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IntegratorBDF Class Reference
Numerical Algorithms -- used internally or by developers to solve numerical problems

Implements the backward-differentiation formula for integrating DAEs. More...

#include <integrator_bdf.hpp>

Inheritance diagram for IntegratorBDF:
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Public Member Functions

virtual Integrator * clone () const
 
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_)
 
 IntegratorBDF ()
 
 IntegratorBDF (const DifferentialEquation &rhs_)
 
 IntegratorBDF (const IntegratorBDF &arg)
 
virtual IntegratorBDF & operator= (const IntegratorBDF &arg)
 
virtual returnValue setDxInitialization (double *dx0)
 
virtual returnValue step (int number)
 
virtual returnValue stop ()
 
virtual returnValue unfreeze ()
 
virtual ~IntegratorBDF ()
 
- Public Member Functions inherited from Integrator
virtual BooleanType canHandleImplicitSwitches () const
 
virtual returnValue deleteAllSeeds ()
 
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
 
returnValue getX (DVector &xEnd) const
 
returnValue getX (VariablesGrid &X) const
 
returnValue getXA (DVector &xaEnd) const
 
returnValue getXA (VariablesGrid &XA) const
 
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)
 
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 ~Integrator ()
 
- 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 ()
 

Protected Member Functions

void allocateMemory ()
 
void applyMTranspose (int index, double *seed1, DMatrix &J, double *seed2)
 
double applyNewtonStep (int index, double *etakplus1, const double *etak, const DMatrix &J, const double *FFF)
 
void constructAll (const IntegratorBDF &arg)
 
void copyBackward (DVector &Dx_x0, DVector &Dx_p, DVector &Dx_u, DVector &Dx_w, const DMatrix &div) const
 
returnValue decomposeJacobian (int index, DMatrix &J)
 
void deleteAll ()
 
void determineBDFEtaGForward (int number)
 
void determineBDFEtaGForward2 (int number)
 
void determineBDFEtaHBackward (int number)
 
void determineBDFEtaHBackward2 (int number)
 
returnValue determineCorrector (int number, BooleanType ini)
 
double determinePredictor (int number, BooleanType ini)
 
void determineRKEtaGForward ()
 
void determineRKEtaGForward2 ()
 
void determineRKEtaHBackward ()
 
void determineRKEtaHBackward2 ()
 
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 int getDimX () 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
 
void initializeButcherTableau ()
 
void initializeVariables ()
 
void interpolate (int number_, DMatrix &div, VariablesGrid &poly)
 
void logCurrentIntegratorStep (const DVector &currentX=emptyConstVector, const DVector &currentXA=emptyConstVector)
 
void prepareDividedDifferences (DMatrix &div)
 
void printBDFfinalResults ()
 
void printBDFfinalResults2 (DMatrix &div)
 
void printBDFIntermediateResults ()
 
void printRKIntermediateResults ()
 
void relaxAlgebraic (double *residuum, double timePoint)
 
returnValue rk_start ()
 
returnValue rk_start_solve (int stepnumber)
 
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 Member Functions inherited from Integrator
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 evaluateTransition (const double time, DVector &xd, const DVector &xa, const DVector &p, const DVector &u, const DVector &w)
 
void initializeOptions ()
 
virtual returnValue setupLogging ()
 
virtual returnValue setupOptions ()
 

Protected Attributes

double ** A
 
double * b4
 
double * b5
 
DVector bseed
 
DVector bseed2
 
double * c
 
DVector c2
 
DVector c2G
 
DVector c2G2
 
DVector c2G3
 
DVector c2H
 
DVector c2H2
 
DVector c2H3
 
RealClock correctorTime
 
DMatrix delta
 
DMatrix deltaG
 
DMatrix deltaG2
 
DMatrix deltaG3
 
DMatrix deltaH
 
DMatrix deltaH2
 
DMatrix deltaH3
 
int dim
 
double ** eta
 
double ** eta2
 
double * eta4
 
double * eta4_
 
double * eta5
 
double * eta5_
 
double * etaG
 
double * etaG2
 
double * etaG3
 
double ** etaH
 
double ** etaH2
 
double ** etaH3
 
double * F
 
double * F2
 
DVector fseed
 
DVector fseed2
 
double * G
 
double * G2
 
double * G3
 
double ** gamma
 
double * H
 
double * H2
 
double * H3
 
double * initial_guess
 
double * initialAlgebraicResiduum
 
double * iseed
 
RealClock jacComputation
 
RealClock jacDecomposition
 
double *** k
 
double *** k2
 
double *** kH
 
double *** kH2
 
double *** kH3
 
double *** l
 
double *** l2
 
DMatrix ** M
 
int * M_index
 
int maxAlloc
 
int maxNM
 
DMatrix nablaG
 
DMatrix nablaG2
 
DMatrix nablaG3
 
DMatrix nablaH
 
DMatrix nablaH2
 
DMatrix nablaH2_
 
DMatrix nablaH3
 
DMatrix nablaH3_
 
DMatrix nablaH_
 
DMatrix nablaY
 
DMatrix nablaY_
 
int ndir
 
int nJacEvaluations
 
int nOfM
 
int * nOfNewtonSteps
 
int nstep
 
DMatrix phi
 
DMatrix phiG
 
DMatrix phiG2
 
DMatrix phiG3
 
double ** psi
 
double * psi_
 
double rel_time_scale
 
double relaxationConstant
 
double t
 
double * x
 
double ** zH
 
double ** zH2
 
double ** zH3
 
- Protected Attributes inherited from Integrator
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
 
- Protected Attributes inherited from AlgorithmicBase
int outputLoggingIdx
 
BooleanType useModuleStandalone
 
UserInteraction * userInteraction
 

Friends

class ShootingMethod
 
class SimulationByIntegration
 

Detailed Description

Implements the backward-differentiation formula for integrating DAEs.

The class IntegratorBDF implements the backward-differentiation formula for integrating differential-algebraic equations (DAEs).

Author
Boris Houska, Hans Joachim Ferreau

Definition at line 52 of file integrator_bdf.hpp.

Constructor & Destructor Documentation

BEGIN_NAMESPACE_ACADO IntegratorBDF::IntegratorBDF ( )

Default constructor.

Definition at line 49 of file integrator_bdf.cpp.

IntegratorBDF::IntegratorBDF ( const DifferentialEquation &  rhs_)

Default constructor.

Definition at line 56 of file integrator_bdf.cpp.

IntegratorBDF::IntegratorBDF ( const IntegratorBDF &  arg)

Copy constructor (deep copy).

Definition at line 62 of file integrator_bdf.cpp.

IntegratorBDF::~IntegratorBDF ( )
virtual

Destructor.

Definition at line 70 of file integrator_bdf.cpp.

Member Function Documentation

void IntegratorBDF::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 111 of file integrator_bdf.cpp.

void IntegratorBDF::applyMTranspose ( int  index,
double *  seed1,
DMatrix &  J,
double *  seed2 
)
protected

applies the transpose of M (needed for automatic differentiation
in backward mode)

Returns
(void)

Definition at line 5168 of file integrator_bdf.cpp.

double IntegratorBDF::applyNewtonStep ( int  index,
double *  etakplus1,
const double *  etak,
const DMatrix &  J,
const double *  FFF 
)
protected

applies a newton step

Returns
the norm of the increment

Definition at line 5140 of file integrator_bdf.cpp.

Integrator * IntegratorBDF::clone ( ) const
virtual

The (virtual) copy constructor

Implements Integrator.

Definition at line 792 of file integrator_bdf.cpp.

void IntegratorBDF::constructAll ( const IntegratorBDF &  arg)
protected

Protected implementation of the copy constructor.

Definition at line 446 of file integrator_bdf.cpp.

void IntegratorBDF::copyBackward ( DVector &  Dx_x0,
DVector &  Dx_p,
DVector &  Dx_u,
DVector &  Dx_w,
const DMatrix &  div 
) const
protected

Definition at line 5282 of file integrator_bdf.cpp.

returnValue IntegratorBDF::decomposeJacobian ( int  index,
DMatrix &  J 
)
protected

Decomposes the Jacobian J.

Returns
SUCCESSFUL_RETURN
RET_THE_DAE_INDEX_IS_TOO_LARGE

Definition at line 5114 of file integrator_bdf.cpp.

void IntegratorBDF::deleteAll ( )
protected

Delete everything.

