capd::pdes::PdeCurve< SeriesT > Class Template Reference

This class is a data structure for storing of a parametric curve together with first order derivatives with respect to initial point. More...

#include <capd/pdes/PdeCurve.h>

Public Types
typedef SeriesT	VectorType
typedef capd::IVector	FiniteVectorType
typedef capd::IMatrix	MatrixType
typedef capd::diffAlgebra::CurveInterface< capd::IMatrix >::HessianType	HessianType
typedef capd::diffAlgebra::CurveInterface< capd::IMatrix >::JetType	JetType
typedef MatrixType::ScalarType	ScalarType
typedef TypeTraits< ScalarType >::Real	Real
typedef MatrixType::size_type	size_type
typedef std::vector< VectorType >	VectorArray
typedef std::vector< VectorArray >	MatrixArray

Public Member Functions
	PdeCurve (size_type dim, size_type order)
virtual	~PdeCurve ()
PdeCurve &	operator= (const PdeCurve &c)
virtual VectorType	operator() (const ScalarType &h) const
virtual VectorType	valueAtCenter (const ScalarType &h) const
virtual VectorType	remainder (const ScalarType &h) const
virtual MatrixType	oneStepDerivativeOfNumericalMethod (const ScalarType &h) const
virtual VectorType	getCenter () const
virtual MatrixType	derivative (const ScalarType &h) const
virtual MatrixType	operator[] (const ScalarType &h) const
virtual void	setOrder (size_type order)
	Sets the order of Taylor interpolation. More...
size_type	getOrder () const
	Returns the order of Taylor interpolation. More...
size_type	getAllocatedOrder () const
	Returns maximal allocated order - used to avoid memory reallocation. More...
size_type	dimension () const
	Returns the dimension in which the relevant dynamics is observed. More...
void	clearCoefficients ()
	sets all coefficients to zero More...
const ScalarType	centerCoefficient (size_type i, size_type j) const
const ScalarType	coefficient (size_type i, size_type j) const
const ScalarType	remainderCoefficient (size_type i, size_type j) const
const ScalarType	coefficient (size_type i, size_type j, size_type k) const
const ScalarType	remainderCoefficient (size_type i, size_type j, size_type k) const
VectorArray &	getCoefficientsAtCenter ()
VectorArray &	getCoefficients ()
VectorArray &	getRemainderCoefficients ()
MatrixArray &	getMatrixCoefficients ()
MatrixArray &	getMatrixRemainderCoefficients ()
MatrixArray &	getDyxCoefficients ()
MatrixArray &	getDyxRemainderCoefficients ()
const VectorArray &	getCoefficientsAtCenter () const
const VectorArray &	getCoefficients () const
const VectorArray &	getRemainderCoefficients () const
const MatrixArray &	getMatrixCoefficients () const
const MatrixArray &	getMatrixRemainderCoefficients () const
const MatrixArray &	getDyxCoefficients () const
const MatrixArray &	getDyxRemainderCoefficients () const
void	setInitMatrix (const MatrixType &M)
void	setInitHessian (const HessianType &)
void	setInitJet (const JetType &)
std::runtime_error	domainErrorMessage (std::string msg, ScalarType h, Real left, Real right) const
virtual HessianType	hessian (const ScalarType &) const
virtual JetType	jet (const ScalarType &) const
virtual void	eval (ScalarType, JetType &) const
virtual void	setDomain (Real left, Real right)
virtual Real	getLeftDomain () const
virtual Real	getRightDomain () const

Protected Member Functions
template<class V >
void	sumTaylorSeries (V &x, const VectorArray &c, ScalarType h, int p, size_type dim) const
void	sumTaylorSeries (MatrixType &A, const MatrixArray &J, ScalarType h, int p, size_type dim) const
void	realloc (size_type dimension)

Protected Attributes
VectorArray	m_coefficientsAtCenter
VectorArray	m_coefficients
VectorArray	m_remainderCoefficients
MatrixArray	m_matrixCoefficients
MatrixArray	m_matrixRemainderCoefficients
MatrixArray	m_dyxCoefficients
MatrixArray	m_dyxRemainderCoefficients
size_type	m_order
MatrixType	initMatrix
Real	m_left
Real	m_right
	domain More...

Detailed Description

template<class SeriesT>
class capd::pdes::PdeCurve< SeriesT >

This class is a data structure for storing of a parametric curve together with first order derivatives with respect to initial point.

More precisely, a curve c(t,x) is represented as c(t,x_0) + d/dx c(t,x)(x-x_0) + smallRemainder(t,x)

This class provides a member functions for accessing of all coefficients.

