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. 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

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(), FLieGenerator< T, N >::end(), imag(), and Attrib::Legacy::Distribution::T.

Referenced by BMultipoleField::Bfield(), BSingleMultipoleField< order >::Bfield(), FDoubleEigen< N >::eigenVectors(), FDoubleEigen< N >::hqr2(), imag(), MapAnalyser::invertMatrix_m(), MapAnalyser::normalizeEigen_m(), sqrt(), and Werrf().

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

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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 endl(), FLieGenerator< T, N >::getBottomIndex(), FTpsData< N >::getExponents(), FLieGenerator< T, N >::getOrder(), FLieGenerator< T, N >::getTopIndex(), Inform::precision(), Inform::setf(), and Attrib::Legacy::Distribution::T.

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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.

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(), FLieGenerator< T, N >::end(), real(), and Attrib::Legacy::Distribution::T.

Referenced by FixedFFTLowPassFilter::apply(), RelativeFFTLowPassFilter::apply(), BMultipoleField::Bfield(), BSingleMultipoleField< order >::Bfield(), FixedFFTLowPassFilter::calc_derivative(), RelativeFFTLowPassFilter::calc_derivative(), GreenWakeFunction::CalcWakeFFT(), DumpEMFields::checkInt(), DumpFields::checkInt(), GreenWakeFunction::compEnergy(), interpolation::complex(), Astra1D_fast::computeFourierCoefficients(), convlv(), erf(), matheval::detail::grammar< real_t, Iterator >::grammar(), FDoubleEigen< N >::hqr2(), MapAnalyser::invertMatrix_m(), GreenWakeFunction::Wake::operator()(), MapAnalyser::printPhaseShift_m(), Astra1DDynamic::readMap(), Astra1DElectroStatic::readMap(), Astra1DMagnetoStatic::readMap(), real(), GreenWakeFunction::setWakeFromFile(), sqrt(), and Werrf().

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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(), FLieGenerator< T, N >::getOrder(), and Attrib::Legacy::Distribution::T.

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