CAPD::DynSys Library  6.0.0
capd::pdes::C1DoubletonSetGeometricTail< Policies > Class Template Reference

#include <capd/pdes/C1DoubletonSetGeometricTail.h>

Public Types

typedef capd::pdes::GeometricBound< capd::intervalVectorType
 
typedef VectorType::MatrixType MatrixType
 
typedef MatrixType::RowVectorType FiniteVectorType
 
typedef MatrixType::ScalarType ScalarType
 
typedef MatrixType::size_type size_type
 
typedef capd::vectalg::MaxNorm< FiniteVectorType, MatrixTypeNormType
 
typedef capd::dynset::C1DoubletonSet< MatrixType, PoliciesFiniteDimensionalBaseSet
 
typedef C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet< MatrixType, Policies > > BaseSet
 
typedef capd::dynset::C1Set< MatrixType >::SetType SetType
 
typedef capd::pdes::PdeSolver< VectorTypeDynSysType
 
typedef capd::dynset::DoubletonData< MatrixTypeData
 
typedef Policies Policy
 
typedef std::vector< VectorTypeVectorArray
 
typedef DynSysType::MatrixArray MatrixArray
 
typedef capd::geomset::CenteredDoubletonSet< MatrixT > C0BaseSet
 
typedef capd::geomset::MatrixDoubletonSet< MatrixT > C1BaseSet
 
typedef BaseSet::ColumnVectorType ColumnVectorType
 
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

 C1DoubletonSetGeometricTail (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())
 
 C1DoubletonSetGeometricTail (const VectorType &x, const FiniteVectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())
 
 C1DoubletonSetGeometricTail (const VectorType &x, const MatrixType &C, const FiniteVectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())
 
 C1DoubletonSetGeometricTail (const VectorType &x, const MatrixType &C, const FiniteVectorType &r0, const MatrixType &B, const FiniteVectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())
 
 C1DoubletonSetGeometricTail (const VectorType &x, const FiniteDimensionalBaseSet &set)
 
void move (DynSysType &dynsys)
 computes image of the set after one step/iterate of the dynamical system More...
 
void move (DynSysType &dynsys, C1DoubletonSetGeometricTail &result) const
 computes image of the set after one step/iterate of the dynamical system and stores it in result More...
 
std::string name () const
 returns set's name More...
 
void initC1 ()
 
const VectorTypeind (VectorArray &J, int j) const
 
const VectorTypeind (MatrixArray &J, int j) const
 
template<class Container >
ScalarType getVyxNorm (Container &J) const
 Here we compute operator norm of f:R^n\to l_\infty In R^n we assume l_2 norm. Hence, operator norm is given by supremum of l_2 norms of rows. This can be also bouned by supremum of l_1 norms of rows. More...
 
void setMaxBlockSize (int newMaxBlockSize)
 
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...
 
void initMove (C0DoubletonSetGeometricTail &result) const
 
void finalizeMove (C0DoubletonSetGeometricTail &result) const
 
void move (DynSysType &dynsys, C0DoubletonSetGeometricTail &result) const
 computes image of the set after one step/iterate of the dynamical system and stores it in result More...
 
void move (DynSysType &dynsys, C1DoubletonSet &result) const
 computes image of the set after one step/iterate of the dynamical system and stores it in result More...
 
ScalarType evalAt (const Functional &f) const
 This method computes value of functor f at interval vector represented by this set. More...
 
VectorType affineTransformation (const MatrixType &A, const VectorType &c) 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...
 
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...
 
 operator VectorType () const
 
const VectorTypegetCurrentSeries () const
 
void setLastEnclosure (const VectorType &enc)
 
const VectorTypegetLastEnclosure () const
 
std::string show () const
 returns a set detailed information More...
 
