Interface for a solver for differential (algebraic) equations. More...

#include <Omu_Integrator.h>

Inheritance diagram for Omu_Integrator:

Public Member Functions
	Omu_Integrator ()
	constructor

virtual	~Omu_Integrator ()
	destructor

virtual const char *	name ()=0
	Name of a specific integrator. More...

Low-level interface for Omuses employing an integrator.
The default implementations call the high-level interface.
virtual void	setup_stages (const Omu_Program *sys)
	Setup stages for integrator. More...

virtual void	setup_struct (int k, const Omu_VariableVec &x, const Omu_VariableVec &u, const Omu_DependentVec &Ft)
	Setup struct for one stage k. More...

virtual void	init_stage (int k, const Omu_VariableVec &x, const Omu_VariableVec &u, const Omu_DependentVec &Ft, bool sa=false)
	Initialize solution of differential equations for stage k. More...

virtual void	solve (int kk, double tstart, double tend, const Omu_VariableVec &x, const Omu_VariableVec &u, Omu_Program *sys, Omu_DependentVec &Ft, Omu_StateVec &xt)
	Solve differential equations over one sample period. More...

High-level interface for derived classes implementing an integrator.
This interface hides details of Omuses, like the classification of variables as discrete-time states, expansion states, and control parameters. Instead it treats continuous-time DAE states and sensitivity parameters.
virtual void	init (int k, const Omu_StateVec &xc, const Omu_Vec &q, const Omu_DependentVec &Fc, bool sa)
	Initialize integrator, like adaptation of array dimensions and test of pre-conditions, like explicit ODE. More...

virtual void	solve (int kk, double tstart, double tend, Omu_StateVec &xc, Omu_StateVec &dxc, Omu_Vec &q, Omu_DependentVec &Fc)
	Solve differential equations over one sample period. More...

virtual void	residual (int kk, double t, const Omu_StateVec &xc, const Omu_StateVec &dxc, const Omu_Vec &q, Omu_DependentVec &Fc)
	Callback to evaluate residuals of continuous-time equations. More...

Member access methods
int	K () const
	get number of stages for which integrator has been set up

Protected Member Functions
Depreciated methods.
These methods are called by the default implementations of hte current versions.
virtual void	init_stage (int k, const Omu_States &x, const Omu_Vector &u, bool sa=false)
	Initialize solution of differential equations for stage k. More...

virtual void	solve (int kk, double tstart, double tend, const Omu_States &x, const Omu_Vector &u, Omu_Program *sys, VECP xt, MATP Sx=MNULL, MATP Su=MNULL)
	Solve differential equations over sample period. More...

Protected Attributes
Omu_Program *	_sys
	Pointer to problem definition that is valid during solve.

int	_K
	number of stages for which integrator was set up

int	_k
	index of current stage

int	_kk
	index of current sample period

int	_nxt
	total number of DAE states

int	_nd
	number of discrete-time states

int	_nv
	number of expansion variables

int	_na
	number of algebraic states (no time derivative)

int	_nx
	number of states treated by optimizer (nx=nxt-nv)

int	_nu
	number of control parameters

int	_nq
	number of sensitivity parameters (nq=nx+nu)

bool	_sa
	Indicate if sensitivity analysis is required together with solution of differential equations.

bool	_serr
	Boolean to indicate if sensitivities should be considered for error tolerance (default: false).

int	_n
	Number of continuous-time states during integration (nxt-nd: total number minus discrete-time states).

int	_m
	Number of control parameters during integration (nd+nu: discrete-time states and actual control parameters).

If_List	_ifList
	container for interface elements

double	_stepsize
	Constant stepsize to be taken by integator. More...

double	_min_stepsize
	Minimal stepsize to be taken by integator. More...

double	_rtol
	Relative integration error tolerance (only for variable stepsize).

double	_atol
	Absolute integration error tolerance (only for variable stepsize).

int	_res_evals
	number of residual evaluations

int	_sen_evals
	number of sensitivity evaluations

int	_jac_evals
	number of Jacobian evaluations

Detailed Description

Interface for a solver for differential (algebraic) equations.