Definition at line 798 of file integrator_bdf.cpp.

void IntegratorBDF::determineBDFEtaGForward ( int  number)
protected

Differentiation of the BDF step:

Definition at line 4353 of file integrator_bdf.cpp.

void IntegratorBDF::determineBDFEtaGForward2 ( int  number)
protected

Differentiation of the BDF step:

Definition at line 4532 of file integrator_bdf.cpp.

void IntegratorBDF::determineBDFEtaHBackward ( int  number)
protected

Differentiation of the BDF step:

Definition at line 4444 of file integrator_bdf.cpp.

void IntegratorBDF::determineBDFEtaHBackward2 ( int  number)
protected

Differentiation of the BDF step:

Definition at line 4671 of file integrator_bdf.cpp.

returnValue IntegratorBDF::determineCorrector ( int  number,
BooleanType  ini 
)
protected

determines the predictor and corrector polynom

Returns
SUCCESFUL_RETURN
RET_INFO_UNDEFINED

Definition at line 2344 of file integrator_bdf.cpp.

double IntegratorBDF::determinePredictor ( int  number,
BooleanType  ini 
)
protected

determines the predictor and starts the corrector iterations.
If a corrector is found a local error estimate will be returned.

Returns
The local error estimate

Definition at line 2231 of file integrator_bdf.cpp.

void IntegratorBDF::determineRKEtaGForward ( )
protected

Differentiation of the RK-Starter:

Definition at line 3029 of file integrator_bdf.cpp.

void IntegratorBDF::determineRKEtaGForward2 ( )
protected

Differentiation of the RK-Starter:

Definition at line 3567 of file integrator_bdf.cpp.

void IntegratorBDF::determineRKEtaHBackward ( )
protected

Differentiation of the RK-Starter:

Definition at line 3103 of file integrator_bdf.cpp.

void IntegratorBDF::determineRKEtaHBackward2 ( )
protected

Differentiation of the RK-Starter:

Definition at line 3657 of file integrator_bdf.cpp.

returnValue IntegratorBDF::evaluate ( const DVector &  x0,
const DVector &  xa,
const DVector &  p,
const DVector &  u,
const DVector &  w,
const Grid &  t_ 
)
protectedvirtual

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

Parameters
x0the initial state
xathe initial algebraic state
pthe parameters
uthe controls
wthe disturbance
t_the time interval

Implements Integrator.

Definition at line 1112 of file integrator_bdf.cpp.

returnValue IntegratorBDF::evaluateSensitivities ( )
protectedvirtual

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

Returns
SUCCESSFUL_RETURN
RET_NO_SEED_ALLOCATED

Implements Integrator.

Definition at line 1650 of file integrator_bdf.cpp.

returnValue IntegratorBDF::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 1047 of file integrator_bdf.cpp.

returnValue IntegratorBDF::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 1032 of file integrator_bdf.cpp.

int IntegratorBDF::getDim ( ) const
protectedvirtual

Returns the dimension of the Differential Equation

Implements Integrator.

Definition at line 5250 of file integrator_bdf.cpp.

int IntegratorBDF::getDimX ( ) const
protectedvirtual

Returns the number of Dynamic Equations in the Differential Equation

Reimplemented from Integrator.

Definition at line 5255 of file integrator_bdf.cpp.

int IntegratorBDF::getNumberOfRejectedSteps ( ) const
virtual

Returns the number of rejected Steps.

Returns
The requested number of rejected steps.

Implements Integrator.

Definition at line 2211 of file integrator_bdf.cpp.

int IntegratorBDF::getNumberOfSteps ( ) const
virtual

Returns the number of accepted Steps.

Returns
The requested number of accepted steps.

Implements Integrator.

Definition at line 2206 of file integrator_bdf.cpp.

returnValue IntegratorBDF::getProtectedBackwardSensitivities ( DVector &  Dx_x0,
DVector &  Dx_p,
DVector &  Dx_u,
DVector &  Dx_w,
int  order 
) const
protectedvirtual

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

Parameters
Dx_x0backward sensitivities w.r.t. the initial states
Dx_pbackward sensitivities w.r.t. the parameters
Dx_ubackward sensitivities w.r.t. the controls
Dx_wbackward sensitivities w.r.t. the disturbance
orderthe order of the derivative

Returns
SUCCESSFUL_RETURN
RET_INPUT_OUT_OF_RANGE

Implements Integrator.

