Abstract base class for all kinds of algorithms for integrating differential equations (ODEs or DAEs). More...

#include <integrator.hpp>

Inheritance diagram for Integrator:

Public Member Functions
virtual BooleanType	canHandleImplicitSwitches () const
virtual Integrator *	clone () const =0
virtual returnValue	deleteAllSeeds ()
virtual returnValue	evaluateSensitivities ()=0
virtual returnValue	freezeAll ()=0
virtual returnValue	freezeMesh ()=0
returnValue	getBackwardSensitivities (DVector &Dx_x0, DVector &Dx_p, DVector &Dx_u, DVector &Dx_w, int order) const
virtual double	getDifferentialEquationSampleTime () const
returnValue	getForwardSensitivities (DVector &Dx, int order) const
returnValue	getForwardSensitivities (VariablesGrid &Dx, int order) const
returnValue	getI (VariablesGrid &I) const
virtual int	getNumberOfRejectedSteps () const =0
virtual int	getNumberOfSteps () const =0
virtual double	getStepSize () const =0
returnValue	getX (DVector &xEnd) const
returnValue	getX (VariablesGrid &X) const
returnValue	getXA (DVector &xaEnd) const
returnValue	getXA (VariablesGrid &XA) const
virtual returnValue	init (const DifferentialEquation &rhs)=0
returnValue	init (const DifferentialEquation &rhs, const Transition &trs)
returnValue	integrate (double t0, double tend, double x0, double xa=0, double p=0, double u=0, double *w=0)
returnValue	integrate (const Grid &t, double x0, double xa=0, double p=0, double u=0, double *w=0)
returnValue	integrate (double t0, double tend, const DVector &x0, const DVector &xa=emptyVector, const DVector &p=emptyVector, const DVector &u=emptyVector, const DVector &w=emptyVector)
returnValue	integrate (const Grid &t, const DVector &x0, const DVector &xa=emptyVector, const DVector &p=emptyVector, const DVector &u=emptyVector, const DVector &w=emptyVector)
returnValue	integrateSensitivities ()
	Integrator ()
	Integrator (const Integrator &arg)
virtual BooleanType	isDifferentialEquationAffine () const
virtual BooleanType	isDifferentialEquationDefined () const
virtual returnValue	printRunTimeProfile () const
returnValue	setBackwardSeed (const int &order, const DVector &seed)
virtual returnValue	setDxInitialization (double *dx0)=0
returnValue	setForwardSeed (const int &order, const DVector &xSeed, const DVector &pSeed=emptyVector, const DVector &uSeed=emptyVector, const DVector &wSeed=emptyVector)
returnValue	setTransition (const Transition &trs)
virtual returnValue	unfreeze ()=0
virtual	~Integrator ()
Protected Member Functions
virtual returnValue	diffTransitionBackward (DVector &DX, DVector &DP, DVector &DU, DVector &DW, int &order)
virtual returnValue	diffTransitionForward (DVector &DX, const DVector &DP, const DVector &DU, const DVector &DW, const int &order)
virtual returnValue	evaluate (const DVector &x0, const DVector &xa, const DVector &p, const DVector &u, const DVector &w, const Grid &t_)=0
virtual returnValue	evaluateTransition (const double time, DVector &xd, const DVector &xa, const DVector &p, const DVector &u, const DVector &w)
virtual int	getDim () const =0
virtual int	getDimX () const
virtual returnValue	getProtectedBackwardSensitivities (DVector &Dx_x0, DVector &Dx_p, DVector &Dx_u, DVector &Dx_w, int order) const =0
virtual returnValue	getProtectedForwardSensitivities (DMatrix *Dx, int order) const =0
virtual returnValue	getProtectedX (DVector *xEnd) const =0
void	initializeOptions ()
virtual returnValue	setProtectedBackwardSeed (const DVector &seed, const int &order)=0
virtual returnValue	setProtectedForwardSeed (const DVector &xSeed, const DVector &pSeed, const DVector &uSeed, const DVector &wSeed, const int &order)=0
virtual returnValue	setupLogging ()
virtual returnValue	setupOptions ()
Protected Attributes
int *	alg_index
int *	control_index
int	count
int	count2
int	count3
int *	ddiff_index
VariablesGrid	ddxStore
int *	diff_index
DVector	diff_scale
int *	disturbance_index
DVector	dP
DVector	dPb
DVector	dU
DVector	dUb
DVector	dW
DVector	dWb
DVector	dX
DVector	dXb
VariablesGrid	dxStore
RealClock	functionEvaluation
double *	h
double	hini
double	hmax
double	hmin
int *	int_control_index
int *	int_parameter_index
VariablesGrid	iStore
int	las
short int	m
short int	ma
int	maxNumberOfSteps
short int	md
short int	mdx
short int	mn
short int	mp
short int	mpi
short int	mu
short int	mui
short int	mw
int	nBDirs
int	nBDirs2
int	nFcnEvaluations
int	nFDirs
int	nFDirs2
int *	parameter_index
int	PrintLevel
DifferentialEquation *	rhs
StateOfAggregation	soa
int	time_index
Grid	timeInterval
double	TOL
RealClock	totalTime
Transition *	transition
double	tune
DVector	xE
VariablesGrid	xStore
Friends
class	ShootingMethod
class	SimulationByIntegration

