLieGenerator< T, N >	PoissonBracket (const FLieGenerator< T, N > &, const FLieGenerator< T, N > &)
	Poisson bracket of two Lie generators. More...
template<class T , int N>
std::ostream &	operator<< (std::ostream &, const FLieGenerator< T, N > &)
	Output. More...

Function Documentation

template<class T , int N>

FLieGenerator<T, N> imag

(

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

)

Take imaginary part of a complex generator.

Definition at line 437 of file FLieGenerator.hpp.

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

Referenced by BMultipoleField::Bfield(), BSingleMultipoleField< order >::Bfield(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), FDoubleEigen< N >::eigenVectors(), DoubleEigen::eigenVectors(), DragtFinnMap< N >::factorBerzForestIrwin(), FNormalForm< N >::FNormalForm(), ComplexEigen::hqr(), FComplexEigen< N >::hqr(), ComplexEigen::hqr2(), FComplexEigen< N >::hqr2(), FDoubleEigen< N >::hqr2(), DoubleEigen::hqr2(), imag(), NormalForm::invariant(), DragtFinnNormalForm< N >::invariant(), FNormalForm< N >::invariant(), MapAnalyser::invertMatrix_m(), MapAnalyser::linTAnalyze(), NormalForm::NormalForm(), NormalForm::orderModes(), DragtFinnNormalForm< N >::orderModes(), FNormalForm< N >::orderModes(), DragtFinnMap< N >::orderModes(), sqrt(), ThinTracker::visitBeamBeam(), and Werrf().

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template<class T , int N>

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

Multiply by scalar.

Definition at line 368 of file FLieGenerator.hpp.

template<class T , int N>

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

Multiply by scalar.

Definition at line 376 of file FLieGenerator.hpp.

template<class T , int N>

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

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

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template<class T , int N>

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

Add.

Definition at line 352 of file FLieGenerator.hpp.

template<class T , int N>

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

Subtract.

Definition at line 360 of file FLieGenerator.hpp.

template<class T , int N>

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

Divide by scalar.

Definition at line 414 of file FLieGenerator.hpp.

template<class T , int N>

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

Output.

Definition at line 515 of file FLieGenerator.hpp.

References endl(), FTpsData< N >::getExponents(), FLieGenerator< T, N >::getOrder(), Inform::precision(), Inform::setf(), and T.

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template<class T , int N>

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

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

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template<class T , int N>

FLieGenerator<T, N> real

(

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

)

Take real part of a complex generator.

Definition at line 422 of file FLieGenerator.hpp.

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

Referenced by FixedFFTLowPassFilter::apply(), RelativeFFTLowPassFilter::apply(), BMultipoleField::Bfield(), BSingleMultipoleField< order >::Bfield(), FixedFFTLowPassFilter::calc_derivative(), RelativeFFTLowPassFilter::calc_derivative(), SpecializedGreensFunction< 3 >::calculate(), P3MPoissonSolver::calculateGridForces(), GreenWakeFunction::CalcWakeFFT(), GreenWakeFunction::compEnergy(), interpolation::complex(), Astra1D_fast::computeFourierCoefficients(), convlv(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), erf(), DragtFinnMap< N >::factorBerzForestIrwin(), FNormalForm< N >::FNormalForm(), Attributes::getString(), Attributes::getStringArray(), matheval::detail::grammar< real_t, Iterator >::grammar(), ComplexEigen::hqr(), FComplexEigen< N >::hqr(), ComplexEigen::hqr2(), FComplexEigen< N >::hqr2(), FDoubleEigen< N >::hqr2(), DoubleEigen::hqr2(), MapAnalyser::invertMatrix_m(), MapAnalyser::linTAnalyze(), NormalForm::NormalForm(), GreenWakeFunction::Wake::operator()(), NormalForm::orderModes(), DragtFinnMap< N >::orderModes(), MapAnalyser::printPhaseShift_m(), Astra1DElectroStatic::readMap(), Astra1DMagnetoStatic::readMap(), Astra1DDynamic::readMap(), real(), GreenWakeFunction::setWakeFromFile(), sqrt(), ThinTracker::visitBeamBeam(), and Werrf().

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template<class T , int N>

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

(

const FLieGenerator< T, N > &

)

Convert real generator to complex.

Definition at line 452 of file FLieGenerator.hpp.

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

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