Definition at line 2158 of file integrator_bdf.cpp.

returnValue IntegratorBDF::getProtectedForwardSensitivities ( DMatrix *  Dx,
int  order 
) const
protectedvirtual

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

Returns
SUCCESSFUL_RETURN
RET_INPUT_OUT_OF_RANGE
Parameters
Dxthe result for the forward sensitivi- ties
orderthe order

Implements Integrator.

Definition at line 2106 of file integrator_bdf.cpp.

returnValue IntegratorBDF::getProtectedX ( DVector *  xEnd) const
protectedvirtual

Returns the result for the state at the time tend.

Returns
SUCCESSFUL_RETURN
Parameters
xEndthe result for the states at the time tend.

Implements Integrator.

Definition at line 2092 of file integrator_bdf.cpp.

double IntegratorBDF::getStepSize ( ) const
virtual

Returns the current step size

Implements Integrator.

Definition at line 2219 of file integrator_bdf.cpp.

returnValue IntegratorBDF::init ( const DifferentialEquation &  rhs_)
virtual

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

Parameters
rhsthe right-hand side of the ODE/DAE.

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

Implements Integrator.

Definition at line 88 of file integrator_bdf.cpp.

returnValue IntegratorBDF::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
rhsthe right-hand side of the ODE/DAE.
trsthe transition to be evaluated at the end.

Returns
SUCCESSFUL_RETURN if all dimension checks succeed.
otherwise: integrator dependent error message.
void IntegratorBDF::initializeButcherTableau ( )
protected

inializes the Butcher Tableau. (only for internal use)

Definition at line 4802 of file integrator_bdf.cpp.

void IntegratorBDF::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 409 of file integrator_bdf.cpp.

void IntegratorBDF::interpolate ( int  number_,
DMatrix &  div,
VariablesGrid &  poly 
)
protected

Definition at line 5310 of file integrator_bdf.cpp.

void IntegratorBDF::logCurrentIntegratorStep ( const DVector &  currentX = emptyConstVector,
const DVector &  currentXA = emptyConstVector 
)
protected

Definition at line 5341 of file integrator_bdf.cpp.

IntegratorBDF & IntegratorBDF::operator= ( const IntegratorBDF &  arg)
virtual

Assignment operator (deep copy).

Definition at line 76 of file integrator_bdf.cpp.

void IntegratorBDF::prepareDividedDifferences ( DMatrix &  div)
protected

Definition at line 5261 of file integrator_bdf.cpp.

void IntegratorBDF::printBDFfinalResults ( )
protected

prints final results of the BDF steps.

Definition at line 4924 of file integrator_bdf.cpp.

void IntegratorBDF::printBDFfinalResults2 ( DMatrix &  div)
protected

prints final results of the BDF steps.

Definition at line 4889 of file integrator_bdf.cpp.

void IntegratorBDF::printBDFIntermediateResults ( )
protected

prints intermediate results of the BDF steps.

Definition at line 4981 of file integrator_bdf.cpp.

void IntegratorBDF::printRKIntermediateResults ( )
protected

prints intermediate results of the Runge Kutta starter

Definition at line 5037 of file integrator_bdf.cpp.

void IntegratorBDF::relaxAlgebraic ( double *  residuum,
double  timePoint 
)
protected

Relax the algebraic equations

Definition at line 5203 of file integrator_bdf.cpp.

returnValue IntegratorBDF::rk_start ( )
protected

computes start values using a diagonal implicit RK-method.

Returns
SUCCESSFUL_RETURN

Definition at line 2520 of file integrator_bdf.cpp.

returnValue IntegratorBDF::rk_start_solve ( int  stepnumber)
protected

starts the newton iteration for the implicit computation of k

Returns
SUCCESSFUL_RETURN

Definition at line 2839 of file integrator_bdf.cpp.

returnValue IntegratorBDF::setBackwardSeed2 ( const DVector &  seed)
protectedvirtual

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

Parameters
seedthe seed matrix

Definition at line 1566 of file integrator_bdf.cpp.

returnValue IntegratorBDF::setDxInitialization ( double *  dx0)
virtual

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

Returns
SUCCESSFUL_RETURN
Parameters
dx0initial guess for the differential state derivatives

Implements Integrator.

