Class for finding the root of a one dimensional function using the Brent algorithm.

It will use the Brent Method for finding function roots in a given interval. First, a grid search is used to bracket the root value with the a step size = (xmax-xmin)/npx. The step size can be controlled via the SetNpx() function. A default value of npx = 100 is used. The default value con be changed using the static method SetDefaultNpx. If the function is unimodal or if its extrema are far apart, setting the fNpx to a small value speeds the algorithm up many times. Then, Brent's method is applied on the bracketed interval. It will use the Brent Method for finding function roots in a given interval. If the Brent method fails to converge the bracketing is repeated on the latest best estimate of the interval. The procedure is repeated with a maximum value (default =10) which can be set for all BrentRootFinder classes with the method SetDefaultNSearch

This class is implemented from TF1::GetX() method.

Definition at line 51 of file BrentRootFinder.h.

Public Member Functions
	BrentRootFinder ()
	Default Constructor.

	~BrentRootFinder () override
	Default Destructor.

virtual int	Iterate ()
	This method is implemented only by the GSLRootFinder and GSLRootFinderDeriv classes and will return an error if it's not one of them.

int	Iterations () const override
	Return number of iteration used to find minimum.

const char *	Name () const override
	Return name of root finder algorithm ("BrentRootFinder").

double	Root () const override
	Returns root value.

virtual bool	SetFunction (const ROOT::Math::IGenFunction &, double, double)
	Set function to solve and the interval in where to look for the root.

bool	SetFunction (const ROOT::Math::IGenFunction &f, double xlow, double xup) override
	Sets the function for the rest of the algorithms.

virtual bool	SetFunction (const ROOT::Math::IGradFunction &, double)
	Set function to solve and the interval in where to look for the root.

void	SetLogScan (bool on)
	Set a log grid scan (default is equidistant bins) will work only if xlow > 0.

void	SetNpx (int npx)
	Set the number of point used to bracket root using a grid.

bool	Solve (int maxIter=100, double absTol=1E-8, double relTol=1E-10) override
	Returns the X value corresponding to the function value fy for (xmin<x<xmax).

int	Status () const override
	Returns status of last estimate.

Static Public Member Functions
static void	SetDefaultNpx (int npx)
	set number of default Npx used at construction time (when SetNpx is not called) Default value is 100

static void	SetDefaultNSearch (int n)
	set number of times the bracketing search in combination with is done to find a good interval Default value is 10

Private Attributes
const IGenFunction *	fFunction
	Pointer to the function.

bool	fLogScan
	flag to control usage of a log scan

int	fNIter
	Number of iterations needed for the last estimation.

int	fNpx
	Number of points to bracket root with initial grid (def is 100)

double	fRoot
	Current estimation of the function root.

int	fStatus
	Status of code of the last estimate.

double	fXMax
	Upper bound of the search interval.

double	fXMin
	Lower bound of the search interval.

#include <Math/BrentRootFinder.h>

Inheritance diagram for ROOT::Math::BrentRootFinder:

Constructor & Destructor Documentation

◆ BrentRootFinder()

ROOT::Math::BrentRootFinder::BrentRootFinder ( )

Default Constructor.

Definition at line 28 of file BrentRootFinder.cxx.

◆ ~BrentRootFinder()

ROOT::Math::BrentRootFinder::~BrentRootFinder ( )

inlineoverride

Default Destructor.

Definition at line 60 of file BrentRootFinder.h.

Member Function Documentation

◆ Iterate()

virtual int ROOT::Math::IRootFinderMethod::Iterate ( )

inlinevirtualinherited

This method is implemented only by the GSLRootFinder and GSLRootFinderDeriv classes and will return an error if it's not one of them.

Reimplemented in ROOT::Math::GSLRootFinder, and ROOT::Math::GSLRootFinderDeriv.

Definition at line 79 of file IRootFinderMethod.h.

◆ Iterations()

int ROOT::Math::BrentRootFinder::Iterations ( ) const

inlineoverridevirtual

Return number of iteration used to find minimum.

Reimplemented from ROOT::Math::IRootFinderMethod.

Definition at line 104 of file BrentRootFinder.h.

◆ Name()

const char * ROOT::Math::BrentRootFinder::Name ( ) const

overridevirtual

Return name of root finder algorithm ("BrentRootFinder").

Implements ROOT::Math::IRootFinderMethod.

Definition at line 62 of file BrentRootFinder.cxx.

◆ Root()

double ROOT::Math::BrentRootFinder::Root ( ) const

inlineoverridevirtual

Returns root value.

Need to call first Solve().

Implements ROOT::Math::IRootFinderMethod.

Definition at line 98 of file BrentRootFinder.h.

◆ SetDefaultNpx()

void ROOT::Math::BrentRootFinder::SetDefaultNpx ( int npx )

static

set number of default Npx used at construction time (when SetNpx is not called) Default value is 100

Definition at line 37 of file BrentRootFinder.cxx.

◆ SetDefaultNSearch()

void ROOT::Math::BrentRootFinder::SetDefaultNSearch ( int n )

static

set number of times the bracketing search in combination with is done to find a good interval Default value is 10

Definition at line 39 of file BrentRootFinder.cxx.

