Class CenteredTripletonSet represents a subset of R^n in the following form. More...

#include <capd/geomset/CenteredTripletonSet.h>

Public Types
typedef MatrixT	MatrixType

typedef MatrixT::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef MatrixType::size_type	size_type

typedef capd::geomset::CenteredDoubletonSet< MatrixT >	BaseSet

typedef BaseSet::ColumnVectorType	ColumnVectorType

typedef MatrixType::template rebind< typename ScalarType::BoundType >::other	RealMatrix

typedef VectorType::template rebind< typename ScalarType::BoundType >::other	RealVector

Public Member Functions
	CenteredTripletonSet (const VectorType &x)

	CenteredTripletonSet (const VectorType &x, const VectorType &r0)

	CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0)

	CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r)

	CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r)

virtual VectorType	affineTransformation (const MatrixType &M, const VectorType &x0) const
	This method computes value of an affine map f at interval vector represented by this set. This set is represented as tripleton X=x+Cr0+intersection(Br,Qq). Then f(X) = M(X-x0) can be computed as M(x-x0) + (MC)r0 + intersection( MB)r, (MQ)*q ) More...

virtual ScalarType	evalAffineFunctional (const VectorType &gradient, const VectorType &x0) const
	This method computes value of an affine functional f at interval vector represented by this set. This set is represented as tripleton X=x+Cr0+intersection(Br,Qq). Then f(X) = grad(X-x0) can be computed as grad(x-x0) + (gradC)r0 + intersection( gradB)r, (gradQ)*q ) More...

	operator VectorType () const

std::string	name () const
	returns set's name More...

const VectorType &	get_r0 () const
	returns r0 More...

const ScalarType &	getElement_r0 (size_type i) const
	returns i-th coordinate of r0 More...

const MatrixType &	get_C () const
	returns matrix C More...

const ScalarType &	getElement_C (size_type i, size_type j) const
	returns element C[i][j] More...

VectorType	getRow_C (size_type i) const
	returns i-th row of C More...

ColumnVectorType	getColumn_C (size_type j) const
	returns j-th column of C More...

std::string	toString () const
	returns set detailed information More...

const VectorType &	get_r0 () const
	returns r0 More...

const ScalarType &	getElement_r0 (size_type i) const
	returns i-th coordinate of r0 More...

void	set_r0 (const VectorType &r)
	sets r0 More...

void	setElement_r0 (size_type i, const ScalarType &s)
	sets i-th coordinate of r0 More...

const MatrixType &	get_C () const
	returns matrix C More...

const ScalarType &	getElement_C (size_type i, size_type j) const
	returns element C[i][j] More...

VectorType	getRow_C (size_type i) const
	returns i-th row of C More...

ColumnVectorType	getColumn_C (size_type j) const
	returns j-th column of C More...

void	set_C (const MatrixType &B)
	sets matrix C:= B More...

void	setElement_C (size_type i, size_type j, const ScalarType &s)
	sets C[i][j] := s More...

template<typename VectorT >
void	setRow_C (size_type i, const VectorT &v)
	sets i-th row of C to v More...

template<typename VectorT >
void	setColumn_C (size_type j, const VectorT &v)
	sets j-th columne of C to v More...

size_type	dimension () const
	returns dimension of a set More...

const VectorType &	get_x () const

const ScalarType &	getElement_x (int i) const

void	set_x (const VectorType &x)

void	setElement_x (size_type i, const ScalarType &s)

const VectorType &	get_r () const

const ScalarType &	getElement_r (size_type i) const

void	set_r (const VectorType &r)

void	setElement_r (size_type i, const ScalarType &s)

const MatrixType &	get_B () const

const MatrixType &	get_invB () const

void	setToIdentity ()

const ScalarType &	getElement_B (size_type i, size_type j) const

VectorType	getRow_B (size_type i) const

ColumnVectorType	getColumn_B (size_type j) const

void	set_B (const MatrixType &B)

void	set_invB (const MatrixType &B)

void	setElement_B (size_type i, size_type j, const ScalarType &s)

template<typename VectorT >
void	setRow_B (size_type i, const VectorT &v)

template<typename VectorT >
void	setColumn_B (size_type j, const VectorT &v)

Public Attributes
VectorType	m_q

MatrixType	m_Q

MatrixType	m_invQ

MatrixType	m_C
	C is a coordinate system of the 'Lipschitz' part. More...

