Class for Multidimensional root finding algorithms bassed on GSL.

This class is used to solve a non-linear system of equations:

f1(x1,....xn) = 0 f2(x1,....xn) = 0 .................. fn(x1,....xn) = 0

See the GSL online manual for information on the GSL MultiRoot finding algorithms

The available GSL algorithms require the derivatives of the supplied functions or not (they are computed internally by GSL). In the first case the user needs to provide a list of multidimensional functions implementing the gradient interface (ROOT::Math::IMultiGradFunction) while in the second case it is enough to supply a list of functions impelmenting the ROOT::Math::IMultiGenFunction interface. The available algorithms requiring derivatives (see also the GSL documentation ) are the followings:

ROOT::Math::GSLMultiRootFinder::kHybridSJ with name <it>"HybridSJ"</it>: modified Powell's hybrid method as implemented in HYBRJ in MINPACK
ROOT::Math::GSLMultiRootFinder::kHybridJ with name <it>"HybridJ"</it>: unscaled version of the previous algorithm
ROOT::Math::GSLMultiRootFinder::kNewton with name <it>"Newton"</it>: Newton method
ROOT::Math::GSLMultiRootFinder::kGNewton with name <it>"GNewton"</it>: modified Newton method

The algorithms without derivatives (see also the GSL documentation ) are the followings:

ROOT::Math::GSLMultiRootFinder::kHybridS with name <it>"HybridS"</it>: same as HybridSJ but using finate difference approximation for the derivatives
ROOT::Math::GSLMultiRootFinder::kHybrid with name <it>"Hybrid"</it>: unscaled version of the previous algorithm
ROOT::Math::GSLMultiRootFinder::kDNewton with name <it>"DNewton"</it>: discrete Newton algorithm
ROOT::Math::GSLMultiRootFinder::kBroyden with name <it>"Broyden"</it>: Broyden algorithm

Definition at line 95 of file GSLMultiRootFinder.h.

Public Types
enum	EDerivType { kHybridSJ, kHybridJ, kNewton, kGNewton }
	enumeration specifying the types of GSL multi root finders requiring the derivatives More...

enum	EType { kHybridS, kHybrid, kDNewton, kBroyden }
	enumeration specifying the types of GSL multi root finders which do not require the derivatives More...

Public Member Functions
	GSLMultiRootFinder (EType type)
	create a multi-root finder based on an algorithm not requiring function derivative More...

	GSLMultiRootFinder (EDerivType type)
	create a multi-root finder based on an algorithm requiring function derivative More...

	GSLMultiRootFinder (const char *name=0)

virtual	~GSLMultiRootFinder ()
	destructor More...

int	AddFunction (const ROOT::Math::IMultiGenFunction &func)

template<class Function >
int	AddFunction (Function &f, int ndim)
	same method as before but using any function implementing the operator(), so can be wrapped in a IMultiGenFunction interface More...

void	Clear ()
	clear list of functions More...

unsigned int	Dim () const
	return the number of sunctions set in the class. More...

const double *	Dx () const
	return the last step size More...

const double *	FVal () const
	return the function values f(X) solving the system i.e. More...

int	Iterations () const
	Return number of iterations. More...

const char *	Name () const
	Return the algorithm name used for solving Note the name is available only after having called solved Otherwise an empyty string is returned. More...

int	PrintLevel () const
	return the print level More...

void	PrintState (std::ostream &os=std::cout)
	print iteration state More...

template<class FuncIterator >
bool	SetFunctionList (FuncIterator begin, FuncIterator end)

void	SetPrintLevel (int level)

void	SetType (EType type)
	set the type for an algorithm without derivatives More...

void	SetType (EDerivType type)
	set the type of algorithm using derivatives More...

void	SetType (const char *name)
	set the type using a string More...

bool	Solve (const double *x, int maxIter=0, double absTol=0, double relTol=0)
	Find the root starting from the point X; Use the number of iteration and tolerance if given otherwise use default parameter values which can be defined by the static method SetDefault... More...

int	Status () const
	Return the status of last root finding. More...

const double *	X () const
	return the root X values solving the system More...

Static Public Member Functions
static void	SetDefaultMaxIterations (int maxiter)
	set maximum number of iterations More...

static void	SetDefaultTolerance (double abstol, double reltol=0)
	set tolerance (absolute and relative) relative tolerance is only use to verify the convergence do it is a minor parameter More...