const MatrixTypeget_R0 () const
 
const MatrixTypeget_R0 () const
 
const ScalarTypegetElement_R0 (size_type i, size_type j) const
 
const ScalarTypegetElement_R0 (size_type i, size_type j) const
 
VectorType getRow_R0 (size_type i) const
 
VectorType getRow_R0 (size_type i) const
 
ColumnVectorType getColumn_R0 (size_type j) const
 
ColumnVectorType getColumn_R0 (size_type j) const
 
const MatrixTypeget_Cjac () const
 
const MatrixTypeget_Cjac () const
 
const ScalarTypegetElement_Cjac (size_type i, size_type j) const
 
const ScalarTypegetElement_Cjac (size_type i, size_type j) const
 
VectorType getRow_Cjac (size_type i) const
 
VectorType getRow_Cjac (size_type i) const
 
ColumnVectorType getColumn_Cjac (size_type j) const
 
ColumnVectorType getColumn_Cjac (size_type j) const
 
const ScalarType getCurrentTime () const
 
ScalarTyperefCurrentTime ()
 
void setCurrentTime (const ScalarType &t)
 
const MatrixT & getLastMatrixEnclosure () const
 
virtual operator MatrixT () const
 returns an enclosure of derivative in the canonical coordinates More...
 
virtual operator MatrixT::RowVectorType () const
 returns an enclosure of the set in the canonical coordinates More...
 
void setCurrentSet (const MatrixT::RowVectorType &x)
 
std::string toString () const
 returns set detailed information More...
 
std::string toString () const
 returns set detailed information 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 ()
 
void setToIdentity (size_type dim)
 
void setToIdentity ()
 sets the set to identity More...
 
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)
 
 operator MatrixType () const
 
virtual MatrixType affineMatrixTransformation (const MatrixType &) const
 returns image of the set after affine transformation More...
 
void set_R0 (const MatrixType &R0)
 
void setElement_R0 (size_type i, size_type j, const ScalarType &s)
 
template<typename VectorT >
void setRow_R0 (size_type i, const VectorT &v)
 
template<typename VectorT >
void setColumn_R0 (size_type j, const VectorT &v)
 
void set_Cjac (const MatrixType &C)
 
void setElement_Cjac (size_type i, size_type j, const ScalarType &s)
 
template<typename VectorT >
void setRow_Cjac (size_type i, const VectorT &v)
 
template<typename VectorT >
void setColumn_Cjac (size_type j, const VectorT &v)
 
const MatrixTypeget_D () const
 
const ScalarTypegetElement_D (size_type i, size_type j) const
 
VectorType getRow_D (size_type i) const
 
ColumnVectorType getColumn_D (size_type j) const
 
void set_D (const MatrixType &Bjac)
 
void setElement_D (size_type i, size_type j, const ScalarType &s)
 
template<typename VectorT >
void setRow_D (size_type i, const VectorT &v)
 
template<typename VectorT >
void setColumn_D (size_type j, const VectorT &v)
 
const MatrixTypeget_R () const
 
const ScalarTypegetElement_R (size_type i, size_type j) const
 
VectorType getRow_R (size_type i) const
 
ColumnVectorType getColumn_R (size_type j) const
 
void set_R (const MatrixType &Bjac)
 
void setElement_R (size_type i, size_type j, const ScalarType &s)
 
template<typename VectorT >
void setRow_R (size_type i, const VectorT &v)
 
template<typename VectorT >
void setColumn_R (size_type j, const VectorT &v)
 
const MatrixTypeget_invBjac () const
 
const MatrixTypeget_Bjac () const
 
const ScalarTypegetElement_Bjac (size_type i, size_type j) const
 
VectorType getRow_Bjac (size_type i) const
 
ColumnVectorType getColumn_Bjac (size_type j) const
 
void set_Bjac (const MatrixType &Bjac)
 
void setElement_Bjac (size_type i, size_type j, const ScalarType &s)
 
template<typename VectorT >
void setRow_Bjac (size_type i, const VectorT &v)
 
template<typename VectorT >
void setColumn_Bjac (size_type j, const VectorT &v)
 

Static Public Member Functions

static void move (const C1BaseSet &set, C1BaseSet &result, MatrixType &bound, Data &data)
 this computes next representation of the set given computed one-step enclosure of the form y + jacPhi*deltaX + rem More...
 
static const size_type degree ()
 

Public Attributes

VectorArray m_dyxId
 
VectorArray m_dyx
 
ScalarType Dxx
 
ScalarType Dyx
 
ScalarType encDyx
 
FiniteVectorType Dy
 
FiniteVectorType encDy
 
MatrixType encDxx
 
bool printLog = false
 
int maxBlockSize = 500
 
int counter
 
VectorType m_x
 x is a center of the set More...
 
VectorType m_r
 r is a interval set in given coordinate system More...
 
VectorType m_enc
 
VectorType m_currentSeries
 
VectorType m_tmp
 
MatrixType m_R0
 r0 is a interval set in given coordinate system that represents 'Lipschitz' part More...
 
MatrixType m_Cjac
 C is a coordinate system of the 'Lipschitz' part. More...
 
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...
 
MatrixType m_B
 B is a coordinate system. More...
 
MatrixType m_invB
 
MatrixType m_D
 D is a center of the set. More...
 
MatrixType m_Bjac
 Bjac is a coordinate system. More...
 
MatrixType m_R
 R is a interval set in given coordinate system. More...
 
MatrixType m_invBjac
 
MatrixType jacRem
 
MatrixType jacEnc
 
VectorType x
 
VectorType deltaX
 
VectorType y
 
VectorType deltaY
 
VectorType rem
 
VectorType enc
 
MatrixType jacPhi
 
MatrixType deltaC
 
MatrixType B
 

Protected Member Functions

void setLastEnclosure (const MatrixT::RowVectorType &enc)
 
void setLastMatrixEnclosure (const MatrixT &M)
 

Protected Attributes

ScalarType m_currentTime
 
MatrixT m_currentMatrix
 
MatrixT m_lastMatrixEnclosure
 
MatrixT::RowVectorType m_currentSet
 
MatrixT::RowVectorType m_lastEnclosure
 

Member Typedef Documentation

◆ BaseSet

◆ C0BaseSet

template<typename MatrixT , typename Policies >
typedef capd::geomset::CenteredDoubletonSet<MatrixT> capd::dynset::C1DoubletonSet< MatrixT, Policies >::C0BaseSet
inherited

◆ C1BaseSet

template<typename MatrixT , typename Policies >
typedef capd::geomset::MatrixDoubletonSet<MatrixT> capd::dynset::C1DoubletonSet< MatrixT, Policies >::C1BaseSet
inherited

◆ ColumnVectorType [1/2]

template<typename MatrixT >
typedef BaseSet::ColumnVectorType capd::geomset::CenteredDoubletonSet< MatrixT >::ColumnVectorType
inherited

◆ ColumnVectorType [2/2]

template<typename MatrixT >
typedef BaseSet::ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::ColumnVectorType
inherited

◆ Data

◆ DynSysType

◆ FiniteDimensionalBaseSet

◆ FiniteVectorType

template<typename Policies >
typedef MatrixType::RowVectorType capd::pdes::C1DoubletonSetGeometricTail< Policies >::FiniteVectorType

◆ MatrixArray

template<typename Policies >
typedef DynSysType::MatrixArray capd::pdes::C1DoubletonSetGeometricTail< Policies >::MatrixArray

◆ MatrixType

template<typename Policies >
typedef VectorType::MatrixType capd::pdes::C1DoubletonSetGeometricTail< Policies >::MatrixType

◆ NormType

◆ Policy

template<typename Policies >
typedef Policies capd::pdes::C1DoubletonSetGeometricTail< Policies >::Policy

◆ 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 Policies >
typedef MatrixType::ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::ScalarType

◆ SetType

◆ size_type

template<typename Policies >
typedef MatrixType::size_type capd::pdes::C1DoubletonSetGeometricTail< Policies >::size_type

◆ VectorArray

template<typename Policies >
typedef std::vector<VectorType> capd::pdes::C1DoubletonSetGeometricTail< Policies >::VectorArray

◆ VectorType

Constructor & Destructor Documentation

◆ C1DoubletonSetGeometricTail() [1/5]

◆ C1DoubletonSetGeometricTail() [2/5]

template<typename Policies >
capd::pdes::C1DoubletonSetGeometricTail< Policies >::C1DoubletonSetGeometricTail ( const VectorType x,
const FiniteVectorType r0,
ScalarType  t = TypeTraits<ScalarType>::zero() 
)
inline

◆ C1DoubletonSetGeometricTail() [3/5]

template<typename Policies >
capd::pdes::C1DoubletonSetGeometricTail< Policies >::C1DoubletonSetGeometricTail ( const VectorType x,
const MatrixType C,
const FiniteVectorType r0,
ScalarType  t = TypeTraits<ScalarType>::zero() 
)
inline

◆ C1DoubletonSetGeometricTail() [4/5]

template<typename Policies >
capd::pdes::C1DoubletonSetGeometricTail< Policies >::C1DoubletonSetGeometricTail ( const VectorType x,
const MatrixType C,
const FiniteVectorType r0,
const MatrixType B,
const FiniteVectorType r,
ScalarType  t = TypeTraits<ScalarType>::zero() 
)
inline

