Abstract base class for all kinds of Runge-Kutta schemes for integrating ODEs. More...

#include <integrator_runge_kutta.hpp>

Inheritance diagram for IntegratorRK:

Public Member Functions
virtual Integrator *	clone () const =0
virtual returnValue	freezeAll ()
virtual returnValue	freezeMesh ()
virtual int	getNumberOfRejectedSteps () const
virtual int	getNumberOfSteps () const
virtual double	getStepSize () const
virtual returnValue	init (const DifferentialEquation &rhs_)
returnValue	init (const DifferentialEquation &rhs_, const Transition &trs_)
	IntegratorRK ()
	IntegratorRK (int dim_, double power_)
	IntegratorRK (const DifferentialEquation &rhs_, int dim_, double power_)
	IntegratorRK (const IntegratorRK &arg)
virtual IntegratorRK &	operator= (const IntegratorRK &arg)
virtual returnValue	setDxInitialization (double *dx0)
virtual returnValue	step (int number)
virtual returnValue	stop ()
virtual returnValue	unfreeze ()
virtual	~IntegratorRK ()
Protected Member Functions
void	allocateMemory ()
void	constructAll (const IntegratorRK &arg)
void	deleteAll ()
double	determineEta45 ()
double	determineEta45 (int number)
void	determineEtaGForward (int number)
void	determineEtaGForward2 (int number)
void	determineEtaHBackward (int number)
void	determineEtaHBackward2 (int number)
virtual returnValue	evaluate (const DVector &x0, const DVector &xa, const DVector &p, const DVector &u, const DVector &w, const Grid &t_)
virtual returnValue	evaluateSensitivities ()
virtual int	getDim () const
virtual returnValue	getProtectedBackwardSensitivities (DVector &Dx_x0, DVector &Dx_p, DVector &Dx_u, DVector &Dx_w, int order) const
virtual returnValue	getProtectedForwardSensitivities (DMatrix *Dx, int order) const
virtual returnValue	getProtectedX (DVector *xEnd) const
virtual void	initializeButcherTableau ()=0
void	initializeVariables ()
void	interpolate (int jj, double e1, double d1, double *e2, VariablesGrid &poly)
void	logCurrentIntegratorStep (const DVector &currentX=emptyConstVector)
void	printIntermediateResults ()
virtual returnValue	setBackwardSeed2 (const DVector &seed)
returnValue	setForwardSeed2 (const DVector &xSeed, const DVector &pSeed, const DVector &uSeed, const DVector &wSeed)
virtual returnValue	setProtectedBackwardSeed (const DVector &seed, const int &order)
virtual returnValue	setProtectedForwardSeed (const DVector &xSeed, const DVector &pSeed, const DVector &uSeed, const DVector &wSeed, const int &order)
Protected Attributes
double **	A
double *	b4
double *	b5
DVector	bseed
DVector	bseed2
double *	c
int	dim
double	err_power
double *	eta4
double *	eta4_
double *	eta5
double *	eta5_
double *	etaG
double *	etaG2
double *	etaG3
double *	etaH
double *	etaH2
double *	etaH3
DVector	fseed
DVector	fseed2
double *	G
double *	G2
double *	G3
double *	H
double *	H2
double *	H3
double **	k
double **	k2
double **	l
double **	l2
int	maxAlloc
double	t
double *	x

Detailed Description

Abstract base class for all kinds of Runge-Kutta schemes for integrating ODEs.

The class IntegratorRK serves as an abstract base class for all kinds of Runge-Kutta schemes for integrating ordinary differential equations (ODEs).

Author:: Boris Houska, Hans Joachim Ferreau

Definition at line 54 of file integrator_runge_kutta.hpp.

Constructor & Destructor Documentation

BEGIN_NAMESPACE_ACADO IntegratorRK::IntegratorRK ( )

Default constructor.

Definition at line 51 of file integrator_runge_kutta.cpp.

IntegratorRK::IntegratorRK	(	int	dim_,
		double	power_
	)

Default constructor.

Definition at line 58 of file integrator_runge_kutta.cpp.

IntegratorRK::IntegratorRK	(	const DifferentialEquation &	rhs_,
		int	dim_,
		double	power_
	)

Default constructor.

