capd::dynsys::Linear3d< MatrixT > Class Template Reference

#include <capd/dynsys/deprecated/Linear3d.h>

Public Types
typedef MatrixT	MatrixType
typedef MatrixType::RowVectorType	VectorType
typedef MatrixType::ScalarType	ScalarType
typedef capd::vectalg::Norm< VectorType, MatrixType >	NormType

Public Member Functions
	Linear3d (const ScalarType &a_a, const ScalarType &a_b, const ScalarType &a_c, const ScalarType &a_d, const ScalarType &a_e, const ScalarType &a_f, const ScalarType &a_g, const ScalarType &a_h, const ScalarType &a_i)
VectorType	Phi (const VectorType &iv) const
MatrixType	JacPhi (const VectorType &iv) const
VectorType	Remainder (const VectorType &iv) const
virtual VectorType	Phi (const ScalarType &t, const VectorType &iv)=0
	Computes value of function (usually numerical scheme for an ODE) at time t and point iv. More...
virtual MatrixType	JacPhi (const ScalarType &t, const VectorType &iv)=0
	Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv. More...
virtual VectorType	Remainder (const ScalarType &t, const VectorType &iv, VectorType &out_enc)=0
	Computes and returns bound for local error of a function (for instance if Phi is finite Taylor series of a map then this method computes bound for Lagrange remainder). If DynSys is an ODE, then out_enc contains enclosure of trajectories over the time step. If the function cannot validate existence of solutions to ODE over the time step, out_enc might be in an inconsistent state. More...
virtual ScalarType	Lipschitz (const ScalarType &t, const VectorType &iv, NormType &n)
	this function returns Lipschitz contants for maps. It should be overriden in classes implementing flows. More...
virtual VectorType	enclosure (const ScalarType &t, const VectorType &x)=0
	Used for ODEs. It verifies the existence of solutions to IVP at time t and set of initial conditions x over the time step. If the function succeeds, a rigorous bound for the trajectories is returned. Otherwise, an exception is thrown. More...
virtual void	encloseC0Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)=0
	For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for: More...
virtual ScalarType	getStep () const
	Returns time step of the dynamical system. By default it returns one - time step for discrete DS (maps). Shall be overridden in classes that implement numerical schemes for ODEs. More...

Protected Attributes
ScalarType	a
ScalarType	b
ScalarType	c
ScalarType	d
ScalarType	e
ScalarType	f
ScalarType	g
ScalarType	h
ScalarType	i

Member Typedef Documentation

MatrixType

template<typename MatrixT >

typedef MatrixT capd::dynsys::Linear3d< MatrixT >::MatrixType

NormType

template<typename MatrixT >

typedef capd::vectalg::Norm<VectorType,MatrixType> capd::dynsys::DynSys< MatrixT >::NormType

inherited

ScalarType

template<typename MatrixT >

typedef MatrixType::ScalarType capd::dynsys::Linear3d< MatrixT >::ScalarType

VectorType

template<typename MatrixT >

typedef MatrixType::RowVectorType capd::dynsys::Linear3d< MatrixT >::VectorType

Constructor & Destructor Documentation

Linear3d()

template<typename MatrixType >

capd::dynsys::Linear3d< MatrixType >::Linear3d ( const ScalarType &  a_a, const ScalarType &  a_b, const ScalarType &  a_c, const ScalarType &  a_d, const ScalarType &  a_e, const ScalarType &  a_f, const ScalarType &  a_g, const ScalarType &  a_h, const ScalarType &  a_i  )

inline

Member Function Documentation

encloseC0Map()

template<typename MatrixT >

virtual void capd::dynsys::DynSys< MatrixT >::encloseC0Map ( const ScalarType &  t, const VectorType &  x, const VectorType &  xx, VectorType &  o_phi, VectorType &  o_rem, VectorType &  o_enc, MatrixType &  o_jacPhi  )

pure virtualinherited

For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for:

• numerical scheme Phi(t,x),
• derivative of numerical scheme D_x Phi(t,xx)
• error of numerical scheme Remainder(t,xx)
• an enclosure for the trajectories over the time step (ODEs only) If the function cannot compute any of the output results, an exception is thrown and the output parameters o_* might be in inconsistent state.

enclosure()

template<typename MatrixT >

virtual VectorType capd::dynsys::DynSys< MatrixT >::enclosure ( const ScalarType &  t, const VectorType &  x  )

pure virtualinherited

Used for ODEs. It verifies the existence of solutions to IVP at time t and set of initial conditions x over the time step. If the function succeeds, a rigorous bound for the trajectories is returned. Otherwise, an exception is thrown.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

getStep()

template<typename MatrixT >

virtual ScalarType capd::dynsys::DynSys< MatrixT >::getStep ( ) const

inlinevirtualinherited

Returns time step of the dynamical system. By default it returns one - time step for discrete DS (maps). Shall be overridden in classes that implement numerical schemes for ODEs.

Reimplemented in capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

JacPhi() [1/2]

template<typename MatrixT >

virtual MatrixType capd::dynsys::DynSys< MatrixT >::JacPhi ( const ScalarType &  t, const VectorType &  iv  )

pure virtualinherited

Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

JacPhi() [2/2]

template<typename MatrixType >

MatrixType capd::dynsys::Linear3d< MatrixType >::JacPhi

(

const VectorType &

iv

)

const

Phi() [1/2]

template<typename MatrixT >

virtual VectorType capd::dynsys::DynSys< MatrixT >::Phi ( const ScalarType &  t, const VectorType &  iv  )

pure virtualinherited

Computes value of function (usually numerical scheme for an ODE) at time t and point iv.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

Phi() [2/2]

template<typename MatrixType >

Linear3d< MatrixType >::VectorType capd::dynsys::Linear3d< MatrixType >::Phi

(

const VectorType &

iv

)

const

Remainder() [1/2]

template<typename MatrixT >

virtual VectorType capd::dynsys::DynSys< MatrixT >::Remainder ( const ScalarType &  t, const VectorType &  iv, VectorType &  out_enc  )

pure virtualinherited

Computes and returns bound for local error of a function (for instance if Phi is finite Taylor series of a map then this method computes bound for Lagrange remainder). If DynSys is an ODE, then out_enc contains enclosure of trajectories over the time step. If the function cannot validate existence of solutions to ODE over the time step, out_enc might be in an inconsistent state.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

Remainder() [2/2]

template<typename MatrixType >

Linear3d< MatrixType >::VectorType capd::dynsys::Linear3d< MatrixType >::Remainder ( const VectorType &  iv ) const

inline

Member Data Documentation

a

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::a

protected

b

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::b

protected

c

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::c

protected

d

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::d

protected

e

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::e

protected

f

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::f

protected

g

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::g

protected

h

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::h

protected

i

template<typename MatrixT >

ScalarType capd::dynsys::Linear3d< MatrixT >::i

protected