Abstract base class that must be inherited by all the numerical integrator classes. More...

Inheritance diagram for flint_base::flint_class:

Collaboration diagram for flint_base::flint_class:

Public Member Functions
procedure(init), deferred	init (me, de, maxsteps, method, atol, rtol, interpon, interpstates, minstepsize, maxstepsize, stepszparams, eventson, eventstepsz, eventoptions, eventtol)
	Init is called once and only to specify new differential equaions, events, and a few integrator options.

procedure(integrate), deferred	integrate (me, x0, y0, xf, yf, stepsz, useconststepsz, stepadvance, intstepson, xint, yint, eventmask, eventstates, stifftest, params)
	Integrate the solution from the initial to final value of the independent variable.

procedure(interpolate), deferred	interpolate (me, xarr, yarr, saveinterpcoeffs)
	If interpolation is enabled, then it outputs the solution at the user-specified grid points.

procedure(info), deferred	info (me, laststatus, statusmsg, nsteps, naccept, nreject, nfcalls, interpready, h0, x0, y0, hf, xf, yf)
	Current FLINT object query function.

Public Attributes
integer(kind(flint_success)), public	status = FLINT_SUCCESS
	Status of the last operation completed.

class(diffeqsys), pointer, public	pdiffeqsys => null()
	Pointer to the user-supplied Differential Equation object.

logical	isscalartol = .TRUE.
	Tolerance related constants: rtol and atol Dimension can be either 1 or n (dimension of the initial condition vector). These are used to compute the scale factor (SC) needed for error computations using the following formula:

real(wp), dimension(:), allocatable	rtol

real(wp), dimension(:), allocatable	atol

integer	totalsteps = 0
	Total number of integrator steps.

integer	acceptedsteps = 0
	Number of accepted integrator steps.

integer	rejectedsteps = 0
	Number of rejected integrator steps.

integer	fcalls = 0
	Total number of Diff Eq. function calls made.

integer	maxsteps = INT_MAXSTEPS
	Maximum number of steps integrator is allowed to take.

logical	interpon = .FALSE.
	True for dense output.

integer, dimension(:), allocatable	interpstates
	States between 1 and n for dense output.

real(wp), dimension(:), allocatable	xint
	Array of the natural integrator steps.

real(wp), dimension(:,:,:), allocatable	bip
	Array to store interpolation coefficients at integrator steps.

real(wp)	minstepsize
	Minimum step size of the integrator. It is always a positive number. Default value is used if user do not specifify it.

real(wp)	maxstepsize
	Maximum step-size of the integrator. It is always a positive number. Default value is the difference between the initial and final value of the independent variable.

real(wp)	initialstepsize
	Initial step size.

real(wp), dimension(6)	stepszparams
	Step size method-specific tuning parameters.

logical	eventson = .FALSE.
	Events checking off by default.

real(wp), dimension(:), allocatable	eventstepsz
	This specifies the maximum time after which the event function must be called for each event detection. A 0 value in EventStepSz means that event will be checked after the integrator takes a natural step always. Otherwise, events will be checked after the interval specified by EventStepSz if that interval size is smaller than the length of the current step size. In case it is bigger, then event will be checked at the integrator's natural step boundary. Setting is for each event spearately.

integer, dimension(:), allocatable	eventoptions
	Event options for each event separately. Must be initialized by the Init Function. Specifies what event related info to return to the user.

real(wp), dimension(:), allocatable	etol
	Event tolerance value for each event in case of root-finding is used for event loation.

real(wp)	x0
	Initial value of the independent variable.

real(wp)	xf
	Final value of the independent variable.

real(wp)	h0
	Initial step-size that was accepted.

real(wp)	hf
	The accepted step-size that was used at the last step.

real(wp), dimension(:), allocatable	y0
	Initial condition.

real(wp), dimension(:), allocatable	yf
	Final solution.

Detailed Description

Abstract base class that must be inherited by all the numerical integrator classes.

Definition at line 125 of file FLINT_base.f90.

Member Function/Subroutine Documentation

◆ info()

procedure (info), deferred flint_base::flint_class::info	(	class(flint_class), intent(inout)	me,
		integer(kind(flint_success)), intent(out)	laststatus,
		character(len=:), intent(out), optional, allocatable	statusmsg,
		integer, intent(out), optional	nsteps,
		integer, intent(out), optional	naccept,
		integer, intent(out), optional	nreject,
		integer, intent(out), optional	nfcalls,
		logical, intent(out), optional	interpready,
		real(wp), intent(out), optional	h0,
		real(wp), intent(out), optional	x0,
		real(wp), dimension(:), intent(out), optional	y0,
		real(wp), intent(out), optional	hf,
		real(wp), intent(out), optional	xf,
		real(wp), dimension(:), intent(out), optional	yf )

pure virtual

Current FLINT object query function.

Parameters

[in,out]	me	Object of class type FLINT
[out]	laststatus	The status code of the last operation completed
[out]	statusmsg	Status message corresponding to the status code in LastStatus
[out]	nsteps	Total number of steps taken
[out]	naccept	Number of Accepted steps
[out]	nreject	Number of rejected steps
[out]	nfcalls	Function calls made not including event calls
[out]	interpready	Whether Interpolation is enabled
[out]	h0	The initial accepted step-size
[out]	x0	The initial value of the independent variable
[out]	y0	Initial condition
[out]	hf	Final accepted step-size
[out]	xf	The final value of the independent variable
[out]	yf	Final solution

Definition at line 209 of file FLINT_base.f90.

◆ init()

procedure (init), deferred flint_base::flint_class::init	(	class(flint_class), intent(inout)	me,
		class(diffeqsys), target	de,
		integer, intent(in)	maxsteps,
		integer, intent(in), optional	method,
		real(wp), dimension(:), intent(in), optional	atol,
		real(wp), dimension(:), intent(in), optional	rtol,
		logical, intent(in), optional	interpon,
		integer, dimension(:), intent(in), optional	interpstates,
		real(wp), intent(in), optional	minstepsize,
		real(wp), intent(in), optional	maxstepsize,
		real(wp), dimension(6), intent(in), optional	stepszparams,
		logical, intent(in), optional	eventson,
		real(wp), dimension(:), intent(in), optional	eventstepsz,
		integer(kind(flint_eventoption_rootfinding)), dimension(:), intent(in), optional	eventoptions,
		real(wp), dimension(:), intent(in), optional	eventtol )

pure virtual

Init is called once and only to specify new differential equaions, events, and a few integrator options.

Parameters

[in,out]	me	Object
	de	Differential Equation system object
[in]	maxsteps	Must specify max no. of steps The implementation can use this number to decide how and how much to allocate internal storage for storing integrator natural steps as well as the interpolation coefficients for delayed interpolation.
[in]	method	Type of Intergrator to use. Implemented methods are: ERK_DOP853 (default) ERK_DOP54 ERK_VERNER98R ERK_VERNER65E
[in]	atol	Absolute tolerance, size must be either 1 or n
[in]	rtol	Relative tolerance, size must be either 1 or n
[in]	interpon	If true, then the interpolation coefficients along with integrator natural steps are computed and stored internally. User can use Interpolate method to compute solutions at any value of the indepedent variable without doing the actual integrating again. Note that if InterpOn is true, then IntStepsOn option of Integrate must be either omitted or set to false.
[in]	interpstates	Specify the interpolation states for which the interpolation coefficients will be computed and stored, e.g. [1,3,4,6,n].
[in]	minstepsize	User can specify minimum and maximum step sizes allowed. Note that these are positive quantities. Sign will be handled bu FLINT.
[in]	maxstepsize	User can specify minimum and maximum step sizes allowed. Note that these are positive quantities. Sign will be handled bu FLINT.
[in]	stepszparams	Step-size computation specific parameters. User can specify these for a specific step-size computation method, otherwise defaults are used. For Hairer's DOPRI5/DOP853 codes: StepSzParams(1): Safety-factor StepSzParams(2): Minimum safety-factor StepSzParams(3): Maximum safety-factor StepSzParams(4): Lund Stabilization parameter beta StepSzParams(5): Lund Stabilization parameter beta multiplier StepSzParams(6): Lund Stabilization PI control term initial value
[in]	eventson	Set true for events detection
[in]	eventstepsz	If events detection is enabled, then user can specify the maximum interval after which events must be checked. If there are even number of sign changes between X and X+EventStepSz, that event cannot be detected. If EventStepSz is not specified, then events are always checked at the integrator's natural steps. Note that these are positive quantities and FLINT will take care of the appropriate sign based on the direction of integration.
[in]	eventoptions	Event Options that control the event information returned by FLINT Default is FLINT_EVENTOPTION_ROOTFINDING.
[in]	eventtol	Event tolerance values used for root-finding if enabled, size must be m

