Module dynset provides various set representations along with algorithms to propagate them using discrete or continuous dynamical systems. Read detailed description of DynSets for more details. More...

Classes
class	capd::dynset::AbstractSet< VectorT >

class	capd::dynset::AffineCoordinateChange< MatrixT >
	Affine Coordinate system Change y = y0 + B*(x-x0) More...

class	capd::dynset::C0AffineSet< MatrixT, Policies >
	The set is represented as: x + B*r; and is moved by the following method. More...

class	capd::dynset::C0BallSet< MatrixT >
	the set is represented as: x + Ball(r). More...

class	capd::dynset::C0DoubletonSet< MatrixT, Policies >
	The set is represented as doubleton: x + Cr0 + Br; and is moved by the following method. More...

class	capd::dynset::C0GraphicalSet< BaseSetT, OutputT >
	C0GraphicalSet is an envelope class for any class derived from C0Set. It adds a possibility of an additional Output after each 'move' of the original set. More...

class	capd::dynset::C0Set< MatrixT >
	Common interface of all sets that stores only C0 information (set position). More...

struct	capd::dynset::SetTraits< C0Set< MatrixT > >
	Specialization of Traits class. More...

class	capd::dynset::C0TripletonSet< MatrixT, Policies >
	Class C0TripletonSet represents a subset of R^n in the following form. More...

class	capd::dynset::C11Rect2< MatrixT, QRPolicy >
	doubleton set with reorganization moved by QR decomposition (3rd method). More...

class	capd::dynset::C1AffineSet< MatrixT, Policies >
	The C1 set is represented as doubleton: x + B*r;. More...

class	capd::dynset::C1DoubletonSet< MatrixT, Policies >
	The C1 set is represented as doubleton: x + Cr0 + Br;. More...

class	capd::dynset::C1GraphicalSet< MatrixT, OutputClass >
	C1GraphicalSet is an envelope class for any class derived from C1Set. It adds a possibility of an additional Output after each 'move' of the original set. More...

class	capd::dynset::C1Set< MatrixT >
	Common interface of all sets that store C1 informations (set position and first derivatives) More...

struct	capd::dynset::SetTraits< C1Set< MatrixT > >

class	capd::dynset::C2DoubletonSet< MatrixT, Policies >
	C2 set in doubleton form. More...

class	capd::dynset::C2Set< MatrixT >
	Common interface of all sets that store C2 information (set position and first and second derivatives) More...

struct	capd::dynset::SetTraits< C2Set< MatrixT > >

class	capd::dynset::CnDoubletonSet< MatrixT, Policies, DEGREE >
	This set stores vector of derivatives with respect to a multiindex alpha as a doubleton. More...

class	capd::dynset::CnRect2Set< MatrixT, Policies, DEGREE >
	Set that stores all derivatives to given order in doubleton form with reorganization moved by QR decomposition method. More...

class	capd::dynset::CnSet< MatrixT, DEGREE >
	Common interface of all sets that store Cn information (set position and derivatives to order n) More...

struct	capd::dynset::SetTraits< CnSet< MatrixT, DEGREE > >

class	capd::dynset::CoordinateSystem< MatrixT >
	Defines coordinate system. More...

class	capd::dynset::IdQRPolicy

class	capd::dynset::DefaultPolicy

struct	capd::dynset::DoubletonData< MatrixT >
	This class is a data structure used in implementation of all types of Doubleton and Tripleton sets. More...

struct	capd::dynset::TripletonData< MatrixT >

struct	capd::dynset::C1DoubletonData< MatrixT >

class	capd::dynset::C0EnclosureHolder< VectorT >
	These classes are used as base classes for all types of C^0-C^n sets. More...

class	capd::dynset::C1EnclosureHolder< MatrixT >

class	capd::dynset::C2EnclosureHolder< MatrixT >

struct	capd::dynset::HOData< BaseData >
	This class is a data structure used in implementation of all types of HO sets. More...

class	capd::dynset::InverseQRPolicy< BasePolicy >

class	capd::dynset::FullQRWithPivoting< BasePolicy >

class	capd::dynset::PartialQRWithPivoting< N, BasePolicy >

class	capd::dynset::SelectiveQRWithPivoting< BasePolicy >
	Vectors are orthogonalized only if they are close to be parallel. More...

class	capd::dynset::CanonicalReorganization< DoubletonT, FactorPolicyT >
	During reorganization we set C and B to Identity and put everything into r0. More...

class	capd::dynset::CoordWiseReorganization< BasePolicy >
	In this reorganization policy column vector B_i corresponding to the biggest coordinate in r (r_i) replaces vector in C_j the 'closest' to B_i and the r_i is moved to r0. More...

class	capd::dynset::InvBByCFactorReorganization< BasePolicy >
	Factor based reorganization for C1 sets. More...

class	capd::dynset::SwapReorganization< BasePolicy >
	Reorganization is performed if r is bigger than r0 but in coordinate system of r. More...

struct	capd::dynset::SetTraits< SetT >
	This class provides a trait of being set of a given type, i.e. More...

Typedefs
typedef MatrixT	capd::dynset::DoubletonData< MatrixT >::MatrixType

typedef MatrixType::RowVectorType	capd::dynset::DoubletonData< MatrixT >::VectorType

typedef MatrixType::ScalarType	capd::dynset::DoubletonData< MatrixT >::ScalarType

typedef MatrixType::size_type	capd::dynset::DoubletonData< MatrixT >::size_type

typedef MatrixT	capd::dynset::TripletonData< MatrixT >::MatrixType

typedef MatrixType::RowVectorType	capd::dynset::TripletonData< MatrixT >::VectorType

typedef MatrixType::ScalarType	capd::dynset::TripletonData< MatrixT >::ScalarType

typedef MatrixType::size_type	capd::dynset::TripletonData< MatrixT >::size_type

typedef MatrixT	capd::dynset::C1DoubletonData< MatrixT >::MatrixType

typedef MatrixType::RowVectorType	capd::dynset::C1DoubletonData< MatrixT >::VectorType

typedef MatrixType::ScalarType	capd::dynset::C1DoubletonData< MatrixT >::ScalarType

typedef MatrixType::size_type	capd::dynset::C1DoubletonData< MatrixT >::size_type

typedef BaseData::MatrixType	capd::dynset::HOData< BaseData >::MatrixType

typedef MatrixType::RowVectorType	capd::dynset::HOData< BaseData >::VectorType

typedef MatrixType::ScalarType	capd::dynset::HOData< BaseData >::ScalarType

typedef MatrixType::size_type	capd::dynset::HOData< BaseData >::size_type

Functions
template<class DS , class V , class M >
void	capd::dynset::computePsi (DS &ds, int p, int q, const typename DS::ScalarType &h, V &psi, M &Dpsi)
	This is an algorithm for computation of polynomial part of Hermite-Obreshkov interpolation Used in all HO-sets. More...

template<typename MatrixT , typename Policies >
C0TripletonSet< MatrixT, Policies >	capd::dynset::operator* (const MatrixT &A, const C0TripletonSet< MatrixT, Policies > &s)

template<class VectorT , class MatrixT >
void	capd::dynset::IdQRPolicy::computeBinvB (MatrixT &B, MatrixT &invB, const VectorT &) const

std::string	capd::dynset::IdQRPolicy::toString () const

std::string	capd::dynset::DefaultPolicy::toString () const

	capd::dynset::DoubletonData< MatrixT >::DoubletonData (size_type dimension)

	capd::dynset::TripletonData< MatrixT >::TripletonData (size_type dimension)

	capd::dynset::C1DoubletonData< MatrixT >::C1DoubletonData (size_type dimension)

	capd::dynset::HOData< BaseData >::HOData (size_type dimension)

void	capd::dynset::HOData< BaseData >::computeC0HORemainder (size_type p, size_type q)

void	capd::dynset::HOData< BaseData >::computeC1HORemainder (size_type p, size_type q, MatrixType &jacRem)

void	capd::dynset::HOData< BaseData >::computeC0HOCoefficients ()

template<class Matrix , class Vector >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::isReorganizationNeeded (const Matrix &invB, const Matrix &C, const Vector &r, const Vector &r0) const

template<class SetType >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::isReorganizationNeeded (const SetType &result) const

template<class SetType >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeIfNeeded (SetType &result) const
	makes reorganization if needed. More...