◆ C1DoubletonSetGeometricTail() [5/5]

template<typename Policies >
capd::pdes::C1DoubletonSetGeometricTail< Policies >::C1DoubletonSetGeometricTail ( const VectorType x,
const FiniteDimensionalBaseSet set 
)
inline

Member Function Documentation

◆ affineTransformation() [1/2]

VectorType capd::pdes::C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet< GeometricBound< capd::interval >::MatrixType, Policies > >::affineTransformation ( const MatrixType A,
const VectorType c 
) const
inlinevirtualinherited

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 )

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

◆ affineTransformation() [2/2]

template<typename Policies >
DoubletonSet< MatrixType >::VectorType capd::geomset::DoubletonSet< MatrixType >::affineTransformation

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 )

◆ degree()

template<typename MatrixT >
static const size_type capd::dynset::C1Set< MatrixT >::degree ( )
inlinestaticinherited

◆ dimension()

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

returns dimension of a set

◆ evalAffineFunctional()

ScalarType capd::pdes::C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet< GeometricBound< capd::interval >::MatrixType, Policies > >::evalAffineFunctional ( const VectorType gradient,
const VectorType x0 
) const
inlinevirtualinherited

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.

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

◆ evalAt()

This method computes value of functor f at interval vector represented by this set.

◆ finalizeMove()

◆ get_B()

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

◆ get_Bjac()

template<typename MatrixT >
const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_Bjac ( ) const
inlineinherited

◆ get_C()

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

returns matrix C

◆ get_Cjac() [1/2]

template<typename MatrixT , typename Policies >
const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_Cjac
inlineinherited

◆ get_Cjac() [2/2]

template<typename MatrixT >
const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_Cjac ( ) const
inlineinherited

◆ get_D()

template<typename MatrixT >
const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_D ( ) const
inlineinherited

◆ get_invB()

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

◆ get_invBjac()

template<typename MatrixT >
const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_invBjac ( ) const
inlineinherited

◆ get_r()

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

◆ get_R()

template<typename MatrixT >
const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_R ( ) const
inlineinherited

◆ get_R0() [1/2]

template<typename MatrixT , typename Policies >
const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_R0
inlineinherited

◆ get_r0()

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

returns r0

◆ get_R0() [2/2]

template<typename MatrixT >
const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_R0 ( ) 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

◆ getColumn_Bjac()

template<typename MatrixT >
ColumnVectorType capd::geomset::MatrixAffineSet< MatrixT >::getColumn_Bjac ( size_type  j) const
inlineinherited

◆ getColumn_C()

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

returns j-th column of C

◆ getColumn_Cjac() [1/2]

template<typename MatrixT , typename Policies >
ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_Cjac
inlineinherited

◆ getColumn_Cjac() [2/2]

template<typename MatrixT >
ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_Cjac ( size_type  j) const
inlineinherited

◆ getColumn_D()

template<typename MatrixT >
ColumnVectorType capd::geomset::MatrixAffineSet< MatrixT >::getColumn_D ( size_type  j) const
inlineinherited

◆ getColumn_R()

template<typename MatrixT >
ColumnVectorType capd::geomset::MatrixAffineSet< MatrixT >::getColumn_R ( size_type  j) const
inlineinherited

◆ getColumn_R0() [1/2]

template<typename MatrixT , typename Policies >
ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_R0
inlineinherited

◆ getColumn_R0() [2/2]

template<typename MatrixT >
ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_R0 ( size_type  j) const
inlineinherited

◆ getCurrentSeries()

◆ getCurrentTime()

const ScalarType capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::getCurrentTime ( ) const
inlineinherited

◆ getElement_B()

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

◆ getElement_Bjac()

template<typename MatrixT >
const ScalarType& capd::geomset::MatrixAffineSet< MatrixT >::getElement_Bjac ( 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
inlineinherited

returns element C[i][j]

◆ getElement_Cjac() [1/2]

template<typename MatrixT , typename Policies >
const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_Cjac
inlineinherited

◆ getElement_Cjac() [2/2]

template<typename MatrixT >
const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_Cjac ( size_type  i,
size_type  j 
) const
inlineinherited

