Module with explicit math functions. More...

Data Types
type	splinedata
	Data type for spline functions. More...

interface	funcvalue
	Evaluates a function. More...

interface	funcderivative
	Evaluates the derivative of a function. More...

Functions/Subroutines
subroutine, private	funcvalue1 (ikf, ifunc, rfunc, x, fn, ierr)
	Evaluates an explicit function. More...

subroutine, private	funcvalue2 (ikf, ifunc, rfunc, x, fn, ierr)
	Evaluates an (possibly) multi-argument explicit function. More...

subroutine, private	funcderivative1 (ikf, iorder, ifunc, rfunc, x, fn, ierr)
	Evaluates the derivative of an explicit function. More...

subroutine, private	funcderivative2 (ikf, iorder, ifunc, rfunc, x, fn, ierr)
	Evaluates the derivative of a multi-argument explicit function. More...

subroutine	funcintegral (ikf, iorder, ifunc, rfunc, x, fn, ierr)
	Integrates an explicit function from 0.0 to x. More...

logical function	canintegrateexplicitly (funcType, intOrder)
	Query function telling if a function can be integrated explicitly. More...

subroutine, private	outofrangeerror (X, X0, X1)
	Prints an error message when function argument is out of range. More...

real(dp) function	func1 (IFUNC, RFUNC, T, X)
	Simple sinusoidal function. More...

real(dp) function	func2 (RFUNC, T, X, useTmin)
	Complex sinusoidal function composed of two sine waves. More...

real(dp) function	func4 (IFUNC, RFUNC, T, X, IERR)
	Complex sinusoidal function composed of many sine waves. More...

real(dp) function	func5 (IKF, IFUNC, RFUNC, constT, IERR)
	Servo simulator function. More...

real(dp) function	func6 (IKF, IFUNC, RFUNC, T, IERR)
	Spline function. More...

subroutine	deallocatesplines ()
	Deallocates all spline function data. More...

subroutine, private	splin3 (X, Y, DERIV, N, Z, FVALUE, FDERIV, M, IOP, IERR)
	Computes a spline approximation from a set of points. More...

real(dp) function	func8 (RFUNC, T, X, IERR)
	Evaluates the streamline wave profile at point X and time T. More...

real(dp) function	func9 (IFUNC, RFUNC, T, X, IERR)
	Evaluates the embedded wave profile at point X and time T. More...

real(dp) function	func10 (IKF, IFUNC, RFUNC, X, IERR)
	Evaluates a piece-wise linear function at the given point. More...

real(dp) function, private	func10diff (IKF, IFUNC, RFUNC, X, IERR)
	Evaluates the derivative of a piece-wise linear function. More...

real(dp) function, private	func10integral (IKF, IFUNC, RFUNC, X, IORD, IERR)
	Integrates a piece-wise linear function from 0.0 to X. More...

real(dp) function	func11 (RFUNC, T)
	Ramp function. More...

real(dp) function, private	rampintegral (IORD, X, OFFSET, SLOPE, X0, X3)
	Integrate a ramp function from 0.0 to X. More...

real(dp) function	func12 (RFUNC, T)
	Step function. More...

real(dp) function	func13 (RFUNC, T)
	Square pulse function. More...

real(dp) function	func14 (RFUNC, T)
	Dirac pulse function. More...

real(dp) function	func15 (RFUNC)
	Constant function. More...

real(dp) function	func16 (RFUNC, T)
	Extended ramp function. More...

real(dp) function	func17 (RFUNC, T)
	Linear function. More...

real(dp) function	func18 (ikf, iFunc, rFunc, arg, ierr)
	Calls a C-function to read and interpolate a function from a file. More...

real(dp) function, private	func18integral (ikf, iFunc, rFunc, arg, iorder, ierr)
	Calls a C-function to read and integrate a function from a file. More...

real(dp) function	func19 (ikf, iFunc, arg, ierr)
	Calls a C-function to get function value of an expression function. More...

real(dp) function	func19diff (ikf, iFunc, arg, ierr)
	Calls a C-function to get derivative of an expression function. More...

real(dp) function	func20 (ikf, iFunc, args, ierr)
	Calls a C-function to get function value of an expression function. More...

real(dp) function	func20diff (ikf, iFunc, args, ierr)
	Calls a C-function to get derivative of an expression function. More...

real(dp) function	func21 (ikf, iFunc, rFunc, args, ierr)
	Calls a C-function to get function value of a user-defined function. More...

real(dp) function	func21diff (ikf, iFunc, rFunc, args, ierr)
	Calls a C-function to get derivative of a user-defined function. More...

real(dp) function	func22 (IKF, RFUNC, T, IERR)
	Smooth trajectory function. More...

