Singly diagonally implizit Runge Kutta method for (stiff) ordinary differential equations (ODEs). More...

#include <Omu_IntSDIRK.h>

Inheritance diagram for Omu_IntSDIRK:

Public Member Functions
	Omu_IntSDIRK ()
	constructor

	~Omu_IntSDIRK ()
	destructor

Implementation of predefined methods.
See Also Omu_Integrator
const char *	name ()
	Name of a specific integrator. More...

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...

Public Member Functions inherited from Omu_Integrator
	Omu_Integrator ()
	constructor

virtual	~Omu_Integrator ()
	destructor

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...

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...

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

Protected Attributes
int	_jac_sbw
	User given semi-bandwidth of Jacobian (default: -1). More...

bool	_banded
	User specification to allow banded solver (default: false). More...

bool	_banded_solver
	internal flag for using banded solver

bool	_sparse_solver
	User specification to allow sparse solver (default: false).

Protected Attributes inherited from Omu_Integrator
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

Additional Inherited Members
Protected Member Functions inherited from Omu_Integrator
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...

Detailed Description

Singly diagonally implizit Runge Kutta method for (stiff) ordinary differential equations (ODEs).

The implementation is based on Hairer/Wanner: "Solving ordinary differential equations II".

Member Function Documentation

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

virtual

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 from Omu_Integrator.

const char* Omu_IntSDIRK::name ( )

inlinevirtual

Name of a specific integrator.

Implements Omu_Integrator.

virtual void Omu_IntSDIRK::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 from Omu_Integrator.

Member Data Documentation

bool Omu_IntSDIRK::_banded

protected

User specification to allow banded solver (default: false).

Banded solvers are used if _banded is true, _jac_sbw < 0, and if the automatic detection indicates that the problem can be solved more efficiently in this way.

int Omu_IntSDIRK::_jac_sbw

protected

User given semi-bandwidth of Jacobian (default: -1).

If a value >= 0 is specified, then it is used instead of the automatic detection.

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

Omu_IntSDIRK.h

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

Member Data Documentation