Definition at line 200 of file FLINT_base.f90.

◆ integrate()

procedure (integrate), deferred flint_base::flint_class::integrate	(	class(flint_class), intent(inout)	me,
		real(wp), intent(in)	x0,
		real(wp), dimension(me%pdiffeqsys%n), intent(in)	y0,
		real(wp), intent(inout)	xf,
		real(wp), dimension(me%pdiffeqsys%n), intent(out)	yf,
		real(wp), intent(inout)	stepsz,
		logical, intent(in), optional	useconststepsz,
		logical, intent(in), optional	stepadvance,
		logical, intent(in), optional	intstepson,
		real(wp), dimension(:), intent(out), optional, allocatable	xint,
		real(wp), dimension(:,:), intent(out), optional, allocatable	yint,
		logical, dimension(me%pdiffeqsys%m), intent(in), optional	eventmask,
		real(wp), dimension(:,:), intent(out), optional, allocatable	eventstates,
		integer, intent(inout), optional	stifftest,
		real(wp), dimension(:), intent(in), optional	params )

pure virtual

Integrate the solution from the initial to final value of the independent variable.

Parameters

[in,out]	me	Object of the class type FLINT
[in]	x0	Initial value of the independent variable
[in]	y0	Initial conditions
[in,out]	xf	Final value of the independent variable
[out]	yf	Final Solution
[in,out]	stepsz	User can specify the initial step-size to use. If it is 0, then FLINT will compute the initial step-size internally. After the completion of the integration, the last accepted step size will be returned back. Note that user must provide the correct sign of the desired step size.
[in]	useconststepsz	If true, then FLINT will not use adaptive step size algorithm, rather it will use the initial step size value given in StepSz as the integrator's natural step. StepSz must take into account the sign of the step otherwise FLINT will return an error. By default, this option is set to False.
[in]	stepadvance	If true, FLINT will only advance the integration by one step and return. By default, this option is set to False.
[in]	intstepson	If true, then FLINT will return the solution at the integrator's natural step size.
[out]	xint	If IntStepsOn=true, user must provide this parameter. FLINT will allocate the memory and return the integrator's natural steps taken in Xint array. FLINT will not explicitly deallocate this memory.
[out]	yint	If IntStepsOn=true, user must provide this parameter. FLINT will allocate the memory and return the solution at the integrator's natural steps in Yint. The first column is the initial condition Y0 and the final column is Yf. FLINT will not explicitly deallocate this memory. In case of an event action changing the solution at the location of the event, the new solution will be returned in Yint.
[in]	eventmask	If EventMask(i)=false, then the event "i" will Not be detected. Default is true. If all the events are masked, then the event detection will be turned off.
[out]	eventstates	Solutions at the event locations for each of the unmasked event. If events are enabled, then user must specify this parameter. FLINT will internally allocate the storage and it will not explicitly deallocate this memory. EventStates(1:(n+2),i) = [Xevent, Yevent, EventID], where EventID is the index of the triggered event (between 1 and m) to which Xevent and Yevent corresponds. In case of an event action changing the solution at the location of the event, EventStates will still return the orginal state.
[in,out]	stifftest	FLINT will use Hairer's DOP853 alogorithm to test for stiffness of the differential equations if StffTest == 1 or StffTest == 2. Test is disabled by default or if Stifftest == 0. StiffTest == 1: If DiffEq are detected to be stiff then -1 is returned in StiffTest and the integration halts at the current step with appropriate status code. StiffTest == 2: If DiffEq are detected to be stiff then -1 is returned in StiffTest but the integration continues.
[in]	params	Parameters for sensitivity analysis. Not implemented yet.

