User Class to find the Root of one dimensional functions.

The GSL Methods are implemented in MathMore and they are loaded automatically via the plug-in manager

The possible types of Root-finding algorithms are:

Root Bracketing Algorithms which do not require function derivatives
1. RootFinder::kBRENT (default method implemented in MathCore)
2. RootFinder::kGSL_BISECTION
3. RootFinder::kGSL_FALSE_POS
4. RootFinder::kGSL_BRENT
Root Finding Algorithms using Derivatives

This class does not cupport copying

Definition at line 73 of file RootFinder.h.

Public Types
enum	EType { kBRENT , kGSL_BISECTION , kGSL_FALSE_POS , kGSL_BRENT , kGSL_NEWTON , kGSL_SECANT , kGSL_STEFFENSON }

Public Member Functions
	RootFinder (RootFinder::EType type=RootFinder::kBRENT)
	Construct a Root-Finder algorithm.

virtual	~RootFinder ()

int	Iterate ()
	Perform a single iteration and return the Status.

int	Iterations () const
	Return the number of iteration performed to find the Root.

const char *	Name () const
	Return the current and latest estimate of the lower value of the Root-finding interval (for bracketing algorithms)

double	Root () const
	Return the current and latest estimate of the Root.

bool	SetFunction (const IGenFunction &f, double xlow, double xup)
	Provide to the solver the function and the initial search interval [xlow, xup] for algorithms not using derivatives (bracketing algorithms) The templated function f must be of a type implementing the operator() method, double operator() ( double x ) Returns non zero if interval is not valid (i.e.

bool	SetFunction (const IGradFunction &f, double xstart)
	Provide to the solver the function and an initial estimate of the root, for algorithms using derivatives.

bool	SetMethod (RootFinder::EType type=RootFinder::kBRENT)

template<class Function , class Derivative >
bool	Solve (Function &f, Derivative &d, double start, int maxIter=100, double absTol=1E-8, double relTol=1E-10)
	Solve `f(x) = 0`, given a derivative `d`.

template<class Function >
bool	Solve (Function &f, double min, double max, int maxIter=100, double absTol=1E-8, double relTol=1E-10)
	Solve `f(x) = 0` numerically.

bool	Solve (int maxIter=100, double absTol=1E-8, double relTol=1E-10)
	Compute the roots iterating until the estimate of the Root is within the required tolerance returning the iteration Status.

int	Status () const
	Return the status of the last estimate of the Root = 0 OK, not zero failure.

Private Member Functions
	RootFinder (const RootFinder &)

RootFinder &	operator= (const RootFinder &rhs)

Private Attributes
IRootFinderMethod *	fSolver

#include <Math/RootFinder.h>

Member Enumeration Documentation

◆ EType

enum ROOT::Math::RootFinder::EType

Enumerator
kBRENT
kGSL_BISECTION
kGSL_FALSE_POS
kGSL_BRENT
kGSL_NEWTON
kGSL_SECANT
kGSL_STEFFENSON

Definition at line 77 of file RootFinder.h.

Constructor & Destructor Documentation

◆ RootFinder() [1/2]

ROOT::Math::RootFinder::RootFinder ( RootFinder::EType type = RootFinder::kBRENT )

Construct a Root-Finder algorithm.

Definition at line 40 of file RootFinder.cxx.

◆ ~RootFinder()

ROOT::Math::RootFinder::~RootFinder ( )

virtual

Definition at line 142 of file RootFinder.cxx.

◆ RootFinder() [2/2]

ROOT::Math::RootFinder::RootFinder ( const RootFinder & )

inlineprivate

Definition at line 90 of file RootFinder.h.

Member Function Documentation

◆ Iterate()

int ROOT::Math::RootFinder::Iterate ( )

inline

Perform a single iteration and return the Status.

Definition at line 153 of file RootFinder.h.

◆ Iterations()

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

inline

Return the number of iteration performed to find the Root.

Definition at line 146 of file RootFinder.h.

◆ Name()

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

inline

Return the current and latest estimate of the lower value of the Root-finding interval (for bracketing algorithms)

Return the current and latest estimate of the upper value of the Root-finding interval (for bracketing algorithms) Get Name of the Root-finding solver algorithm

Definition at line 190 of file RootFinder.h.