Variables
integer, parameter, private	dp = kind(1.0D0)
	8-byte real (double) More...

real(dp), parameter, private	pi = 3.141592653589793238_dp
	The value of π. More...

real(dp), parameter, private	twopi = PI+PI
	The value of 2π. More...

real(dp), parameter, private	epsarg_p = 1.0e-15_dp
	Argument tolerance. More...

integer, parameter	maxfunc_p = 22
	Number of function types. More...

integer, parameter	sinusoidal_p = 1

integer, parameter	compl_sinus_p = 2

integer, parameter	delayed_compl_sinus_p = 3

integer, parameter	wave_sinus_p = 4

integer, parameter	lin_vel_var_p = 5

integer, parameter	spline_p = 6

integer, parameter	wave_stokes5_p = 7

integer, parameter	wave_streamline_p = 8

integer, parameter	wave_embedded_p = 9

integer, parameter	lin_var_p = 10

integer, parameter	ramp_p = 11

integer, parameter	step_p = 12

integer, parameter	square_puls_p = 13

integer, parameter	dirac_puls_p = 14

integer, parameter	constant_p = 15

integer, parameter	lim_ramp_p = 16

integer, parameter	scale_p = 17

integer, parameter	device_function_p = 18

integer, parameter	math_expression_p = 19

integer, parameter	user_defined_p = 21

integer, parameter	smooth_traj_p = 22

character(len=19), dimension(maxfunc_p), parameter	functype_p = (/ 'SINUSOIDAL ', 'COMPL_SINUS ', 'DELAYED_COMPL_SINUS', 'WAVE_SINUS ', 'LIN_VEL_VAR ', 'SPLINE ', 'WAVE_STOKES5 ', 'WAVE_STREAMLINE ', 'WAVE_EMBEDDED ', 'LIN_VAR ', 'RAMP ', 'STEP ', 'SQUARE_PULS ', 'DIRAC_PULS ', 'CONSTANT ', 'LIM_RAMP ', 'SCALE ', 'DEVICE_FUNCTION ', 'MATH_EXPRESSION ', 'MATH_EXPRESSION ', 'USER_DEFINED ', 'SMOOTH_TRAJ ' /)
	Function type names. More...

integer, save	dbgfunc = 0
	File unit number of debug print. More...

integer, parameter	nspln_p = 6
	Max. number of spline functions in core. More...

type(splinedata), dimension(nspln_p), save, private	spl
	Internal spline data buffer. More...

integer, dimension(nspln_p), save	last = 0
	Identifier for splines in core. More...

Detailed Description

Module with explicit math functions.

This module contains a collection of Fortran functions for evaluating explicit math functions. It consists of the following functions:

FUNC1 : SIN-function
FUNC2 : Two SIN-functions summed, either TMAX or TMIN given
FUNC4 : Wave function (SIN-functions with random phase)
FUNC5 : Servo simulator
FUNC6 : Spline function
FUNC8 : Streamline wave function
FUNC9 : Wave function with embedded streamline functions
FUNC10 : Piece-wise linear function
FUNC11 : Ramp function
FUNC12 : Step function
FUNC13 : Square pulse function
FUNC14 : Dirac pulse function
FUNC15 : Constant function
FUNC16 : Extended ramp function
FUNC17 : Scaling function
FUNC18 : External device function
FUNC19 : General math expression function
FUNC20 : Multi-variable math expression function
FUNC21 : Multi-variable user-defined function (plug-in)
FUNC22 : Smooth trajectory based on SIN2

Originally, this module was writtene by Ole Iver Sivertsen (OIS) in 1984, and later converted to Fortran90 by Bjorn Haugen in 1999.

Function/Subroutine Documentation

◆ canintegrateexplicitly()

logical function explicitfunctionsmodule::canintegrateexplicitly	(	integer, intent(in)	funcType,
		integer, intent(in)	intOrder
	)

Query function telling if a function can be integrated explicitly.

Author: Knut Morten Okstad

Date: 15 Dec 2004

◆ deallocatesplines()

subroutine explicitfunctionsmodule::deallocatesplines

Deallocates all spline function data.

◆ func1()

real(dp) function explicitfunctionsmodule::func1	(	integer, dimension(3), intent(in)	IFUNC,
		real(dp), dimension(:), intent(in)	RFUNC,
		real(dp), intent(in)	T,
		real(dp), intent(in)	X
	)

Simple sinusoidal function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PROGRAM CATEGORY : Fortran function
*
* PURPOSE          : To describe a scaling function
*
* PURPOSE          : To describe a simple sinusoidal function.
*                    A sine wave can be delayed and displaced.
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Position...................................X
*                    Period velocity........................OMEGA=RF1*2*pi
*                    Period delay.............................EPS=RF2*2*pi
*                    Amplitude................................AMP=RF3
*                    Amplitude displacement.................DELTA=RF4
*                    Maximum time for the function to apply..TMAX=RF5
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC1(IFUNC,RFUNC,T,X)
*
***********************************************************************

Author: Ole Ivar Sivertsen SINTEF avd. for maskinkonstruksjon

Date: 1984

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◆ func10()

real(dp) function explicitfunctionsmodule::func10	(	integer, intent(in)	IKF,
		integer, dimension(:), intent(in)	IFUNC,
		real(dp), dimension(:,:), intent(in)	RFUNC,
		real(dp), intent(in)	X,
		integer, intent(inout)	IERR
	)

Evaluates a piece-wise linear function at the given point.

