Classes
class	RootFind
	Root finder for 1D problems. More...

struct	RootFind::rfTable
	Structure containing the iteration history. More...

class	solveProb
	Method to solve a pseudo steady state of a nonlinear problem. More...

Functions
	RootFind (ResidEval *resid)
	Constructor for the object.

	RootFind (const RootFind &r)
	Copy constructor.

	~RootFind ()
	Destructor. Deletes the integrator.

RootFind &	operator= (const RootFind &right)
	Assignment operator.

doublereal	delXNonzero (doublereal x1) const
	Calculate a deltaX from an input value of x.

doublereal	delXMeaningful (doublereal x1) const
	Calculate a deltaX from an input value of x.

doublereal	deltaXControlled (doublereal x2, doublereal x1) const
	Calculate a controlled, nonzero delta between two numbers.

bool	theSame (doublereal x2, doublereal x1, doublereal factor=1.0) const
	Function to decide whether two real numbers are the same or not.

int	solve (doublereal xmin, doublereal xmax, int itmax, doublereal &funcTargetValue, doublereal *xbest)
	Using a line search method, find the root of a 1D function.

doublereal	func (doublereal x)
	Return the function value.

void	setTol (doublereal rtolf, doublereal atolf, doublereal rtolx=0.0, doublereal atolx=0.0)
	Set the tolerance parameters for the rootfinder.

void	setPrintLvl (int printLvl)
	Set the print level from the rootfinder.

void	setFuncIsGenerallyIncreasing (bool value)
	Set the function behavior flag.

void	setFuncIsGenerallyDecreasing (bool value)
	Set the function behavior flag.

void	setDeltaX (doublereal deltaXNorm)
	Set the minimum value of deltaX.

void	setDeltaXMax (doublereal deltaX)
	Set the maximum value of deltaX.

void	printTable ()
	Print the iteration history table.

Variables
ResidEval *	m_residFunc
	Pointer to the residual function evaluator.

doublereal	m_funcTargetValue
	Target value for the function. We seek the value of f that is equal to this value.

doublereal	m_atolf
	Absolute tolerance for the value of f.

doublereal	m_atolx
	Absolute tolerance for the value of x.

doublereal	m_rtolf
	Relative tolerance for the value of f and x.

doublereal	m_rtolx
	Relative tolerance for the value of x.

doublereal	m_maxstep
	Maximum number of step sizes.

int	printLvl
	Print level.

bool	writeLogAllowed_
	Boolean to turn on the possibility of writing a log file.

doublereal	DeltaXnorm_
	Delta X norm. This is the nominal value of deltaX that will be used by the program.

int	specifiedDeltaXnorm_
	Boolean indicating whether DeltaXnorm_ has been specified by the user or not.

doublereal	DeltaXMax_
	Delta X Max. This is the maximum value of deltaX that will be used by the program.

int	specifiedDeltaXMax_
	Boolean indicating whether DeltaXMax_ has been specified by the user or not.

bool	FuncIsGenerallyIncreasing_
	Boolean indicating whether the function is an increasing with x.

bool	FuncIsGenerallyDecreasing_
	Boolean indicating whether the function is decreasing with x.

doublereal	deltaXConverged_
	Value of delta X that is needed for convergence.

doublereal	x_maxTried_
	Internal variable tracking largest x tried.

doublereal	fx_maxTried_
	Internal variable tracking f(x) of largest x tried.

doublereal	x_minTried_
	Internal variable tracking smallest x tried.

doublereal	fx_minTried_
	Internal variable tracking f(x) of smallest x tried.

std::vector< struct rfTable >	rfHistory_
	Vector of iteration histories.

Constant which determines the return integer from the routine
#define	ROOTFIND_SUCCESS 0
	This means that the root solver was a success.

#define	ROOTFIND_SUCCESS_XCONVERGENCEONLY 1
	This return value means that the root finder resolved a solution in the x coordinate However, convergence in F was not achieved.

#define	ROOTFIND_FAILEDCONVERGENCE -1
	This means that the root solver failed to achieve convergence.

#define	ROOTFIND_BADINPUT -2
	This means that the input to the root solver was defective.

#define	ROOTFIND_SOLNLOWERTHANXMIN -3
	This means that the rootfinder believes the solution is lower than xmin.

#define	ROOTFIND_SOLNHIGHERTHANXMAX -4
	This means that the rootfinder believes the solution is higher than xmax.

int	its

int	TP_its

double	slope

double	xval

double	fval

int	foundPos

int	foundNeg

double	deltaXConverged

double	deltaFConverged

double	delX

std::string	reasoning

void	clear ()

Detailed Description

Macro Definition Documentation

#define ROOTFIND_SUCCESS 0

This means that the root solver was a success.