Protected Member Functions
void	ClearFunctions ()

std::pair< bool, int >	GetType (const char *name)

Private Member Functions
	GSLMultiRootFinder (const GSLMultiRootFinder &)

GSLMultiRootFinder &	operator= (const GSLMultiRootFinder &)

Private Attributes
std::vector< ROOT::Math::IMultiGenFunction * >	fFunctions

int	fIter

int	fPrintLevel

GSLMultiRootBaseSolver *	fSolver

int	fStatus

int	fType

bool	fUseDerivAlgo

#include <Math/GSLMultiRootFinder.h>

Member Enumeration Documentation

◆ EDerivType

enum ROOT::Math::GSLMultiRootFinder::EDerivType

enumeration specifying the types of GSL multi root finders requiring the derivatives

Enumerator
kHybridSJ
kHybridJ
kNewton
kGNewton

Definition at line 104 of file GSLMultiRootFinder.h.

◆ EType

enum ROOT::Math::GSLMultiRootFinder::EType

enumeration specifying the types of GSL multi root finders which do not require the derivatives

Enumerator
kHybridS
kHybrid
kDNewton
kBroyden

Definition at line 115 of file GSLMultiRootFinder.h.

Constructor & Destructor Documentation

◆ GSLMultiRootFinder() [1/4]

ROOT::Math::GSLMultiRootFinder::GSLMultiRootFinder ( EType type )

create a multi-root finder based on an algorithm not requiring function derivative

Definition at line 67 of file GSLMultiRootFinder.cxx.

◆ GSLMultiRootFinder() [2/4]

ROOT::Math::GSLMultiRootFinder::GSLMultiRootFinder ( EDerivType type )

create a multi-root finder based on an algorithm requiring function derivative

Definition at line 76 of file GSLMultiRootFinder.cxx.

◆ GSLMultiRootFinder() [3/4]

ROOT::Math::GSLMultiRootFinder::GSLMultiRootFinder ( const char * name = 0 )

Definition at line 85 of file GSLMultiRootFinder.cxx.

◆ ~GSLMultiRootFinder()

ROOT::Math::GSLMultiRootFinder::~GSLMultiRootFinder ( )

virtual

destructor

Definition at line 95 of file GSLMultiRootFinder.cxx.

◆ GSLMultiRootFinder() [4/4]

ROOT::Math::GSLMultiRootFinder::GSLMultiRootFinder ( const GSLMultiRootFinder & )

private

Definition at line 102 of file GSLMultiRootFinder.cxx.

Member Function Documentation

◆ AddFunction() [1/2]

int ROOT::Math::GSLMultiRootFinder::AddFunction ( const ROOT::Math::IMultiGenFunction & func )

Definition at line 122 of file GSLMultiRootFinder.cxx.

◆ AddFunction() [2/2]

template<class Function >

int ROOT::Math::GSLMultiRootFinder::AddFunction	(	Function &	f,
		int	ndim
	)

inline

same method as before but using any function implementing the operator(), so can be wrapped in a IMultiGenFunction interface

Definition at line 192 of file GSLMultiRootFinder.h.

◆ Clear()

void ROOT::Math::GSLMultiRootFinder::Clear ( )

clear list of functions

Definition at line 139 of file GSLMultiRootFinder.cxx.

◆ ClearFunctions()

void ROOT::Math::GSLMultiRootFinder::ClearFunctions ( )

protected

Definition at line 130 of file GSLMultiRootFinder.cxx.

◆ Dim()

unsigned int ROOT::Math::GSLMultiRootFinder::Dim ( ) const

inline

return the number of sunctions set in the class.

The number must be equal to the dimension of the functions

Definition at line 202 of file GSLMultiRootFinder.h.

◆ Dx()

const double * ROOT::Math::GSLMultiRootFinder::Dx ( ) const

return the last step size

Definition at line 151 of file GSLMultiRootFinder.cxx.

◆ FVal()

const double * ROOT::Math::GSLMultiRootFinder::FVal ( ) const

return the function values f(X) solving the system i.e.

they must be close to zero at the solution

Definition at line 155 of file GSLMultiRootFinder.cxx.

◆ GetType()

std::pair< bool, int > ROOT::Math::GSLMultiRootFinder::GetType ( const char * name )

protected

Definition at line 219 of file GSLMultiRootFinder.cxx.

◆ Iterations()

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

inline

Return number of iterations.

Definition at line 227 of file GSLMultiRootFinder.h.

◆ Name()

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

Return the algorithm name used for solving Note the name is available only after having called solved Otherwise an empyty string is returned.

Definition at line 159 of file GSLMultiRootFinder.cxx.

◆ operator=()

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

private

Definition at line 106 of file GSLMultiRootFinder.cxx.

◆ PrintLevel()

int ROOT::Math::GSLMultiRootFinder::PrintLevel ( ) const

inline

return the print level

Definition at line 248 of file GSLMultiRootFinder.h.

◆ PrintState()

void ROOT::Math::GSLMultiRootFinder::PrintState ( std::ostream & os = std::cout )

print iteration state

Definition at line 333 of file GSLMultiRootFinder.cxx.