Definition at line 80 of file integrator_runge_kutta.cpp.

IntegratorRK::IntegratorRK ( const IntegratorRK & arg )

Copy constructor (deep copy).

Definition at line 103 of file integrator_runge_kutta.cpp.

IntegratorRK::~IntegratorRK ( ) [virtual]

Destructor.

Definition at line 110 of file integrator_runge_kutta.cpp.

Member Function Documentation

void IntegratorRK::allocateMemory ( ) [protected]

This routine is protected and sets up all
variables (i.e. allocates memory etc.).
Note that this routine assumes that the
dimensions are already set correctly and is
thus for internal use only.

Definition at line 151 of file integrator_runge_kutta.cpp.

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

The (virtual) copy constructor

Implements Integrator.

Implemented in IntegratorDiscretizedODE, IntegratorRK23, IntegratorRK45, IntegratorRK78, and IntegratorRK12.

void IntegratorRK::constructAll ( const IntegratorRK & arg ) [protected]

Implementation of the copy constructor.

Definition at line 407 of file integrator_runge_kutta.cpp.

void IntegratorRK::deleteAll ( ) [protected]

Implementation of the delete operator.

Definition at line 291 of file integrator_runge_kutta.cpp.

double IntegratorRK::determineEta45 ( ) [protected]

computes eta4 and eta5 (only for internal use)

Returns:: The error estimate.

Definition at line 1625 of file integrator_runge_kutta.cpp.

double IntegratorRK::determineEta45 ( int number ) [protected]

computes eta4 and eta5 (only for internal use)

Returns:: The error estimate.

Definition at line 1689 of file integrator_runge_kutta.cpp.

void IntegratorRK::determineEtaGForward ( int number ) [protected]

computes etaG in forward direction (only for internal use)

Definition at line 1748 of file integrator_runge_kutta.cpp.

void IntegratorRK::determineEtaGForward2 ( int number ) [protected]

computes etaG and etaG2 in forward direction
(only for internal use)

Definition at line 1779 of file integrator_runge_kutta.cpp.

void IntegratorRK::determineEtaHBackward ( int number ) [protected]

computes etaH in backward direction (only for internal use)

Definition at line 1817 of file integrator_runge_kutta.cpp.

void IntegratorRK::determineEtaHBackward2 ( int number ) [protected]

computes etaH2 in backward direction (only for internal use)

Definition at line 1851 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::evaluate	(	const DVector &	x0,
		const DVector &	xa,
		const DVector &	p,
		const DVector &	u,
		const DVector &	w,
		const Grid &	t_
	)		`[protected, 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

Implements Integrator.

Definition at line 645 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::evaluateSensitivities ( ) [protected, virtual]

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

Returns:: SUCCESSFUL_RETURN
RET_NO_SEED_ALLOCATED

Implements Integrator.

Definition at line 1075 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::freezeAll ( ) [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

Implements Integrator.

Definition at line 621 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::freezeMesh ( ) [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

Implements Integrator.

Definition at line 605 of file integrator_runge_kutta.cpp.

int IntegratorRK::getDim ( ) const [protected, virtual]

Returns the dimension of the Differential Equation

Implements Integrator.

Definition at line 2059 of file integrator_runge_kutta.cpp.

int IntegratorRK::getNumberOfRejectedSteps ( ) const [virtual]

Returns the number of rejected Steps.

Returns:: The requested number of rejected steps.

Implements Integrator.

Definition at line 1603 of file integrator_runge_kutta.cpp.

int IntegratorRK::getNumberOfSteps ( ) const [virtual]

Returns the number of accepted Steps.

Returns:: The requested number of accepted steps.

Implements Integrator.

Definition at line 1598 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::getProtectedBackwardSensitivities	(	DVector &	Dx_x0,
		DVector &	Dx_p,
		DVector &	Dx_u,
		DVector &	Dx_w,
		int	order
	)		const `[protected, 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

Implements Integrator.

Definition at line 1509 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::getProtectedForwardSensitivities	(	DMatrix *	Dx,
		int	order
	)		const `[protected, 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

Implements Integrator.

Definition at line 1475 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::getProtectedX ( DVector * xEnd ) const [protected, 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.

Implements Integrator.