Definition at line 2181 of file integrator_bdf.cpp.

returnValue IntegratorBDF::setForwardSeed2 ( const DVector &  xSeed,
const DVector &  pSeed,
const DVector &  uSeed,
const DVector &  wSeed 
)
protected

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

Parameters
xSeedthe seed w.r.t the initial states
pSeedthe seed w.r.t the parameters
uSeedthe seed w.r.t the controls
wSeedthe seed w.r.t the disturbances

Definition at line 1429 of file integrator_bdf.cpp.

returnValue IntegratorBDF::setProtectedBackwardSeed ( const DVector &  seed,
const int &  order 
)
protectedvirtual

Define a backward seed

Returns
SUCCESFUL_RETURN
RET_INPUT_OUT_OF_RANGE
Parameters
seedthe seed matrix
orderthe order of the seed.

Implements Integrator.

Definition at line 1503 of file integrator_bdf.cpp.

returnValue IntegratorBDF::setProtectedForwardSeed ( const DVector &  xSeed,
const DVector &  pSeed,
const DVector &  uSeed,
const DVector &  wSeed,
const int &  order 
)
protectedvirtual

Define a forward seed matrix.

Returns
SUCCESFUL RETURN
RET_INPUT_OUT_OF_RANGE
Parameters
xSeedthe seed w.r.t the initial states
pSeedthe seed w.r.t the parameters
uSeedthe seed w.r.t the controls
wSeedthe seed w.r.t the disturbances
orderthe order of the seed.

Implements Integrator.

Definition at line 1359 of file integrator_bdf.cpp.

returnValue IntegratorBDF::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
numberthe step number

Definition at line 1787 of file integrator_bdf.cpp.

returnValue IntegratorBDF::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 2085 of file integrator_bdf.cpp.

returnValue IntegratorBDF::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.

Returns
SUCCESSFUL_RETURN
RET_ALREADY_UNFROZED

Implements Integrator.

Definition at line 1061 of file integrator_bdf.cpp.

Friends And Related Function Documentation

friend class ShootingMethod
friend

Definition at line 56 of file integrator_bdf.hpp.

friend class SimulationByIntegration
friend

Definition at line 55 of file integrator_bdf.hpp.

Member Data Documentation

double** IntegratorBDF::A
protected

the coefficient A of the Butcher Tableau.

Definition at line 517 of file integrator_bdf.hpp.

double* IntegratorBDF::b4
protected

the 4th order coefficients of the Butcher Tableau.

Definition at line 518 of file integrator_bdf.hpp.

double* IntegratorBDF::b5
protected

the 5th order coefficients of the Butcher Tableau.

Definition at line 519 of file integrator_bdf.hpp.

DVector IntegratorBDF::bseed
protected

The backward seed (only internal use)

Definition at line 576 of file integrator_bdf.hpp.

DVector IntegratorBDF::bseed2
protected

The backward seed 2 (only internal use)

Definition at line 579 of file integrator_bdf.hpp.

double* IntegratorBDF::c
protected

the time coefficients of the Butcher Tableau.

Definition at line 520 of file integrator_bdf.hpp.

DVector IntegratorBDF::c2
protected

the constant in the derivative of the corrector
polynom.

Definition at line 546 of file integrator_bdf.hpp.

DVector IntegratorBDF::c2G
protected

Sensitivity matrix (only internal use)

Definition at line 586 of file integrator_bdf.hpp.

DVector IntegratorBDF::c2G2
protected

Sensitivity matrix (only internal use)

Definition at line 598 of file integrator_bdf.hpp.

DVector IntegratorBDF::c2G3
protected

Sensitivity matrix (only internal use)

Definition at line 599 of file integrator_bdf.hpp.

DVector IntegratorBDF::c2H
protected

Sensitivity matrix (only internal use)

Definition at line 606 of file integrator_bdf.hpp.

DVector IntegratorBDF::c2H2
protected

Sensitivity matrix (only internal use)

Definition at line 620 of file integrator_bdf.hpp.

DVector IntegratorBDF::c2H3
protected

Sensitivity matrix (only internal use)

Definition at line 621 of file integrator_bdf.hpp.

RealClock IntegratorBDF::correctorTime
protected

Definition at line 638 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::delta
protected

sums over the modified divided differences

Definition at line 545 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::deltaG
protected

Sensitivity matrix (only internal use)

Definition at line 585 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::deltaG2
protected

Sensitivity matrix (only internal use)

Definition at line 596 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::deltaG3
protected

Sensitivity matrix (only internal use)

Definition at line 597 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::deltaH
protected

Sensitivity matrix (only internal use)

Definition at line 605 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::deltaH2
protected

Sensitivity matrix (only internal use)

Definition at line 618 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::deltaH3
protected

Sensitivity matrix (only internal use)

Definition at line 619 of file integrator_bdf.hpp.

int IntegratorBDF::dim
protected

the dimension of the Butcher Tableau.