Definition at line 203 of file FLINT_base.f90.

◆ interpolate()

procedure (interpolate), deferred flint_base::flint_class::interpolate	(	class(flint_class), intent(inout)	me,
		real(wp), dimension(1:), intent(in)	xarr,
		real(wp), dimension(size(me%interpstates),size(xarr)), intent(out)	yarr,
		logical, intent(in), optional	saveinterpcoeffs )

pure virtual

If interpolation is enabled, then it outputs the solution at the user-specified grid points.

Parameters

[in,out]	me	Object of class type FLINT
[in]	xarr	Xarr is provided by the user with values of the independent variable at which the solution is sought. Xarr must be in ascending order and the min and max values must not be smaller and larger than X0 and Xf, respectively.
[out]	yarr	Yarr provides the solution at each point specified in Xarr.
[in]	saveinterpcoeffs	If SaveInterpCoeffs=False, then the internal memory which stores interpolation coefficients is freed. After that, Interpolate function can not be called again without calling Integrate first. By default, SaveInterpCoeffs=False. In order to be able to call Interpolate again, user must set it to Trueat for every call to Interpolate.

Definition at line 206 of file FLINT_base.f90.

Member Data Documentation

◆ acceptedsteps

integer flint_base::flint_class::acceptedsteps = 0

Number of accepted integrator steps.

Definition at line 144 of file FLINT_base.f90.

◆ atol

real(wp), dimension(:), allocatable flint_base::flint_class::atol

Definition at line 141 of file FLINT_base.f90.

◆ bip

real(wp), dimension(:,:,:), allocatable flint_base::flint_class::bip

Array to store interpolation coefficients at integrator steps.

Definition at line 157 of file FLINT_base.f90.

◆ etol

real(wp), dimension(:), allocatable flint_base::flint_class::etol

Event tolerance value for each event in case of root-finding is used for event loation.

Definition at line 187 of file FLINT_base.f90.

◆ eventoptions

integer, dimension(:), allocatable flint_base::flint_class::eventoptions

Event options for each event separately. Must be initialized by the Init Function. Specifies what event related info to return to the user.

Definition at line 184 of file FLINT_base.f90.

◆ eventson

logical flint_base::flint_class::eventson = .FALSE.

Events checking off by default.

Definition at line 172 of file FLINT_base.f90.

◆ eventstepsz

real(wp), dimension(:), allocatable flint_base::flint_class::eventstepsz

This specifies the maximum time after which the event function must be called for each event detection. A 0 value in EventStepSz means that event will be checked after the integrator takes a natural step always. Otherwise, events will be checked after the interval specified by EventStepSz if that interval size is smaller than the length of the current step size. In case it is bigger, then event will be checked at the integrator's natural step boundary. Setting is for each event spearately.

Definition at line 180 of file FLINT_base.f90.

◆ fcalls

integer flint_base::flint_class::fcalls = 0

Total number of Diff Eq. function calls made.

Definition at line 147 of file FLINT_base.f90.

◆ h0

real(wp) flint_base::flint_class::h0

Initial step-size that was accepted.

Definition at line 191 of file FLINT_base.f90.

◆ hf

real(wp) flint_base::flint_class::hf

The accepted step-size that was used at the last step.

Definition at line 192 of file FLINT_base.f90.

◆ initialstepsize

real(wp) flint_base::flint_class::initialstepsize

Initial step size.

Definition at line 168 of file FLINT_base.f90.

◆ interpon

logical flint_base::flint_class::interpon = .FALSE.