Parameters

[in]	IKF	Function identification number
[in]	IFUNC	Integer function input parameters
[in]	RFUNC	Real function input parameters
[in]	X	Function argument
[out]	ierr	Error indicator

Returns: Function value at point X

Author: Knut Morten Okstad

Date: 17 Nov 2014

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◆ func10diff()

real(dp) function, private explicitfunctionsmodule::func10diff	(	integer, intent(in)	IKF,
		integer, dimension(:), intent(in)	IFUNC,
		real(dp), dimension(:,:), intent(in)	RFUNC,
		real(dp), intent(in)	X,
		integer, intent(inout)	IERR
	)

private

Evaluates the derivative of a piece-wise linear function.

Parameters

[in]	IKF	Function identification number
[in]	IFUNC	Integer function input parameters
[in]	RFUNC	Real function input parameters
[in]	X	Function argument
[out]	ierr	Error indicator

Returns: Function derivative at point X

Author: Knut Morten Okstad

Date: 17 Nov 2014

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◆ func10integral()

real(dp) function, private explicitfunctionsmodule::func10integral	(	integer, intent(in)	IKF,
		integer, dimension(:), intent(in)	IFUNC,
		real(dp), dimension(:,:), intent(in)	RFUNC,
		real(dp), intent(in)	X,
		integer, intent(in)	IORD,
		integer, intent(inout)	IERR
	)

private

Integrates a piece-wise linear function from 0.0 to X.

Parameters

[in]	IKF	Function identification number
[in]	IFUNC	Integer function input parameters
[in]	RFUNC	Real function input parameters
[in]	X	Function argument, upper range of integration domain
[in]	IORD	Integration order (0, 1, or 2)
[out]	ierr	Error indicator

Returns: Function integral at point X

Author: Bjorn Haugen

Date: 1998

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◆ func11()

real(dp) function explicitfunctionsmodule::func11	(	real(dp), dimension(3), intent(in)	RFUNC,
		real(dp), intent(in)	T
	)

Ramp function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a ramp funtion
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Offset ...............................OFFSET=RF1
*                    Ramp slope ............................SLOPE=RF2
*                    Start time for ramp....................STIME=RF3
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC11(RFUNC,T)
*
***********************************************************************

Author: Torleif Iversen (OIS) SINTEF avd. for reguleringsteknikk

Date: 1989

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◆ func12()

real(dp) function explicitfunctionsmodule::func12	(	real(dp), dimension(3), intent(in)	RFUNC,
		real(dp), intent(in)	T
	)

Step function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a step funtion
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Offset ...............................OFFSET=RF1
*                    Step amplitude...........................AMP=RF2
*                    Start time for ramp....................STIME=RF3
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC12(RFUNC,T)
*
***********************************************************************

Author: Torleif Iversen (OIS) SINTEF avd. for reguleringsteknikk

Date: 1989

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◆ func13()

real(dp) function explicitfunctionsmodule::func13	(	real(dp), dimension(4), intent(in)	RFUNC,
		real(dp), intent(in)	T
	)

Square pulse function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a square puls function
*
* ENTRY ARGUMENTS  : Time ......................................T
*                    Offset ...............................OFFSET=RF1
*                    Step amplitude ..........................AMP=RF2
*                    Period ...............................PERIOD=RF4
*                    Phrase angle .........................PANGLE=RF4
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC13(RFUNC,T)
*
***********************************************************************

Author: Torleif Iversen (OIS) SINTEF avd. for reguleringsteknikk

Date: 1989

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◆ func14()

real(dp) function explicitfunctionsmodule::func14	(	real(dp), dimension(4), intent(in)	RFUNC,
		real(dp), intent(in)	T
	)

Dirac pulse function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a dirac puls function
*
* ENTRY ARGUMENTS  : Time ......................................T
*                    Offset ...............................OFFSET=RF1
*                    Step amplitude ..........................AMP=RF2
*                    Start time for puls....................STIME=RF3
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC14(RFUNC,T)
*
***********************************************************************

Author: Torleif Iversen (OIS) SINTEF avd. for reguleringsteknikk

Date: 1989

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◆ func15()

real(dp) function explicitfunctionsmodule::func15 ( real(dp), dimension(1), intent(in) RFUNC )

Constant function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a constant function
*
* ENTRY ARGUMENTS  : Constant.............................. CONST=RF1
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC15(RFUNC)
*
***********************************************************************

Author: Torleif Iversen (OIS) SINTEF avd. for reguleringsteknikk

Date: 1989

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◆ func16()

real(dp) function explicitfunctionsmodule::func16	(	real(dp), dimension(4), intent(in)	RFUNC,
		real(dp), intent(in)	T
	)

Extended ramp function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe an extended ramp funtion
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Offset ...............................OFFSET=RF1
*                    Ramp slope ............................SLOPE=RF2
*                    Start time for ramp....................STIME=RF3
*                    Stop time for ramp.....................STOPT=RF4
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC16(RFUNC,T)
 
