Sample implementation of FadMap. This class implements the vector field for the Lorenz system. Template parameters are: Scalar: double, interval, MpFloat, MpInterval, etc. D: in this case either 3 or 0. If D=3 then vectors and matrices are allocated on stack and the computations are much faster but we must know they dimension at compile time. This forces separate compilation of all the classes like vectors and matrices for this particular dimension. D=0 means that vectors and matrices are allocated on the storage and they can be of arbitrary dimension specified at runtime. More...

#include <capd/dynsys/FadMap.h>

Public Types
typedef capd::dynsys::FadMap< Scalar, D >::HessianType	HessianType

typedef capd::dynsys::FadMap< Scalar, D >::MatrixType	MatrixType

typedef capd::dynsys::FadMap< Scalar, D >::VectorType	VectorType

typedef FadFunction< VectorType >	FunctionType

typedef Scalar	ScalarType

Public Member Functions
	LorenzFadMap ()

	LorenzFadMap (Scalar _s, Scalar _r, Scalar _q)

template<typename AVector >
AVector	operator() (const AVector &in) const
	This operator computes vector field of the Lorenz system. More...

template<typename TimeT , typename AVector >
AVector	operator() (const TimeT &, const AVector &in) const
	This operator computes vector field of the Lorenz system. The system is autonomous, but the operator must have two arguments in order to fit requested signature. More...

MatrixType	derivative (const Scalar &t, const VectorType &u) const
	This operator should compute derivative of the vector field. One can specify own implementation or use in the implementation a template function computeDerivative from file differentiate.h (as in the example of the Lorenz system below) which performs FAD to compute derivative of a map. More...

VectorType	operator() (Scalar t, const VectorType &x, MatrixType &o_der) const
	computes simultaneously value and derivative of the map for a given vector and time More...

MatrixType	operator[] (const VectorType &u) const
	For backward compatibility. It computes derivative of the vector field for an autonomous vector field. More...

void	setParameter (int i, Scalar value)

unsigned	dimension () const

template<typename Description >
void	setParameter (Description, Scalar)
	This function should set parameter value of the vector field as a Description we may use integers or strings, etc. More...

unsigned	dimension ()
	You must implement this method. It must return the dimension of the phase space. More...

unsigned	degree ()
	Maximal order of spacial derivatives that this map can compute. More...

Public Attributes
std::vector< Scalar >	parameters

Detailed Description

template<class Scalar, unsigned D>
class capd::dynsys::LorenzFadMap< Scalar, D >

Sample implementation of FadMap. This class implements the vector field for the Lorenz system. Template parameters are: Scalar: double, interval, MpFloat, MpInterval, etc. D: in this case either 3 or 0. If D=3 then vectors and matrices are allocated on stack and the computations are much faster but we must know they dimension at compile time. This forces separate compilation of all the classes like vectors and matrices for this particular dimension. D=0 means that vectors and matrices are allocated on the storage and they can be of arbitrary dimension specified at runtime.

Member Typedef Documentation

◆ FunctionType

template<class Scalar , unsigned D>

typedef FadFunction<VectorType> capd::dynsys::LorenzFadMap< Scalar, D >::FunctionType

◆ HessianType

template<class Scalar , unsigned D>

typedef capd::dynsys::FadMap<Scalar,D>::HessianType capd::dynsys::LorenzFadMap< Scalar, D >::HessianType

◆ MatrixType

template<class Scalar , unsigned D>

typedef capd::dynsys::FadMap<Scalar,D>::MatrixType capd::dynsys::LorenzFadMap< Scalar, D >::MatrixType

◆ ScalarType

template<typename Scalar , unsigned D>

typedef Scalar capd::dynsys::FadMap< Scalar, D >::ScalarType

inherited

◆ VectorType

template<class Scalar , unsigned D>

typedef capd::dynsys::FadMap<Scalar,D>::VectorType capd::dynsys::LorenzFadMap< Scalar, D >::VectorType

Constructor & Destructor Documentation

◆ LorenzFadMap() [1/2]

template<class Scalar , unsigned D>

capd::dynsys::LorenzFadMap< Scalar, D >::LorenzFadMap ( )

inline

◆ LorenzFadMap() [2/2]

template<class Scalar , unsigned D>

capd::dynsys::LorenzFadMap< Scalar, D >::LorenzFadMap	(	Scalar	_s,
		Scalar	_r,
		Scalar	_q
	)

inline

Member Function Documentation

◆ degree()

template<typename Scalar , unsigned D>

unsigned capd::dynsys::FadMap< Scalar, D >::degree ( )

inlineinherited

Maximal order of spacial derivatives that this map can compute.

