#include <capd/pdes/PdeSolver.h>

Public Types
typedef SeriesT	VectorType

typedef StepControlT	StepControlType

typedef capd::IVector	FiniteVectorType

typedef PdeCurve< VectorType >	CurveType

typedef PdeCurve< VectorType >	SolutionCurve

typedef capd::IMatrix	MatrixType

typedef MatrixType::ScalarType	ScalarType

typedef TypeTraits< ScalarType >::Real	Real

typedef MatrixType::size_type	size_type

typedef DissipativeVectorField< VectorType >	VectorFieldType

typedef CurveType::VectorArray	VectorArray

typedef CurveType::MatrixArray	MatrixArray

typedef capd::diffAlgebra::CurveInterface< capd::IMatrix >::HessianType	HessianType

typedef capd::diffAlgebra::CurveInterface< capd::IMatrix >::JetType	JetType

Public Member Functions
	PdeSolver (VectorFieldType &f, size_type order)

	~PdeSolver ()

const CurveType &	getCurve () const

CurveType &	getCurve ()

const CurveType &	getImplicitCurve () const

template<typename SetType >
void	operator() (SetType &set)

template<typename SetType >
void	operator() (SetType &set, SetType &result)
	Computes image of the set (in set's representation) and stores it in the result set. More...

VectorFieldType &	getVectorField ()

void	encloseC0Map (const FiniteVectorType &x0, const VectorType &x, VectorType &y, FiniteVectorType &o_phi, FiniteVectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)

void	encloseC1Map (const FiniteVectorType &x0, const VectorType &x, const FiniteVectorType &inDy, VectorType &y, FiniteVectorType &o_phi, FiniteVectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi, MatrixType &o_jacRem, MatrixType &o_jacEnc, VectorArray &DyxId, VectorArray &Dyx, FiniteVectorType &outDy, FiniteVectorType &encDy)

void	computeImplicitCoefficients (const FiniteVectorType &x0, const VectorType &x, size_type q)

void	initRemainderCoefficients (ScalarType, const VectorType &, unsigned)

void	computeTimeStep (const ScalarType &t, const VectorType &x)

void	setStep (ScalarType h)

void	adjustTimeStep (ScalarType h)

ScalarType	getStep ()

ScalarType	getCoeffNorm (size_type, size_type degree) const

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	coefficient (size_type i, size_type j, size_type k) const

const ScalarType	remainderCoefficient (size_type i, size_type j) const

const ScalarType	remainderCoefficient (size_type i, size_type j, size_type k) const

VectorArray &	getCoefficientsAtCenter ()

const VectorArray &	getCoefficientsAtCenter () const

VectorArray &	getCoefficients ()

const VectorArray &	getCoefficients () const

VectorArray &	getRemainderCoefficients ()

const VectorArray &	getRemainderCoefficients () const

MatrixArray &	getMatrixCoefficients ()

const MatrixArray &	getMatrixCoefficients () const

MatrixArray &	getMatrixRemainderCoefficients ()

const MatrixArray &	getMatrixRemainderCoefficients () const

MatrixArray &	getDyxCoefficients ()

const MatrixArray &	getDyxCoefficients () const

MatrixArray &	getDyxRemainderCoefficients ()

const MatrixArray &	getDyxRemainderCoefficients () const

void	setInitMatrix (const MatrixType &M)

void	setInitMatrix (const MatrixType &)

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

void	turnOnStepControl ()

void	turnOffStepControl ()

void	onOffStepControl (bool _onOffStepControl)

const StepControlType &	getStepControl () const

void	setStepControl (const StepControlType &stepControl)

bool	isStepChangeAllowed () const

void	setAbsoluteTolerance (TolScalarType tol)

void	setRelativeTolerance (TolScalarType tol)

TolScalarType	getAbsoluteTolerance () const

TolScalarType	getRelativeTolerance () const

SeriesT::ScalarType	getMaxStep () const

void	setMaxStep (SeriesT::ScalarType maxStep)

Static Public Member Functions
static TolScalarType	getEffectiveTolerance (Solver &solver, const SetType &s)

Protected Types
typedef std::tuple< VectorArray &, MatrixArray &, MatrixArray & >	C1Data

Protected Member Functions
template<class V >
bool	checkRemainderInclusion (const V &T, const FiniteVectorType &rem, ScalarType &beta)
	this function is used to check, that predicted enclosure is indeed an enclosure for leading modes used both in C^0 and C^1 computation More...