template<class Matrix , class Vector >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeIfNeeded (Matrix &B, Matrix &invB, Vector &r, Matrix &C, Vector &r0) const

template<class SetType >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::isC1ReorganizationNeeded (const SetType &result) const

template<class Matrix >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::isC1ReorganizationNeeded (const Matrix &invB, const Matrix &C, const Matrix &R, const Matrix &R0) const

template<class Matrix >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeC1IfNeeded (Matrix &B, Matrix &invB, Matrix &R, Matrix &C, Matrix &R0) const

template<class SetType >
bool	capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeC1IfNeeded (SetType &result) const
	makes reorganization if needed. return true if reorganization was performed More...

std::string	capd::dynset::InvBByCFactorReorganization< BasePolicy >::name () const

template<class DynSysT >
void	capd::dynset::CnDoubletonSet< MatrixT, Policies, DEGREE >::move (DynSysT &cndynsys, CnDoubletonSet &result) const

template<class DynSysT >
void	capd::dynset::CnRect2Set< MatrixT, Policies, DEGREE >::move (DynSysT &cndynsys, CnRect2Set &result) const

Variables
VectorType	capd::dynset::DoubletonData< MatrixT >::x

VectorType	capd::dynset::DoubletonData< MatrixT >::deltaX

VectorType	capd::dynset::DoubletonData< MatrixT >::y

VectorType	capd::dynset::DoubletonData< MatrixT >::deltaY

VectorType	capd::dynset::DoubletonData< MatrixT >::rem

VectorType	capd::dynset::DoubletonData< MatrixT >::enc

MatrixType	capd::dynset::DoubletonData< MatrixT >::jacPhi

MatrixType	capd::dynset::DoubletonData< MatrixT >::deltaC

MatrixType	capd::dynset::DoubletonData< MatrixT >::B

VectorType	capd::dynset::TripletonData< MatrixT >::qr

MatrixType	capd::dynset::TripletonData< MatrixT >::Q

MatrixType	capd::dynset::C1DoubletonData< MatrixT >::jacRem

MatrixType	capd::dynset::C1DoubletonData< MatrixT >::jacEnc

VectorType	capd::dynset::HOData< BaseData >::psiPlus

VectorType	capd::dynset::HOData< BaseData >::psiMinus

VectorType	capd::dynset::HOData< BaseData >::pBound

VectorType	capd::dynset::HOData< BaseData >::cBound

MatrixType	capd::dynset::HOData< BaseData >::JPlus

MatrixType	capd::dynset::HOData< BaseData >::JMinus

MatrixType	capd::dynset::HOData< BaseData >::midJMinusInverse

MatrixType	capd::dynset::HOData< BaseData >::T

Detailed Description

Module dynset provides various set representations along with algorithms to propagate them using discrete or continuous dynamical systems. Read detailed description of DynSets for more details.