VectorType	m_r0
	r0 is a interval set in given coordinate system that represents 'Lipschitz' part More...

VectorType	m_x
	x is a center of the set More...

MatrixType	m_B
	B is a coordinate system. More...

MatrixType	m_invB

VectorType	m_r
	r is a interval set in given coordinate system More...

Protected Member Functions
	CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r, const MatrixType &Q, const VectorType &q)

void	copyQ ()

Detailed Description

template<typename MatrixT>
class capd::geomset::CenteredTripletonSet< MatrixT >

Class CenteredTripletonSet represents a subset of R^n in the following form.

x + C*r0 + intersection(B*r , Q*q )

where x is a point vector C,B,Q are point matrices, where B and Q are invertible and Q is close to orthogonal r0,r are interval vectors

Moreover it stores rigorous inverse matrices of B and Q

Member Typedef Documentation

◆ BaseSet

template<typename MatrixT >

typedef capd::geomset::CenteredDoubletonSet<MatrixT> capd::geomset::CenteredTripletonSet< MatrixT >::BaseSet

◆ ColumnVectorType

template<typename MatrixT >

typedef BaseSet::ColumnVectorType capd::geomset::CenteredDoubletonSet< MatrixT >::ColumnVectorType

inherited

◆ MatrixType

template<typename MatrixT >

typedef MatrixT capd::geomset::CenteredTripletonSet< MatrixT >::MatrixType

◆ RealMatrix

template<typename MatrixT >

typedef MatrixType::template rebind<typename ScalarType::BoundType>::other capd::geomset::AffineSet< MatrixT >::RealMatrix

inherited

◆ RealVector

template<typename MatrixT >

typedef VectorType::template rebind<typename ScalarType::BoundType>::other capd::geomset::AffineSet< MatrixT >::RealVector

inherited

◆ ScalarType

template<typename MatrixT >

typedef MatrixType::ScalarType capd::geomset::CenteredTripletonSet< MatrixT >::ScalarType

◆ size_type

template<typename MatrixT >

typedef MatrixType::size_type capd::geomset::CenteredTripletonSet< MatrixT >::size_type

◆ VectorType

template<typename MatrixT >

typedef MatrixT::RowVectorType capd::geomset::CenteredTripletonSet< MatrixT >::VectorType

Member Function Documentation

◆ dimension()

template<typename MatrixT >

size_type capd::geomset::AffineSet< MatrixT >::dimension ( ) const

inlineinherited

returns dimension of a set

◆ get_B()

template<typename MatrixT >

const MatrixType& capd::geomset::AffineSet< MatrixT >::get_B ( ) const

inlineinherited

◆ get_C() [1/2]

template<typename MatrixT >

const MatrixType& capd::geomset::DoubletonSet< MatrixT >::get_C

inline

returns matrix C

◆ get_C() [2/2]

template<typename MatrixT >

const MatrixType& capd::geomset::DoubletonSet< MatrixT >::get_C ( ) const

inlineinherited

returns matrix C

◆ get_invB()

template<typename MatrixT >

const MatrixType& capd::geomset::AffineSet< MatrixT >::get_invB ( ) const

inlineinherited

◆ get_r()

template<typename MatrixT >

const VectorType& capd::geomset::AffineSet< MatrixT >::get_r ( ) const

inlineinherited

◆ get_r0() [1/2]

template<typename MatrixT >

const VectorType& capd::geomset::DoubletonSet< MatrixT >::get_r0

inline

returns r0

◆ get_r0() [2/2]

template<typename MatrixT >

const VectorType& capd::geomset::DoubletonSet< MatrixT >::get_r0 ( ) const

inlineinherited

returns r0

◆ get_x()

template<typename MatrixT >

const VectorType& capd::geomset::AffineSet< MatrixT >::get_x ( ) const

inlineinherited

◆ getColumn_B()

template<typename MatrixT >

ColumnVectorType capd::geomset::AffineSet< MatrixT >::getColumn_B ( size_type j ) const