void	makeSelfConsistentBound (VectorArray &enc)

void	computeODECoefficients (VectorArray &a, size_type p)

void	scaleRemByStepPower (const VectorArray &enc, ScalarType s)

bool	checkRemainderInclusion (const VectorArray &, ScalarType &beta)

void	predictEnclosure (const VectorArray &X, VectorArray &enc, ScalarType R, ScalarType I, ScalarType IP)

void	makeSelfConsistentBound (C1Data enc)

void	computeODECoefficients (C1Data a, size_type p)

void	scaleRemByStepPower (C1Data enc, ScalarType s)

bool	checkRemainderInclusion (C1Data, ScalarType &beta)

void	predictEnclosure (C1Data X, C1Data enc, ScalarType R, ScalarType I, ScalarType IP)

void	predictEnclosure (const VectorArray &X, VectorArray &enc, FiniteVectorType &rem, ScalarType R, ScalarType I, ScalarType IP)
	this function is used to predict enclosure for C^0 part and for finite number of column in C^1 algorithm More...

void	initEncloseOneStep (const FiniteVectorType &x0, const VectorType &x)
	this function realizes initial computation usd in both for C^0 and C^1 algorithms More...

void	sumTaylorSeriesOfLeadingModes (size_type m, VectorType &x, FiniteVectorType &o_phi, FiniteVectorType &o_rem, MatrixType &o_jacPhi)
	computes output from one step of both C^0 and C^1 algorithms, that is o_phi, o_jacPhi and o_rem More...

template<class EncType >
void	highOrderEnclosure (const EncType &X, EncType &enc)

void	highOrderEnclosure ()

void	setInitialCondition (const FiniteVectorType &x0, const VectorType &x, CurveType &curve)

void	saveCurrentSet (const capd::diffAlgebra::TimeRange< ScalarType > &)

void	saveCurrentSet (const capd::dynset::C1Set< MatrixType > &set)

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
CurveType	m_implicitCurve

VectorFieldType &	m_vectorField

ScalarType	m_step

ScalarType	m_fixedTimeStep

MatrixType	m_jacPhi

MatrixType	m_jacRem

MatrixType	m_dyxPhi

MatrixType	m_dyxRem

FiniteVectorType	m_phi

FiniteVectorType	m_deltaX

FiniteVectorType	m_rem

FiniteVectorType	predicted_rem

std::vector< FiniteVectorType >	predicted_jacRem

std::vector< FiniteVectorType >	predicted_dyxRem

int	m_numberOfExplicitColumns

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...

StepControlType	m_stepControl

bool	m_onOffStepControl

TolScalarType	m_absoluteTolerance

TolScalarType	m_relativeTolerance

SeriesT::ScalarType	m_maxStep

Member Typedef Documentation

◆ C1Data

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef std::tuple<VectorArray&,MatrixArray&,MatrixArray&> capd::pdes::PdeSolver< SeriesT, StepControlT >::C1Data

protected

◆ CurveType

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef PdeCurve<VectorType> capd::pdes::PdeSolver< SeriesT, StepControlT >::CurveType

◆ FiniteVectorType

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef capd::IVector capd::pdes::PdeSolver< SeriesT, StepControlT >::FiniteVectorType

◆ HessianType

template<class SeriesT >

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

inherited

◆ JetType

template<class SeriesT >

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

inherited

◆ MatrixArray

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef CurveType::MatrixArray capd::pdes::PdeSolver< SeriesT, StepControlT >::MatrixArray

◆ MatrixType

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef capd::IMatrix capd::pdes::PdeSolver< SeriesT, StepControlT >::MatrixType

◆ Real

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef TypeTraits<ScalarType>::Real capd::pdes::PdeSolver< SeriesT, StepControlT >::Real

◆ ScalarType

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef MatrixType::ScalarType capd::pdes::PdeSolver< SeriesT, StepControlT >::ScalarType

◆ size_type

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef MatrixType::size_type capd::pdes::PdeSolver< SeriesT, StepControlT >::size_type

◆ SolutionCurve

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef PdeCurve<VectorType> capd::pdes::PdeSolver< SeriesT, StepControlT >::SolutionCurve

◆ StepControlType

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef StepControlT capd::pdes::PdeSolver< SeriesT, StepControlT >::StepControlType