Detailed Description

Abstract base class for all kinds of algorithms for integrating differential equations (ODEs or DAEs).

The class Integrator serves as an abstract base class for all kinds of algorithms for integrating differential equations (ODEs or DAEs).

Author:: Boris Houska, Hans Joachim Ferreau

Definition at line 61 of file integrator.hpp.

Constructor & Destructor Documentation

BEGIN_NAMESPACE_ACADO Integrator::Integrator ( )

Default constructor.

Definition at line 56 of file integrator.cpp.

Integrator::Integrator ( const Integrator & arg )

Copy constructor.

Definition at line 131 of file integrator.cpp.

Integrator::~Integrator ( ) [virtual]

Default destructor.

Definition at line 139 of file integrator.cpp.

Member Function Documentation

BooleanType Integrator::canHandleImplicitSwitches ( ) const [virtual]

Returns if integrator is able to handle implicit switches.

Returns:: BT_TRUE: if integrator can handle implicit switches.
BT_FALSE: otherwise

Definition at line 459 of file integrator.cpp.

virtual Integrator* Integrator::clone ( ) const [pure virtual]

The (virtual) copy constructor

Implemented in IntegratorDiscretizedODE, IntegratorBDF, IntegratorLYAPUNOV, IntegratorRK, IntegratorLYAPUNOV45, IntegratorRK23, IntegratorRK45, IntegratorRK78, and IntegratorRK12.

returnValue Integrator::deleteAllSeeds ( ) [virtual]

Deletes all seeds that have been set with the methods above.
This function will also give the corresponding memory free.

Returns:: SUCCESSFUL_RETURN
RET_NO_SEED_ALLOCATED

Definition at line 488 of file integrator.cpp.

returnValue Integrator::diffTransitionBackward	(	DVector &	DX,
		DVector &	DP,
		DVector &	DU,
		DVector &	DW,
		int &	order
	)		`[protected, virtual]`

Definition at line 542 of file integrator.cpp.

returnValue Integrator::diffTransitionForward	(	DVector &	DX,
		const DVector &	DP,
		const DVector &	DU,
		const DVector &	DW,
		const int &	order
	)		`[protected, virtual]`

Definition at line 521 of file integrator.cpp.

virtual returnValue Integrator::evaluate	(	const DVector &	x0,
		const DVector &	xa,
		const DVector &	p,
		const DVector &	u,
		const DVector &	w,
		const Grid &	t_
	)		`[protected, pure virtual]`

Starts integration: cf. integrate(...) for
more details.

