CAPD DynSys Library  5.2.0
Public Types | Public Member Functions | List of all members
capd::pdes::PdeAbstractSection< VectorT, MatrixT > Class Template Referenceabstract
Pdes

#include <capd/pdes/PdeAbstractSection.h>

Public Types

typedef MatrixT MatrixType
 
typedef VectorT VectorType
 
typedef MatrixType::RowVectorType FiniteVectorType
 
typedef MatrixType::ScalarType ScalarType
 
typedef VectorType::size_type size_type
 integral type used to index containers (vectors, matrices, etc) More...
 
typedef capd::dynset::AbstractSet< FiniteVectorType > Set
 type of abstract base class for all sets More...
 
typedef PdeSectionDerivativesEnclosure< VectorType, MatrixType > SectionDerivativesEnclosureType
 
typedef capd::diffAlgebra::Hessian< ScalarType, FiniteVectorType::csDim, FiniteVectorType::csDim > HessianType
 
typedef capd::diffAlgebra::Jet< MatrixT, 0 > JetType
 

Public Member Functions

virtual ScalarType operator() (const VectorType &v) const =0
 evaluates function at a given vector More...
 
virtual VectorType gradient (const VectorType &u) const =0
 returns gradient of the function computed at vector u More...
 
virtual ScalarType gradientByVector (const VectorType &x, const VectorType &u) const =0
 
virtual const capd::poincare::AbstractSection< MatrixType > & getProjection (size_type) const =0
 
virtual bool isSpecialSection () const
 This is very important function. More...
 
virtual ScalarType evalAt (const Set &set) const
 This function computes value of section function on a given set. More...
 
virtual MatrixType computeDP (const VectorType &P, const VectorType &vfOnP, const MatrixType &Dxx, const FiniteVectorType &Dy, const ScalarType &Dyx, FiniteVectorType &Py, ScalarType &Pyx) const
 Simultaneous computation of gradient of return time and derivative of Poincare Map dP. More...
 

Member Typedef Documentation

◆ FiniteVectorType

template<class VectorT , class MatrixT >
typedef MatrixType::RowVectorType capd::pdes::PdeAbstractSection< VectorT, MatrixT >::FiniteVectorType

◆ HessianType

template<class VectorT , class MatrixT >
typedef capd::diffAlgebra::Hessian<ScalarType,FiniteVectorType::csDim,FiniteVectorType::csDim> capd::pdes::PdeAbstractSection< VectorT, MatrixT >::HessianType

◆ JetType

template<class VectorT , class MatrixT >
typedef capd::diffAlgebra::Jet<MatrixT,0> capd::pdes::PdeAbstractSection< VectorT, MatrixT >::JetType

◆ MatrixType

template<class VectorT , class MatrixT >
typedef MatrixT capd::pdes::PdeAbstractSection< VectorT, MatrixT >::MatrixType

◆ ScalarType

template<class VectorT , class MatrixT >
typedef MatrixType::ScalarType capd::pdes::PdeAbstractSection< VectorT, MatrixT >::ScalarType

◆ SectionDerivativesEnclosureType

template<class VectorT , class MatrixT >
typedef PdeSectionDerivativesEnclosure<VectorType,MatrixType> capd::pdes::PdeAbstractSection< VectorT, MatrixT >::SectionDerivativesEnclosureType

◆ Set

template<class VectorT , class MatrixT >
typedef capd::dynset::AbstractSet<FiniteVectorType> capd::pdes::PdeAbstractSection< VectorT, MatrixT >::Set

type of abstract base class for all sets

◆ size_type

template<class VectorT , class MatrixT >
typedef VectorType::size_type capd::pdes::PdeAbstractSection< VectorT, MatrixT >::size_type

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

◆ VectorType

template<class VectorT , class MatrixT >
typedef VectorT capd::pdes::PdeAbstractSection< VectorT, MatrixT >::VectorType

Member Function Documentation

◆ computeDP()

template<class VectorT , class MatrixT >
virtual MatrixType capd::pdes::PdeAbstractSection< VectorT, MatrixT >::computeDP ( const VectorType &  P,
const VectorType &  vfOnP,
const MatrixType &  Dxx,
const FiniteVectorType &  Dy,
const ScalarType &  Dyx,
FiniteVectorType &  Py,
ScalarType &  Pyx 
) const
inlinevirtual

Simultaneous computation of gradient of return time and derivative of Poincare Map dP.

Parameters
[in]P- value of Poincare map
[in]D- finite block of solution to first variational equation computed at return time
[out]vfOnP- vector field evaluated on P

◆ evalAt()

template<class VectorT , class MatrixT >
virtual ScalarType capd::pdes::PdeAbstractSection< VectorT, MatrixT >::evalAt ( const Set &  set) const
inlinevirtual

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

Reimplemented in capd::pdes::PdeCoordinateSection< VectorT, MatrixT >, and capd::pdes::PdeAffineSection< VectorT, MatrixT >.

◆ getProjection()

template<class VectorT , class MatrixT >
virtual const capd::poincare::AbstractSection<MatrixType>& capd::pdes::PdeAbstractSection< VectorT, MatrixT >::getProjection ( size_type  ) const
pure virtual

Implemented in capd::pdes::PdeCoordinateSection< VectorT, MatrixT >, and capd::pdes::PdeAffineSection< VectorT, MatrixT >.

◆ gradient()

template<class VectorT , class MatrixT >
virtual VectorType capd::pdes::PdeAbstractSection< VectorT, MatrixT >::gradient ( const VectorType &  u) const
pure virtual

returns gradient of the function computed at vector u

Implemented in capd::pdes::PdeAffineSection< VectorT, MatrixT >, and capd::pdes::PdeCoordinateSection< VectorT, MatrixT >.

◆ gradientByVector()

template<class VectorT , class MatrixT >
virtual ScalarType capd::pdes::PdeAbstractSection< VectorT, MatrixT >::gradientByVector ( const VectorType &  x,
const VectorType &  u 
) const
pure virtual

Implemented in capd::pdes::PdeAffineSection< VectorT, MatrixT >, and capd::pdes::PdeCoordinateSection< VectorT, MatrixT >.

◆ isSpecialSection()

template<class VectorT , class MatrixT >
virtual bool capd::pdes::PdeAbstractSection< VectorT, 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 in capd::pdes::PdeCoordinateSection< VectorT, MatrixT >.

◆ operator()()

template<class VectorT , class MatrixT >
virtual ScalarType capd::pdes::PdeAbstractSection< VectorT, MatrixT >::operator() ( const VectorType &  v) const
pure virtual

evaluates function at a given vector

Implemented in capd::pdes::PdeCoordinateSection< VectorT, MatrixT >, and capd::pdes::PdeAffineSection< VectorT, MatrixT >.