◆ SetFunction() [1/3]

virtual bool ROOT::Math::IRootFinderMethod::SetFunction	(	const ROOT::Math::IGenFunction &	,
		double	,
		double	)

inlinevirtual

Set function to solve and the interval in where to look for the root.

@param f Function to be minimized. @param xlow Lower bound of the search interval. @param xup Upper bound of the search interval.

Reimplemented from ROOT::Math::IRootFinderMethod.

Definition at line 53 of file IRootFinderMethod.h.

◆ SetFunction() [2/3]

bool ROOT::Math::BrentRootFinder::SetFunction	(	const ROOT::Math::IGenFunction &	,
		double	,
		double	)

overridevirtual

Sets the function for the rest of the algorithms.

The parameters set the interval where the root has to be calculated.

Reimplemented from ROOT::Math::IRootFinderMethod.

Definition at line 42 of file BrentRootFinder.cxx.

◆ SetFunction() [3/3]

virtual bool ROOT::Math::IRootFinderMethod::SetFunction	(	const ROOT::Math::IGradFunction &	,
		double	)

inlinevirtual

Set function to solve and the interval in where to look for the root.

@param f Function to be minimized. @param xlow Lower bound of the search interval. @param xup Upper bound of the search interval.

Reimplemented from ROOT::Math::IRootFinderMethod.

Definition at line 45 of file IRootFinderMethod.h.

◆ SetLogScan()

void ROOT::Math::BrentRootFinder::SetLogScan ( bool on )

inline

Set a log grid scan (default is equidistant bins) will work only if xlow > 0.

Definition at line 95 of file BrentRootFinder.h.

◆ SetNpx()

void ROOT::Math::BrentRootFinder::SetNpx ( int npx )

inline

Set the number of point used to bracket root using a grid.

Definition at line 89 of file BrentRootFinder.h.

◆ Solve()

bool ROOT::Math::BrentRootFinder::Solve	(	int	maxIter = 100,
		double	absTol = 1E-8,
		double	relTol = 1E-10 )

overridevirtual

Returns the X value corresponding to the function value fy for (xmin<x<xmax).

Method: First, the grid search is used to bracket the maximum with the step size = (xmax-xmin)/fNpx. This way, the step size can be controlled via the SetNpx() function. If the function is unimodal or if its extrema are far apart, setting the fNpx to a small value speeds the algorithm up many times. Then, Brent's method is applied on the bracketed interval.

@param maxIter maximum number of iterations. @param absTol desired absolute error in the minimum position. @param absTol desired relative error in the minimum position.

Implements ROOT::Math::IRootFinderMethod.

Definition at line 66 of file BrentRootFinder.cxx.

◆ Status()

int ROOT::Math::BrentRootFinder::Status ( ) const

inlineoverridevirtual

Returns status of last estimate.

If = 0 is OK

Implements ROOT::Math::IRootFinderMethod.

Definition at line 101 of file BrentRootFinder.h.

Member Data Documentation

◆ fFunction

const IGenFunction* ROOT::Math::BrentRootFinder::fFunction

private

Pointer to the function.

Definition at line 124 of file BrentRootFinder.h.

◆ fLogScan

bool ROOT::Math::BrentRootFinder::fLogScan

private

flag to control usage of a log scan

Definition at line 125 of file BrentRootFinder.h.

◆ fNIter

int ROOT::Math::BrentRootFinder::fNIter

private

Number of iterations needed for the last estimation.

Definition at line 126 of file BrentRootFinder.h.

◆ fNpx

int ROOT::Math::BrentRootFinder::fNpx

private

Number of points to bracket root with initial grid (def is 100)

Definition at line 127 of file BrentRootFinder.h.

◆ fRoot

double ROOT::Math::BrentRootFinder::fRoot

private

Current estimation of the function root.

Definition at line 131 of file BrentRootFinder.h.

◆ fStatus

int ROOT::Math::BrentRootFinder::fStatus

private

Status of code of the last estimate.

Definition at line 128 of file BrentRootFinder.h.

◆ fXMax

double ROOT::Math::BrentRootFinder::fXMax

private

Upper bound of the search interval.

Definition at line 130 of file BrentRootFinder.h.

◆ fXMin

double ROOT::Math::BrentRootFinder::fXMin

private

Lower bound of the search interval.

Definition at line 129 of file BrentRootFinder.h.

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

math/mathcore/inc/Math/BrentRootFinder.h
math/mathcore/src/BrentRootFinder.cxx

Public Member Functions

Static Public Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ BrentRootFinder()

◆ ~BrentRootFinder()

Member Function Documentation

◆ Iterate()

◆ Iterations()

◆ Name()

◆ Root()

◆ SetDefaultNpx()

◆ SetDefaultNSearch()

◆ SetFunction() [1/3]

◆ SetFunction() [2/3]

◆ SetFunction() [3/3]

◆ SetLogScan()

◆ SetNpx()

◆ Solve()

◆ Status()

Member Data Documentation

◆ fFunction

◆ fLogScan

◆ fNIter

◆ fNpx

◆ fRoot

◆ fStatus

◆ fXMax

◆ fXMin