Namespaces
	Cephes

	Minim1D

	Util

Classes
class	BasicFitMethodFunction

class	BasicMinimizer

class	Derivator

struct	EvaluatorOneDim

struct	EvaluatorOneDim< const ROOT::Math::IParamMultiFunction & >

class	Functor

class	Functor1D

class	FunctorGradHandler

class	FunctorHandler

class	FunctorImpl

class	GenAlgoOptions

class	GeneticMinimizer

struct	GeneticMinimizerParameters

class	GradFunctor

class	GradFunctor1D

class	GSL1DMinimizerWrapper

class	GSLDerivator

class	GSLFunctionAdapter

class	GSLFunctionDerivWrapper

class	GSLFunctionWrapper

class	GSLMinimizer

class	GSLMinimizer1D

class	GSLMultiFit

class	GSLMultiFitFunctionAdapter

class	GSLMultiFitFunctionWrapper

class	GSLMultiMinDerivFunctionWrapper

struct	GSLMultiMinFunctionAdapter

class	GSLMultiMinFunctionWrapper

class	GSLMultiMinimizer

class	GSLNLSMinimizer

class	GSLRandomEngine

class	GSLRngCMRG

class	GSLRngGFSR4

class	GSLRngMinStd

class	GSLRngMixMax

class	GSLRngMRG

class	GSLRngMT

class	GSLRngRand

class	GSLRngRanLux

class	GSLRngRanLuxD1

class	GSLRngRanLuxD2

class	GSLRngRanLuxS1

class	GSLRngRanLuxS2

class	GSLRngRanMar

struct	GSLRngROOTWrapper

class	GSLRngTaus

class	GSLRngWrapper

class	GSLSimAnFunc

class	GSLSimAnMinimizer

class	GSLSimAnnealing

struct	GSLSimAnParams

class	IBaseFunctionMultiDimTempl

class	IBaseFunctionOneDim

class	IBaseParam

class	IGradientFunctionMultiDimTempl

class	IGradientFunctionOneDim

class	IGradientMultiDimTempl

class	IGradientOneDim

class	IMinimizer1D

class	IOptions

class	IParametricFunctionMultiDimTempl

class	IParametricFunctionOneDim

class	IParametricGradFunctionMultiDimTempl

class	IParametricGradFunctionOneDim

class	KahanSum
	The Kahan compensate summation algorithm significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers. This is done by keeping a separate running compensation (a variable to accumulate small errors). . More...

class	LSResidualFunc

class	MemFunHandler

class	MemGradFunHandler

class	Minimizer

class	MinimizerOptions

class	MinimizerVariableTransformation

class	MinimTransformFunction

class	MinimTransformVariable

class	MixMaxEngine

class	MixMaxEngineImpl

class	MixMaxEngineImpl< ROOT_MM_N >

class	MultiNumGradFunction

struct	NullTypeFunc1D

class	OneDimMultiFunctionAdapter

class	OneDimParamFunctionAdapter

class	RandomFunctions

class	RandomFunctions< EngineType, ROOT::Math::GSLRandomEngine >

class	RandomFunctionsImpl

class	RandomFunctionsImpl< TRandomEngine >

class	SinVariableTransformation

class	SqrtLowVariableTransformation

class	SqrtUpVariableTransformation

class	TRandomEngine

class	WrappedFunction

class	WrappedMemFunction

class	WrappedMemMultiFunction

class	WrappedMultiFunction

class	WrappedParamFunction

class	WrappedParamFunctionGen

Typedefs
typedef TRandomEngine	DefaultEngineType

typedef BasicFitMethodFunction< ROOT::Math::IMultiGenFunction >	FitMethodFunction

typedef BasicFitMethodFunction< ROOT::Math::IMultiGradFunction >	FitMethodGradFunction

typedef double(*	FreeFunctionPtr) (double)

typedef double(*	FreeMultiFunctionPtr) (const double *)

typedef double(*	FreeParamMultiFunctionPtr) (const double , const double )

typedef void(*	GSLFdfPointer) (double, void , double , double *)

typedef double(*	GSLFuncPointer) (double, void *)

typedef void(*	GSLMultiFitDfPointer) (const gsl_vector , void , gsl_matrix *)

typedef void(*	GSLMultiFitFdfPointer) (const gsl_vector , void , gsl_vector , gsl_matrix )

typedef double(*	GSLMultiFitFPointer) (const gsl_vector , void , gsl_vector *)

typedef void(*	GSLMultiMinDfPointer) (const gsl_vector , void , gsl_vector *)

typedef void(*	GSLMultiMinFdfPointer) (const gsl_vector , void , double , gsl_vector )

typedef double(*	GSLMultiMinFuncPointer) (const gsl_vector , void )

typedef GSLRngRanLuxS1	GSLRngRanLux1

typedef GSLRngRanLuxS2	GSLRngRanLux2

typedef GSLRngRanLuxD2	GSLRngRanLux48

using	IBaseFunctionMultiDim = IBaseFunctionMultiDimTempl< double >

typedef IBaseFunctionOneDim	IGenFunction

typedef IGradientFunctionOneDim	IGradFunction

using	IGradientFunctionMultiDim = IGradientFunctionMultiDimTempl< double >

using	IGradientMultiDim = IGradientMultiDimTempl< double >

using	IMultiGenFunction = IMultiGenFunctionTempl< double >

template<class T >
using	IMultiGenFunctionTempl = IBaseFunctionMultiDimTempl< T >

typedef IGradientFunctionMultiDim	IMultiGradFunction

using	IParametricFunctionMultiDim = IParametricFunctionMultiDimTempl< double >

using	IParametricGradFunctionMultiDim = IParametricGradFunctionMultiDimTempl< double >

typedef IParametricFunctionOneDim	IParamFunction

typedef IParametricGradFunctionOneDim	IParamGradFunction

typedef IParametricFunctionMultiDim	IParamMultiFunction

template<class T >
using	IParamMultiFunctionTempl = IParametricFunctionMultiDimTempl< T >

typedef IParametricGradFunctionMultiDim	IParamMultiGradFunction

template<class T >
using	IParamMultiGradFunctionTempl = IParametricGradFunctionMultiDimTempl< T >

typedef MixMaxEngine< 17, 0 >	MixMaxEngine17

typedef MixMaxEngine< 240, 0 >	MixMaxEngine240

typedef MixMaxEngine< 256, 2 >	MixMaxEngine256

Enumerations
enum	EGSLMinimizerType { kConjugateFR , kConjugatePR , kVectorBFGS , kVectorBFGS2 , kSteepestDescent }

enum	EMinimVariableType { kDefault , kFix , kBounds , kLowBound , kUpBound }

Functions
double	beta_cdf (double x, double a, double b)

double	beta_cdf_c (double x, double a, double b)

double	binomial_cdf (unsigned int k, double p, unsigned int n)

double	binomial_cdf_c (unsigned int k, double p, unsigned int n)

double	breitwigner_cdf (double x, double gamma, double x0=0)

double	breitwigner_cdf_c (double x, double gamma, double x0=0)

double	cauchy_cdf (double x, double b, double x0=0)

double	cauchy_cdf_c (double x, double b, double x0=0)

double	chisquared_cdf (double x, double r, double x0=0)

double	chisquared_cdf_c (double x, double r, double x0=0)

double	crystalball_cdf (double x, double alpha, double n, double sigma, double x0=0)

double	crystalball_cdf_c (double x, double alpha, double n, double sigma, double x0=0)

double	crystalball_integral (double x, double alpha, double n, double sigma, double x0=0)

double	expm1 (double x)
	exp(x) -1 with error cancellation when x is small More...

double	exponential_cdf (double x, double lambda, double x0=0)

double	exponential_cdf_c (double x, double lambda, double x0=0)

double	fdistribution_cdf (double x, double n, double m, double x0=0)

double	fdistribution_cdf_c (double x, double n, double m, double x0=0)

double	gamma_cdf (double x, double alpha, double theta, double x0=0)

double	gamma_cdf_c (double x, double alpha, double theta, double x0=0)

double	gaussian_cdf (double x, double sigma=1, double x0=0)
	Alternative name for same function. More...