◆ getElement_D()

template<typename MatrixT >
const ScalarType& capd::geomset::MatrixAffineSet< MatrixT >::getElement_D ( 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_R()

template<typename MatrixT >
const ScalarType& capd::geomset::MatrixAffineSet< MatrixT >::getElement_R ( size_type  i,
size_type  j 
) const
inlineinherited

◆ getElement_r0()

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

returns i-th coordinate of r0

◆ getElement_R0() [1/2]

template<typename MatrixT , typename Policies >
const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_R0
inlineinherited

◆ getElement_R0() [2/2]

template<typename MatrixT >
const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_R0 ( size_type  i,
size_type  j 
) const
inlineinherited

◆ getElement_x()

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

◆ getLastEnclosure()

◆ getLastMatrixEnclosure()

template<class MatrixT >
const MatrixT& capd::dynset::C1EnclosureHolder< MatrixT >::getLastMatrixEnclosure ( ) const
inlineinherited

◆ getRow_B()

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

◆ getRow_Bjac()

template<typename MatrixT >
VectorType capd::geomset::MatrixAffineSet< MatrixT >::getRow_Bjac ( size_type  i) const
inlineinherited

◆ getRow_C()

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

returns i-th row of C

◆ getRow_Cjac() [1/2]

template<typename MatrixT , typename Policies >
VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_Cjac
inlineinherited

◆ getRow_Cjac() [2/2]

template<typename MatrixT >
VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_Cjac ( size_type  i) const
inlineinherited

◆ getRow_D()

template<typename MatrixT >
VectorType capd::geomset::MatrixAffineSet< MatrixT >::getRow_D ( size_type  i) const
inlineinherited

◆ getRow_R()

template<typename MatrixT >
VectorType capd::geomset::MatrixAffineSet< MatrixT >::getRow_R ( size_type  i) const
inlineinherited

◆ getRow_R0() [1/2]

template<typename MatrixT , typename Policies >
VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_R0
inlineinherited

◆ getRow_R0() [2/2]

template<typename MatrixT >
VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_R0 ( size_type  i) const
inlineinherited

◆ getVyxNorm()

template<typename Policies >
template<class Container >
ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::getVyxNorm ( Container &  J) const
inline

Here we compute operator norm of f:R^n\to l_\infty In R^n we assume l_2 norm. Hence, operator norm is given by supremum of l_2 norms of rows. This can be also bouned by supremum of l_1 norms of rows.

first check finite number of rows, where the coefficients are given explicitly.

check the first row which is bounded uniformly as a geometric series.

◆ ind() [1/2]

template<typename Policies >
const VectorType& capd::pdes::C1DoubletonSetGeometricTail< Policies >::ind ( MatrixArray J,
int  j 
) const
inline

◆ ind() [2/2]

template<typename Policies >
const VectorType& capd::pdes::C1DoubletonSetGeometricTail< Policies >::ind ( VectorArray J,
int  j 
) const
inline

◆ initC1()

template<typename Policies >
void capd::pdes::C1DoubletonSetGeometricTail< Policies >::initC1 ( )
inline

◆ initMove()

◆ move() [1/4]

template<typename MatrixType , typename Policies >
void capd::dynset::C1DoubletonSet< MatrixType, Policies >::move ( const C1BaseSet set,
C1BaseSet result,
MatrixType bound,
Data data 
)
staticinherited

this computes next representation of the set given computed one-step enclosure of the form y + jacPhi*deltaX + rem

this computes next representation of the set given computed one-step enclosure of the form y + jacPhi*deltaX + rem

◆ move() [2/4]

template<typename Policies >
void capd::pdes::C1DoubletonSetGeometricTail< Policies >::move ( DynSysType dynsys)
inlinevirtual

computes image of the set after one step/iterate of the dynamical system

Reimplemented from capd::dynset::C1DoubletonSet< MatrixT, Policies >.

◆ move() [3/4]

computes image of the set after one step/iterate of the dynamical system and stores it in result

◆ move() [4/4]

template<typename MatrixType , typename Policies >
void capd::dynset::C1DoubletonSet< MatrixType, Policies >::move ( DynSysType dynsys,
C1DoubletonSet< MatrixT, Policies > &  result 
) const
inherited

computes image of the set after one step/iterate of the dynamical system and stores it in result

◆ name()

template<typename Policies >
std::string capd::pdes::C1DoubletonSetGeometricTail< Policies >::name ( ) const
inlinevirtual

returns set's name

Reimplemented from capd::dynset::C1DoubletonSet< MatrixT, Policies >.