Member Typedef Documentation

FiniteVectorType

template<class SeriesT >

typedef capd::IVector capd::pdes::PdeCurve< SeriesT >::FiniteVectorType

HessianType

template<class SeriesT >

typedef capd::diffAlgebra::CurveInterface<capd::IMatrix>::HessianType capd::pdes::PdeCurve< SeriesT >::HessianType

JetType

template<class SeriesT >

typedef capd::diffAlgebra::CurveInterface<capd::IMatrix>::JetType capd::pdes::PdeCurve< SeriesT >::JetType

MatrixArray

template<class SeriesT >

typedef std::vector<VectorArray> capd::pdes::PdeCurve< SeriesT >::MatrixArray

MatrixType

template<class SeriesT >

typedef capd::IMatrix capd::pdes::PdeCurve< SeriesT >::MatrixType

Real

template<class SeriesT >

typedef TypeTraits<ScalarType>::Real capd::pdes::PdeCurve< SeriesT >::Real

ScalarType

template<class SeriesT >

typedef MatrixType::ScalarType capd::pdes::PdeCurve< SeriesT >::ScalarType

size_type

template<class SeriesT >

typedef MatrixType::size_type capd::pdes::PdeCurve< SeriesT >::size_type

VectorArray

template<class SeriesT >

typedef std::vector<VectorType> capd::pdes::PdeCurve< SeriesT >::VectorArray

VectorType

template<class SeriesT >

typedef SeriesT capd::pdes::PdeCurve< SeriesT >::VectorType

Constructor & Destructor Documentation

~PdeCurve()

template<class SeriesT >

virtual capd::pdes::PdeCurve< SeriesT >::~PdeCurve ( )

inlinevirtual

Member Function Documentation

derivative()

template<class SeriesT >

virtual MatrixType capd::pdes::PdeCurve< SeriesT >::derivative ( const ScalarType &  h ) const

inlinevirtual

Implements capd::diffAlgebra::ParametricCurve< capd::IMatrix, SeriesT >.

domainErrorMessage()

std::runtime_error capd::diffAlgebra::CurveInterface< capd::IMatrix >::domainErrorMessage ( std::string  msg, ScalarType  h, Real  left, Real  right  ) const

inlineinherited

eval()

virtual void capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::eval ( ScalarType  , JetType &    ) const

inlinevirtualinherited

getAllocatedOrder()

template<class SeriesT >

size_type capd::pdes::PdeCurve< SeriesT >::getAllocatedOrder

(

)

const

Returns maximal allocated order - used to avoid memory reallocation.

getCenter()

template<class SeriesT >

virtual VectorType capd::pdes::PdeCurve< SeriesT >::getCenter ( ) const

inlinevirtual

getCoefficients() [1/2]

template<class SeriesT >

VectorArray& capd::pdes::PdeCurve< SeriesT >::getCoefficients ( )

inline

getCoefficients() [2/2]

template<class SeriesT >

const VectorArray& capd::pdes::PdeCurve< SeriesT >::getCoefficients ( ) const

inline

getCoefficientsAtCenter() [1/2]

template<class SeriesT >

VectorArray& capd::pdes::PdeCurve< SeriesT >::getCoefficientsAtCenter ( )

inline

getCoefficientsAtCenter() [2/2]

template<class SeriesT >

const VectorArray& capd::pdes::PdeCurve< SeriesT >::getCoefficientsAtCenter ( ) const

inline

getDyxCoefficients() [1/2]

template<class SeriesT >

MatrixArray& capd::pdes::PdeCurve< SeriesT >::getDyxCoefficients ( )

inline

getDyxCoefficients() [2/2]

template<class SeriesT >

const MatrixArray& capd::pdes::PdeCurve< SeriesT >::getDyxCoefficients ( ) const

inline

getDyxRemainderCoefficients() [1/2]

template<class SeriesT >

MatrixArray& capd::pdes::PdeCurve< SeriesT >::getDyxRemainderCoefficients ( )

inline

getDyxRemainderCoefficients() [2/2]

template<class SeriesT >

const MatrixArray& capd::pdes::PdeCurve< SeriesT >::getDyxRemainderCoefficients ( ) const

inline

getLeftDomain()

