TimeMap class provides class that serves as Poincare section of the form x_i = c. More...

#include <capd/poincare/CoordinateSection.h>

Public Types
typedef MatrixT	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef VectorType::size_type	size_type
	integral type used to index containers (vectors, matrices, etc) More...

typedef capd::dynset::AbstractSet< VectorType >	Set
	type of abstract base class for all sets More...

typedef AbstractSection< MatrixT >::JetType	JetType

typedef capd::diffAlgebra::Hessian< ScalarType, VectorType::csDim, VectorType::csDim >	HessianType

typedef SectionDerivativesEnclosure< MatrixType >	SectionDerivativesEnclosureType

Public Member Functions
	CoordinateSection (size_type D, size_type _i, ScalarType _c=TypeTraits< ScalarType >::zero())
	(indices start at 0)$ More...

ScalarType	operator() (const VectorType &v) const
	evaluates function at a given vector More...

void	setDirection (size_type i)

void	setConstant (ScalarType _c)

VectorType	getNormalVector () const

VectorType	gradient (const VectorType &) const
	returns gradient of the function computed at vector u More...

ScalarType	gradientByVector (const VectorType &, const VectorType &u) const

bool	isSpecialSection () const
	This is very important function. More...

ScalarType	evalAt (const capd::dynset::AbstractSet< VectorType > &s) const

void	computeDT (const JetType &Px, const JetType &vfOnPx, JetType &dT, size_type degree) const

virtual ScalarType	evalAt (const Set &set) const =0
	This function computes value of section function on a given set. More...

virtual void	computeDT (const MatrixType &derivativeOfFlow, const VectorType &gradientOnPx, const ScalarType &denominator, VectorType &result) const
	computes gradient of return time More...

virtual MatrixType	computeDP (const VectorType &Px, const MatrixType &derivativeOfFlow, const VectorType &fieldOnPx, VectorType &dT) const
	Simultaneous computation of gradient of return time and derivative of Poincare Map dP. More...

virtual void	computeDP (const VectorType &Px, const MatrixType &derivativeOfFlow, const HessianType &hessianOfFlow, const VectorType &fieldOnPx, const VectorType &d2Phidt2, const MatrixType &derOfVectorFieldOnPx, MatrixType &DP, HessianType &D2P, VectorType &dT, MatrixType &d2T) const
	Simultaneous computation of first and second Taylor coefficients of return time and Poincare map. More...

Detailed Description

template<typename MatrixT>
class capd::poincare::CoordinateSection< MatrixT >

TimeMap class provides class that serves as Poincare section of the form x_i = c.

The section is defined by:

integer - index of variable
constant c that defines affine hyperplane x_i=c

Member Typedef Documentation

◆ HessianType

template<class MatrixT >

typedef capd::diffAlgebra::Hessian<ScalarType,VectorType::csDim,VectorType::csDim> capd::poincare::AbstractSection< MatrixT >::HessianType

inherited

◆ JetType

template<typename MatrixT >

typedef AbstractSection<MatrixT>::JetType capd::poincare::CoordinateSection< MatrixT >::JetType

◆ MatrixType

template<typename MatrixT >

typedef MatrixT capd::poincare::CoordinateSection< MatrixT >::MatrixType

◆ ScalarType

template<typename MatrixT >

typedef MatrixType::ScalarType capd::poincare::CoordinateSection< MatrixT >::ScalarType

◆ SectionDerivativesEnclosureType

template<class MatrixT >

typedef SectionDerivativesEnclosure<MatrixType> capd::poincare::AbstractSection< MatrixT >::SectionDerivativesEnclosureType

inherited

◆ Set

template<typename MatrixT >

typedef capd::dynset::AbstractSet<VectorType> capd::poincare::CoordinateSection< MatrixT >::Set

type of abstract base class for all sets

◆ size_type

template<typename MatrixT >

typedef VectorType::size_type capd::poincare::CoordinateSection< MatrixT >::size_type

integral type used to index containers (vectors, matrices, etc)