Definition at line 30 of file RootFind.h.

Referenced by RedlichKwongMFTP::densSpinodalGas(), RedlichKwongMFTP::densSpinodalLiquid(), and RootFind::solve().

#define ROOTFIND_SUCCESS_XCONVERGENCEONLY 1

This return value means that the root finder resolved a solution in the x coordinate However, convergence in F was not achieved.

A common situation for this to happen is that f(x) is discontinuous about f(x) = f_0, where we seek the x where the function is equal to f_0. f(x) spans the f_0 while not being equal to f_0 anywhere.

Definition at line 38 of file RootFind.h.

Referenced by RootFind::solve().

#define ROOTFIND_FAILEDCONVERGENCE -1

This means that the root solver failed to achieve convergence.

Definition at line 40 of file RootFind.h.

Referenced by RootFind::solve().

#define ROOTFIND_BADINPUT -2

This means that the input to the root solver was defective.

Definition at line 42 of file RootFind.h.

Referenced by RootFind::solve().

#define ROOTFIND_SOLNLOWERTHANXMIN -3

This means that the rootfinder believes the solution is lower than xmin.

Definition at line 44 of file RootFind.h.

Referenced by RootFind::solve().

#define ROOTFIND_SOLNHIGHERTHANXMAX -4

This means that the rootfinder believes the solution is higher than xmax.

Definition at line 49 of file RootFind.h.

Referenced by RootFind::solve().

Function Documentation

RootFind ( ResidEval * resid )

Constructor for the object.

Parameters

resid Pointer to the residual function to be used to calculate f(x)

Definition at line 71 of file RootFind.cpp.

RootFind ( const RootFind & r )

Copy constructor.

Parameters

r	object to be copied

Definition at line 96 of file RootFind.cpp.

~RootFind ( )

Destructor. Deletes the integrator.

Definition at line 122 of file RootFind.cpp.

RootFind & operator= ( const RootFind & right )

Assignment operator.

Parameters

right object to be copied

Returns: returns a reference to the current object

Definition at line 126 of file RootFind.cpp.

References RootFind::deltaXConverged_, RootFind::DeltaXMax_, RootFind::DeltaXnorm_, RootFind::FuncIsGenerallyDecreasing_, RootFind::FuncIsGenerallyIncreasing_, RootFind::fx_maxTried_, RootFind::fx_minTried_, RootFind::m_atolf, RootFind::m_atolx, RootFind::m_funcTargetValue, RootFind::m_maxstep, RootFind::m_residFunc, RootFind::m_rtolf, RootFind::m_rtolx, RootFind::printLvl, RootFind::specifiedDeltaXMax_, RootFind::specifiedDeltaXnorm_, RootFind::writeLogAllowed_, RootFind::x_maxTried_, and RootFind::x_minTried_.

doublereal delXNonzero ( doublereal x1 ) const

private

Calculate a deltaX from an input value of x.

This routine ensure that the deltaX will be greater or equal to DeltaXNorm_ or 1.0E-14 x

Parameters

x1	input value of x

Definition at line 162 of file RootFind.cpp.

References RootFind::DeltaXnorm_.

Referenced by RootFind::deltaXControlled(), and RootFind::delXMeaningful().

doublereal delXMeaningful ( doublereal x1 ) const

private

Calculate a deltaX from an input value of x.

This routine ensure that the deltaX will be greater or equal to DeltaXNorm_ or 1.0E-14 x or deltaXConverged_.

Parameters

x1	input value of x

Definition at line 179 of file RootFind.cpp.

References RootFind::deltaXConverged_, and RootFind::delXNonzero().

Referenced by RootFind::solve(), and RootFind::theSame().

double deltaXControlled	(	doublereal	x2,
		doublereal	x1
	)		const

private

Calculate a controlled, nonzero delta between two numbers.

The delta is designed to be greater than or equal to delXMeaningful(x) defined above with the same sign as the original delta. Therefore if you subtract it from either of the two original numbers, you get a different number.

Parameters

x2	first number
x1	second number

Definition at line 197 of file RootFind.cpp.

References RootFind::delXNonzero().

Referenced by RootFind::solve().

bool theSame	(	doublereal	x2,
		doublereal	x1,
		doublereal	factor = `1.0`
	)		const

private

Function to decide whether two real numbers are the same or not.

A comparison is made between the two numbers to decide whether they are close to one another. This is defined as being within factor * delXMeaningful() of each other.

The basic premise here is that if the two numbers are too close, the noise will prevent an accurate calculation of the function and its slope.