Parameters:

x0	the initial state
xa	the initial algebraic state
p	the parameters
u	the controls
w	the disturbance
t_	the time interval

Implemented in IntegratorLYAPUNOV, IntegratorRK, and IntegratorBDF.

virtual returnValue Integrator::evaluateSensitivities ( ) [pure virtual]

Implemented in IntegratorRK, IntegratorBDF, and IntegratorLYAPUNOV.

returnValue Integrator::evaluateTransition	(	const double	time,
		DVector &	xd,
		const DVector &	xa,
		const DVector &	p,
		const DVector &	u,
		const DVector &	w
	)		`[protected, virtual]`

Evaluates the transtion (protected, only for internal use).

Parameters:

time	the time
xd	the state
xa	the algebraic state
p	the parameters
u	the controls
w	the disturbance

Definition at line 505 of file integrator.cpp.

virtual returnValue Integrator::freezeAll ( ) [pure virtual]

Freezes the mesh as well as all intermediate values. This function
is necessary for the case that automatic differentiation in backward
mode should is used. (Note: This function might for large right hand
sides lead to memory problems as all intemediate values will be
stored!)

Returns:: SUCCESSFUL_RETURN
RET_ALREADY_FROZEN

Implemented in IntegratorRK, IntegratorLYAPUNOV, and IntegratorBDF.

virtual returnValue Integrator::freezeMesh ( ) [pure virtual]

Freezes the mesh: Storage of the step sizes. If the integrator is
freezed, the mesh will be stored when calling the function integrate
for the first time. If the function integrate is called more than
once the same mesh will be reused (i.e. the step size control will
be turned off). Note that the mesh should be frozen if any kind of
sensitivity generation is used.

Returns:: SUCCESSFUL_RETURN
RET_ALREADY_FROZEN

Implemented in IntegratorRK, IntegratorLYAPUNOV, and IntegratorBDF.

returnValue Integrator::getBackwardSensitivities	(	DVector &	Dx_x0,
		DVector &	Dx_p,
		DVector &	Dx_u,
		DVector &	Dx_w,
		int	order
	)		const

Returns the result for the backward sensitivities at the time tend.

Parameters:

Dx_x0	backward sensitivities w.r.t. the initial states
Dx_p	backward sensitivities w.r.t. the parameters
Dx_u	backward sensitivities w.r.t. the controls
Dx_w	backward sensitivities w.r.t. the disturbance

Returns:: SUCCESSFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Definition at line 424 of file integrator.cpp.

double Integrator::getDifferentialEquationSampleTime ( ) const [virtual]

Returns the

Definition at line 478 of file integrator.cpp.

virtual int Integrator::getDim ( ) const [protected, pure virtual]

Returns the dimension of the Differential Equation

Implemented in IntegratorBDF, IntegratorLYAPUNOV, and IntegratorRK.

int Integrator::getDimX ( ) const [protected, virtual]

Returns the number of Dynamic Equations in the Differential Equation

Reimplemented in IntegratorBDF.

Definition at line 618 of file integrator.cpp.

returnValue Integrator::getForwardSensitivities	(	DVector &	Dx,
		int	order
	)		const

Returns the result for the forward sensitivities at the time tend.

Parameters:

Dx	the result for the forward sensitivities.
order	the order.

Returns:: SUCCESSFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Definition at line 406 of file integrator.cpp.

returnValue Integrator::getForwardSensitivities	(	VariablesGrid &	Dx,
		int	order
	)		const

Returns the result for the forward sensitivities on the grid.

Parameters:

Dx	the result for the forward sensitivities.
order	the order.

Returns:: SUCCESSFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Definition at line 414 of file integrator.cpp.

returnValue Integrator::getI ( VariablesGrid & I ) const [inline]

Returns the requested output on the specified grid.
The intermediate states constructed based on linear
interpolation.

Parameters:

I	the intermediates states on the grid.

Returns:: SUCCESSFUL_RETURN
RET_TRAJECTORY_NOT_FROZEN

virtual int Integrator::getNumberOfRejectedSteps ( ) const [pure virtual]

Returns the number of rejected Steps.