◆ VectorArray

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef CurveType::VectorArray capd::pdes::PdeSolver< SeriesT, StepControlT >::VectorArray

◆ VectorFieldType

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef DissipativeVectorField<VectorType> capd::pdes::PdeSolver< SeriesT, StepControlT >::VectorFieldType

◆ VectorType

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

typedef SeriesT capd::pdes::PdeSolver< SeriesT, StepControlT >::VectorType

Constructor & Destructor Documentation

◆ PdeSolver()

template<class SeriesT , class StepControlT >

capd::pdes::PdeSolver< SeriesT, StepControlT >::PdeSolver	(	VectorFieldType &	f,
		size_type	order
	)

inline

◆ ~PdeSolver()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

capd::pdes::PdeSolver< SeriesT, StepControlT >::~PdeSolver ( )

inline

Member Function Documentation

◆ adjustTimeStep()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::adjustTimeStep ( ScalarType h )

inline

◆ checkRemainderInclusion() [1/3]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

bool capd::pdes::PdeSolver< SeriesT, StepControlT >::checkRemainderInclusion	(	C1Data	,
		ScalarType &	beta
	)

inlineprotected

◆ checkRemainderInclusion() [2/3]

template<class SeriesT , class StepControlT >

template<class V >

bool capd::pdes::PdeSolver< SeriesT, StepControlT >::checkRemainderInclusion	(	const V &	T,
		const FiniteVectorType &	rem,
		ScalarType &	beta
	)

protected

this function is used to check, that predicted enclosure is indeed an enclosure for leading modes used both in C^0 and C^1 computation

◆ checkRemainderInclusion() [3/3]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

bool capd::pdes::PdeSolver< SeriesT, StepControlT >::checkRemainderInclusion	(	const VectorArray &	,
		ScalarType &	beta
	)

inlineprotected

◆ computeImplicitCoefficients()

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::computeImplicitCoefficients	(	const FiniteVectorType &	x0,
		const VectorType &	x,
		size_type	q
	)

◆ computeODECoefficients() [1/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::computeODECoefficients	(	C1Data	a,
		size_type	p
	)

inlineprotected

◆ computeODECoefficients() [2/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::computeODECoefficients	(	VectorArray &	a,
		size_type	p
	)

inlineprotected

◆ computeTimeStep()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::computeTimeStep	(	const ScalarType &	t,
		const VectorType &	x
	)

inline

◆ derivative()

template<class SeriesT >

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

inlinevirtualinherited

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

◆ encloseC0Map()

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::encloseC0Map	(	const FiniteVectorType &	x0,
		const VectorType &	x,
		VectorType &	y,
		FiniteVectorType &	o_phi,
		FiniteVectorType &	o_rem,
		VectorType &	o_enc,
		MatrixType &	o_jacPhi
	)

◆ encloseC1Map()

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::encloseC1Map	(	const FiniteVectorType &	x0,
		const VectorType &	x,
		const FiniteVectorType &	inDy,
		VectorType &	y,
		FiniteVectorType &	o_phi,
		FiniteVectorType &	o_rem,
		VectorType &	o_enc,
		MatrixType &	o_jacPhi,
		MatrixType &	o_jacRem,
		MatrixType &	o_jacEnc,
		VectorArray &	DyxId,
		VectorArray &	Dyx,
		FiniteVectorType &	outDy,
		FiniteVectorType &	encDy
	)

◆ eval()

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

inlinevirtualinherited

◆ getAbsoluteTolerance()

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::getAbsoluteTolerance ( ) const

inlineinherited

◆ getAllocatedOrder()

template<class SeriesT >

size_type capd::pdes::PdeCurve< SeriesT >::getAllocatedOrder ( ) const

inherited

Returns maximal allocated order - used to avoid memory reallocation.