***********************************************************************

Author: Terje Rolvag (OIS) SINTEF avd. for reguleringsteknikk

Date: 1989

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◆ func17()

real(dp) function explicitfunctionsmodule::func17	(	real(dp), dimension(1), intent(in)	RFUNC,
		real(dp), intent(in)	T
	)

Linear function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PROGRAM CATEGORY : Fortran function
*
* PURPOSE          : To describe a scaling function
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Scale Factor...........................SCALE=RF1
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC17(RFUNC,T)
*
***********************************************************************

Author: Jens Lien Fedem AS

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◆ func18()

real(dp) function explicitfunctionsmodule::func18	(	integer, intent(in)	ikf,
		integer, dimension(5), intent(in)	iFunc,
		real(dp), dimension(2), intent(in)	rFunc,
		real(dp), intent(in)	arg,
		integer, intent(inout)	ierr
	)

Calls a C-function to read and interpolate a function from a file.

Author: Tommy Jorstad / Knut Morten Okstad

Date: 14 Jun 2002

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◆ func18integral()

real(dp) function, private explicitfunctionsmodule::func18integral	(	integer, intent(in)	ikf,
		integer, dimension(5), intent(in)	iFunc,
		real(dp), dimension(2), intent(in)	rFunc,
		real(dp), intent(in)	arg,
		integer, intent(in)	iorder,
		integer, intent(inout)	ierr
	)

private

Calls a C-function to read and integrate a function from a file.

Author: Knut Morten Okstad

Date: 15 Dec 2004

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◆ func19()

real(dp) function explicitfunctionsmodule::func19	(	integer, intent(in)	ikf,
		integer, dimension(3), intent(in)	iFunc,
		real(dp), intent(in)	arg,
		integer, intent(inout)	ierr
	)

Calls a C-function to get function value of an expression function.

Author: Tommy Jorstad

Date: 15 Aug 2002

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◆ func19diff()

real(dp) function explicitfunctionsmodule::func19diff	(	integer, intent(in)	ikf,
		integer, dimension(3), intent(in)	iFunc,
		real(dp), intent(in)	arg,
		integer, intent(inout)	ierr
	)

Calls a C-function to get derivative of an expression function.

Author: Knut Morten Okstad

Date: 15 Sep 2009

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◆ func2()

real(dp) function explicitfunctionsmodule::func2	(	real(dp), dimension(:), intent(in)	RFUNC,
		real(dp), intent(in)	T,
		real(dp), intent(in)	X,
		logical, intent(in)	useTmin
	)

Complex sinusoidal function composed of two sine waves.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a complex sinusoidal made up of
*                    2 sine waves which separately can be delayed.
*                    The sine waves are added together and a total
*                    dispacement can be specified.
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Position...................................X
*                    Period velocity  wave1................OMEGA1=RF1
*                    Period velocity  wave2................OMEGA2=RF2
*                    Period delay  wave1.....................EPS1=RF3
*                    Period delay  wave2.....................EPS2=RF4
*                    Amplitude  wave1........................AMP1=RF5
*                    Amplitude  wave2........................AMP2=RF5
*                    Amplitude displacement.................DELTA=RF7
*                    Starting point for function to apply....TMIN=RF8
*                    Maximum time for the function to apply..TMAX=RF8
*                    Flag for specifying TMIN or TMAX.....useTmin
*
* EXIT ARGUMENTS   : Value of function at time T................F
*
* CALLING SEQUENCE : FN=FUNC2(RFUNC,T,X,useTmin)
*
***********************************************************************

Author: Sjur Lassesen SINTEF avd. for maskinkonstruksjon

Date: 1986

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◆ func20()

real(dp) function explicitfunctionsmodule::func20	(	integer, intent(in)	ikf,
		integer, dimension(4), intent(in)	iFunc,
		real(dp), dimension(:), intent(in)	args,
		integer, intent(inout)	ierr
	)

Calls a C-function to get function value of an expression function.

Author: Knut Morten Okstad

Date: 15 Sep 2009

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◆ func20diff()

real(dp) function explicitfunctionsmodule::func20diff	(	integer, intent(in)	ikf,
		integer, dimension(4), intent(in)	iFunc,
		real(dp), dimension(:), intent(in)	args,
		integer, intent(inout)	ierr
	)

Calls a C-function to get derivative of an expression function.

Author: Knut Morten Okstad

Date: 15 Sep 2009

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◆ func21()

real(dp) function explicitfunctionsmodule::func21	(	integer, intent(in)	ikf,
		integer, dimension(4), intent(in)	iFunc,
		real(dp), dimension(:), intent(in)	rFunc,
		real(dp), dimension(:), intent(in)	args,
		integer, intent(inout)	ierr
	)

Calls a C-function to get function value of a user-defined function.