Definition at line 516 of file integrator_bdf.hpp.

double** IntegratorBDF::eta
protected

the predictor and corrector approximations

Definition at line 556 of file integrator_bdf.hpp.

double** IntegratorBDF::eta2
protected

the predictor and corrector approximations

Definition at line 557 of file integrator_bdf.hpp.

double* IntegratorBDF::eta4
protected

the result of order 4

Definition at line 525 of file integrator_bdf.hpp.

double* IntegratorBDF::eta4_
protected

the result of order 4

Definition at line 527 of file integrator_bdf.hpp.

double* IntegratorBDF::eta5
protected

the result of order 5

Definition at line 526 of file integrator_bdf.hpp.

double* IntegratorBDF::eta5_
protected

the result of order 5

Definition at line 528 of file integrator_bdf.hpp.

double* IntegratorBDF::etaG
protected

Sensitivity matrix (only internal use)

Definition at line 582 of file integrator_bdf.hpp.

double* IntegratorBDF::etaG2
protected

Sensitivity matrix (only internal use)

Definition at line 590 of file integrator_bdf.hpp.

double* IntegratorBDF::etaG3
protected

Sensitivity matrix (only internal use)

Definition at line 591 of file integrator_bdf.hpp.

double** IntegratorBDF::etaH
protected

Sensitivity matrix (only internal use)

Definition at line 602 of file integrator_bdf.hpp.

double** IntegratorBDF::etaH2
protected

Sensitivity matrix (only internal use)

Definition at line 612 of file integrator_bdf.hpp.

double** IntegratorBDF::etaH3
protected

Sensitivity matrix (only internal use)

Definition at line 613 of file integrator_bdf.hpp.

double* IntegratorBDF::F
protected

Definition at line 561 of file integrator_bdf.hpp.

double* IntegratorBDF::F2
protected

Definition at line 562 of file integrator_bdf.hpp.

DVector IntegratorBDF::fseed
protected

The forward seed (only internal use)

Definition at line 575 of file integrator_bdf.hpp.

DVector IntegratorBDF::fseed2
protected

The forward seed 2 (only internal use)

Definition at line 578 of file integrator_bdf.hpp.

double* IntegratorBDF::G
protected

Sensitivity matrix (only internal use)

Definition at line 581 of file integrator_bdf.hpp.

double* IntegratorBDF::G2
protected

Sensitivity matrix (only internal use)

Definition at line 588 of file integrator_bdf.hpp.

double* IntegratorBDF::G3
protected

Sensitivity matrix (only internal use)

Definition at line 589 of file integrator_bdf.hpp.

double** IntegratorBDF::gamma
protected

intermediate coefficients

Definition at line 541 of file integrator_bdf.hpp.

double* IntegratorBDF::H
protected

Sensitivity matrix (only internal use)

Definition at line 601 of file integrator_bdf.hpp.

double* IntegratorBDF::H2
protected

Sensitivity matrix (only internal use)

Definition at line 610 of file integrator_bdf.hpp.

double* IntegratorBDF::H3
protected

Sensitivity matrix (only internal use)

Definition at line 611 of file integrator_bdf.hpp.

double* IntegratorBDF::initial_guess
protected

an initial guess for dot_x and xa

Definition at line 567 of file integrator_bdf.hpp.

double* IntegratorBDF::initialAlgebraicResiduum
protected

Definition at line 509 of file integrator_bdf.hpp.

double* IntegratorBDF::iseed
protected

the intermediate seeds

Definition at line 533 of file integrator_bdf.hpp.

RealClock IntegratorBDF::jacComputation
protected

Definition at line 636 of file integrator_bdf.hpp.