ParametricCurve< capd::IMatrix , SeriesT >::Real capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::getLeftDomain

inlinevirtualinherited

getMatrixCoefficients() [1/2]

template<class SeriesT >

MatrixArray& capd::pdes::PdeCurve< SeriesT >::getMatrixCoefficients ( )

inline

getMatrixCoefficients() [2/2]

template<class SeriesT >

const MatrixArray& capd::pdes::PdeCurve< SeriesT >::getMatrixCoefficients ( ) const

inline

getMatrixRemainderCoefficients() [1/2]

template<class SeriesT >

MatrixArray& capd::pdes::PdeCurve< SeriesT >::getMatrixRemainderCoefficients ( )

inline

getMatrixRemainderCoefficients() [2/2]

template<class SeriesT >

const MatrixArray& capd::pdes::PdeCurve< SeriesT >::getMatrixRemainderCoefficients ( ) const

inline

getRemainderCoefficients() [1/2]

template<class SeriesT >

VectorArray& capd::pdes::PdeCurve< SeriesT >::getRemainderCoefficients ( )

inline

getRemainderCoefficients() [2/2]

template<class SeriesT >

const VectorArray& capd::pdes::PdeCurve< SeriesT >::getRemainderCoefficients ( ) const

inline

getRightDomain()

ParametricCurve< capd::IMatrix , SeriesT >::Real capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::getRightDomain

inlinevirtualinherited

hessian()

virtual HessianType capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::hessian ( const ScalarType &  ) const

inlinevirtualinherited

jet()

virtual JetType capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::jet ( const ScalarType &  ) const

inlinevirtualinherited

oneStepDerivativeOfNumericalMethod()

template<class SeriesT >

virtual MatrixType capd::pdes::PdeCurve< SeriesT >::oneStepDerivativeOfNumericalMethod ( const ScalarType &  h ) const

inlinevirtual

operator()()

template<class SeriesT >

virtual VectorType capd::pdes::PdeCurve< SeriesT >::operator() ( const ScalarType &  h ) const

inlinevirtual

Implements capd::diffAlgebra::ParametricCurve< capd::IMatrix, SeriesT >.

operator=()

template<class SeriesT >

PdeCurve& capd::pdes::PdeCurve< SeriesT >::operator=

(

const PdeCurve< SeriesT > &

c

)

operator[]()

template<class SeriesT >

virtual MatrixType capd::pdes::PdeCurve< SeriesT >::operator[] ( const ScalarType &  h ) const

inlinevirtual

Implements capd::diffAlgebra::ParametricCurve< capd::IMatrix, SeriesT >.

remainder()

template<class SeriesT >

virtual VectorType capd::pdes::PdeCurve< SeriesT >::remainder ( const ScalarType &  h ) const

inlinevirtual

remainderCoefficient()

template<class SeriesT >

const ScalarType capd::pdes::PdeCurve< SeriesT >::remainderCoefficient	(	size_type	i,
		size_type	j,
		size_type	k
	)		const

setDomain()

void capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::setDomain ( Real  left, Real  right  )

inlinevirtualinherited

setInitHessian()

void capd::diffAlgebra::CurveInterface< capd::IMatrix >::setInitHessian ( const HessianType &  )

inlineinherited

setInitJet()

void capd::diffAlgebra::CurveInterface< capd::IMatrix >::setInitJet ( const JetType &  )

inlineinherited

setInitMatrix()

template<class SeriesT >

void capd::pdes::PdeCurve< SeriesT >::setInitMatrix ( const MatrixType &  M )

inline

valueAtCenter()

template<class SeriesT >

virtual VectorType capd::pdes::PdeCurve< SeriesT >::valueAtCenter ( const ScalarType &  h ) const

inlinevirtual

Member Data Documentation

initMatrix

template<class SeriesT >

MatrixType capd::pdes::PdeCurve< SeriesT >::initMatrix

protected

m_coefficients

template<class SeriesT >

VectorArray capd::pdes::PdeCurve< SeriesT >::m_coefficients

protected

m_coefficientsAtCenter

template<class SeriesT >

VectorArray capd::pdes::PdeCurve< SeriesT >::m_coefficientsAtCenter

protected

m_dyxCoefficients

template<class SeriesT >

MatrixArray capd::pdes::PdeCurve< SeriesT >::m_dyxCoefficients

protected

m_dyxRemainderCoefficients

template<class SeriesT >

MatrixArray capd::pdes::PdeCurve< SeriesT >::m_dyxRemainderCoefficients

protected

m_left

Real capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::m_left

protectedinherited

m_matrixCoefficients

template<class SeriesT >

MatrixArray capd::pdes::PdeCurve< SeriesT >::m_matrixCoefficients

protected

m_matrixRemainderCoefficients

template<class SeriesT >

MatrixArray capd::pdes::PdeCurve< SeriesT >::m_matrixRemainderCoefficients

protected

m_order

template<class SeriesT >

size_type capd::pdes::PdeCurve< SeriesT >::m_order

protected

m_remainderCoefficients

template<class SeriesT >

VectorArray capd::pdes::PdeCurve< SeriesT >::m_remainderCoefficients

protected

m_right

Real capd::diffAlgebra::ParametricCurve< capd::IMatrix , SeriesT >::m_right

protectedinherited

domain