FNormalForm< N > Class Template Reference

Normal form of a truncated Taylor series map. More...

#include <FNormalForm.h>

Collaboration diagram for FNormalForm< N >:

Public Member Functions
	FNormalForm (const FVps< double, N > &map)
	Constructor. More...
	FNormalForm ()
	FNormalForm (const FNormalForm &)
	~FNormalForm ()
int	degreesOfFreedom () const
	Get number of stable degrees of freedom. More...
const FTps< double, N > &	normalForm () const
	Get normal-form map as a Lie transform. More...
const FTps< double, N > &	normalisingMap () const
	Get normalising map as a Lie transform. More...
const FVector< std::complex < double >, N > &	eigenValues () const
	Get eigenvalues of the linear part as a complex vector. More...
const FMatrix< double, N, N > &	eigenVectors () const
	Get eigenvectors of the linear part in packed form. More...
FMatrix< double, N/2, N/2 >	anharmonicity () const
	Get anharmonicities as a matrix. More...
FTps< double, N >	invariant (int i) const
	Get invariant polynomial for mode i. More...

Protected Member Functions
void	orderModes (FVector< std::complex< double >, N >, FMatrix< double, N, N >)

Private Member Functions
void	operator= (const FNormalForm &)

Private Attributes
int	freedom
FTps< double, N >	A_Lie
FTps< double, N >	N_Lie
FVector< std::complex< double > , N >	lambda
FMatrix< double, N, N >	V

Detailed Description

template<int N>
class FNormalForm< N >

Normal form of a truncated Taylor series map.

Definition at line 51 of file FNormalForm.h.

Constructor & Destructor Documentation

template<int N>

FNormalForm< N >::FNormalForm ( const FVps< double, N > &  map )

explicit

Constructor.

Definition at line 142 of file FNormalForm.h.

References FNormalForm< N >::A_Lie, abs(), arg(), FDoubleEigen< N >::eigenValues(), ExpMap(), FVps< T, N >::filter(), FNormalForm< N >::freedom, FTpsData< N >::getExponents(), FVps< T, N >::getTopOrder(), imag(), FNormalForm< N >::lambda, FVps< T, N >::linearTerms(), log(), FNormalForm< N >::N_Lie, FNormalForm< N >::orderModes(), FDoubleEigen< N >::packedEigenVectors(), pi, pow(), real(), FTps< T, N >::scaleMonomials(), FTps< T, N >::setCoefficient(), FVps< T, N >::substitute(), FTps< T, N >::substitute(), and FNormalForm< N >::V.

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template<int N>

FNormalForm< N >::FNormalForm

(

)

Definition at line 129 of file FNormalForm.h.

template<int N>

FNormalForm< N >::FNormalForm

(

const FNormalForm< N > &

form

)

Definition at line 135 of file FNormalForm.h.

template<int N>

FNormalForm< N >::~FNormalForm

(

)

Definition at line 297 of file FNormalForm.h.

Member Function Documentation

template<int N>

FMatrix< double, N/2, N/2 > FNormalForm< N >::anharmonicity

(

)

const

Get anharmonicities as a matrix.

Definition at line 308 of file FNormalForm.h.

References Physics::pi, and pi.

template<int N>

int FNormalForm< N >::degreesOfFreedom

(

)

const

Get number of stable degrees of freedom.

Definition at line 302 of file FNormalForm.h.

template<int N>

const FVector< std::complex< double >, N > & FNormalForm< N >::eigenValues

(

)

const

Get eigenvalues of the linear part as a complex vector.

Definition at line 374 of file FNormalForm.h.

template<int N>

const FMatrix< double, N, N > & FNormalForm< N >::eigenVectors

(

)

const

Get eigenvectors of the linear part in packed form.

Definition at line 380 of file FNormalForm.h.

Referenced by Period::fill().

template<int N>

FTps< double, N > FNormalForm< N >::invariant

(

int

i

)

const

Get invariant polynomial for mode i.

Definition at line 342 of file FNormalForm.h.

References abs(), imag(), and FTps< T, N >::setCoefficient().

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template<int N>

const FTps< double, N > & FNormalForm< N >::normalForm

(

)

const

Get normal-form map as a Lie transform.

Definition at line 362 of file FNormalForm.h.

template<int N>

const FTps< double, N > & FNormalForm< N >::normalisingMap

(

)

const

Get normalising map as a Lie transform.

Definition at line 368 of file FNormalForm.h.

Referenced by Period::fill().

template<int N>

void FNormalForm< N >::operator= ( const FNormalForm< N > &  )

private

template<int N>

void FNormalForm< N >::orderModes ( FVector< std::complex< double >, N >  tlam, FMatrix< double, N, N >  tmat  )

protected

Definition at line 386 of file FNormalForm.h.

References abs(), Physics::c, FArray2D< T, M, N >::col_begin(), FArray2D< T, M, N >::col_end(), interpolation::im(), imag(), interpolation::re(), sqrt(), and FArray2D< T, M, N >::swapColumns().

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

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Member Data Documentation

template<int N>

FTps<double, N> FNormalForm< N >::A_Lie

private

Definition at line 100 of file FNormalForm.h.

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

template<int N>

int FNormalForm< N >::freedom

private

Definition at line 97 of file FNormalForm.h.

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

template<int N>

FVector<std::complex<double>, N> FNormalForm< N >::lambda

private

Definition at line 106 of file FNormalForm.h.

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

template<int N>

FTps<double, N> FNormalForm< N >::N_Lie

private

Definition at line 103 of file FNormalForm.h.

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

template<int N>

FMatrix<double, N, N> FNormalForm< N >::V

private

Definition at line 109 of file FNormalForm.h.

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

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

• src/Classic/FixedAlgebra/FNormalForm.h