◆ getCenter()

template<class SeriesT >

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

inlinevirtualinherited

◆ getCoefficients() [1/2]

template<class SeriesT >

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

inlineinherited

◆ getCoefficients() [2/2]

template<class SeriesT >

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

inlineinherited

◆ getCoefficientsAtCenter() [1/2]

template<class SeriesT >

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

inlineinherited

◆ getCoefficientsAtCenter() [2/2]

template<class SeriesT >

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

inlineinherited

◆ getCoeffNorm()

template<class SeriesT , class StepControlT >

PdeSolver< SeriesT, StepControlT >::ScalarType capd::pdes::PdeSolver< SeriesT, StepControlT >::getCoeffNorm	(	size_type	r,
		size_type	degree
	)		const

◆ getCurve() [1/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

CurveType& capd::pdes::PdeSolver< SeriesT, StepControlT >::getCurve ( )

inline

◆ getCurve() [2/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

const CurveType& capd::pdes::PdeSolver< SeriesT, StepControlT >::getCurve ( ) const

inline

◆ getDyxCoefficients() [1/2]

template<class SeriesT >

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

inlineinherited

◆ getDyxCoefficients() [2/2]

template<class SeriesT >

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

inlineinherited

◆ getDyxRemainderCoefficients() [1/2]

template<class SeriesT >

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

inlineinherited

◆ getDyxRemainderCoefficients() [2/2]

template<class SeriesT >

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

inlineinherited

◆ getEffectiveTolerance()

static TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::getEffectiveTolerance	(	Solver &	solver,
		const SetType &	s
	)

inlinestaticinherited

◆ getImplicitCurve()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

const CurveType& capd::pdes::PdeSolver< SeriesT, StepControlT >::getImplicitCurve ( ) 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 ( )

inlineinherited

◆ getMatrixCoefficients() [2/2]

template<class SeriesT >

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

inlineinherited

◆ getMatrixRemainderCoefficients() [1/2]

template<class SeriesT >

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

inlineinherited

◆ getMatrixRemainderCoefficients() [2/2]

template<class SeriesT >

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

inlineinherited

◆ getMaxStep()

SeriesT::ScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::getMaxStep ( ) const

inlineinherited

◆ getRelativeTolerance()

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::getRelativeTolerance ( ) const

inlineinherited

◆ getRemainderCoefficients() [1/2]

template<class SeriesT >

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

inlineinherited

◆ getRemainderCoefficients() [2/2]

template<class SeriesT >

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

inlineinherited

◆ getRightDomain()

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

inlinevirtualinherited

◆ getStep()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

ScalarType capd::pdes::PdeSolver< SeriesT, StepControlT >::getStep ( )

inline

◆ getStepControl()

const StepControlType& capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::getStepControl ( ) const

inlineinherited

◆ getVectorField()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

VectorFieldType& capd::pdes::PdeSolver< SeriesT, StepControlT >::getVectorField ( )

inline

◆ hessian()

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

inlinevirtualinherited

◆ highOrderEnclosure() [1/2]

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::highOrderEnclosure

protected

◆ highOrderEnclosure() [2/2]

template<class SeriesT , class StepControlT >

template<class EncType >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::highOrderEnclosure	(	const EncType &	X,
		EncType &	enc
	)

protected

◆ initEncloseOneStep()

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::initEncloseOneStep	(	const FiniteVectorType &	x0,
		const VectorType &	x
	)

protected

this function realizes initial computation usd in both for C^0 and C^1 algorithms

◆ initRemainderCoefficients()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::initRemainderCoefficients	(	ScalarType	,
		const VectorType &	,
		unsigned
	)

inline

◆ isStepChangeAllowed()

bool capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::isStepChangeAllowed ( ) const

inlineinherited

◆ jet()

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

inlinevirtualinherited

◆ makeSelfConsistentBound() [1/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::makeSelfConsistentBound ( C1Data enc )

inlineprotected

◆ makeSelfConsistentBound() [2/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::makeSelfConsistentBound ( VectorArray & enc )

inlineprotected

◆ oneStepDerivativeOfNumericalMethod()

template<class SeriesT >

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

inlinevirtualinherited

◆ onOffStepControl()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::onOffStepControl ( bool _onOffStepControl )

inlineinherited

◆ operator()() [1/3]

template<class SeriesT >

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

inlinevirtualinherited

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

◆ operator()() [2/3]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

template<typename SetType >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::operator() ( SetType & set )

inline

◆ operator()() [3/3]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

template<typename SetType >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::operator()	(	SetType &	set,
		SetType &	result
	)

inline

Computes image of the set (in set's representation) and stores it in the result set.