Author: Knut Morten Okstad

Date: 15 Jan 2010

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◆ func21diff()

real(dp) function explicitfunctionsmodule::func21diff	(	integer, intent(in)	ikf,
		integer, dimension(4), intent(in)	iFunc,
		real(dp), dimension(:), intent(in)	rFunc,
		real(dp), dimension(:), intent(in)	args,
		integer, intent(inout)	ierr
	)

Calls a C-function to get derivative of a user-defined function.

Author: Knut Morten Okstad

Date: 15 Jan 2010

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◆ func22()

real(dp) function explicitfunctionsmodule::func22	(	integer, intent(in)	IKF,
		real(dp), dimension(4), intent(in)	RFUNC,
		real(dp), intent(in)	T,
		integer, intent(inout)	IERR
	)

Smooth trajectory function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a trajectory with continuity in speed,
*                    acceleration and jerk.
*                    The trajectiory is based on a second order
*                    sinusoidal function.
*
* ENTRY ARGUMENTS  : Time.........................................T
*                    Starting time for trajection generation....RF1
*                    Total trajectory time......................RF2
*                    Maximum acceleration.......................RF3
*                    Maximum speed..............................RF4
*
* EXIT ARGUMENTS   : Value of function at time T.................FN
*                    Error indicator...........................IERR
*
* CALLING SEQUENCE : FN=FUNC22(IKF,RFUNC,T,IERR)
*
* ERROR INDICATION : IERR < 0 --> An error has occurred
*                     -10 : Zero or negative maximum acceleration
*                     -15 : Zero or negative maximum speed
*                     -20 : Can not reach maximum speed
*                           before deacceleration
*
***********************************************************************

Author: Hans Petter Hildre 503914, NTH Institutt for maskinkonstruksjon

Date: 27 Mar 1990

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◆ func4()

real(dp) function explicitfunctionsmodule::func4	(	integer, dimension(:), intent(in)	IFUNC,
		real(dp), dimension(:), intent(in)	RFUNC,
		real(dp), intent(in)	T,
		real(dp), intent(in)	X,
		integer, intent(inout)	IERR
	)

Complex sinusoidal function composed of many sine waves.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a complex sinusoidal made up of
*                    an arbitrary number of sine waves with separate
*                    amplitudes, frequencies and phase shifts.
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Position...................................X
*                    Number of sine waves, N .............IFUNC(3)
*                    Amplitude, A(i) ...................RFUNC(1,i)
*                    Angular frequency, omega(i) .......RFUNC(2,i)
*                    Phase shift, epsilon(i) ...........RFUNC(3,i)
*
* EXIT ARGUMENTS   : Value of function at time T................F
*                    Error indicator.........................IERR
*
* CALLING SEQUENCE : FN=FUNC4(IFUNC,RFUNC,T,X,IERR)
*
* ERROR INDICATION : IERR
*
***********************************************************************

Author: Knut Morten Okstad

Date: 16 Jan 2007

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◆ func5()

real(dp) function explicitfunctionsmodule::func5	(	integer, intent(in)	IKF,
		integer, dimension(:), intent(in)	IFUNC,
		real(dp), dimension(:), intent(in)	RFUNC,
		real(dp), intent(in)	constT,
		integer, intent(inout)	IERR
	)

Servo simulator function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : To describe a curve starting in 0.0 and varying
*                    linearly between -1.0 and 1.0.
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    Time incident for change in gradient.....RF1
*                     .       .     .    .    .    .           .
*                    Time incident for change in gradient.....RF8
*
* EXIT ARGUMENTS   : Value of function at time T...............FN
*                    Error indicator.........................IERR
*
* CALLING SEQUENCE : FN=FUNC5(IKF,IFUNC,RFUNC,T,IERR)
*
* ERROR INDICATION : IERR < 0  -->  Error has occurred
*
*           NNN =  5        Negative starting time
*           NNN = 10        2. change in grad. earlier than 1.
*           NNN = 15        3. change in grad. earlier than 2.
*           NNN = 20        4. change in grad. earlier than 3.
*           NNN = 25        5. change in grad. earlier than 4.
*           NNN = 30        6. change in grad. earlier than 5.
*           NNN = 35        7. change in grad. earlier than 6.
*           NNN = 40        8. change in grad. earlier than 7.
*
***********************************************************************

Author: Ole Ivar Sivertsen SINTEF avd. for maskinkonstruksjon

Date: 1984

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◆ func6()

real(dp) function explicitfunctionsmodule::func6	(	integer, intent(in)	IKF,
		integer, dimension(:), intent(in)	IFUNC,
		real(dp), dimension(:,:), intent(in)	RFUNC,
		real(dp), intent(in)	T,
		integer, intent(inout)	IERR
	)

Spline function.

