Solving autonomous ordinary differential equations using Taylor series expansion. More...

#include <Omu_IntOdeTs.h>

Inheritance diagram for Omu_IntOdeTs:

Public Member Functions
	Omu_IntOdeTs (int)
	constructor

	Omu_IntOdeTs ()
	constructor

	~Omu_IntOdeTs ()
	destructor

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

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

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...

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 (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...

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

Protected Attributes
int	_max_deg
	maximum degree of the taylor series expansion of the ode

double	_tau
	time scaling of the taylor series

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

Solving autonomous ordinary differential equations using Taylor series expansion.

The implementation is adapted from the driver routine forodec of the adol-c automatic differentiation code.

Member Function Documentation

void Omu_IntOdeTs::init_stage	(	int	k,
		const Omu_VariableVec &	x,
		const Omu_VariableVec &	u,
		const Omu_DependentVec &	Ft,
		bool	sa
	)

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 from Omu_Integrator.

const char* Omu_IntOdeTs::name ( )

inlinevirtual

Name of a specific integrator.

Implements Omu_Integrator.

void Omu_IntOdeTs::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 from Omu_Integrator.

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

Omu_IntOdeTs.h

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation