Validated integrator for ODEs based on Taylor models with ellipsoidal remainder term. More...

#include <ellipsoidal_integrator.hpp>

Inheritance diagram for EllipsoidalIntegrator:

Public Member Functions
Tmatrix< Interval >	boundQ () const

	EllipsoidalIntegrator ()

	EllipsoidalIntegrator (const DifferentialEquation &rhs_, const int &N_=3)

	EllipsoidalIntegrator (const EllipsoidalIntegrator &arg)

template<typename T >
Tmatrix< Interval >	getStateBound (const Tmatrix< T > &x) const

returnValue	init (const DifferentialEquation &rhs_, const int &N_=3)

Tmatrix< Interval >	integrate (double t0, double tf, int M, const Tmatrix< Interval > &x)

Tmatrix< Interval >	integrate (double t0, double tf, int M, const Tmatrix< Interval > &x, const Tmatrix< Interval > &p)

Tmatrix< Interval >	integrate (double t0, double tf, int M, const Tmatrix< Interval > &x, const Tmatrix< Interval > &p, const Tmatrix< Interval > &w)

template<typename T >
returnValue	integrate (double t0, double tf, Tmatrix< T > x, Tmatrix< T > p=0, Tmatrix< T > *w=0)

virtual EllipsoidalIntegrator &	operator= (const EllipsoidalIntegrator &arg)

template<typename T >
double	step (const double &t, const double &tf, Tmatrix< T > x, Tmatrix< T > p=0, Tmatrix< T > *w=0)

virtual	~EllipsoidalIntegrator ()

Public Member Functions inherited from AlgorithmicBase
int	addLogRecord (LogRecord &_record)

returnValue	addOption (OptionsName name, int value)

returnValue	addOption (OptionsName name, double value)

returnValue	addOption (uint idx, OptionsName name, int value)

returnValue	addOption (uint idx, OptionsName name, double value)

returnValue	addOptionsList ()

	AlgorithmicBase ()

	AlgorithmicBase (UserInteraction *_userInteraction)

	AlgorithmicBase (const AlgorithmicBase &rhs)

returnValue	get (OptionsName name, int &value) const

returnValue	get (OptionsName name, double &value) const

returnValue	get (OptionsName name, std::string &value) const

returnValue	get (uint idx, OptionsName name, int &value) const

returnValue	get (uint idx, OptionsName name, double &value) const

returnValue	getAll (LogName _name, MatrixVariablesGrid &values) const

returnValue	getFirst (LogName _name, DMatrix &firstValue) const

returnValue	getFirst (LogName _name, VariablesGrid &firstValue) const

returnValue	getLast (LogName _name, DMatrix &lastValue) const

returnValue	getLast (LogName _name, VariablesGrid &lastValue) const

Options	getOptions (uint idx) const

BooleanType	haveOptionsChanged () const

BooleanType	haveOptionsChanged (uint idx) const

AlgorithmicBase &	operator= (const AlgorithmicBase &rhs)

returnValue	plot (PlotFrequency _frequency=PLOT_IN_ANY_CASE)

returnValue	printLogRecord (std::ostream &_stream, int idx, LogPrintMode _mode=PRINT_ITEM_BY_ITEM) const

returnValue	replot (PlotFrequency _frequency=PLOT_IN_ANY_CASE)

returnValue	set (OptionsName name, int value)

returnValue	set (OptionsName name, double value)

returnValue	set (OptionsName name, const std::string &value)

returnValue	set (uint idx, OptionsName name, int value)

returnValue	set (uint idx, OptionsName name, double value)

returnValue	setAll (LogName _name, const MatrixVariablesGrid &values)

returnValue	setLast (LogName _name, int lastValue, double time=-INFTY)

returnValue	setLast (LogName _name, double lastValue, double time=-INFTY)

returnValue	setLast (LogName _name, const DVector &lastValue, double time=-INFTY)

returnValue	setLast (LogName _name, const DMatrix &lastValue, double time=-INFTY)

returnValue	setLast (LogName _name, const VariablesGrid &lastValue, double time=-INFTY)

returnValue	setOptions (const Options &arg)

returnValue	setOptions (uint idx, const Options &arg)

virtual	~AlgorithmicBase ()