The following is from the original FORTRAN-77 documententation:

***********************************************************************
*
* PURPOSE          : Computes a spline approximation of third order.
*
* ENTRY ARGUMENTS  : Time.......................................T
*                    X(i) .........................RFUNC(2*i-1,j)
*                    Y(X) .........................RFUNC(2*i  ,j)
*
* EXIT ARGUMENTS   : Value of function at time T................F
*                    Error indicator.........................IERR
*
* CALLING SEQUENCE : FN=FUNC6(IKF,IFUNC,RFUNC,T,IERR)
*
***********************************************************************

Author: Ole Ivar Sivertsen SINTEF avd. for maskinkonstruksjon

Date: 1984

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◆ func8()

real(dp) function explicitfunctionsmodule::func8	(	real(dp), dimension(:), intent(in)	RFUNC,
		real(dp), intent(in)	T,
		real(dp), intent(in)	X,
		integer, intent(inout)	IERR
	)

Evaluates the streamline wave profile at point X and time T.

Parameters

[in]	RFUNC	Wave data, output from wavefunctionsmodule::initfunc8
[in]	T	Current time
[in]	X	Current position
[out]	IERR	Error indicator

Returns: Current wave height above z = 0

Author: Knut Morten Okstad

Date: 9 May 2011

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◆ func9()

real(dp) function explicitfunctionsmodule::func9	(	integer, dimension(:), intent(in)	IFUNC,
		real(dp), dimension(:), intent(in)	RFUNC,
		real(dp), intent(in)	T,
		real(dp), intent(in)	X,
		integer, intent(inout)	IERR
	)

Evaluates the embedded wave profile at point X and time T.

Parameters

[in]	IFUNC	Wave data, output from wavefunctionsmodule::initfunc9
[in]	RFUNC	Wave data, output from wavefunctionsmodule::initfunc9
[in]	T	Current time
[in]	X	Current position
[out]	IERR	Error indicator

Returns: Current wave height above z = 0

Author: Knut Morten Okstad

Date: 14 May 2012

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◆ funcderivative1()

subroutine, private explicitfunctionsmodule::funcderivative1	(	integer, intent(in)	ikf,
		integer, intent(in)	iorder,
		integer, dimension(:), intent(in)	ifunc,
		real(dp), dimension(:), intent(in)	rfunc,
		real(dp), intent(in)	x,
		real(dp), intent(out)	fn,
		integer, intent(out)	ierr
	)

private

Evaluates the derivative of an explicit function.

Parameters

[in]	ikf	Function identification number
[in]	iorder	Derivative order
[in]	ifunc	Integer function input parameters
[in]	rfunc	Real function input parameters
[in]	x	Function argument
[out]	fn	Derivative of function
[out]	ierr	Error indicator

Author: Knut Morten Okstad

Date: 15 Dec 2005

◆ funcderivative2()

subroutine, private explicitfunctionsmodule::funcderivative2	(	integer, intent(in)	ikf,
		integer, intent(in)	iorder,
		integer, dimension(:), intent(in)	ifunc,
		real(dp), dimension(:), intent(in)	rfunc,
		real(dp), dimension(:), intent(in)	x,
		real(dp), intent(out)	fn,
		integer, intent(out)	ierr
	)

private

Evaluates the derivative of a multi-argument explicit function.

Parameters

[in]	ikf	Function identification number
[in]	iorder	Derivative order
[in]	ifunc	Integer function input parameters
[in]	rfunc	Real function input parameters
[in]	x	Function arguments
[out]	fn	Derivative of function
[out]	ierr	Error indicator

Author: Knut Morten Okstad

Date: 15 Oct 2009

◆ funcintegral()

subroutine explicitfunctionsmodule::funcintegral	(	integer, intent(in)	ikf,
		integer, intent(in)	iorder,
		integer, dimension(:), intent(in)	ifunc,
		real(dp), dimension(:), intent(in)	rfunc,
		real(dp), intent(in)	x,
		real(dp), intent(out)	fn,
		integer, intent(inout)	ierr
	)

Integrates an explicit function from 0.0 to x.

Parameters

[in]	ikf	Function identification number
[in]	iorder	Integration order
[in]	ifunc	Integer function input parameters
[in]	rfunc	Real function input parameters
[in]	x	Function arguments
[out]	fn	Integral of function
[out]	ierr	Error indicator

Author: Knut Morten Okstad

Date: 15 Dec 2004

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◆ funcvalue1()

subroutine, private explicitfunctionsmodule::funcvalue1	(	integer, intent(in)	ikf,
		integer, dimension(:), intent(in)	ifunc,
		real(dp), dimension(:), intent(in)	rfunc,
		real(dp), intent(in)	x,
		real(dp), intent(out)	fn,
		integer, intent(inout)	ierr
	)

private

Evaluates an explicit function.

Parameters

[in]	ikf	Function identification number
[in]	ifunc	Integer function input parameters
[in]	rfunc	Real function input parameters
[in]	x	Function argument
[out]	fn	Value of function
[out]	ierr	Error indicator

Author: Ole Ivar Sivertsen SINTEF avd. for maskinkonstruksjon

Date: 1989

◆ funcvalue2()

subroutine, private explicitfunctionsmodule::funcvalue2	(	integer, intent(in)	ikf,
		integer, dimension(:), intent(in)	ifunc,
		real(dp), dimension(:), intent(in)	rfunc,
		real(dp), dimension(:), intent(in)	x,
		real(dp), intent(out)	fn,
		integer, intent(inout)	ierr
	)

private

Evaluates an (possibly) multi-argument explicit function.