Typedef Documentation

◆ MatrixType [1/4]

template<class MatrixT >

typedef MatrixT capd::dynset::DoubletonData< MatrixT >::MatrixType

◆ MatrixType [2/4]

template<class BaseData >

typedef BaseData::MatrixType capd::dynset::HOData< BaseData >::MatrixType

◆ MatrixType [3/4]

template<class MatrixT >

typedef MatrixT capd::dynset::TripletonData< MatrixT >::MatrixType

◆ MatrixType [4/4]

template<class MatrixT >

typedef MatrixT capd::dynset::C1DoubletonData< MatrixT >::MatrixType

◆ ScalarType [1/4]

template<class MatrixT >

typedef MatrixType::ScalarType capd::dynset::DoubletonData< MatrixT >::ScalarType

◆ ScalarType [2/4]

template<class BaseData >

typedef MatrixType::ScalarType capd::dynset::HOData< BaseData >::ScalarType

◆ ScalarType [3/4]

template<class MatrixT >

typedef MatrixType::ScalarType capd::dynset::TripletonData< MatrixT >::ScalarType

◆ ScalarType [4/4]

template<class MatrixT >

typedef MatrixType::ScalarType capd::dynset::C1DoubletonData< MatrixT >::ScalarType

◆ size_type [1/4]

template<class MatrixT >

typedef MatrixType::size_type capd::dynset::DoubletonData< MatrixT >::size_type

◆ size_type [2/4]

template<class BaseData >

typedef MatrixType::size_type capd::dynset::HOData< BaseData >::size_type

◆ size_type [3/4]

template<class MatrixT >

typedef MatrixType::size_type capd::dynset::TripletonData< MatrixT >::size_type

◆ size_type [4/4]

template<class MatrixT >

typedef MatrixType::size_type capd::dynset::C1DoubletonData< MatrixT >::size_type

◆ VectorType [1/4]

template<class MatrixT >

typedef MatrixType::RowVectorType capd::dynset::DoubletonData< MatrixT >::VectorType

◆ VectorType [2/4]

template<class BaseData >

typedef MatrixType::RowVectorType capd::dynset::HOData< BaseData >::VectorType

◆ VectorType [3/4]

template<class MatrixT >

typedef MatrixType::RowVectorType capd::dynset::TripletonData< MatrixT >::VectorType

◆ VectorType [4/4]

template<class MatrixT >

typedef MatrixType::RowVectorType capd::dynset::C1DoubletonData< MatrixT >::VectorType

Function Documentation

◆ C1DoubletonData()

template<class MatrixT >

capd::dynset::C1DoubletonData< MatrixT >::C1DoubletonData ( size_type dimension )

inlineexplicit

◆ computeBinvB()

template<class VectorT , class MatrixT >

void capd::dynset::IdQRPolicy::computeBinvB	(	MatrixT &	B,
		MatrixT &	invB,
		const VectorT &
	)		const

inline

◆ computeC0HOCoefficients()

template<class BaseData >

void capd::dynset::HOData< BaseData >::computeC0HOCoefficients ( )

inline

◆ computeC0HORemainder()

template<class BaseData >

void capd::dynset::HOData< BaseData >::computeC0HORemainder	(	size_type	p,
		size_type	q
	)

inline

◆ computeC1HORemainder()

template<class BaseData >

void capd::dynset::HOData< BaseData >::computeC1HORemainder	(	size_type	p,
		size_type	q,
		MatrixType &	jacRem
	)

inline

◆ computePsi()

template<class DS , class V , class M >

void capd::dynset::computePsi	(	DS &	ds,
		int	p,
		int	q,
		const typename DS::ScalarType &	h,
		V &	psi,
		M &	Dpsi
	)

This is an algorithm for computation of polynomial part of Hermite-Obreshkov interpolation Used in all HO-sets.

Assumptions:

Parameters

	ds	dynamical system. We assume that it has computed coefficients for the main part and variational equations
	p,q	two numners such that p+q=order
[out]	psi	computed polynomial interpolation
[out]	Dpsi	derivative of psi wrt

NOTE: In the present implementation order cannot be bigger than 33. This is due to the capacity of long type when compute binomial.

