CAPD DynSys Library 5.2.0
capd::dynset Namespace Reference

Various set representations that can be moved with dynamical systems. More...

Classes

class  AbstractSet
 
class  AffineCoordinateChange
 Affine Coordinate system Change y = y0 + B*(x-x0) More...
 
class  C0AffineSet
 The set is represented as: x + B*r; and is moved by the following method. More...
 
class  C0BallSet
 the set is represented as: x + Ball(r). More...
 
class  C0DoubletonSet
 The set is represented as doubleton: x + C*r0 + B*r; and is moved by the following method. More...
 
class  C0EnclosureHolder
 These classes are used as base classes for all types of C^0-C^n sets. More...
 
class  C0FlowballSet
 
class  C0GraphicalSet
 C0GraphicalSet is an envelope class for any class derived from C0Set. It adds a possibility of an additional Output after each 'move' of the original set. More...
 
class  C0HODoubletonSet
 Class C0HODoubletonSet represents a subset of R^n as doubleton, i.e. More...
 
class  C0HOSet
 This class uses representation of subset of R^n inherited from template parameter. More...
 
class  C0HOTripletonSet
 Class C0HOTripletonSet represents a subset of $ R^n $ in the following form. More...
 
class  C0Set
 Common interface of all sets that stores only C0 information (set position). More...
 
class  C0TripletonSet
 Class C0TripletonSet represents a subset of R^n in the following form. More...
 
class  C11Rect2
 $C^1$ doubleton set with reorganization moved by QR decomposition (3rd method). More...
 
class  C11Rect2Set
 
class  C1AffineSet
 The C1 set is represented as doubleton: x + B*r;. More...
 
struct  C1DoubletonData
 
class  C1DoubletonSet
 The C1 set is represented as doubleton: x + C*r0 + B*r;. More...
 
class  C1EnclosureHolder
 
class  C1GraphicalSet
 C1GraphicalSet is an envelope class for any class derived from C1Set. It adds a possibility of an additional Output after each 'move' of the original set. More...
 
class  C1HOSet
 This class uses representation of subset of R^n inherited from template parameter. More...
 
class  C1Set
 Common interface of all sets that store C1 informations (set position and first derivatives) More...
 
class  C2DoubletonSet
 C2 set in doubleton form. More...
 
class  C2EnclosureHolder
 
class  C2Set
 Common interface of all sets that store C2 information (set position and first and second derivatives) More...
 
class  CanonicalReorganization
 During reorganization we set C and B to Identity and put everything into r0. More...
 
class  CnDoubletonSet
 This set stores vector of derivatives with respect to a multiindex alpha as a doubleton. More...
 
class  CnRect2Set
 Set that stores all derivatives to given order in doubleton form with reorganization moved by QR decomposition method. More...
 
class  CnSet
 Common interface of all sets that store Cn information (set position and derivatives to order n) More...
 
class  CoordinateSystem
 Defines coordinate system. More...
 
class  CoordWiseReorganization
 In this reorganization policy column vector B_i corresponding to the biggest coordinate in r (r_i) replaces vector in C_j the 'closest' to B_i and the r_i is moved to r0. More...
 
class  DefaultPolicy
 
struct  DoubletonData
 This class is a data structure used in implementation of all types of Doubleton and Tripleton sets. More...
 
class  FactorPolicy
 
class  FactorReorganization
 Factor based reorganization. More...
 
class  FullQRWithPivoting
 
struct  HOData
 This class is a data structure used in implementation of all types of HO sets. More...
 
class  IdQRPolicy
 
class  InvBByCFactorReorganization
 Factor based reorganization for C1 sets. More...
 
class  InverseQRPolicy
 
class  NoReorganization
 Reorganization that does nothing. More...
 
class  PartialQRWithPivoting
 
class  QRReorganization
 During reorganization we orthogonalize B. More...
 
class  SelectiveQRWithPivoting
 Vectors are orthogonalized only if they are close to be parallel. More...
 
struct  SetTraits
 
struct  SetTraits< C0Set< MatrixT > >
 Specialization of Traits class. More...
 
struct  SetTraits< C1Set< MatrixT > >
 
struct  SetTraits< C2Set< MatrixT > >
 
struct  SetTraits< CnSet< MatrixT, DEGREE > >
 
class  SwapReorganization
 Reorganization is performed if r is bigger than r0 but in coordinate system of r. More...
 
struct  TripletonData
 

Typedefs

typedef FactorReorganization< FullQRWithPivoting<> > C11Rect2Policies
 In C1Rect2Set both C0 and C1 parts are represented as: x + C*r0 + B*r. More...
 

Functions

template<class DS , class V , class M >
void computePsi (DS &ds, int p, int q, const typename DS::ScalarType &h, V &psi, M &Dpsi)
 This is an algorithm for computation of polynomial part of Hermite-Obreshkov interpolation Used in all HO-sets. More...
 
template<typename MatrixT , typename Policies >
C0TripletonSet< MatrixT, Policies > operator* (const MatrixT &A, const C0TripletonSet< MatrixT, Policies > &s)
 

Detailed Description

Various set representations that can be moved with dynamical systems.

Typedef Documentation

◆ C11Rect2Policies

In C1Rect2Set both C0 and C1 parts are represented as: x + C*r0 + B*r.

where:

  • x - set center
  • C*r0 - 'Lipschitz' part
  • B*r - 'errors' computed via QR method