Parameters

[in]	ikf	Function identification number
[in]	ifunc	Integer function input parameters
[in]	rfunc	Real function input parameters
[in]	x	Function arguments
[out]	fn	Value of function
[out]	ierr	Error indicator

Author: Knut Morten Okstad

Date: 15 Oct 2009

◆ outofrangeerror()

subroutine, private explicitfunctionsmodule::outofrangeerror	(	real(dp), intent(in)	X,
		real(dp), intent(in)	X0,
		real(dp), intent(in)	X1
	)

private

Prints an error message when function argument is out of range.

◆ rampintegral()

real(dp) function, private explicitfunctionsmodule::rampintegral	(	integer, intent(in)	IORD,
		real(dp), intent(in)	X,
		real(dp), intent(in)	OFFSET,
		real(dp), intent(in)	SLOPE,
		real(dp), intent(in)	X0,
		real(dp), intent(in), optional	X3
	)

private

Integrate a ramp function from 0.0 to X.

Parameters

[in]	IORD	Integration order (1 or 2)
[in]	X	End point of integration
[in]	OFFSET	Function value offset
[in]	SLOPE	Ramp slope
[in]	X0	Start point for ramp
[in]	X3	End point for ramp

Returns: Function integral at point X

Author: Knut Morten Okstad

Date: 2006

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◆ splin3()

subroutine, private explicitfunctionsmodule::splin3	(	real(dp), dimension(:), intent(in)	X,
		real(dp), dimension(:), intent(in)	Y,
		real(dp), dimension(:,:), intent(inout)	DERIV,
		integer, intent(in)	N,
		real(dp), dimension(:), intent(in)	Z,
		real(dp), dimension(:), intent(out)	FVALUE,
		real(dp), dimension(:,:), intent(out)	FDERIV,
		integer, intent(in)	M,
		integer, intent(in)	IOP,
		integer, intent(out)	IERR
	)

private

Computes a spline approximation from a set of points.

The following is from the original FORTRAN-77 documententation:

CERN LIBRARY PROGRAM NO E-209.
nummat library PROGRAM no e201.
 
revised version july 1973.
 
purpose : to compute a natural spline approximation of third
          order for a FUNCTION y(X) given in the n points
          (x(i),y(i)) , i=1...n.
 
parameters(in list).
 
x       = an array storing the input arguments.dimension x(n).
y       = an array storing the input FUNCTION values.the element
          y(i) represent the FUNCTION value y(X) for x=x(I).
deriv   = an array used for storing the computed derivatives of
          the FUNCTION y(X).in deriv(I,1) and deriv(I,2) are
          stored the first- and second-order derivatives of y(x)
          for x=x(i) respectively.
n       = number of input FUNCTION values.
z       = an array storing the arguments for the interpolated
          values to be computed.
fvalue  = an array storing the computed interpolated values.
          fvalue(j) represent the FUNCTION value fvalue(Z) for
          z=z(j).
fderiv  = an array used for storing the derivatives of the com-
          puted interpolated values.explanation as for deriv.
m       = number of interpolated values to be computed.
iop     = option PARAMETER.for iop.LE.0 the derivatives for each
          sub-interval in the spline approximation are computed.
          <0, the second order END-POINT DERIVATIVES are
              computed by linear extrapolation.
          =0, the second order END-POINT DERIVATIVES ASSUMED to
              be given.
          =1, compute spline approximations for the arguments
              given in the array z,the derivatives beeing
              assumed to have been calculated in a previous call
              on the routine.
ierr    = error PARAMETER.
          =0, no errors occurred.
          =1, the number of points too small i.e. n less than 4.
          =2, the arguments x(i) not in increasing order.
          =3, argument to be used in interpolation above range.
          =4, argument to be used in interpolation below range.
 
local variables(static).
 
secd1   = VALUE of the second derivative d2y(x)/dx2 for the
          input argument x=x(1).
secdn   = VALUE of the second derivative d2y(x)/dx2 for the
          input argument x=x(n).
          nb. values have to be assigned to secd1 and secdn in
          the calling program.IF a natural spline fit is wanted,
          put secd1=secdn=0.
vofint  = computed approximation for the integral of y(x) taken
          from x(1) to x(n).
nxy     = n(see above),has to be stored for entries
          corresponding to iop=1.

Variable Documentation

◆ compl_sinus_p

integer, parameter explicitfunctionsmodule::compl_sinus_p = 2

◆ constant_p

integer, parameter explicitfunctionsmodule::constant_p = 15

◆ dbgfunc

integer, save explicitfunctionsmodule::dbgfunc = 0

File unit number of debug print.

◆ delayed_compl_sinus_p

integer, parameter explicitfunctionsmodule::delayed_compl_sinus_p = 3

◆ device_function_p

integer, parameter explicitfunctionsmodule::device_function_p = 18

◆ dirac_puls_p

integer, parameter explicitfunctionsmodule::dirac_puls_p = 14

◆ dp

integer, parameter, private explicitfunctionsmodule::dp = kind(1.0D0)

private

8-byte real (double)

◆ epsarg_p

real(dp), parameter, private explicitfunctionsmodule::epsarg_p = 1.0e-15_dp

private

Argument tolerance.