◆ derivative()

template<class Scalar , unsigned D>

MatrixType capd::dynsys::LorenzFadMap< Scalar, D >::derivative	(	const Scalar &	,
		const VectorType &
	)		const

inlinevirtual

This operator should compute derivative of the vector field. One can specify own implementation or use in the implementation a template function computeDerivative from file differentiate.h (as in the example of the Lorenz system below) which performs FAD to compute derivative of a map.

Implements capd::dynsys::FadMap< Scalar, D >.

◆ dimension() [1/2]

template<typename Scalar , unsigned D>

unsigned capd::dynsys::FadMap< Scalar, D >::dimension ( )

inlineinherited

You must implement this method. It must return the dimension of the phase space.

◆ dimension() [2/2]

template<class Scalar , unsigned D>

unsigned capd::dynsys::LorenzFadMap< Scalar, D >::dimension ( ) const

inline

◆ operator()() [1/3]

template<class Scalar , unsigned D>

template<typename AVector >

AVector capd::dynsys::LorenzFadMap< Scalar, D >::operator() ( const AVector & in ) const

inline

This operator computes vector field of the Lorenz system.

◆ operator()() [2/3]

template<class Scalar , unsigned D>

template<typename TimeT , typename AVector >

AVector capd::dynsys::LorenzFadMap< Scalar, D >::operator()	(	const TimeT &	,
		const AVector &	in
	)		const

inline

This operator computes vector field of the Lorenz system. The system is autonomous, but the operator must have two arguments in order to fit requested signature.

◆ operator()() [3/3]

template<class Scalar , unsigned D>

VectorType capd::dynsys::LorenzFadMap< Scalar, D >::operator()	(	Scalar	t,
		const VectorType &	x,
		MatrixType &	o_der
	)		const

inlinevirtual

computes simultaneously value and derivative of the map for a given vector and time

Implements capd::dynsys::FadMap< Scalar, D >.

◆ operator[]()

template<class Scalar , unsigned D>

MatrixType capd::dynsys::LorenzFadMap< Scalar, D >::operator[] ( const VectorType & ) const

inlinevirtual

For backward compatibility. It computes derivative of the vector field for an autonomous vector field.

Implements capd::dynsys::FadMap< Scalar, D >.

◆ setParameter() [1/2]

template<typename Scalar , unsigned D>

template<typename Description >

void capd::dynsys::FadMap< Scalar, D >::setParameter	(	Description	,
		Scalar
	)

inlineinherited

This function should set parameter value of the vector field as a Description we may use integers or strings, etc.

◆ setParameter() [2/2]

template<class Scalar , unsigned D>

void capd::dynsys::LorenzFadMap< Scalar, D >::setParameter	(	int	i,
		Scalar	value
	)

inline

Member Data Documentation

◆ parameters

template<class Scalar , unsigned D>

std::vector<Scalar> capd::dynsys::LorenzFadMap< Scalar, D >::parameters

Public Types

Public Member Functions

Public Attributes

Detailed Description

template<class Scalar, unsigned D> class capd::dynsys::LorenzFadMap< Scalar, D >

Member Typedef Documentation

◆ FunctionType

◆ HessianType

◆ MatrixType

◆ ScalarType

◆ VectorType

Constructor & Destructor Documentation

◆ LorenzFadMap() [1/2]

◆ LorenzFadMap() [2/2]

Member Function Documentation

◆ degree()

◆ derivative()

◆ dimension() [1/2]

◆ dimension() [2/2]

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

◆ operator[]()

◆ setParameter() [1/2]

◆ setParameter() [2/2]

Member Data Documentation

◆ parameters

template<class Scalar, unsigned D>
class capd::dynsys::LorenzFadMap< Scalar, D >