The solver is employed internally to numerically integrate continuous-time model equations over sample periods and discrete-time stages.

Member Function Documentation

virtual void Omu_Integrator::init	(	int	k,
		const Omu_StateVec &	xc,
		const Omu_Vec &	q,
		const Omu_DependentVec &	Fc,
		bool	sa
	)

inlinevirtual

Initialize integrator, like adaptation of array dimensions and test of pre-conditions, like explicit ODE.

An explicit ODE is present if Fc.Jdx.is_scalar() and Fc.Jdx[0][0] != 0.0. An algebraic state j, 0<=j<_n can be identified with Fc.Jdx.is_zero_column[j]. Note that the init method should not find consistent initial conditions of a DAE as parameters may jump between sample periods kk afterwards.

Parameters

k	stage
xc	continuous-time states, dim(xc)=_n
q	sensitivity parameters, dim(q)=_nq
Fc	pre-initialized data structures for evaluating residuals, dim(Fc)=_n, including structurally analyzed Jacobians, dim(Fc.Jx)=_n._n, dim(Fc.Jxp)=_n._n, dim(Fc.Jq)=_n._nq
sa	indicates if sensitivity analysis is required

Reimplemented in Omu_IntGRK4, Omu_IntDASPK, Omu_IntSDIRK, Omu_IntIMP, and Omu_IntODE.

virtual void Omu_Integrator::init_stage	(	int	k,
		const Omu_VariableVec &	x,
		const Omu_VariableVec &	u,
		const Omu_DependentVec &	Ft,
		bool	sa = `false`
	)

virtual

Initialize solution of differential equations for stage k.

Note: The numbers of variables and equation structure (given in F) shall be the same for all sample periods of a stage.

Parameters

k	stage
x	state variables for optimization, including bounds etc.
u	control parameters for optimization
Ft	pre-initialized data structures for resisuals and Jacobians
sa	true if sensitivity analysis shall be performed

Reimplemented in Omu_IntOdeTs.

virtual void Omu_Integrator::init_stage	(	int	k,
		const Omu_States &	x,
		const Omu_Vector &	u,
		bool	sa = `false`
	)

inlineprotectedvirtual

Initialize solution of differential equations for stage k.

Reimplemented in Omu_IntODE.

virtual const char* Omu_Integrator::name ( )

pure virtual

Name of a specific integrator.

Implemented in Omu_IntGRK4, Omu_IntDASPK, Omu_IntOdeTs, Omu_IntRK4, Omu_IntSDIRK, Omu_IntIMP, Omu_IntEuler, and Omu_IntRKsuite.

virtual void Omu_Integrator::residual	(	int	kk,
		double	t,
		const Omu_StateVec &	xc,
		const Omu_StateVec &	dxc,
		const Omu_Vec &	q,
		Omu_DependentVec &	Fc
	)

virtual

Callback to evaluate residuals of continuous-time equations.

Parameters

kk	sample period
t	time for evaluation
xc	continuous-time states, dim(xc)=_n
dxc	derivatives of continuous-time states wrt time, dim(dxc)=_n
q	sensitivity parameters, dim(q)=_nq

Return values

Fc	residuals for continuous-time equations, dim(Fc)=_n; Jacobians Fc.Jx, Fc.Jdx, Fc.Jq if Fc.is_required_J() is true

virtual void Omu_Integrator::setup_stages ( const Omu_Program * sys )

virtual

Setup stages for integrator.

This method is called once after Omu_Program's setup_stages has been performed.

Parameters

sys	pointer to problem definition

virtual void Omu_Integrator::setup_struct	(	int	k,
		const Omu_VariableVec &	x,
		const Omu_VariableVec &	u,
		const Omu_DependentVec &	Ft
	)

virtual

Setup struct for one stage k.