◆ SetDefaultMaxIterations()

void ROOT::Math::GSLMultiRootFinder::SetDefaultMaxIterations ( int maxiter )

static

set maximum number of iterations

Definition at line 62 of file GSLMultiRootFinder.cxx.

◆ SetDefaultTolerance()

void ROOT::Math::GSLMultiRootFinder::SetDefaultTolerance	(	double	abstol,
		double	reltol = `0`
	)

static

set tolerance (absolute and relative) relative tolerance is only use to verify the convergence do it is a minor parameter

Definition at line 57 of file GSLMultiRootFinder.cxx.

◆ SetFunctionList()

template<class FuncIterator >

bool ROOT::Math::GSLMultiRootFinder::SetFunctionList	(	FuncIterator	begin,
		FuncIterator	end
	)

inline

Definition at line 171 of file GSLMultiRootFinder.h.

◆ SetPrintLevel()

void ROOT::Math::GSLMultiRootFinder::SetPrintLevel ( int level )

inline

Definition at line 245 of file GSLMultiRootFinder.h.

◆ SetType() [1/3]

void ROOT::Math::GSLMultiRootFinder::SetType ( EType type )

inline

set the type for an algorithm without derivatives

Definition at line 149 of file GSLMultiRootFinder.h.

◆ SetType() [2/3]

void ROOT::Math::GSLMultiRootFinder::SetType ( EDerivType type )

inline

set the type of algorithm using derivatives

Definition at line 154 of file GSLMultiRootFinder.h.

◆ SetType() [3/3]

void ROOT::Math::GSLMultiRootFinder::SetType ( const char * name )

set the type using a string

Definition at line 114 of file GSLMultiRootFinder.cxx.

◆ Solve()

bool ROOT::Math::GSLMultiRootFinder::Solve	(	const double *	x,
		int	maxIter = `0`,
		double	absTol = `0`,
		double	relTol = `0`
	)

Find the root starting from the point X; Use the number of iteration and tolerance if given otherwise use default parameter values which can be defined by the static method SetDefault...

Definition at line 236 of file GSLMultiRootFinder.cxx.

◆ Status()

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

inline

Return the status of last root finding.

Definition at line 232 of file GSLMultiRootFinder.h.

◆ X()

const double * ROOT::Math::GSLMultiRootFinder::X ( ) const

return the root X values solving the system

Definition at line 147 of file GSLMultiRootFinder.cxx.

Member Data Documentation

◆ fFunctions

std::vector<ROOT::Math::IMultiGenFunction *> ROOT::Math::GSLMultiRootFinder::fFunctions

private

Definition at line 286 of file GSLMultiRootFinder.h.

◆ fIter

int ROOT::Math::GSLMultiRootFinder::fIter

private

Definition at line 275 of file GSLMultiRootFinder.h.

◆ fPrintLevel

int ROOT::Math::GSLMultiRootFinder::fPrintLevel

private

Definition at line 277 of file GSLMultiRootFinder.h.

◆ fSolver

GSLMultiRootBaseSolver* ROOT::Math::GSLMultiRootFinder::fSolver

private

Definition at line 285 of file GSLMultiRootFinder.h.

◆ fStatus

int ROOT::Math::GSLMultiRootFinder::fStatus

private

Definition at line 276 of file GSLMultiRootFinder.h.

◆ fType

int ROOT::Math::GSLMultiRootFinder::fType

private

Definition at line 282 of file GSLMultiRootFinder.h.

◆ fUseDerivAlgo

bool ROOT::Math::GSLMultiRootFinder::fUseDerivAlgo

private

Definition at line 283 of file GSLMultiRootFinder.h.

Libraries for ROOT::Math::GSLMultiRootFinder:

[legend]

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Member Enumeration Documentation

◆ EDerivType

◆ EType

Constructor & Destructor Documentation

◆ GSLMultiRootFinder() [1/4]

◆ GSLMultiRootFinder() [2/4]

◆ GSLMultiRootFinder() [3/4]

◆ ~GSLMultiRootFinder()

◆ GSLMultiRootFinder() [4/4]

Member Function Documentation

◆ AddFunction() [1/2]

◆ AddFunction() [2/2]

◆ Clear()

◆ ClearFunctions()

◆ Dim()

◆ Dx()

◆ FVal()

◆ GetType()

◆ Iterations()

◆ Name()

◆ operator=()

◆ PrintLevel()

◆ PrintState()

◆ SetDefaultMaxIterations()

◆ SetDefaultTolerance()

◆ SetFunctionList()

◆ SetPrintLevel()

◆ SetType() [1/3]

◆ SetType() [2/3]

◆ SetType() [3/3]

◆ Solve()

◆ Status()

◆ X()

Member Data Documentation

◆ fFunctions

◆ fIter

◆ fPrintLevel

◆ fSolver

◆ fStatus

◆ fType

◆ fUseDerivAlgo