CAPD::DynSys Library
6.0.0
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#include <capd/pdes/C1DoubletonSetGeometricTail.h>
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 VectorType & | ind (VectorArray &J, int j) const |
const VectorType & | ind (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 VectorType & | getCurrentSeries () const |
void | setLastEnclosure (const VectorType &enc) |
const VectorType & | getLastEnclosure () const |
std::string | show () const |
returns a set detailed information More... | |
const MatrixType & | get_R0 () const |
const MatrixType & | get_R0 () const |
const ScalarType & | getElement_R0 (size_type i, size_type j) const |
const ScalarType & | getElement_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 MatrixType & | get_Cjac () const |
const MatrixType & | get_Cjac () const |
const ScalarType & | getElement_Cjac (size_type i, size_type j) const |
const ScalarType & | getElement_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 |
ScalarType & | refCurrentTime () |
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 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 () |
void | setToIdentity (size_type dim) |
void | setToIdentity () |
sets the set to identity More... | |
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) |
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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) |
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void | setRow_Cjac (size_type i, const VectorT &v) |
template<typename VectorT > | |
void | setColumn_Cjac (size_type j, const VectorT &v) |
const MatrixType & | get_D () const |
const ScalarType & | getElement_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) |
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void | setRow_D (size_type i, const VectorT &v) |
template<typename VectorT > | |
void | setColumn_D (size_type j, const VectorT &v) |
const MatrixType & | get_R () const |
const ScalarType & | getElement_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 MatrixType & | get_invBjac () const |
const MatrixType & | get_Bjac () const |
const ScalarType & | getElement_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 () |
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 |
typedef C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet<MatrixType,Policies> > capd::pdes::C1DoubletonSetGeometricTail< Policies >::BaseSet |
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typedef capd::dynset::DoubletonData<MatrixType> capd::pdes::C1DoubletonSetGeometricTail< Policies >::Data |
typedef capd::pdes::PdeSolver<VectorType> capd::pdes::C1DoubletonSetGeometricTail< Policies >::DynSysType |
typedef capd::dynset::C1DoubletonSet<MatrixType,Policies> capd::pdes::C1DoubletonSetGeometricTail< Policies >::FiniteDimensionalBaseSet |
typedef MatrixType::RowVectorType capd::pdes::C1DoubletonSetGeometricTail< Policies >::FiniteVectorType |
typedef DynSysType::MatrixArray capd::pdes::C1DoubletonSetGeometricTail< Policies >::MatrixArray |
typedef VectorType::MatrixType capd::pdes::C1DoubletonSetGeometricTail< Policies >::MatrixType |
typedef capd::vectalg::MaxNorm<FiniteVectorType,MatrixType> capd::pdes::C1DoubletonSetGeometricTail< Policies >::NormType |
typedef Policies capd::pdes::C1DoubletonSetGeometricTail< Policies >::Policy |
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typedef MatrixType::ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::ScalarType |
typedef capd::dynset::C1Set<MatrixType>::SetType capd::pdes::C1DoubletonSetGeometricTail< Policies >::SetType |
typedef MatrixType::size_type capd::pdes::C1DoubletonSetGeometricTail< Policies >::size_type |
typedef std::vector<VectorType> capd::pdes::C1DoubletonSetGeometricTail< Policies >::VectorArray |
typedef capd::pdes::GeometricBound<capd::interval> capd::pdes::C1DoubletonSetGeometricTail< Policies >::VectorType |
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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 >.
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 )
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returns dimension of a set
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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 >.
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This method computes value of functor f at interval vector represented by this set.
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returns matrix C
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returns r0
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returns j-th column of C
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returns element C[i][j]
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returns i-th coordinate of r0
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returns i-th row of C
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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.
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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
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computes image of the set after one step/iterate of the dynamical system
Reimplemented from capd::dynset::C1DoubletonSet< MatrixT, Policies >.
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computes image of the set after one step/iterate of the dynamical system and stores it in result
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computes image of the set after one step/iterate of the dynamical system and stores it in result
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returns set's name
Reimplemented from capd::dynset::C1DoubletonSet< MatrixT, Policies >.
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returns an enclosure of derivative in the canonical coordinates
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returns an enclosure of the set in the canonical coordinates
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sets matrix C:= B
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sets r0
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sets j-th columne of C to v
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sets C[i][j] := s
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sets i-th coordinate of r0
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sets i-th row of C to v
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returns a set detailed information
Implements capd::dynset::AbstractSet< MatrixT::RowVectorType >.
int capd::pdes::C1DoubletonSetGeometricTail< Policies >::counter |
ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::Dxx |
FiniteVectorType capd::pdes::C1DoubletonSetGeometricTail< Policies >::Dy |
ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::Dyx |
MatrixType capd::pdes::C1DoubletonSetGeometricTail< Policies >::encDxx |
FiniteVectorType capd::pdes::C1DoubletonSetGeometricTail< Policies >::encDy |
ScalarType capd::pdes::C1DoubletonSetGeometricTail< Policies >::encDyx |
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B is a coordinate system.
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Bjac is a coordinate system.
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C is a coordinate system of the 'Lipschitz' part.
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C is a coordinate system of the 'Lipschitz' part.
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D is a center of the set.
VectorArray capd::pdes::C1DoubletonSetGeometricTail< Policies >::m_dyx |
VectorArray capd::pdes::C1DoubletonSetGeometricTail< Policies >::m_dyxId |
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R is a interval set in given coordinate system.
VectorType capd::geomset::AffineSet< MatrixT >::m_r |
r is a interval set in given coordinate system
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r0 is a interval set in given coordinate system that represents 'Lipschitz' part
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r0 is a interval set in given coordinate system that represents 'Lipschitz' part
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VectorType capd::geomset::AffineSet< MatrixT >::m_x |
x is a center of the set
int capd::pdes::C1DoubletonSetGeometricTail< Policies >::maxBlockSize = 500 |
bool capd::pdes::C1DoubletonSetGeometricTail< Policies >::printLog = false |