Parameters

[in]	set	C^0 or C^1 set representing initial conditions
[out]	result	on return contains image of the set

◆ operator[]()

template<class SeriesT >

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

inlinevirtualinherited

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

◆ predictEnclosure() [1/3]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::predictEnclosure	(	C1Data	X,
		C1Data	enc,
		ScalarType	R,
		ScalarType	I,
		ScalarType	IP
	)

inlineprotected

◆ predictEnclosure() [2/3]

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::predictEnclosure	(	const VectorArray &	X,
		VectorArray &	enc,
		FiniteVectorType &	rem,
		ScalarType	R,
		ScalarType	I,
		ScalarType	IP
	)

protected

this function is used to predict enclosure for C^0 part and for finite number of column in C^1 algorithm

◆ predictEnclosure() [3/3]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::predictEnclosure	(	const VectorArray &	X,
		VectorArray &	enc,
		ScalarType	R,
		ScalarType	I,
		ScalarType	IP
	)

inlineprotected

◆ remainder()

template<class SeriesT >

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

inlinevirtualinherited

◆ remainderCoefficient()

template<class SeriesT >

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

inherited

◆ saveCurrentSet() [1/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::saveCurrentSet ( const capd::diffAlgebra::TimeRange< ScalarType > & )

inlineprotected

◆ saveCurrentSet() [2/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::saveCurrentSet ( const capd::dynset::C1Set< MatrixType > & set )

inlineprotected

◆ scaleRemByStepPower() [1/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::scaleRemByStepPower	(	C1Data	enc,
		ScalarType	s
	)

inlineprotected

◆ scaleRemByStepPower() [2/2]

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::scaleRemByStepPower	(	const VectorArray &	enc,
		ScalarType	s
	)

inlineprotected

◆ setAbsoluteTolerance()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::setAbsoluteTolerance ( TolScalarType tol )

inlineinherited

◆ 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

◆ setInitialCondition()

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::setInitialCondition	(	const FiniteVectorType &	x0,
		const VectorType &	x,
		CurveType &	curve
	)

protected

◆ setInitJet()

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

inlineinherited

◆ setInitMatrix() [1/2]

void capd::diffAlgebra::CurveInterface< capd::IMatrix >::setInitMatrix ( const MatrixType & )

inlineinherited

◆ setInitMatrix() [2/2]

template<class SeriesT >

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

inlineinherited

◆ setMaxStep()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::setMaxStep ( SeriesT::ScalarType maxStep )

inlineinherited

◆ setRelativeTolerance()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::setRelativeTolerance ( TolScalarType tol )

inlineinherited

◆ setStep()

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

void capd::pdes::PdeSolver< SeriesT, StepControlT >::setStep ( ScalarType h )

inline

◆ setStepControl()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::setStepControl ( const StepControlType & stepControl )

inlineinherited

◆ sumTaylorSeriesOfLeadingModes()

template<class SeriesT , class StepControlT >

void capd::pdes::PdeSolver< SeriesT, StepControlT >::sumTaylorSeriesOfLeadingModes	(	size_type	m,
		VectorType &	x,
		FiniteVectorType &	o_phi,
		FiniteVectorType &	o_rem,
		MatrixType &	o_jacPhi
	)

protected

computes output from one step of both C^0 and C^1 algorithms, that is o_phi, o_jacPhi and o_rem

◆ turnOffStepControl()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::turnOffStepControl ( )

inlineinherited

◆ turnOnStepControl()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::turnOnStepControl ( )

inlineinherited

◆ valueAtCenter()

template<class SeriesT >

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

inlinevirtualinherited

Member Data Documentation

◆ initMatrix

template<class SeriesT >

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

protectedinherited

◆ m_absoluteTolerance

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::m_absoluteTolerance

protectedinherited

◆ m_coefficients

template<class SeriesT >

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

protectedinherited

◆ m_coefficientsAtCenter

template<class SeriesT >

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

protectedinherited

◆ m_deltaX

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

FiniteVectorType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_deltaX

protected

◆ m_dyxCoefficients

template<class SeriesT >

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

protectedinherited

◆ m_dyxPhi

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

MatrixType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_dyxPhi

protected

◆ m_dyxRem

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

MatrixType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_dyxRem

protected

◆ m_dyxRemainderCoefficients

template<class SeriesT >

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

protectedinherited

◆ m_fixedTimeStep

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

ScalarType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_fixedTimeStep

protected

◆ m_implicitCurve

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

CurveType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_implicitCurve

protected

◆ m_jacPhi

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

MatrixType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_jacPhi

protected

◆ m_jacRem

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

MatrixType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_jacRem

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

protectedinherited

◆ m_matrixRemainderCoefficients

template<class SeriesT >

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

protectedinherited

◆ m_maxStep

SeriesT::ScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::m_maxStep

protectedinherited

◆ m_numberOfExplicitColumns

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

int capd::pdes::PdeSolver< SeriesT, StepControlT >::m_numberOfExplicitColumns

protected

◆ m_onOffStepControl

bool capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::m_onOffStepControl

