CAPD DynSys Library 5.2.0
capd::geomset::DoubletonSet< MatrixT > Class Template Reference

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< typenameScalarType::BoundType >::other RealMatrix
 
typedef VectorType::template rebind< typenameScalarType::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
 
DoubletonSetoperator= (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+C*r0+intersection(B*r,Q*q). Then f(X) = M*(X-x0) can be computed as M*(x-x0) + (M*C)*r0 + intersection( M*B)*r, (M*Q)*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+C*r0+B*r. Then f(X) = grad*(X-x0) can be computed as grad*(x-x0) + (grad*C)*r0 + (grad*B)*r. More...
 
std::string toString () const
 returns set detailed information More...
 
virtual std::string name () const
 returns set's name More...
 
const VectorTypeget_r0 () const
 returns r0 More...
 
const ScalarTypegetElement_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 MatrixTypeget_C () const
 returns matrix C More...
 
const ScalarTypegetElement_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 VectorTypeget_x () const
 
const ScalarTypegetElement_x (int i) const
 
void set_x (const VectorType &x)
 
void setElement_x (size_type i, const ScalarType &s)
 
const VectorTypeget_r () const
 
const ScalarTypegetElement_r (size_type i) const
 
void set_r (const VectorType &r)
 
void setElement_r (size_type i, const ScalarType &s)
 
const MatrixTypeget_B () const
 
const MatrixTypeget_invB () const
 
void setToIdentity ()
 
const ScalarTypegetElement_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<typenameScalarType::BoundType>::other capd::geomset::AffineSet< MatrixT >::RealMatrix
inherited

◆ RealVector

template<typename MatrixT >
typedef VectorType::template rebind<typenameScalarType::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_C()

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

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()

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

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()

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

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()

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

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()

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

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()

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

returns i-th row of C

◆ name()

◆ 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_C()

template<typename MatrixT >
void capd::geomset::DoubletonSet< MatrixT >::set_C ( const MatrixType B)
inline

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)
inline

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 
)
inline

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 
)
inline

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 
)
inline

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 
)
inline

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

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