inlineinherited

◆ getColumn_C() [1/2]

template<typename MatrixT >

ColumnVectorType capd::geomset::DoubletonSet< MatrixT >::getColumn_C

inline

returns j-th column of C

◆ getColumn_C() [2/2]

template<typename MatrixT >

ColumnVectorType capd::geomset::DoubletonSet< MatrixT >::getColumn_C ( size_type j ) const

inlineinherited

returns j-th column of C

◆ getElement_B()

template<typename MatrixT >

const ScalarType& capd::geomset::AffineSet< MatrixT >::getElement_B	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ getElement_C() [1/2]

template<typename MatrixT >

const ScalarType& capd::geomset::DoubletonSet< MatrixT >::getElement_C

inline

returns element C[i][j]

◆ getElement_C() [2/2]

template<typename MatrixT >

const ScalarType& capd::geomset::DoubletonSet< MatrixT >::getElement_C	(	size_type	i,
		size_type	j
	)		const

inlineinherited

returns element C[i][j]

◆ getElement_r()

template<typename MatrixT >

const ScalarType& capd::geomset::AffineSet< MatrixT >::getElement_r ( size_type i ) const

inlineinherited

◆ getElement_r0() [1/2]

template<typename MatrixT >

const ScalarType& capd::geomset::DoubletonSet< MatrixT >::getElement_r0

inline

returns i-th coordinate of r0

◆ getElement_r0() [2/2]

template<typename MatrixT >

const ScalarType& capd::geomset::DoubletonSet< MatrixT >::getElement_r0 ( size_type i ) const

inlineinherited

returns i-th coordinate of r0

◆ getElement_x()

template<typename MatrixT >

const ScalarType& capd::geomset::AffineSet< MatrixT >::getElement_x ( int i ) const

inlineinherited

◆ getRow_B()

template<typename MatrixT >

VectorType capd::geomset::AffineSet< MatrixT >::getRow_B ( size_type i ) const

inlineinherited

◆ getRow_C() [1/2]

template<typename MatrixT >

VectorType capd::geomset::DoubletonSet< MatrixT >::getRow_C

inline

returns i-th row of C

◆ getRow_C() [2/2]

template<typename MatrixT >

VectorType capd::geomset::DoubletonSet< MatrixT >::getRow_C ( size_type i ) const

inlineinherited

returns i-th row of C

◆ name()

template<typename MatrixT >

std::string capd::geomset::CenteredTripletonSet< MatrixT >::name ( ) const

inlinevirtual

returns set's name

Reimplemented from capd::geomset::CenteredDoubletonSet< MatrixT >.

◆ operator VectorType()

template<typename MatrixT >

capd::geomset::CenteredTripletonSet< MatrixT >::operator VectorType ( ) const

inline

◆ set_B()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_B ( const MatrixType & B )

inlineinherited

◆ set_C()

template<typename MatrixT >

void capd::geomset::DoubletonSet< MatrixT >::set_C ( const MatrixType & B )

inlineinherited

sets matrix C:= B

◆ set_invB()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_invB ( const MatrixType & B )

inlineinherited

◆ set_r()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_r ( const VectorType & r )

inlineinherited

◆ set_r0()

template<typename MatrixT >

void capd::geomset::DoubletonSet< MatrixT >::set_r0 ( const VectorType & r )

inlineinherited

sets r0

◆ set_x()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_x ( const VectorType & x )

inlineinherited

◆ setColumn_B()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::AffineSet< MatrixT >::setColumn_B	(	size_type	j,
		const VectorT &	v
	)

inlineinherited

◆ setColumn_C()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::DoubletonSet< MatrixT >::setColumn_C	(	size_type	j,
		const VectorT &	v
	)

inlineinherited

sets j-th columne of C to v

◆ setElement_B()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setElement_B	(	size_type	i,
		size_type	j,
		const ScalarType &	s
	)

inlineinherited

◆ setElement_C()

template<typename MatrixT >

void capd::geomset::DoubletonSet< MatrixT >::setElement_C	(	size_type	i,
		size_type	j,
		const ScalarType &	s
	)

inlineinherited

sets C[i][j] := s

◆ setElement_r()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setElement_r	(	size_type	i,
		const ScalarType &	s
	)

inlineinherited

◆ setElement_r0()

template<typename MatrixT >

void capd::geomset::DoubletonSet< MatrixT >::setElement_r0	(	size_type	i,
		const ScalarType &	s
	)

inlineinherited

sets i-th coordinate of r0

◆ setElement_x()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setElement_x	(	size_type	i,
		const ScalarType &	s
	)

inlineinherited

◆ setRow_B()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::AffineSet< MatrixT >::setRow_B	(	size_type	i,
		const VectorT &	v
	)

inlineinherited

◆ setRow_C()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::DoubletonSet< MatrixT >::setRow_C	(	size_type	i,
		const VectorT &	v
	)

inlineinherited

sets i-th row of C to v

◆ setToIdentity()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setToIdentity ( )

inlineinherited

Member Data Documentation

◆ m_B

template<typename MatrixT >

MatrixType capd::geomset::AffineSet< MatrixT >::m_B

inherited

B is a coordinate system.

◆ m_C

template<typename MatrixT >

MatrixType capd::geomset::DoubletonSet< MatrixT >::m_C

inherited

C is a coordinate system of the 'Lipschitz' part.

◆ m_invB

template<typename MatrixT >

MatrixType capd::geomset::AffineSet< MatrixT >::m_invB

inherited

◆ m_invQ

template<typename MatrixT >

MatrixType capd::geomset::CenteredTripletonSet< MatrixT >::m_invQ

◆ m_q

template<typename MatrixT >

VectorType capd::geomset::CenteredTripletonSet< MatrixT >::m_q

◆ m_Q

template<typename MatrixT >

MatrixType capd::geomset::CenteredTripletonSet< MatrixT >::m_Q

◆ m_r

template<typename MatrixT >

VectorType capd::geomset::AffineSet< MatrixT >::m_r

inherited

r is a interval set in given coordinate system

◆ m_r0

template<typename MatrixT >

VectorType capd::geomset::DoubletonSet< MatrixT >::m_r0

inherited

r0 is a interval set in given coordinate system that represents 'Lipschitz' part

◆ m_x

template<typename MatrixT >

VectorType capd::geomset::AffineSet< MatrixT >::m_x

inherited

x is a center of the set

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

capd/geomset/CenteredTripletonSet.h
capd/geomset/CenteredTripletonSet.hpp

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Detailed Description

template<typename MatrixT> class capd::geomset::CenteredTripletonSet< MatrixT >

Member Typedef Documentation

◆ BaseSet

◆ ColumnVectorType

◆ MatrixType

◆ RealMatrix

◆ RealVector

◆ ScalarType

◆ size_type

◆ VectorType

Member Function Documentation

◆ dimension()

◆ get_B()

◆ get_C() [1/2]

◆ get_C() [2/2]

◆ get_invB()

◆ get_r()

◆ get_r0() [1/2]

◆ get_r0() [2/2]

◆ get_x()

◆ getColumn_B()

◆ getColumn_C() [1/2]

◆ getColumn_C() [2/2]

◆ getElement_B()

◆ getElement_C() [1/2]

◆ getElement_C() [2/2]

◆ getElement_r()

◆ getElement_r0() [1/2]

◆ getElement_r0() [2/2]

◆ getElement_x()

◆ getRow_B()

◆ getRow_C() [1/2]

◆ getRow_C() [2/2]

◆ name()

◆ operator VectorType()

◆ set_B()

◆ set_C()

◆ set_invB()

◆ set_r()

◆ set_r0()

◆ set_x()

◆ setColumn_B()

◆ setColumn_C()

◆ setElement_B()

◆ setElement_C()

◆ setElement_r()

◆ setElement_r0()

◆ setElement_x()

◆ setRow_B()

◆ setRow_C()

◆ setToIdentity()

Member Data Documentation

◆ m_B

◆ m_C

◆ m_invB

◆ m_invQ

◆ m_q

◆ m_Q

◆ m_r

◆ m_r0

◆ m_x

template<typename MatrixT>
class capd::geomset::CenteredTripletonSet< MatrixT >