protectedinherited

◆ m_order

template<class SeriesT >

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

protectedinherited

◆ m_phi

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

FiniteVectorType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_phi

protected

◆ m_relativeTolerance

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::m_relativeTolerance

protectedinherited

◆ m_rem

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

FiniteVectorType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_rem

protected

◆ m_remainderCoefficients

template<class SeriesT >

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

protectedinherited

◆ m_right

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

protectedinherited

domain

◆ m_step

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

ScalarType capd::pdes::PdeSolver< SeriesT, StepControlT >::m_step

protected

◆ m_stepControl

StepControlType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , SeriesT::ScalarType >::m_stepControl

protectedinherited

◆ m_vectorField

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

VectorFieldType& capd::pdes::PdeSolver< SeriesT, StepControlT >::m_vectorField

protected

◆ predicted_dyxRem

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

std::vector<FiniteVectorType> capd::pdes::PdeSolver< SeriesT, StepControlT >::predicted_dyxRem

protected

◆ predicted_jacRem

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

std::vector<FiniteVectorType> capd::pdes::PdeSolver< SeriesT, StepControlT >::predicted_jacRem

protected

◆ predicted_rem

template<class SeriesT , class StepControlT = capd::dynsys::ILastTermsStepControl>

FiniteVectorType capd::pdes::PdeSolver< SeriesT, StepControlT >::predicted_rem

protected

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

capd/pdes/PdeSolver.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ C1Data

◆ CurveType

◆ FiniteVectorType

◆ HessianType

◆ JetType

◆ MatrixArray

◆ MatrixType

◆ Real

◆ ScalarType

◆ size_type

◆ SolutionCurve

◆ StepControlType

◆ VectorArray

◆ VectorFieldType

◆ VectorType

Constructor & Destructor Documentation

◆ PdeSolver()

◆ ~PdeSolver()

Member Function Documentation

◆ adjustTimeStep()

◆ checkRemainderInclusion() [1/3]

◆ checkRemainderInclusion() [2/3]

◆ checkRemainderInclusion() [3/3]

◆ computeImplicitCoefficients()

◆ computeODECoefficients() [1/2]

◆ computeODECoefficients() [2/2]

◆ computeTimeStep()

◆ derivative()

◆ domainErrorMessage()

◆ encloseC0Map()

◆ encloseC1Map()

◆ eval()

◆ getAbsoluteTolerance()

◆ getAllocatedOrder()

◆ getCenter()

◆ getCoefficients() [1/2]

◆ getCoefficients() [2/2]

◆ getCoefficientsAtCenter() [1/2]

◆ getCoefficientsAtCenter() [2/2]

◆ getCoeffNorm()

◆ getCurve() [1/2]

◆ getCurve() [2/2]

◆ getDyxCoefficients() [1/2]

◆ getDyxCoefficients() [2/2]

◆ getDyxRemainderCoefficients() [1/2]

◆ getDyxRemainderCoefficients() [2/2]

◆ getEffectiveTolerance()

◆ getImplicitCurve()

◆ getLeftDomain()

◆ getMatrixCoefficients() [1/2]

◆ getMatrixCoefficients() [2/2]

◆ getMatrixRemainderCoefficients() [1/2]

◆ getMatrixRemainderCoefficients() [2/2]

◆ getMaxStep()

◆ getRelativeTolerance()

◆ getRemainderCoefficients() [1/2]

◆ getRemainderCoefficients() [2/2]

◆ getRightDomain()

◆ getStep()

◆ getStepControl()

◆ getVectorField()

◆ hessian()

◆ highOrderEnclosure() [1/2]

◆ highOrderEnclosure() [2/2]

◆ initEncloseOneStep()

◆ initRemainderCoefficients()

◆ isStepChangeAllowed()

◆ jet()

◆ makeSelfConsistentBound() [1/2]

◆ makeSelfConsistentBound() [2/2]

◆ oneStepDerivativeOfNumericalMethod()

◆ onOffStepControl()

◆ operator()() [1/3]