Private Member Functions
template<typename T >
Tmatrix< Interval >	bound (const Tmatrix< T > &x) const

template<typename T >
void	center (Tmatrix< T > &x) const

void	copy (const EllipsoidalIntegrator &arg)

Tmatrix< Interval >	evalC (const Tmatrix< double > &C, double h) const

Tmatrix< double >	evalC2 (const Tmatrix< double > &C, double h) const

template<typename T >
Tmatrix< T >	evaluate (Function &f, double t, Tmatrix< T > x, Tmatrix< T > p, Tmatrix< T > *w) const

template<typename T >
Tmatrix< T >	evaluate (Function &f, Interval t, Tmatrix< T > x, Tmatrix< T > p, Tmatrix< T > *w) const

template<typename T >
Tmatrix< T >	getPolynomial (const Tmatrix< T > &x) const

template<typename T >
Tmatrix< Interval >	getRemainder (const Tmatrix< T > &x) const

template<typename T >
Tmatrix< double >	hat (const Tmatrix< T > &x) const

BooleanType	isIncluded (const Tmatrix< Interval > &A, const Tmatrix< Interval > &B) const

double	norm (const Tmatrix< Interval > &E, Tmatrix< Interval > &X) const

template<typename T >
void	phase0 (double t, Tmatrix< T > x, Tmatrix< T > p, Tmatrix< T > *w, Tmatrix< T > &coeff, Tmatrix< double > &C)

template<typename T >
double	phase1 (double t, double tf, Tmatrix< T > x, Tmatrix< T > p, Tmatrix< T > *w, Tmatrix< T > &coeff, Tmatrix< double > &C)

template<typename T >
void	phase2 (double t, double h, Tmatrix< T > x, Tmatrix< T > p, Tmatrix< T > *w, Tmatrix< T > &coeff, Tmatrix< double > &C)

template<typename T >
Tmatrix< T >	phi (const Tmatrix< T > &coeff, const double &h) const

double	scale (const Interval &E, const Interval &X) const

void	setInfinity ()

virtual returnValue	setupOptions ()

void	updateQ (Tmatrix< double > C, Tmatrix< Interval > R)

Private Attributes
Function	ddg

Function	dg

Function	g

Function	gr

int	N

int	nx

RealClock	Phase0Time

RealClock	Phase1Time

Tmatrix< double >	Q

RealClock	totalTime

Additional Inherited Members
Protected Attributes inherited from AlgorithmicBase
int	outputLoggingIdx

BooleanType	useModuleStandalone

UserInteraction *	userInteraction

Detailed Description

Validated integrator for ODEs based on Taylor models with ellipsoidal remainder term.

Author: Mario Villanueva, Boris Houska

Definition at line 60 of file ellipsoidal_integrator.hpp.

Constructor & Destructor Documentation

◆ EllipsoidalIntegrator() [1/3]

BEGIN_NAMESPACE_ACADO EllipsoidalIntegrator::EllipsoidalIntegrator ( )

Default constructor.

Definition at line 44 of file ellipsoidal_integrator.cpp.

◆ EllipsoidalIntegrator() [2/3]

EllipsoidalIntegrator::EllipsoidalIntegrator	(	const DifferentialEquation &	rhs_,
		const int &	N_ = `3`
	)

Constructor that takes the differential equation and the order (default 3) as an argument.

\param rhs_  The differential equation.
\param N_    The order of the intergrator (default = 3).

Definition at line 46 of file ellipsoidal_integrator.cpp.