◆ DoubletonData()

template<class MatrixT >

capd::dynset::DoubletonData< MatrixT >::DoubletonData ( size_type dimension )

inlineexplicit

◆ HOData()

template<class BaseData >

capd::dynset::HOData< BaseData >::HOData ( size_type dimension )

inlineexplicit

◆ isC1ReorganizationNeeded() [1/2]

template<typename BasePolicy = DefaultPolicy>

template<class Matrix >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::isC1ReorganizationNeeded	(	const Matrix &	invB,
		const Matrix &	C,
		const Matrix &	R,
		const Matrix &	R0
	)		const

inline

◆ isC1ReorganizationNeeded() [2/2]

template<typename BasePolicy = DefaultPolicy>

template<class SetType >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::isC1ReorganizationNeeded ( const SetType & result ) const

inline

◆ isReorganizationNeeded() [1/2]

template<typename BasePolicy = DefaultPolicy>

template<class Matrix , class Vector >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::isReorganizationNeeded	(	const Matrix &	invB,
		const Matrix &	C,
		const Vector &	r,
		const Vector &	r0
	)		const

inline

◆ isReorganizationNeeded() [2/2]

template<typename BasePolicy = DefaultPolicy>

template<class SetType >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::isReorganizationNeeded ( const SetType & result ) const

inline

◆ move() [1/2]

template<typename MatrixT , typename Policies , __size_type DEGREE>

template<typename DynSysT >

void capd::dynset::CnDoubletonSet< MatrixT, Policies, DEGREE >::move	(	DynSysT &	cndynsys,
		CnDoubletonSet< MatrixT, Policies, DEGREE > &	result
	)		const

◆ move() [2/2]

template<typename MatrixType , typename Policies , __size_type DEGREE>

template<class DynSysT >

void capd::dynset::CnRect2Set< MatrixType, Policies, DEGREE >::move	(	DynSysT &	cndynsys,
		CnRect2Set< MatrixT, Policies, DEGREE > &	result
	)		const

◆ name()

template<typename BasePolicy = DefaultPolicy>

std::string capd::dynset::InvBByCFactorReorganization< BasePolicy >::name ( ) const

inline

◆ operator*()

template<typename MatrixT , typename Policies >

C0TripletonSet< MatrixT, Policies > capd::dynset::operator*	(	const MatrixT &	A,
		const C0TripletonSet< MatrixT, Policies > &	s
	)

◆ reorganizeC1IfNeeded() [1/2]

template<typename BasePolicy = DefaultPolicy>

template<class Matrix >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeC1IfNeeded	(	Matrix &	B,
		Matrix &	invB,
		Matrix &	R,
		Matrix &	C,
		Matrix &	R0
	)		const

inline

◆ reorganizeC1IfNeeded() [2/2]

template<typename BasePolicy = DefaultPolicy>

template<class SetType >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeC1IfNeeded ( SetType & result ) const

inline

makes reorganization if needed. return true if reorganization was performed

◆ reorganizeIfNeeded() [1/2]

template<typename BasePolicy = DefaultPolicy>

template<class Matrix , class Vector >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeIfNeeded	(	Matrix &	B,
		Matrix &	invB,
		Vector &	r,
		Matrix &	C,
		Vector &	r0
	)		const

inline

◆ reorganizeIfNeeded() [2/2]

template<typename BasePolicy = DefaultPolicy>

template<class SetType >

bool capd::dynset::InvBByCFactorReorganization< BasePolicy >::reorganizeIfNeeded ( SetType & result ) const

inline

makes reorganization if needed.

◆ toString() [1/2]

std::string capd::dynset::IdQRPolicy::toString ( ) const

inline

◆ toString() [2/2]

std::string capd::dynset::DefaultPolicy::toString ( ) const

inline

◆ TripletonData()

template<class MatrixT >

capd::dynset::TripletonData< MatrixT >::TripletonData ( size_type dimension )