◆ VectorType

template<typename MatrixT >

typedef MatrixType::RowVectorType capd::poincare::CoordinateSection< MatrixT >::VectorType

Constructor & Destructor Documentation

◆ CoordinateSection()

template<typename MatrixT >

capd::poincare::CoordinateSection< MatrixT >::CoordinateSection	(	size_type	D,
		size_type	_i,
		ScalarType	_c = `TypeTraits<ScalarType>::zero()`
	)

inline

(indices start at 0)$

Parameters

D	phase space dimension
_i	index of coordinate which defines section (counted from 0)
_c	value that defines section

Member Function Documentation

◆ computeDT()

template<typename MatrixT >

void capd::poincare::CoordinateSection< MatrixT >::computeDT	(	const JetType &	Px,
		const JetType &	vfOnPx,
		JetType &	dT,
		size_type	degree
	)		const

inline

◆ evalAt() [1/2]

template<typename MatrixT >

ScalarType capd::poincare::CoordinateSection< MatrixT >::evalAt ( const capd::dynset::AbstractSet< VectorType > & s ) const

inline

◆ evalAt() [2/2]

template<class MatrixT >

virtual ScalarType capd::poincare::AbstractSection< MatrixT >::evalAt ( const Set & set ) const

pure virtualinherited

This function computes value of section function on a given set.

◆ getNormalVector()

template<typename MatrixT >

VectorType capd::poincare::CoordinateSection< MatrixT >::getNormalVector ( ) const

inline

◆ gradient()

template<typename MatrixT >

VectorType capd::poincare::CoordinateSection< MatrixT >::gradient ( const VectorType & u ) const

inlinevirtual

returns gradient of the function computed at vector u

Implements capd::poincare::AbstractSection< MatrixT >.

◆ gradientByVector()

template<typename MatrixT >

ScalarType capd::poincare::CoordinateSection< MatrixT >::gradientByVector	(	const VectorType &	,
		const VectorType &	u
	)		const

inlinevirtual

Reimplemented from capd::poincare::AbstractSection< MatrixT >.

◆ isSpecialSection()

template<typename MatrixT >

bool capd::poincare::CoordinateSection< MatrixT >::isSpecialSection ( ) const

inlinevirtual

This is very important function.

If it returns true, class PoincareMap delegates computation of value of section(set) to the section. Otherwise it is assumed that the set has more information to compute value of section(set) in most optimal way. This is quite natural as the set knows its own representation. This function returns true for instance if the PoincareSection is given by x_i=c, where x_i is i-th coordinate and c is constant.

Reimplemented from capd::poincare::AbstractSection< MatrixT >.

◆ operator()()

template<typename MatrixT >

ScalarType capd::poincare::CoordinateSection< MatrixT >::operator() ( const VectorType & v ) const

inlinevirtual

evaluates function at a given vector

Implements capd::poincare::AbstractSection< MatrixT >.

◆ setConstant()

template<typename MatrixT >

void capd::poincare::CoordinateSection< MatrixT >::setConstant ( ScalarType _c )

inline

◆ setDirection()

template<typename MatrixT >

void capd::poincare::CoordinateSection< MatrixT >::setDirection ( size_type i )

inline

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

capd/poincare/CoordinateSection.h

Public Types

Public Member Functions

Detailed Description

template<typename MatrixT> class capd::poincare::CoordinateSection< MatrixT >

Member Typedef Documentation

◆ HessianType

◆ JetType

◆ MatrixType

◆ ScalarType

◆ SectionDerivativesEnclosureType

◆ Set

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ CoordinateSection()

Member Function Documentation

◆ computeDT()

◆ evalAt() [1/2]

◆ evalAt() [2/2]

◆ getNormalVector()

◆ gradient()

◆ gradientByVector()

◆ isSpecialSection()

◆ operator()()

◆ setConstant()

◆ setDirection()

template<typename MatrixT>
class capd::poincare::CoordinateSection< MatrixT >