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 ()
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

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

BEGIN_NAMESPACE_ACADO EllipsoidalIntegrator::EllipsoidalIntegrator ( )

Default constructor.

Definition at line 44 of file ellipsoidal_integrator.cpp.

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

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

Parameters:

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

Definition at line 46 of file ellipsoidal_integrator.cpp.

EllipsoidalIntegrator::EllipsoidalIntegrator ( const EllipsoidalIntegrator & arg )

Copy constructor (deep copy).

Definition at line 53 of file ellipsoidal_integrator.cpp.

EllipsoidalIntegrator::~EllipsoidalIntegrator ( ) [virtual]

Destructor.

Definition at line 55 of file ellipsoidal_integrator.cpp.

Member Function Documentation

template<typename T >

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

Tmatrix< Interval > EllipsoidalIntegrator::boundQ ( ) const

Definition at line 258 of file ellipsoidal_integrator.cpp.

template<typename T >

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

void EllipsoidalIntegrator::copy ( const EllipsoidalIntegrator & arg ) [private]

Definition at line 166 of file ellipsoidal_integrator.cpp.

Tmatrix< Interval > EllipsoidalIntegrator::evalC	(	const Tmatrix< double > &	C,
		double	h
	)		const `[private]`

Definition at line 178 of file ellipsoidal_integrator.cpp.

Tmatrix< double > EllipsoidalIntegrator::evalC2	(	const Tmatrix< double > &	C,
		double	h
	)		const `[private]`

Definition at line 193 of file ellipsoidal_integrator.cpp.

template<typename T >

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

template<typename T >

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

template<typename T >

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

template<typename T >

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

template<typename T >

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

template<typename T >

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

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

Definition at line 68 of file ellipsoidal_integrator.cpp.

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

Definition at line 102 of file ellipsoidal_integrator.cpp.

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.

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

Definition at line 118 of file ellipsoidal_integrator.cpp.

template<typename T >

returnValue EllipsoidalIntegrator::integrate	(	double	t0,
		double	tf,
		Tmatrix< T > *	x,
		Tmatrix< T > *	p = `0`,
		Tmatrix< T > *	w = `0`
	)

BooleanType EllipsoidalIntegrator::isIncluded	(	const Tmatrix< Interval > &	A,
		const Tmatrix< Interval > &	B
	)		const `[private]`

Definition at line 265 of file ellipsoidal_integrator.cpp.

double EllipsoidalIntegrator::norm	(	const Tmatrix< Interval > &	E,
		Tmatrix< Interval > &	X
	)		const `[private]`

Definition at line 218 of file ellipsoidal_integrator.cpp.

EllipsoidalIntegrator & EllipsoidalIntegrator::operator= ( const EllipsoidalIntegrator & arg ) [virtual]

Assignment operator (deep copy).

Definition at line 57 of file ellipsoidal_integrator.cpp.

template<typename T >

void EllipsoidalIntegrator::phase0	(	double	t,
		Tmatrix< T > *	x,
		Tmatrix< T > *	p,
		Tmatrix< T > *	w,
		Tmatrix< T > &	coeff,
		Tmatrix< double > &	C
	)		`[private]`

template<typename T >

double EllipsoidalIntegrator::phase1	(	double	t,
		double	tf,
		Tmatrix< T > *	x,
		Tmatrix< T > *	p,
		Tmatrix< T > *	w,
		Tmatrix< T > &	coeff,
		Tmatrix< double > &	C
	)		`[private]`

template<typename T >

void EllipsoidalIntegrator::phase2	(	double	t,
		double	h,
		Tmatrix< T > *	x,
		Tmatrix< T > *	p,
		Tmatrix< T > *	w,
		Tmatrix< T > &	coeff,
		Tmatrix< double > &	C
	)		`[private]`