This method is called once during problem setup. Note: The numbers of variables and equation structure (given in Ft) shall be the same for all sample periods of a stage.

Parameters

k	stage
x	state variables for optimization, including bounds etc.
u	control parameters for optimization
Ft	pre-initialized data structures for resisuals and Jacobians

virtual void Omu_Integrator::solve	(	int	kk,
		double	tstart,
		double	tend,
		const Omu_VariableVec &	x,
		const Omu_VariableVec &	u,
		Omu_Program *	sys,
		Omu_DependentVec &	Ft,
		Omu_StateVec &	xt
	)

virtual

Solve differential equations over one sample period.

The differential-algebraic equations can be evaluated by calling Omu_Program::continuous for sys. Note that the first _nd elements of xt are discrete-time states that need to be treated like control parameters u by an integrator. Furthermore, the last _nv elements of xt are expansion variables that are not seen by the optimizer and accordingly no sensitivities are required with respect to them. The default implementation of solve calls the high-level version.

Parameters

kk	sample period
tstart	start time for integration
tend	end time for integration
x	state variables for optimization, including bounds etc.
u	control parameters for optimization
sys	problem definition for calling Omu_Program::continuous
Ft	pre-initialized data structures for resisuals and Jacobians
xt	start values for integration at tstart, dim(xt)=_nxt; initial sensitivity matrices xt.Sx, dim(xt.Sx)=_nxt._nx, and xt.Su, dim(xt.Su)=_nxt._nu, if _sa is true

Return values

xt	result at tend; xt.Sx and xt.Su at tend if _sa is true

Exceptions

E_CONV indicate that the integrator failed to converge; may be caught during optimization step length test

Reimplemented in Omu_IntOdeTs, and Omu_IntODE.

virtual void Omu_Integrator::solve	(	int	kk,
		double	tstart,
		double	tend,
		Omu_StateVec &	xc,
		Omu_StateVec &	dxc,
		Omu_Vec &	q,
		Omu_DependentVec &	Fc
	)

virtual

Solve differential equations over one sample period.

Additionally solve sensitivity equations if _sa is true. The default implementation calls the depreciated solve method.

Parameters

kk	sample period
tstart	start time for integration
tend	end time for integration
xc	continuous-time states at tstart, dim(xc)=_n; sensitivities xc.Sq at tstart, dim(xc.Sq)=_n._nq, if _sa is true
dxc	pre-allocated time derivatives of continuous-time states, dim(dxc)=_n
q	sensitivity parameters, dim(q)=_nq
Fc	pre-allocated argument for residual calls, dim(Fc)=_n, including structurally analyzed Jacobians Fc.Jx, Fc.Jdx, Fc.Jq

Return values

xc	continuous-time states at tend; sensitivities xc.Sq at tend if _sa is true

Exceptions

E_CONV indicate that the integrator failed to converge; may be caught during optimization step length test

Reimplemented in Omu_IntGRK4, Omu_IntDASPK, Omu_IntSDIRK, and Omu_IntIMP.

virtual void Omu_Integrator::solve	(	int	kk,
		double	tstart,
		double	tend,
		const Omu_States &	x,
		const Omu_Vector &	u,
		Omu_Program *	sys,
		VECP	xt,
		MATP	Sx = `MNULL`,
		MATP	Su = `MNULL`
	)

inlineprotectedvirtual

Solve differential equations over sample period.

Member Data Documentation

double Omu_Integrator::_min_stepsize

protected

Minimal stepsize to be taken by integator.

Default: 0.0, i.e. no limitation.

double Omu_Integrator::_stepsize

protected

Constant stepsize to be taken by integator.

For stepsize>0, an integrator takes ceil((tend-tstart)/stepsize) equidistant steps in the sampling interval [tstart,tend]. Default: 0.0, i.e. integrator chooses own stepsize.

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

Omu_Integrator.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

Member Data Documentation