◆ functype_p

character(len=19), dimension(maxfunc_p), parameter explicitfunctionsmodule::functype_p = (/ 'SINUSOIDAL ', 'COMPL_SINUS ', 'DELAYED_COMPL_SINUS', 'WAVE_SINUS ', 'LIN_VEL_VAR ', 'SPLINE ', 'WAVE_STOKES5 ', 'WAVE_STREAMLINE ', 'WAVE_EMBEDDED ', 'LIN_VAR ', 'RAMP ', 'STEP ', 'SQUARE_PULS ', 'DIRAC_PULS ', 'CONSTANT ', 'LIM_RAMP ', 'SCALE ', 'DEVICE_FUNCTION ', 'MATH_EXPRESSION ', 'MATH_EXPRESSION ', 'USER_DEFINED ', 'SMOOTH_TRAJ ' /)

Function type names.

◆ last

integer, dimension(nspln_p), save explicitfunctionsmodule::last = 0

Identifier for splines in core.

◆ lim_ramp_p

integer, parameter explicitfunctionsmodule::lim_ramp_p = 16

◆ lin_var_p

integer, parameter explicitfunctionsmodule::lin_var_p = 10

◆ lin_vel_var_p

integer, parameter explicitfunctionsmodule::lin_vel_var_p = 5

◆ math_expression_p

integer, parameter explicitfunctionsmodule::math_expression_p = 19

◆ maxfunc_p

integer, parameter explicitfunctionsmodule::maxfunc_p = 22

Number of function types.

◆ nspln_p

integer, parameter explicitfunctionsmodule::nspln_p = 6

Max. number of spline functions in core.

◆ pi

real(dp), parameter, private explicitfunctionsmodule::pi = 3.141592653589793238_dp

private

The value of π.

◆ ramp_p

integer, parameter explicitfunctionsmodule::ramp_p = 11

◆ scale_p

integer, parameter explicitfunctionsmodule::scale_p = 17

◆ sinusoidal_p

integer, parameter explicitfunctionsmodule::sinusoidal_p = 1

◆ smooth_traj_p

integer, parameter explicitfunctionsmodule::smooth_traj_p = 22

◆ spl

type(splinedata), dimension(nspln_p), save, private explicitfunctionsmodule::spl

private

Internal spline data buffer.

◆ spline_p

integer, parameter explicitfunctionsmodule::spline_p = 6

◆ square_puls_p

integer, parameter explicitfunctionsmodule::square_puls_p = 13

◆ step_p

integer, parameter explicitfunctionsmodule::step_p = 12

◆ twopi

real(dp), parameter, private explicitfunctionsmodule::twopi = PI+PI

private

The value of 2π.

◆ user_defined_p

integer, parameter explicitfunctionsmodule::user_defined_p = 21

◆ wave_embedded_p

integer, parameter explicitfunctionsmodule::wave_embedded_p = 9

◆ wave_sinus_p

integer, parameter explicitfunctionsmodule::wave_sinus_p = 4

◆ wave_stokes5_p

integer, parameter explicitfunctionsmodule::wave_stokes5_p = 7

◆ wave_streamline_p

integer, parameter explicitfunctionsmodule::wave_streamline_p = 8

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ canintegrateexplicitly()

◆ deallocatesplines()

◆ func1()

◆ func10()

◆ func10diff()

◆ func10integral()

◆ func11()

◆ func12()

◆ func13()

◆ func14()

◆ func15()

◆ func16()

◆ func17()

◆ func18()

◆ func18integral()

◆ func19()

◆ func19diff()

◆ func2()

◆ func20()

◆ func20diff()

◆ func21()

◆ func21diff()

◆ func22()

◆ func4()

◆ func5()

◆ func6()

◆ func8()

◆ func9()

◆ funcderivative1()

◆ funcderivative2()

◆ funcintegral()

◆ funcvalue1()

◆ funcvalue2()

◆ outofrangeerror()

◆ rampintegral()

◆ splin3()

Variable Documentation

◆ compl_sinus_p

◆ constant_p

◆ dbgfunc

◆ delayed_compl_sinus_p

◆ device_function_p

◆ dirac_puls_p

◆ dp

◆ epsarg_p

◆ functype_p

◆ last

◆ lim_ramp_p

◆ lin_var_p

◆ lin_vel_var_p

◆ math_expression_p

◆ maxfunc_p

◆ nspln_p

◆ pi

◆ ramp_p

◆ scale_p

◆ sinusoidal_p

◆ smooth_traj_p

◆ spl

◆ spline_p

◆ square_puls_p

◆ step_p

◆ twopi

◆ user_defined_p

◆ wave_embedded_p

◆ wave_sinus_p

◆ wave_stokes5_p

◆ wave_streamline_p