Parameters

x1	First number
x2	second number
factor	Multiplicative factor to multiple deltaX with

Returns: Returns a boolean indicating whether the two numbers are the same or not.

Definition at line 223 of file RootFind.cpp.

References RootFind::delXMeaningful(), and ckr::max().

Referenced by RootFind::solve().

int solve	(	doublereal	xmin,
		doublereal	xmax,
		int	itmax,
		doublereal &	funcTargetValue,
		doublereal *	xbest
	)

Using a line search method, find the root of a 1D function.

This routine solves the following equation.

\[ R(x) = f(x) - f_o = 0 \]

Parameters

xmin	Minimum value of x to be used.
xmax	Maximum value of x to be used
itmax	maximum number of iterations. Usually, it can be less than 50.
funcTargetValue	Value of \( f_o \) in the equation. On return, it contains the value of the function actually obtained.
xbest	Returns the x that satisfies the function On input, xbest should contain the best estimate of the solution. An attempt to find the solution near xbest is made.

Returns: : 0 = ROOTFIND_SUCCESS Found function -1 = ROOTFIND_FAILEDCONVERGENCE Failed to find the answer -2 = ROOTFIND_BADINPUT Bad input was detected

Definition at line 245 of file RootFind.cpp.

References AssertThrow, RootFind::deltaXControlled(), RootFind::deltaXConverged_, RootFind::DeltaXMax_, RootFind::DeltaXnorm_, RootFind::delXMeaningful(), Cantera::fp2str(), RootFind::func(), RootFind::FuncIsGenerallyDecreasing_, RootFind::FuncIsGenerallyIncreasing_, RootFind::m_atolf, RootFind::m_atolx, RootFind::m_funcTargetValue, RootFind::m_rtolf, RootFind::m_rtolx, ckr::max(), ckr::min(), Cantera::print_funcEval(), RootFind::printLvl, RootFind::printTable(), RootFind::rfHistory_, ROOTFIND_BADINPUT, ROOTFIND_FAILEDCONVERGENCE, ROOTFIND_SOLNHIGHERTHANXMAX, ROOTFIND_SOLNLOWERTHANXMIN, ROOTFIND_SUCCESS, ROOTFIND_SUCCESS_XCONVERGENCEONLY, RootFind::specifiedDeltaXMax_, RootFind::specifiedDeltaXnorm_, RootFind::theSame(), Cantera::writelog(), RootFind::writeLogAllowed_, Cantera::writelogf(), RootFind::x_maxTried_, and RootFind::x_minTried_.

Referenced by RedlichKwongMFTP::densSpinodalGas(), and RedlichKwongMFTP::densSpinodalLiquid().

doublereal func ( doublereal x )

Return the function value.

This routine evaluates the following equation.

\[ R(x) = f(x) - f_o = 0 \]

Parameters

x	Value of the independent variable

Returns: The routine returns the value of \( R(x) \)

Definition at line 1182 of file RootFind.cpp.

References mdp::checkFinite(), RootFind::fx_maxTried_, RootFind::fx_minTried_, RootFind::m_funcTargetValue, RootFind::m_residFunc, RootFind::x_maxTried_, and RootFind::x_minTried_.

Referenced by RootFind::solve().

void setTol	(	doublereal	rtolf,
		doublereal	atolf,
		doublereal	rtolx = `0.0`,
		doublereal	atolx = `0.0`
	)

Set the tolerance parameters for the rootfinder.

These tolerance parameters are used on the function value and the independent value to determine convergence

Parameters

rtolf	Relative tolerance. The default is 10^-5
atolf	absolute tolerance. The default is 10^-11
rtolx	Relative tolerance. The default is 10^-5 Default parameter is 0.0, in which case rtolx is set equal to rtolf
atolx	absolute tolerance. The default is 10^-11 Default parameter is 0.0, in which case atolx is set equal to atolf

Definition at line 1212 of file RootFind.cpp.

References RootFind::m_atolf, RootFind::m_atolx, RootFind::m_rtolf, and RootFind::m_rtolx.

Referenced by RedlichKwongMFTP::densSpinodalGas(), and RedlichKwongMFTP::densSpinodalLiquid().

void setPrintLvl ( int printLvl )

Set the print level from the rootfinder.

0 -> absolutely nothing is printed for a single time step. 1 -> One line summary per solve_nonlinear call 2 -> short description, points of interest: Table of nonlinear solve - one line per iteration 3 -> Table is included -> More printing per nonlinear iteration (default) that occurs during the table 4 -> Summaries of the nonlinear solve iteration as they are occurring -> table no longer printed 5 -> Algorithm information on the nonlinear iterates are printed out 6 -> Additional info on the nonlinear iterates are printed out 7 -> Additional info on the linear solve is printed out. 8 -> Info on a per iterate of the linear solve is printed out.