RealClock IntegratorBDF::jacDecomposition
protected

Definition at line 637 of file integrator_bdf.hpp.

double*** IntegratorBDF::k
protected

the intermediate results

Definition at line 529 of file integrator_bdf.hpp.

double*** IntegratorBDF::k2
protected

the intermediate results

Definition at line 530 of file integrator_bdf.hpp.

double*** IntegratorBDF::kH
protected

Sensitivity matrix (only internal use)

Definition at line 607 of file integrator_bdf.hpp.

double*** IntegratorBDF::kH2
protected

Sensitivity matrix (only internal use)

Definition at line 622 of file integrator_bdf.hpp.

double*** IntegratorBDF::kH3
protected

Sensitivity matrix (only internal use)

Definition at line 624 of file integrator_bdf.hpp.

double*** IntegratorBDF::l
protected

the intermediate results

Definition at line 531 of file integrator_bdf.hpp.

double*** IntegratorBDF::l2
protected

the intermediate results

Definition at line 532 of file integrator_bdf.hpp.

DMatrix** IntegratorBDF::M
protected

the Jacobians for Newton's method

Definition at line 549 of file integrator_bdf.hpp.

int* IntegratorBDF::M_index
protected

the index of the inverse approximation

Definition at line 551 of file integrator_bdf.hpp.

int IntegratorBDF::maxAlloc
protected

size of the memory that is allocated to store
the trajectory and the mesh.

Definition at line 630 of file integrator_bdf.hpp.

int IntegratorBDF::maxNM
protected

number of allocated Jacobian storage positions

Definition at line 553 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaG
protected

Sensitivity matrix (only internal use)

Definition at line 583 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaG2
protected

Sensitivity matrix (only internal use)

Definition at line 592 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaG3
protected

Sensitivity matrix (only internal use)

Definition at line 593 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaH
protected

Sensitivity matrix (only internal use)

Definition at line 603 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaH2
protected

Sensitivity matrix (only internal use)

Definition at line 614 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaH2_
protected

Sensitivity matrix (only internal use)

Definition at line 616 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaH3
protected

Sensitivity matrix (only internal use)

Definition at line 615 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaH3_
protected

Sensitivity matrix (only internal use)

Definition at line 617 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaH_
protected

Sensitivity matrix (only internal use)

Definition at line 604 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaY
protected

the devided differences

Definition at line 542 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::nablaY_
protected

the devided differences (backup)

Definition at line 543 of file integrator_bdf.hpp.

int IntegratorBDF::ndir
protected

number of dependecy directions (only internal use)

Definition at line 573 of file integrator_bdf.hpp.

int IntegratorBDF::nJacEvaluations
protected

Definition at line 639 of file integrator_bdf.hpp.

int IntegratorBDF::nOfM
protected

number of distinct inverse Jacobian approximations

Definition at line 552 of file integrator_bdf.hpp.

int* IntegratorBDF::nOfNewtonSteps
protected

the number of newton steps (for each BDF-step)

Definition at line 555 of file integrator_bdf.hpp.

int IntegratorBDF::nstep
protected

the horizon length of the multistep method

Definition at line 538 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::phi
protected

the modified divided differences

Definition at line 544 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::phiG
protected

Sensitivity matrix (only internal use)

Definition at line 584 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::phiG2
protected

Sensitivity matrix (only internal use)

Definition at line 594 of file integrator_bdf.hpp.

DMatrix IntegratorBDF::phiG3
protected

Sensitivity matrix (only internal use)

Definition at line 595 of file integrator_bdf.hpp.

double** IntegratorBDF::psi
protected

the time differences (multi-step-sizes).

Definition at line 539 of file integrator_bdf.hpp.

double* IntegratorBDF::psi_
protected

the time differences (multi-step-sizes). (backup)

Definition at line 540 of file integrator_bdf.hpp.

double IntegratorBDF::rel_time_scale
protected

relative time scale (intermediate variable)

Definition at line 568 of file integrator_bdf.hpp.

double IntegratorBDF::relaxationConstant
protected

Definition at line 510 of file integrator_bdf.hpp.

double IntegratorBDF::t
protected

the actual time

Definition at line 558 of file integrator_bdf.hpp.

double* IntegratorBDF::x
protected

the actual state (only internal use)

Definition at line 559 of file integrator_bdf.hpp.

double** IntegratorBDF::zH
protected

Sensitivity matrix (only internal use)

Definition at line 608 of file integrator_bdf.hpp.

double** IntegratorBDF::zH2
protected

Sensitivity matrix (only internal use)

Definition at line 623 of file integrator_bdf.hpp.

double** IntegratorBDF::zH3
protected

Sensitivity matrix (only internal use)

Definition at line 625 of file integrator_bdf.hpp.

The documentation for this class was generated from the following files:

acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:25