◆ operator=()

RootFinder & ROOT::Math::RootFinder::operator= ( const RootFinder & rhs )

inlineprivate

Definition at line 91 of file RootFinder.h.

◆ Root()

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

inline

Return the current and latest estimate of the Root.

Definition at line 160 of file RootFinder.h.

◆ SetFunction() [1/2]

bool ROOT::Math::RootFinder::SetFunction	(	const IGenFunction &	f,
		double	xlow,
		double	xup
	)

inline

Provide to the solver the function and the initial search interval [xlow, xup] for algorithms not using derivatives (bracketing algorithms) The templated function f must be of a type implementing the operator() method, double operator() ( double x ) Returns non zero if interval is not valid (i.e.

does not contains a root)

Definition at line 109 of file RootFinder.h.

◆ SetFunction() [2/2]

bool ROOT::Math::RootFinder::SetFunction	(	const IGradFunction &	f,
		double	xstart
	)

inline

Provide to the solver the function and an initial estimate of the root, for algorithms using derivatives.

The templated function f must be of a type implementing the operator() and the Gradient() methods. double operator() ( double x ) Returns non zero if starting point is not valid

Definition at line 123 of file RootFinder.h.

◆ SetMethod()

bool ROOT::Math::RootFinder::SetMethod ( RootFinder::EType type = RootFinder::kBRENT )

Definition at line 47 of file RootFinder.cxx.

◆ Solve() [1/3]

template<class Function , class Derivative >

bool ROOT::Math::RootFinder::Solve	(	Function &	f,
		Derivative &	d,
		double	start,
		int	maxIter = `100`,
		double	absTol = `1E-8`,
		double	relTol = `1E-10`
	)

Solve f(x) = 0, given a derivative d.

Parameters

f	Function whose root should be found.
d	Derivative of the function.
start	Starting point for iteration.
maxIter	Maximum number of iterations, passed to Solve(int,double,double)
absTol	Absolute tolerance, as in Solve(int,double,double)
relTol	Relative tolerance, passed to Solve(int,double,double)

Returns: true if a root was found. Retrieve the result using Root().

Definition at line 224 of file RootFinder.h.

◆ Solve() [2/3]

template<class Function >

bool ROOT::Math::RootFinder::Solve	(	Function &	f,
		double	min,
		double	max,
		int	maxIter = `100`,
		double	absTol = `1E-8`,
		double	relTol = `1E-10`
	)

Solve f(x) = 0 numerically.

Parameters

f	Function whose root should be found.
min	Minimum allowed value of `x`.
max	Maximum allowed value of `x`.
maxIter	Maximum number of iterations, passed to Solve(int,double,double)
absTol	Absolute tolerance, as in Solve(int,double,double)
relTol	Relative tolerance, passed to Solve(int,double,double)

Returns: true if a root was found. Retrieve the result using Root().

Definition at line 245 of file RootFinder.h.

◆ Solve() [3/3]

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

inline

Compute the roots iterating until the estimate of the Root is within the required tolerance returning the iteration Status.

Definition at line 139 of file RootFinder.h.

◆ Status()

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

inline

Return the status of the last estimate of the Root = 0 OK, not zero failure.

Definition at line 168 of file RootFinder.h.

Member Data Documentation

◆ fSolver

IRootFinderMethod* ROOT::Math::RootFinder::fSolver

private

Definition at line 200 of file RootFinder.h.

Libraries for ROOT::Math::RootFinder:

[legend]

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

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

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Member Enumeration Documentation

◆ EType

Constructor & Destructor Documentation

◆ RootFinder() [1/2]

◆ ~RootFinder()

◆ RootFinder() [2/2]

Member Function Documentation

◆ Iterate()

◆ Iterations()

◆ Name()

◆ operator=()

◆ Root()

◆ SetFunction() [1/2]

◆ SetFunction() [2/2]

◆ SetMethod()

◆ Solve() [1/3]

◆ Solve() [2/3]

◆ Solve() [3/3]

◆ Status()

Member Data Documentation

◆ fSolver