◆ operator MatrixT()

template<class MatrixT >
virtual capd::dynset::C1EnclosureHolder< MatrixT >::operator MatrixT ( ) const
inlinevirtualinherited

returns an enclosure of derivative in the canonical coordinates

◆ operator MatrixT::RowVectorType()

virtual capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::operator MatrixT::RowVectorType ( ) const
inlinevirtualinherited

returns an enclosure of the set in the canonical coordinates

◆ operator MatrixType()

template<typename MatrixT >
capd::geomset::MatrixDoubletonSet< MatrixT >::operator MatrixType ( ) const
inherited

◆ operator VectorType()

◆ refCurrentTime()

ScalarType& capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::refCurrentTime ( )
inlineinherited

◆ set_B()

template<typename MatrixT >
void capd::geomset::AffineSet< MatrixT >::set_B ( const MatrixType B)
inlineinherited

◆ set_Bjac()

template<typename MatrixT >
void capd::geomset::MatrixAffineSet< MatrixT >::set_Bjac ( const MatrixType Bjac)
inlineinherited

◆ set_C()

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

sets matrix C:= B

◆ set_Cjac()

template<typename MatrixT >
void capd::geomset::MatrixDoubletonSet< MatrixT >::set_Cjac ( const MatrixType C)
inlineinherited

◆ set_D()

template<typename MatrixT >
void capd::geomset::MatrixAffineSet< MatrixT >::set_D ( const MatrixType Bjac)
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::MatrixAffineSet< MatrixT >::set_R ( const MatrixType Bjac)
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::MatrixDoubletonSet< MatrixT >::set_R0 ( const MatrixType R0)
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_Bjac()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixAffineSet< MatrixT >::setColumn_Bjac ( 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

◆ setColumn_Cjac()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixDoubletonSet< MatrixT >::setColumn_Cjac ( size_type  j,
const VectorT &  v 
)
inlineinherited

◆ setColumn_D()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixAffineSet< MatrixT >::setColumn_D ( size_type  j,
const VectorT &  v 
)
inlineinherited

◆ setColumn_R()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixAffineSet< MatrixT >::setColumn_R ( size_type  j,
const VectorT &  v 
)
inlineinherited

◆ setColumn_R0()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixDoubletonSet< MatrixT >::setColumn_R0 ( size_type  j,
const VectorT &  v 
)
inlineinherited

◆ setCurrentSet()

void capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::setCurrentSet ( const VectorT &  x)
inlineinherited

◆ setCurrentTime()

void capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::setCurrentTime ( const ScalarType t)
inlineinherited

◆ setElement_B()

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

◆ setElement_Bjac()

template<typename MatrixT >
void capd::geomset::MatrixAffineSet< MatrixT >::setElement_Bjac ( 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_Cjac()

template<typename MatrixT >
void capd::geomset::MatrixDoubletonSet< MatrixT >::setElement_Cjac ( size_type  i,
size_type  j,
const ScalarType s 
)
inlineinherited

◆ setElement_D()

template<typename MatrixT >
void capd::geomset::MatrixAffineSet< MatrixT >::setElement_D ( 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_R()

template<typename MatrixT >
void capd::geomset::MatrixAffineSet< MatrixT >::setElement_R ( size_type  i,
size_type  j,
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_R0()

template<typename MatrixT >
void capd::geomset::MatrixDoubletonSet< MatrixT >::setElement_R0 ( size_type  i,
size_type  j,
const ScalarType s 
)
inlineinherited

◆ setElement_x()

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

◆ setLastEnclosure() [1/2]

void capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::setLastEnclosure ( const VectorT &  enc)
inlineprotectedinherited

◆ setLastEnclosure() [2/2]

◆ setLastMatrixEnclosure()

template<class MatrixT >
void capd::dynset::C1EnclosureHolder< MatrixT >::setLastMatrixEnclosure ( const MatrixT &  M)
inlineprotectedinherited

◆ setMaxBlockSize()

template<typename Policies >
void capd::pdes::C1DoubletonSetGeometricTail< Policies >::setMaxBlockSize ( int  newMaxBlockSize)
inline

◆ setRow_B()

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

◆ setRow_Bjac()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixAffineSet< MatrixT >::setRow_Bjac ( 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