Returns:: The requested number of rejected steps.

Implemented in IntegratorBDF, IntegratorRK, and IntegratorLYAPUNOV.

virtual int Integrator::getNumberOfSteps ( ) const [pure virtual]

Returns the number of accepted Steps.

Returns:: The requested number of accepted steps.

Implemented in IntegratorBDF, IntegratorRK, and IntegratorLYAPUNOV.

virtual returnValue Integrator::getProtectedBackwardSensitivities	(	DVector &	Dx_x0,
		DVector &	Dx_p,
		DVector &	Dx_u,
		DVector &	Dx_w,
		int	order
	)		const `[protected, pure virtual]`

Returns the result for the backward sensitivities at the time tend.

Parameters:

Dx_x0	backward sensitivities w.r.t. the initial states
Dx_p	backward sensitivities w.r.t. the parameters
Dx_u	backward sensitivities w.r.t. the controls
Dx_w	backward sensitivities w.r.t. the disturbance
order	the order of the derivative

Returns:: SUCCESSFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Implemented in IntegratorLYAPUNOV, IntegratorRK, and IntegratorBDF.

virtual returnValue Integrator::getProtectedForwardSensitivities	(	DMatrix *	Dx,
		int	order
	)		const `[protected, pure virtual]`

Returns the result for the forward sensitivities at the time tend.

Returns:: SUCCESSFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Parameters:

Dx	the result for the forward sensitivi- ties
order	the order

Implemented in IntegratorLYAPUNOV, and IntegratorRK.

virtual returnValue Integrator::getProtectedX ( DVector * xEnd ) const [protected, pure virtual]

Returns the result for the state at the time tend.

Returns:: SUCCESSFUL_RETURN

Parameters:

xEnd	the result for the states at the time tend.

Implemented in IntegratorLYAPUNOV, IntegratorRK, and IntegratorBDF.

virtual double Integrator::getStepSize ( ) const [pure virtual]

Returns the current step size

Implemented in IntegratorBDF, IntegratorRK, and IntegratorLYAPUNOV.

returnValue Integrator::getX ( DVector & xEnd ) const [inline]

Returns the result for the differential states at the
time tend.

Parameters:

xEnd	the result for the states at the time tend.

Returns:: SUCCESSFUL_RETURN

returnValue Integrator::getX ( VariablesGrid & X ) const [inline]

Returns the requested output on the specified grid. Note
that the output X will be evaluated based on polynomial
interpolation depending on the order of the integrator.

Parameters:

X	the differential states on the grid.

Returns:: SUCCESSFUL_RETURN
RET_TRAJECTORY_NOT_FROZEN

returnValue Integrator::getXA ( DVector & xaEnd ) const [inline]

Returns the result for the algebraic states at the
time tend.

Parameters:

xaEnd the result for the algebraic states at the time tend.

Returns:: SUCCESSFUL_RETURN

returnValue Integrator::getXA ( VariablesGrid & XA ) const [inline]

Returns the requested output on the specified grid. Note
that the output X will be evaluated based on polynomial
interpolation depending on the order of the integrator.

Parameters:

XA	the algebraic states on the grid.

Returns:: SUCCESSFUL_RETURN
RET_TRAJECTORY_NOT_FROZEN

virtual returnValue Integrator::init ( const DifferentialEquation & rhs ) [pure virtual]

The initialization routine which takes the right-hand side of
the differential equation to be integrated.

Parameters:

rhs	the right-hand side of the ODE/DAE.

Returns:: SUCCESSFUL_RETURN if all dimension checks succeed.
otherwise: integrator dependent error message.

Implemented in IntegratorLYAPUNOV, IntegratorRK, IntegratorBDF, IntegratorDiscretizedODE, and IntegratorRK12.

returnValue Integrator::init	(	const DifferentialEquation &	rhs,
		const Transition &	trs
	)

The initialization routine which takes the right-hand side of
the differential equation to be integrated. In addition a
transition function can be set which is evaluated at the end
of the integration interval.