◆ EllipsoidalIntegrator() [3/3]

EllipsoidalIntegrator::EllipsoidalIntegrator ( const EllipsoidalIntegrator & arg )

Copy constructor (deep copy).

Definition at line 53 of file ellipsoidal_integrator.cpp.

◆ ~EllipsoidalIntegrator()

EllipsoidalIntegrator::~EllipsoidalIntegrator ( )

virtual

Destructor.

Definition at line 55 of file ellipsoidal_integrator.cpp.

Member Function Documentation

◆ bound()

template<typename T >

Tmatrix<Interval> EllipsoidalIntegrator::bound ( const Tmatrix< T > & x ) const

private

◆ boundQ()

Tmatrix< Interval > EllipsoidalIntegrator::boundQ ( ) const

Definition at line 258 of file ellipsoidal_integrator.cpp.

◆ center()

template<typename T >

void EllipsoidalIntegrator::center ( Tmatrix< T > & x ) const

private

◆ copy()

void EllipsoidalIntegrator::copy ( const EllipsoidalIntegrator & arg )

private

Definition at line 166 of file ellipsoidal_integrator.cpp.

◆ evalC()

Tmatrix< Interval > EllipsoidalIntegrator::evalC	(	const Tmatrix< double > &	C,
		double	h
	)		const

private

Definition at line 178 of file ellipsoidal_integrator.cpp.

◆ evalC2()

Tmatrix< double > EllipsoidalIntegrator::evalC2	(	const Tmatrix< double > &	C,
		double	h
	)		const

private

Definition at line 193 of file ellipsoidal_integrator.cpp.

◆ evaluate() [1/2]

template<typename T >

Tmatrix<T> EllipsoidalIntegrator::evaluate	(	Function &	f,
		double	t,
		Tmatrix< T > *	x,
		Tmatrix< T > *	p,
		Tmatrix< T > *	w
	)		const

private

◆ evaluate() [2/2]

template<typename T >

Tmatrix<T> EllipsoidalIntegrator::evaluate	(	Function &	f,
		Interval	t,
		Tmatrix< T > *	x,
		Tmatrix< T > *	p,
		Tmatrix< T > *	w
	)		const

private

◆ getPolynomial()

template<typename T >

Tmatrix<T> EllipsoidalIntegrator::getPolynomial ( const Tmatrix< T > & x ) const

private

◆ getRemainder()

template<typename T >

Tmatrix<Interval> EllipsoidalIntegrator::getRemainder ( const Tmatrix< T > & x ) const

private

◆ getStateBound()

template<typename T >

Tmatrix<Interval> EllipsoidalIntegrator::getStateBound ( const Tmatrix< T > & x ) const

◆ hat()

template<typename T >

Tmatrix<double> EllipsoidalIntegrator::hat ( const Tmatrix< T > & x ) const

private

◆ init()

returnValue EllipsoidalIntegrator::init	(	const DifferentialEquation &	rhs_,
		const int &	N_ = `3`
	)

Definition at line 68 of file ellipsoidal_integrator.cpp.

◆ integrate() [1/4]

Tmatrix< Interval > EllipsoidalIntegrator::integrate	(	double	t0,
		double	tf,
		int	M,
		const Tmatrix< Interval > &	x
	)

Definition at line 102 of file ellipsoidal_integrator.cpp.

◆ integrate() [2/4]

Tmatrix< Interval > EllipsoidalIntegrator::integrate	(	double	t0,
		double	tf,
		int	M,
		const Tmatrix< Interval > &	x,
		const Tmatrix< Interval > &	p
	)

Definition at line 110 of file ellipsoidal_integrator.cpp.

◆ integrate() [3/4]

Tmatrix< Interval > EllipsoidalIntegrator::integrate	(	double	t0,
		double	tf,
		int	M,
		const Tmatrix< Interval > &	x,
		const Tmatrix< Interval > &	p,
		const Tmatrix< Interval > &	w
	)