◆ setRow_Cjac()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixDoubletonSet< MatrixT >::setRow_Cjac ( size_type  i,
const VectorT &  v 
)
inlineinherited

◆ setRow_D()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixAffineSet< MatrixT >::setRow_D ( size_type  i,
const VectorT &  v 
)
inlineinherited

◆ setRow_R()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixAffineSet< MatrixT >::setRow_R ( size_type  i,
const VectorT &  v 
)
inlineinherited

◆ setRow_R0()

template<typename MatrixT >
template<typename VectorT >
void capd::geomset::MatrixDoubletonSet< MatrixT >::setRow_R0 ( size_type  i,
const VectorT &  v 
)
inlineinherited

◆ setToIdentity()

template<typename MatrixT >
void capd::geomset::AffineSet< MatrixT >::setToIdentity ( )
inlineinherited

◆ show()

template<typename MatrixType , typename Policies >
std::string capd::dynset::C1DoubletonSet< MatrixType, Policies >::show ( void  ) const
virtualinherited

returns a set detailed information

Implements capd::dynset::AbstractSet< MatrixT::RowVectorType >.

Member Data Documentation

◆ counter

template<typename Policies >
int capd::pdes::C1DoubletonSetGeometricTail< Policies >::counter

◆ Dxx

template<typename Policies >
ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::Dxx

◆ Dy

◆ Dyx

template<typename Policies >
ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::Dyx

◆ encDxx

template<typename Policies >
MatrixType capd::pdes::C1DoubletonSetGeometricTail< Policies >::encDxx

◆ encDy

template<typename Policies >
FiniteVectorType capd::pdes::C1DoubletonSetGeometricTail< Policies >::encDy

◆ encDyx

template<typename Policies >
ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::encDyx

◆ m_B

template<typename MatrixT >
MatrixType capd::geomset::AffineSet< MatrixT >::m_B
inherited

B is a coordinate system.

◆ m_Bjac

template<typename MatrixT >
MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_Bjac
inherited

Bjac 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_Cjac

template<typename MatrixT , typename Policies >
MatrixType capd::geomset::MatrixDoubletonSet< MatrixT >::m_Cjac
inherited

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

◆ m_currentMatrix

template<class MatrixT >
MatrixT capd::dynset::C1EnclosureHolder< MatrixT >::m_currentMatrix
protectedinherited

◆ m_currentSeries

◆ m_currentSet

MatrixT::RowVectorType capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::m_currentSet
protectedinherited

◆ m_currentTime

ScalarType capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::m_currentTime
protectedinherited

◆ m_D

template<typename MatrixT >
MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_D
inherited

D is a center of the set.

◆ m_dyx

template<typename Policies >
VectorArray capd::pdes::C1DoubletonSetGeometricTail< Policies >::m_dyx

◆ m_dyxId

template<typename Policies >
VectorArray capd::pdes::C1DoubletonSetGeometricTail< Policies >::m_dyxId

◆ m_enc

◆ m_invB

template<typename MatrixT >
MatrixType capd::geomset::AffineSet< MatrixT >::m_invB
inherited

◆ m_invBjac

template<typename MatrixT >
MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_invBjac
inherited

◆ m_lastEnclosure

MatrixT::RowVectorType capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::m_lastEnclosure
protectedinherited

◆ m_lastMatrixEnclosure

template<class MatrixT >
MatrixT capd::dynset::C1EnclosureHolder< MatrixT >::m_lastMatrixEnclosure
protectedinherited

◆ m_R

template<typename MatrixT >
MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_R
inherited

R is a interval set in given coordinate system.

◆ m_r

template<typename Policies >
VectorType capd::geomset::AffineSet< MatrixT >::m_r

r is a interval set in given coordinate system

◆ m_R0

template<typename MatrixT , typename Policies >
MatrixType capd::geomset::MatrixDoubletonSet< MatrixT >::m_R0
inherited

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

◆ 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_tmp

◆ m_x

template<typename Policies >
VectorType capd::geomset::AffineSet< MatrixT >::m_x

x is a center of the set

◆ maxBlockSize

template<typename Policies >
int capd::pdes::C1DoubletonSetGeometricTail< Policies >::maxBlockSize = 500

◆ printLog

template<typename Policies >
bool capd::pdes::C1DoubletonSetGeometricTail< Policies >::printLog = false

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