Parameters:

rhs	the right-hand side of the ODE/DAE.
trs	the transition to be evaluated at the end.

Returns:: SUCCESSFUL_RETURN if all dimension checks succeed.
otherwise: integrator dependent error message.

Reimplemented in IntegratorRK, IntegratorLYAPUNOV, and IntegratorBDF.

Definition at line 185 of file integrator.cpp.

void Integrator::initializeOptions ( ) [protected]

Initializes the options. This routine should be called by the
integrators derived from this class in order to initialize
the following members based on the user options:

maxNumberOfSteps hmin hmax tune TOL las (cf. SETTINGS for more details)

Definition at line 587 of file integrator.cpp.

returnValue Integrator::integrate	(	double	t0,
		double	tend,
		double *	x0,
		double *	xa = `0`,
		double *	p = `0`,
		double *	u = `0`,
		double *	w = `0`
	)

Starts the integration of the right hand side at time t0.
If neither the maximum number of allowed iteration is
exceeded nor any other error occurs the functions stops the
integration at time tend.

Returns:: SUCCESFUL_RETURN or
a error message that depends on the specific
integration routine. (cf. the corresponding header
file that implements the integration routine)

Parameters:

t0	the start time
tend	the end time
x0	the initial state
xa	the initial algebraic state
p	the parameters
u	the controls
w	the disturbance

Definition at line 207 of file integrator.cpp.

returnValue Integrator::integrate	(	const Grid &	t,
		double *	x0,
		double *	xa = `0`,
		double *	p = `0`,
		double *	u = `0`,
		double *	w = `0`
	)

Starts the integration of the right hand side at time t0.
If neither the maximum number of allowed iteration is
exceeded nor any other error occurs the functions stops the
integration at time tend.
In addition, results at intermediate grid points can be
stored. Note that these grid points are for storage only and
have nothing to do the integrator steps.

Returns:: SUCCESFUL_RETURN or
a error message that depends on the specific
integration routine. (cf. the corresponding header
file that implements the integration routine)

Parameters:

t	the grid [t0,tend]
x0	the initial state
xa	the initial algebraic state
p	the parameters
u	the controls
w	the disturbance

Definition at line 220 of file integrator.cpp.

returnValue Integrator::integrate	(	double	t0,
		double	tend,
		const DVector &	x0,
		const DVector &	xa = `emptyVector`,
		const DVector &	p = `emptyVector`,
		const DVector &	u = `emptyVector`,
		const DVector &	w = `emptyVector`
	)

Starts the integration of the right hand side at time t0.
If neither the maximum number of allowed iteration is
exceeded nor any other error occurs the functions stops the
integration at time tend.

Returns:: SUCCESFUL_RETURN or
a error message that depends on the specific
integration routine. (cf. the corresponding header
file that implements the integration routine)

Parameters:

t0	the start time
tend	the end time
x0	the initial state
xa	the initial algebraic state
p	the parameters
u	the controls
w	the disturbance

Definition at line 241 of file integrator.cpp.

returnValue Integrator::integrate	(	const Grid &	t,
		const DVector &	x0,
		const DVector &	xa = `emptyVector`,
		const DVector &	p = `emptyVector`,
		const DVector &	u = `emptyVector`,
		const DVector &	w = `emptyVector`
	)

Starts the integration of the right hand side at time t0.
If neither the maximum number of allowed iteration is
exceeded nor any other error occurs the functions stops the
integration at time tend.
In addition, results at intermediate grid points can be
stored. Note that these grid points are for storage only and
have nothing to do the integrator steps.

Returns:: SUCCESFUL_RETURN or
a error message that depends on the specific
integration routine. (cf. the corresponding header
file that implements the integration routine)

Parameters:

t	the grid [t0,tend]
x0	the initial state
xa	the initial algebraic state
p	the parameters
u	the controls
w	the disturbance

Definition at line 255 of file integrator.cpp.

returnValue Integrator::integrateSensitivities ( )

< Integrates forward and/or backward depending on the specified seeds.