Definition at line 1461 of file integrator_runge_kutta.cpp.

double IntegratorRK::getStepSize ( ) const [virtual]

Returns the current step size

Implements Integrator.

Definition at line 1609 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::init ( const DifferentialEquation & rhs_ ) [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.

Implements Integrator.

Reimplemented in IntegratorDiscretizedODE, and IntegratorRK12.

Definition at line 116 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::init	(	const DifferentialEquation &	rhs_,
		const Transition &	trs_
	)		`[inline]`

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 from Integrator.

virtual void IntegratorRK::initializeButcherTableau ( ) [protected, pure virtual]

This routine initializes the coefficients of the Butcher Tableau.

Implemented in IntegratorRK12, IntegratorRK23, IntegratorRK45, and IntegratorRK78.

void IntegratorRK::initializeVariables ( ) [protected]

This routine is protected and is basically used
to set all pointer-valued member to the NULL pointer.
In addition some dimensions are initialized with 0 as
a default value.

Definition at line 134 of file integrator_runge_kutta.cpp.

void IntegratorRK::interpolate	(	int	jj,
		double *	e1,
		double *	d1,
		double *	e2,
		VariablesGrid &	poly
	)		`[protected]`

Definition at line 2042 of file integrator_runge_kutta.cpp.

void IntegratorRK::logCurrentIntegratorStep ( const DVector & currentX = emptyConstVector ) [protected]

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

Assignment operator (deep copy).

Definition at line 395 of file integrator_runge_kutta.cpp.

void IntegratorRK::printIntermediateResults ( ) [protected]

prints intermediate results for the case that the PrintLevel is
HIGH.

Definition at line 1891 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::setBackwardSeed2 ( const DVector & seed ) [protected, virtual]

Initializes a second backward seed. (only for internal use)

Parameters:

seed	the seed matrix

Definition at line 1029 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::setDxInitialization ( double * dx0 ) [virtual]

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

Returns:: SUCCESSFUL_RETURN

Parameters:

dx0	initial guess for the differential state derivatives

Implements Integrator.

Definition at line 1615 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::setForwardSeed2	(	const DVector &	xSeed,
		const DVector &	pSeed,
		const DVector &	uSeed,
		const DVector &	wSeed
	)		`[protected]`

Initializes a second forward seed. (only for internal use)

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

Definition at line 909 of file integrator_runge_kutta.cpp.

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

Define a backward seed

Returns:: SUCCESFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Parameters:

seed	the seed matrix
order	the order of the seed.

Implements Integrator.

Definition at line 981 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::setProtectedForwardSeed	(	const DVector &	xSeed,
		const DVector &	pSeed,
		const DVector &	uSeed,
		const DVector &	wSeed,
		const int &	order
	)		`[protected, 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.

Implements Integrator.

Definition at line 835 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::step ( int number ) [virtual]

Executes the next single step. This function can be used to
call the integrator step wise. Note that this function is e.g.
useful in real-time simulations where after each step a time
out limit has to be checked. This function will usually return

Returns:: RET_FINAL_STEP_NOT_PERFORMED_YET
for the case that the final step has not been
performed yet, i.e. the integration routine is not yet
at the time tend.
Otherwise it will either return; SUCCESSFUL_RETURN
or any other error message that might occur during
an integration step.

In most real situations you can define the maximum number of
step sizes to be 1 before calling the function integrate
Then the function integrate should return after one step with
the message
RET_MAXIMUM_NUMBER_OF_STEPS_EXCEEDED. After that you can call
step() until the final time is reached.
(You can use the PrintLevel NONE to avoid that the message
RET_MAXIMUM_NUMBER_OF_STEPS_EXCEEDED is printed.)

Parameters:

number the step number

Reimplemented in IntegratorDiscretizedODE, and IntegratorRK12.

Definition at line 1194 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::stop ( ) [virtual]

Stops the integration even if the final time has not been
reached yet. This function will also give all memory free.
In particular, the function unfreeze() will be called.
(This function is designed for the usage in real-time
contexts in order to deal with error messages without
deleting and re-initializing the integrator.)

Returns:: SUCCESSFUL_RETURN

Definition at line 1455 of file integrator_runge_kutta.cpp.

returnValue IntegratorRK::unfreeze ( ) [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.