Parameters

printLvl integer value

Definition at line 1243 of file RootFind.cpp.

References RootFind::printLvl.

Referenced by RedlichKwongMFTP::densSpinodalGas(), and RedlichKwongMFTP::densSpinodalLiquid().

void setFuncIsGenerallyIncreasing ( bool value )

Set the function behavior flag.

If this is true, the function is generally an increasing function of x. In particular, if the algorithm is seeking a higher value of f, it will look in the positive x direction.

This type of function is needed because this algorithm must deal with regions of f(x) where f is not changing with x.

Parameters

value boolean value

Definition at line 1259 of file RootFind.cpp.

References RootFind::FuncIsGenerallyDecreasing_, and RootFind::FuncIsGenerallyIncreasing_.

Referenced by RedlichKwongMFTP::densSpinodalGas().

void setFuncIsGenerallyDecreasing ( bool value )

Set the function behavior flag.

If this is true, the function is generally a decreasing function of x. In particular, if the algorithm is seeking a higher value of f, it will look in the negative x direction.

This type of function is needed because this algorithm must deal with regions of f(x) where f is not changing with x.

Parameters

value boolean value

Definition at line 1278 of file RootFind.cpp.

References RootFind::FuncIsGenerallyDecreasing_, and RootFind::FuncIsGenerallyIncreasing_.

Referenced by RedlichKwongMFTP::densSpinodalLiquid().

void setDeltaX ( doublereal deltaXNorm )

Set the minimum value of deltaX.

This sets the value of deltaXNorm_

Parameters

deltaXNorm

Definition at line 1292 of file RootFind.cpp.

References RootFind::DeltaXnorm_, and RootFind::specifiedDeltaXnorm_.

void setDeltaXMax ( doublereal deltaX )

Set the maximum value of deltaX.

This sets the value of deltaXMax_

Parameters

deltaX

Definition at line 1304 of file RootFind.cpp.

References RootFind::DeltaXMax_, and RootFind::specifiedDeltaXMax_.

void printTable ( )

Print the iteration history table.

Definition at line 1312 of file RootFind.cpp.

References RootFind::m_funcTargetValue, and RootFind::rfHistory_.

Referenced by RootFind::solve().

Variable Documentation

ResidEval* m_residFunc

Pointer to the residual function evaluator.

Definition at line 338 of file RootFind.h.

Referenced by RootFind::func(), and RootFind::operator=().

doublereal m_funcTargetValue

Target value for the function. We seek the value of f that is equal to this value.

Definition at line 341 of file RootFind.h.

Referenced by RootFind::func(), RootFind::operator=(), RootFind::printTable(), and RootFind::solve().

doublereal m_atolf

Absolute tolerance for the value of f.

Definition at line 344 of file RootFind.h.

Referenced by RootFind::operator=(), RootFind::setTol(), and RootFind::solve().

doublereal m_atolx

Absolute tolerance for the value of x.

Definition at line 347 of file RootFind.h.

Referenced by RootFind::operator=(), RootFind::setTol(), and RootFind::solve().

doublereal m_rtolf

Relative tolerance for the value of f and x.

Definition at line 350 of file RootFind.h.

Referenced by RootFind::operator=(), RootFind::setTol(), and RootFind::solve().

doublereal m_rtolx

Relative tolerance for the value of x.

Definition at line 353 of file RootFind.h.

Referenced by RootFind::operator=(), RootFind::setTol(), and RootFind::solve().

doublereal m_maxstep

Maximum number of step sizes.

Definition at line 356 of file RootFind.h.

Referenced by RootFind::operator=().

int printLvl

protected

Print level.

0 No printing of any kind 1 Single print line indicating success or failure of the routine. 2 Summary table printed at the end of the routine, with a convergence history 3 Printouts during the iteration are added. Summary table is printed out at the end. if writeLogAllowed_ is turned on, a file is written out with the convergence history.

Definition at line 368 of file RootFind.h.

Referenced by RootFind::operator=(), RootFind::setPrintLvl(), and RootFind::solve().

bool writeLogAllowed_

Boolean to turn on the possibility of writing a log file.

Definition at line 373 of file RootFind.h.

Referenced by RootFind::operator=(), and RootFind::solve().

doublereal DeltaXnorm_

protected

Delta X norm. This is the nominal value of deltaX that will be used by the program.

Definition at line 377 of file RootFind.h.

Referenced by RootFind::delXNonzero(), RootFind::operator=(), RootFind::setDeltaX(), and RootFind::solve().

int specifiedDeltaXnorm_