Returns:: SUCCESSFUL_RETURN
RET_NO_SEED_ALLOCATED

Definition at line 357 of file integrator.cpp.

BooleanType Integrator::isDifferentialEquationAffine ( ) const [virtual]

Returns if the differential equation of the integrator is affine.

Returns:: BT_TRUE: if differential equation is affine.
BT_FALSE: otherwise

Definition at line 471 of file integrator.cpp.

BooleanType Integrator::isDifferentialEquationDefined ( ) const [virtual]

Returns if the differential equation of the integrator is defined.

Returns:: BT_TRUE: if differential equation is defined.
BT_FALSE: otherwise

Definition at line 465 of file integrator.cpp.

returnValue Integrator::printRunTimeProfile ( ) const [virtual]

Prints the run-time profile. This routine
can be used after an integration run in
order to assess the performance.
Integrates forward and/or backward depending on the specified seeds.

Returns:: SUCCESSFUL_RETURN
RET_NO_SEED_ALLOCATED

Definition at line 624 of file integrator.cpp.

returnValue Integrator::setBackwardSeed	(	const int &	order,
		const DVector &	seed
	)

Define a backward seed

Returns:: SUCCESFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Parameters:

order	the order of the seed.
seed	the backward seed

Definition at line 338 of file integrator.cpp.

virtual returnValue Integrator::setDxInitialization ( double * dx0 ) [pure virtual]

Sets an initial guess for the differential state derivatives
(consistency condition)

Returns:: SUCCESSFUL_RETURN

Parameters:

dx0	initial guess for the differential state derivatives

Implemented in IntegratorRK, IntegratorLYAPUNOV, and IntegratorBDF.

returnValue Integrator::setForwardSeed	(	const int &	order,
		const DVector &	xSeed,
		const DVector &	pSeed = `emptyVector`,
		const DVector &	uSeed = `emptyVector`,
		const DVector &	wSeed = `emptyVector`
	)

Define a forward seed matrix.

Returns:: SUCCESFUL RETURN
RET_INPUT_OUT_OF_RANGE

Parameters:

order	the order of the seed.
xSeed	the seed w.r.t states
pSeed	the seed w.r.t parameters
uSeed	the seed w.r.t controls
wSeed	the seed w.r.t disturbances

Definition at line 308 of file integrator.cpp.

virtual returnValue Integrator::setProtectedBackwardSeed	(	const DVector &	seed,
		const int &	order
	)		`[protected, pure virtual]`

Define a backward seed

Returns:: SUCCESFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Parameters:

seed	the seed matrix
order	the order of the seed.

Implemented in IntegratorLYAPUNOV, IntegratorRK, and IntegratorBDF.

virtual returnValue Integrator::setProtectedForwardSeed	(	const DVector &	xSeed,
		const DVector &	pSeed,
		const DVector &	uSeed,
		const DVector &	wSeed,
		const int &	order
	)		`[protected, pure virtual]`

Define a forward seed.

Returns:: SUCCESFUL RETURN
RET_INPUT_OUT_OF_RANGE

Parameters:

xSeed	the seed w.r.t the initial states
pSeed	the seed w.r.t the parameters
uSeed	the seed w.r.t the controls
wSeed	the seed w.r.t the disturbances
order	the order of the seed.

Implemented in IntegratorLYAPUNOV, IntegratorRK, and IntegratorBDF.

returnValue Integrator::setTransition ( const Transition & trs )

Definition at line 198 of file integrator.cpp.

returnValue Integrator::setupLogging ( ) [protected, virtual]

Definition at line 599 of file integrator.cpp.

returnValue Integrator::setupOptions ( ) [protected, virtual]

Definition at line 566 of file integrator.cpp.

virtual returnValue Integrator::unfreeze ( ) [pure virtual]

Unfreezes the mesh: Gives the memory free that has previously
been allocated by "freeze". If you use the function
integrate after unfreezing the usual step size control will be
switched on.