inlineexplicit

Variable Documentation

◆ B

template<class MatrixT >

MatrixType capd::dynset::DoubletonData< MatrixT >::B

◆ cBound

template<class BaseData >

VectorType capd::dynset::HOData< BaseData >::cBound

◆ deltaC

template<class MatrixT >

MatrixType capd::dynset::DoubletonData< MatrixT >::deltaC

◆ deltaX

template<class MatrixT >

VectorType capd::dynset::DoubletonData< MatrixT >::deltaX

◆ deltaY

template<class MatrixT >

VectorType capd::dynset::DoubletonData< MatrixT >::deltaY

◆ enc

template<class MatrixT >

VectorType capd::dynset::DoubletonData< MatrixT >::enc

◆ jacEnc

template<class MatrixT >

MatrixType capd::dynset::C1DoubletonData< MatrixT >::jacEnc

◆ jacPhi

template<class MatrixT >

MatrixType capd::dynset::DoubletonData< MatrixT >::jacPhi

◆ jacRem

template<class MatrixT >

MatrixType capd::dynset::C1DoubletonData< MatrixT >::jacRem

◆ JMinus

template<class BaseData >

MatrixType capd::dynset::HOData< BaseData >::JMinus

◆ JPlus

template<class BaseData >

MatrixType capd::dynset::HOData< BaseData >::JPlus

◆ midJMinusInverse

template<class BaseData >

MatrixType capd::dynset::HOData< BaseData >::midJMinusInverse

◆ pBound

template<class BaseData >

VectorType capd::dynset::HOData< BaseData >::pBound

◆ psiMinus

template<class BaseData >

VectorType capd::dynset::HOData< BaseData >::psiMinus

◆ psiPlus

template<class BaseData >

VectorType capd::dynset::HOData< BaseData >::psiPlus

◆ Q

template<class MatrixT >

MatrixType capd::dynset::TripletonData< MatrixT >::Q

◆ qr

template<class MatrixT >

VectorType capd::dynset::TripletonData< MatrixT >::qr

◆ rem

template<class MatrixT >

VectorType capd::dynset::DoubletonData< MatrixT >::rem

◆ T

template<class BaseData >

MatrixType capd::dynset::HOData< BaseData >::T

◆ x

template<class MatrixT >

VectorType capd::dynset::DoubletonData< MatrixT >::x

◆ y

template<class MatrixT >

VectorType capd::dynset::DoubletonData< MatrixT >::y

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ MatrixType [1/4]

◆ MatrixType [2/4]

◆ MatrixType [3/4]

◆ MatrixType [4/4]

◆ ScalarType [1/4]

◆ ScalarType [2/4]

◆ ScalarType [3/4]

◆ ScalarType [4/4]

◆ size_type [1/4]

◆ size_type [2/4]

◆ size_type [3/4]

◆ size_type [4/4]

◆ VectorType [1/4]

◆ VectorType [2/4]

◆ VectorType [3/4]

◆ VectorType [4/4]

Function Documentation

◆ C1DoubletonData()

◆ computeBinvB()

◆ computeC0HOCoefficients()

◆ computeC0HORemainder()

◆ computeC1HORemainder()

◆ computePsi()

◆ DoubletonData()

◆ HOData()

◆ isC1ReorganizationNeeded() [1/2]

◆ isC1ReorganizationNeeded() [2/2]

◆ isReorganizationNeeded() [1/2]

◆ isReorganizationNeeded() [2/2]

◆ move() [1/2]

◆ move() [2/2]

◆ name()

◆ operator*()

◆ reorganizeC1IfNeeded() [1/2]

◆ reorganizeC1IfNeeded() [2/2]

◆ reorganizeIfNeeded() [1/2]

◆ reorganizeIfNeeded() [2/2]

◆ toString() [1/2]

◆ toString() [2/2]

◆ TripletonData()

Variable Documentation

◆ B

◆ cBound

◆ deltaC

◆ deltaX

◆ deltaY

◆ enc

◆ jacEnc

◆ jacPhi

◆ jacRem

◆ JMinus

◆ JPlus

◆ midJMinusInverse

◆ pBound

◆ psiMinus

◆ psiPlus

◆ Q

◆ qr

◆ rem

◆ T

◆ x

◆ y