Root finder for 1D problems. More...

#include <RootFind.h>

Collaboration diagram for RootFind:

Classes
struct	rfTable
	Structure containing the iteration history. More...

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

	RootFind (const RootFind &r)

RootFind &	operator= (const RootFind &right)

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

doublereal	func (doublereal x)
	Return the function value. More...

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

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

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

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

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

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

void	printTable ()
	Print the iteration history table. More...

Public Attributes
ResidEval *	m_residFunc
	Pointer to the residual function evaluator. More...

doublereal	m_funcTargetValue
	Target value for the function. More...

doublereal	m_atolf
	Absolute tolerance for the value of f. More...

doublereal	m_atolx
	Absolute tolerance for the value of x. More...

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

doublereal	m_rtolx
	Relative tolerance for the value of x. More...

doublereal	m_maxstep
	Maximum number of step sizes. More...

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

Protected Attributes
int	printLvl
	Print level. More...

doublereal	DeltaXnorm_
	Delta X norm. More...

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

doublereal	DeltaXMax_
	Delta X Max. More...

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

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

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

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

doublereal	x_maxTried_
	Internal variable tracking largest x tried. More...

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

doublereal	x_minTried_
	Internal variable tracking smallest x tried. More...

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

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

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

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

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

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

Detailed Description

Root finder for 1D problems.

Deprecated:: Unused. To be removed after Cantera 2.3. See boost::math::tools::toms748_solve for an alternative.

The root finder solves a single nonlinear equation described below.

\[ f(x) = f_0 \]

\( f(x) \) is assumed to be single valued as a function of x. \( f(x) \) is not assumed to be continuous nor is its derivative assumed to be well formed.

Root finders are significantly different in the sense that do not have to rely solely on Newton's method to find the answer to the problem. Instead they use a method to bound the solution between high and low values and then use a method to refine that bound. The eventual solution to the problem is presented as x_best and as a bound, delta_X, on the solution component. Because of this, they are far more stable for functions and Jacobians that have discontinuities or noise associated with them.

The algorithm is a convolution of a local Secant method with an approach of finding a straddle in x. The Jacobian is never required.

There is a general breakdown of the algorithm into stages. The first stage seeks to find a straddle of the function. The second stage seeks to reduce the bounds in x and f in order to satisfy the specification of the stopping criteria. In the last stage the algorithm seeks to find the base value of x that satisfies the original equation given what it current knows about the function.

Globalization strategy

Specifying the General Changes in x

Supplying Hints with General Function Behavior Flags

Stopping Criteria

Specification of the Stopping Criteria

Additional constraints

Bounds Criteria For the Routine

Example

// Define a residual. The definition of a residual involves a lot more work than is shown here.
ResidEval * ec;
// Instantiate the root finder with the residual to be solved, ec.
RootFind rf(&ec);
// Set the relative and absolute tolerances for f and x.
rf.setTol(1.0E-5, 1.0E-10, 1.0E-5, 1.0E-11);
// Give a hint about the function's dependence on x. This is needed, for example, if the function has
// flat regions.
rf.setFuncIsGenerallyIncreasing(true);
rf.setDeltaX(0.01);
// Supply an initial guess for the solution
double xbest = phiM;
double oldP = printLvl_;
// Set the print level for the solver. Zero produces no output. Two produces a summary table of each iteration.
rf.setPrintLvl(2);
// Define a minimum and maximum for the independent variable.
double phimin = 1.3;
double phimax = 2.2;
// Define a maximum iteration number
int itmax = 100;
// Define the f_0 value, and on return will contain the actual value of f(x) obtained
double currentObtained;
// Call the solver
status = rf.solve(phimin, phimax, 100, currentObtained, &xbest);
if (status == 0) {
  if (printLvl_ > 1) {
    printf("Electrode::integrateConstantCurrent(): Volts (%g amps) = %g\n", currentObtained, xbest);
  }
} else {
  if (printLvl_) {
     printf("Electrode::integrateConstantCurrent(): bad status = %d Volts (%g amps) = %g\n",
            status, currentObtained, xbest);
  }
}

Todo:

Noise

General Search to be done when all else fails

Definition at line 133 of file RootFind.h.

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

Classes

Public Member Functions

Public Attributes

Protected Attributes

Private Member Functions

Detailed Description