True for dense output.

Definition at line 151 of file FLINT_base.f90.

◆ interpstates

integer, dimension(:), allocatable flint_base::flint_class::interpstates

States between 1 and n for dense output.

Definition at line 152 of file FLINT_base.f90.

◆ isscalartol

logical flint_base::flint_class::isscalartol = .TRUE.

Tolerance related constants: rtol and atol Dimension can be either 1 or n (dimension of the initial condition vector). These are used to compute the scale factor (SC) needed for error computations using the following formula:

$SC_i = atol_i + rtol_i |Y_{i}| \quad i=1..n,$

where $|Y|$ is the absolute value of the current solution vector.

Definition at line 139 of file FLINT_base.f90.

◆ maxsteps

integer flint_base::flint_class::maxsteps = INT_MAXSTEPS

Maximum number of steps integrator is allowed to take.

Definition at line 149 of file FLINT_base.f90.

◆ maxstepsize

real(wp) flint_base::flint_class::maxstepsize

Maximum step-size of the integrator. It is always a positive number. Default value is the difference between the initial and final value of the independent variable.

Definition at line 166 of file FLINT_base.f90.

◆ minstepsize

real(wp) flint_base::flint_class::minstepsize

Minimum step size of the integrator. It is always a positive number. Default value is used if user do not specifify it.

Definition at line 161 of file FLINT_base.f90.

◆ pdiffeqsys

class(diffeqsys), pointer, public flint_base::flint_class::pdiffeqsys => null()

Pointer to the user-supplied Differential Equation object.

Definition at line 131 of file FLINT_base.f90.

◆ rejectedsteps

integer flint_base::flint_class::rejectedsteps = 0

Number of rejected integrator steps.

Definition at line 145 of file FLINT_base.f90.

◆ rtol

real(wp), dimension(:), allocatable flint_base::flint_class::rtol

Definition at line 140 of file FLINT_base.f90.

◆ status

integer(kind(flint_success)), public flint_base::flint_class::status = FLINT_SUCCESS

Status of the last operation completed.

Definition at line 128 of file FLINT_base.f90.

◆ stepszparams

real(wp), dimension(6) flint_base::flint_class::stepszparams

Step size method-specific tuning parameters.

Definition at line 170 of file FLINT_base.f90.

◆ totalsteps

integer flint_base::flint_class::totalsteps = 0

Total number of integrator steps.

Definition at line 143 of file FLINT_base.f90.

◆ x0

real(wp) flint_base::flint_class::x0

Initial value of the independent variable.

Definition at line 189 of file FLINT_base.f90.

◆ xf

real(wp) flint_base::flint_class::xf

Final value of the independent variable.

Definition at line 190 of file FLINT_base.f90.

◆ xint

real(wp), dimension(:), allocatable flint_base::flint_class::xint

Array of the natural integrator steps.

Definition at line 154 of file FLINT_base.f90.

◆ y0

real(wp), dimension(:), allocatable flint_base::flint_class::y0

Initial condition.

Definition at line 193 of file FLINT_base.f90.

◆ yf

real(wp), dimension(:), allocatable flint_base::flint_class::yf

Final solution.

Definition at line 194 of file FLINT_base.f90.

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

src/FLINT_base.f90

Public Member Functions

Public Attributes

Detailed Description

Member Function/Subroutine Documentation

◆ info()

◆ init()

◆ integrate()

◆ interpolate()

Member Data Documentation

◆ acceptedsteps

◆ atol

◆ bip

◆ etol

◆ eventoptions

◆ eventson

◆ eventstepsz

◆ fcalls

◆ h0

◆ hf

◆ initialstepsize

◆ interpon

◆ interpstates

◆ isscalartol

◆ maxsteps

◆ maxstepsize

◆ minstepsize

◆ pdiffeqsys

◆ rejectedsteps

◆ rtol

◆ status

◆ stepszparams

◆ totalsteps

◆ x0

◆ xf

◆ xint

◆ y0

◆ yf