Doubleton representation of the form x0 + C*r0 + B*r . More...

#include <capd/geomset/DoubletonSet.h>

Public Types
typedef AffineSet< MatrixT >	BaseSet

typedef BaseSet::MatrixType	MatrixType

typedef BaseSet::VectorType	VectorType

typedef BaseSet::ColumnVectorType	ColumnVectorType

typedef BaseSet::ScalarType	ScalarType

typedef MatrixType::size_type	size_type

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

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

Public Member Functions
	DoubletonSet (size_type)
	x:=0, r0:=0, C:=Id, r:=0, r:=Id More...

	DoubletonSet (const VectorType &x)
	x:=mid(v), r0:=[-radius(v),radius(v)], C:=Id, r:=0, r:=Id More...

	DoubletonSet (const VectorType &r0, bool)
	x:=0, r0:=r0, C:=Id, r:=0, r:=Id More...

	DoubletonSet (const VectorType &x, const VectorType &r0)
	x:=x, r0:=r0, C:=Id, r:=0, r:=Id More...

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

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

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

	operator VectorType () const

DoubletonSet &	operator= (const VectorType &v)

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 the vector represented by this set. This set is represented as doubleton X=x+Cr0+Br. Then f(X) = grad(X-x0) can be computed as grad(x-x0) + (gradC)r0 + (gradB)r. More...

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

virtual std::string	name () const
	returns set's name 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_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 Attributes
VectorType	m_r0
	r0 is a interval set in given coordinate system that represents 'Lipschitz' part More...

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

Detailed Description

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

Doubleton representation of the form x0 + C*r0 + B*r .

We define sets representation of the form

x + C*r0 + B * r

where

the vector x is a center,
the matrices C and B are coordinate systems,
the vector r0 is a product of intervals and represents the set in a given coordinate system,
the vector r is used mainly to store computational errors

Member Typedef Documentation

◆ BaseSet

template<typename MatrixT >

typedef AffineSet<MatrixT> capd::geomset::DoubletonSet< MatrixT >::BaseSet

◆ ColumnVectorType

template<typename MatrixT >

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

◆ MatrixType

template<typename MatrixT >

typedef BaseSet::MatrixType capd::geomset::DoubletonSet< 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 BaseSet::ScalarType capd::geomset::DoubletonSet< MatrixT >::ScalarType

◆ size_type

template<typename MatrixT >

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

◆ VectorType

template<typename MatrixT >

typedef BaseSet::VectorType capd::geomset::DoubletonSet< 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_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_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

◆ getElement_B()

template<typename MatrixT >

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

inlineinherited

◆ getElement_r()

template<typename MatrixT >

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

inlineinherited

◆ 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

◆ name()

template<typename MatrixT >

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

inlinevirtual

returns set's name

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

Reimplemented in capd::pdes::C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet< GeometricBound::MatrixType, Policies > >, capd::dynset::C0HODoubletonSet< MatrixT, Policies >, capd::dynset::C1DoubletonSet< MatrixT, Policies >, capd::dynset::C1DoubletonSet< GeometricBound::MatrixType, Policies >, capd::dynset::C0DoubletonSet< MatrixT, Policies >, capd::dynset::C0DoubletonSet< GeometricBound::MatrixType, capd::C0Rect2Policies >, capd::dynset::C2DoubletonSet< MatrixT, Policies >, capd::geomset::CenteredDoubletonSet< MatrixT >, capd::geomset::CenteredTripletonSet< MatrixT >, capd::geomset::CenteredDoubletonSet< GeometricBound::MatrixType >, and capd::dynset::C11Rect2Set< MatrixT >.

◆ operator VectorType()

template<typename MatrixT >

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

◆ set_B()

template<typename MatrixT >

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

inlineinherited

◆ 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_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

◆ setElement_B()

template<typename MatrixT >

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

inlineinherited

◆ setElement_r()

template<typename MatrixT >

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

inlineinherited

◆ 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

◆ 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

B is a coordinate system.

◆ m_C

template<typename MatrixT >

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

protected

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

◆ m_invB

template<typename MatrixT >

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

◆ m_r

template<typename MatrixT >

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

r is a interval set in given coordinate system

◆ m_r0

template<typename MatrixT >

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

protected

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

x is a center of the set

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

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

Member Typedef Documentation

◆ BaseSet

◆ ColumnVectorType

◆ MatrixType

◆ RealMatrix

◆ RealVector

◆ ScalarType

◆ size_type

◆ VectorType

Member Function Documentation

◆ dimension()

◆ get_B()

◆ get_invB()

◆ get_r()

◆ get_x()

◆ getColumn_B()

◆ getElement_B()

◆ getElement_r()

◆ getElement_x()

◆ getRow_B()

◆ name()

◆ operator VectorType()

◆ set_B()

◆ set_invB()

◆ set_r()

◆ set_x()

◆ setColumn_B()

◆ setElement_B()

◆ setElement_r()

◆ setElement_x()

◆ setRow_B()

◆ setToIdentity()

Member Data Documentation

◆ m_B

◆ m_C

◆ m_invB

◆ m_r

◆ m_r0

◆ m_x

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