capd::normalForms Namespace Reference

Functions
template<typename MatrixType , unsigned DEGREE>
capd::diffAlgebra::Jet< MatrixType, DEGREE >	linearSubstitution (const MatrixType &N, const capd::diffAlgebra::Jet< MatrixType, DEGREE > &s, const MatrixType &M)
template<typename MatrixType , unsigned DEGREE>
capd::diffAlgebra::Jet< MatrixType, DEGREE >	linearSubstitutionPowerSeries (const MatrixType &N, const capd::diffAlgebra::Jet< MatrixType, DEGREE > &s, const MatrixType &M)
template<typename MatrixType , unsigned DEGREE>
void	derivativesToSeries (capd::diffAlgebra::Jet< MatrixType, DEGREE > &s)
template<typename MatrixType , unsigned DEGREE>
void	seriesToDerivatives (capd::diffAlgebra::Jet< MatrixType, DEGREE > &s)
template<typename T >
bool	checkLambda (std::complex< T > lambda)
template<typename T_Bound , typename T_Rnd >
std::complex< capd::intervals::Interval< T_Bound, T_Rnd > >	operator/ (const std::complex< capd::intervals::Interval< T_Bound, T_Rnd > > &x, const std::complex< capd::intervals::Interval< T_Bound, T_Rnd > > &y)
template<typename T_Bound , typename T_Rnd >
std::complex< capd::intervals::Interval< T_Bound, T_Rnd > >	operator/ (const std::complex< capd::intervals::Interval< T_Bound, T_Rnd > > &x, int y)
template<typename ScalarType >
void	computeEigensystem (const capd::vectalg::Matrix< ScalarType, 2, 2 > &c, capd::vectalg::Matrix< std::complex< ScalarType >, 2, 2 > &eigenvectors, capd::vectalg::Vector< std::complex< ScalarType >, 2 > &eigenvalues)
template<typename ScalarType , unsigned DEGREE>
capd::diffAlgebra::Jet< capd::vectalg::Matrix< std::complex< ScalarType >, 2, 2 >, DEGREE >	planarLinearSubstitution (const capd::diffAlgebra::Jet< capd::vectalg::Matrix< ScalarType, 2, 2 >, DEGREE > &s)
template<typename ScalarType , unsigned DEGREE>
std::complex< ScalarType > &	takeCoeff (capd::diffAlgebra::Jet< capd::vectalg::Matrix< std::complex< ScalarType >, 2, 2 >, DEGREE > &s, int i, int j, int k)
template<typename ScalarType , unsigned DEGREE>
capd::vectalg::Vector< std::complex< ScalarType >, 0 >	computePlanarEllipticNormalForm (capd::diffAlgebra::Jet< capd::vectalg::Matrix< ScalarType, 2, 2 >, DEGREE > &c)
template<typename ScalarType >
capd::vectalg::Vector< std::complex< ScalarType >, 0 >	computePlanarEllipticNormalForm (capd::diffAlgebra::Jet< capd::vectalg::Matrix< ScalarType, 0, 0 >, 0 > &c)

Function Documentation

checkLambda()

template<typename T >

bool capd::normalForms::checkLambda

(

std::complex< T >

lambda

)

computeEigensystem()

template<typename ScalarType >

void capd::normalForms::computeEigensystem	(	const capd::vectalg::Matrix< ScalarType, 2, 2 > &	c,
		capd::vectalg::Matrix< std::complex< ScalarType >, 2, 2 > &	eigenvectors,
		capd::vectalg::Vector< std::complex< ScalarType >, 2 > &	eigenvalues
	)

computePlanarEllipticNormalForm() [1/2]

template<typename ScalarType >

capd::vectalg::Vector<std::complex<ScalarType>,0> capd::normalForms::computePlanarEllipticNormalForm

(

capd::diffAlgebra::Jet< capd::vectalg::Matrix< ScalarType, 0, 0 >, 0 > &

c

)

computePlanarEllipticNormalForm() [2/2]

template<typename ScalarType , unsigned DEGREE>

capd::vectalg::Vector<std::complex<ScalarType>,0> capd::normalForms::computePlanarEllipticNormalForm

(

capd::diffAlgebra::Jet< capd::vectalg::Matrix< ScalarType, 2, 2 >, DEGREE > &

c

)

derivativesToSeries()

template<typename MatrixType , unsigned DEGREE>

void capd::normalForms::derivativesToSeries

(

capd::diffAlgebra::Jet< MatrixType, DEGREE > &

s

)

linearSubstitution()

template<typename MatrixType , unsigned DEGREE>

capd::diffAlgebra::Jet<MatrixType,DEGREE> capd::normalForms::linearSubstitution	(	const MatrixType &	N,
		const capd::diffAlgebra::Jet< MatrixType, DEGREE > &	s,
		const MatrixType &	M
	)

linearSubstitutionPowerSeries()

template<typename MatrixType , unsigned DEGREE>

capd::diffAlgebra::Jet<MatrixType,DEGREE> capd::normalForms::linearSubstitutionPowerSeries	(	const MatrixType &	N,
		const capd::diffAlgebra::Jet< MatrixType, DEGREE > &	s,
		const MatrixType &	M
	)

operator/() [1/2]

template<typename T_Bound , typename T_Rnd >

std::complex< capd::intervals::Interval<T_Bound,T_Rnd> > capd::normalForms::operator/	(	const std::complex< capd::intervals::Interval< T_Bound, T_Rnd > > &	x,
		const std::complex< capd::intervals::Interval< T_Bound, T_Rnd > > &	y
	)

operator/() [2/2]

template<typename T_Bound , typename T_Rnd >

std::complex< capd::intervals::Interval<T_Bound,T_Rnd> > capd::normalForms::operator/	(	const std::complex< capd::intervals::Interval< T_Bound, T_Rnd > > &	x,
		int	y
	)

planarLinearSubstitution()

template<typename ScalarType , unsigned DEGREE>

capd::diffAlgebra::Jet< capd::vectalg::Matrix< std::complex<ScalarType>,2,2>,DEGREE > capd::normalForms::planarLinearSubstitution

(

const capd::diffAlgebra::Jet< capd::vectalg::Matrix< ScalarType, 2, 2 >, DEGREE > &

s

)

seriesToDerivatives()

template<typename MatrixType , unsigned DEGREE>

void capd::normalForms::seriesToDerivatives

(

capd::diffAlgebra::Jet< MatrixType, DEGREE > &

s

)

takeCoeff()

template<typename ScalarType , unsigned DEGREE>

std::complex<ScalarType>& capd::normalForms::takeCoeff	(	capd::diffAlgebra::Jet< capd::vectalg::Matrix< std::complex< ScalarType >, 2, 2 >, DEGREE > &	s,
		int	i,
		int	j,
		int	k
	)