double	gaussian_cdf_c (double x, double sigma=1, double x0=0)
	Alternative name for same function. More...

double	landau_cdf (double x, double xi=1, double x0=0)

double	landau_cdf_c (double x, double xi=1, double x0=0)

double	landau_xm1 (double x, double xi=1, double x0=0)

double	landau_xm2 (double x, double xi=1, double x0=0)

double	log1p (double x)
	log(1+x) with error cancelatio when x is small More...

double	lognormal_cdf (double x, double m, double s, double x0=0)

double	lognormal_cdf_c (double x, double m, double s, double x0=0)

double	negative_binomial_cdf (unsigned int k, double p, double n)

double	negative_binomial_cdf_c (unsigned int k, double p, double n)

double	normal_cdf (double x, double sigma=1, double x0=0)

double	normal_cdf_c (double x, double sigma=1, double x0=0)

double	Pi ()

double	poisson_cdf (unsigned int n, double mu)

double	poisson_cdf_c (unsigned int n, double mu)

double	Polynomial1eval (double x, double *a, unsigned int N)

double	Polynomialeval (double x, double *a, unsigned int N)

double	tdistribution_cdf (double x, double r, double x0=0)

double	tdistribution_cdf_c (double x, double r, double x0=0)

double	uniform_cdf (double x, double a, double b, double x0=0)

double	uniform_cdf_c (double x, double a, double b, double x0=0)

Probability Density Functions from MathCore
Additional PDF's are provided in the MathMore library (see PDF functions from MathMore)
double	beta_pdf (double x, double a, double b)

double	binomial_pdf (unsigned int k, double p, unsigned int n)

double	negative_binomial_pdf (unsigned int k, double p, double n)

double	breitwigner_pdf (double x, double gamma, double x0=0)

double	cauchy_pdf (double x, double b=1, double x0=0)

double	chisquared_pdf (double x, double r, double x0=0)

double	crystalball_function (double x, double alpha, double n, double sigma, double x0=0)

double	crystalball_pdf (double x, double alpha, double n, double sigma, double x0=0)

double	exponential_pdf (double x, double lambda, double x0=0)

double	fdistribution_pdf (double x, double n, double m, double x0=0)

double	gamma_pdf (double x, double alpha, double theta, double x0=0)

double	gaussian_pdf (double x, double sigma=1, double x0=0)

double	bigaussian_pdf (double x, double y, double sigmax=1, double sigmay=1, double rho=0, double x0=0, double y0=0)

double	landau_pdf (double x, double xi=1, double x0=0)

double	lognormal_pdf (double x, double m, double s, double x0=0)

double	normal_pdf (double x, double sigma=1, double x0=0)

double	poisson_pdf (unsigned int n, double mu)

double	tdistribution_pdf (double x, double r, double x0=0)

double	uniform_pdf (double x, double a, double b, double x0=0)

Special Functions from MathCore
double	erf (double x)

double	erfc (double x)

double	tgamma (double x)

double	lgamma (double x)

double	inc_gamma (double a, double x)

double	inc_gamma_c (double a, double x)

double	beta (double x, double y)

double	inc_beta (double x, double a, double b)

double	sinint (double x)

double	cosint (double x)

Typedef Documentation

◆ DefaultEngineType

typedef TRandomEngine ROOT::Math::DefaultEngineType

Documentation for the RandomFunction class

Definition at line 47 of file RandomFunctions.h.

◆ FitMethodFunction

typedef BasicFitMethodFunction< ROOT::Math::IMultiGenFunction > ROOT::Math::FitMethodFunction

Definition at line 43 of file Fitter.h.

◆ FitMethodGradFunction

typedef BasicFitMethodFunction< ROOT::Math::IMultiGradFunction > ROOT::Math::FitMethodGradFunction

Definition at line 44 of file Fitter.h.

◆ FreeFunctionPtr

typedef double(* ROOT::Math::FreeFunctionPtr) (double)

Definition at line 39 of file WrappedFunction.h.

◆ FreeMultiFunctionPtr

typedef double(* ROOT::Math::FreeMultiFunctionPtr)(const double *)

Definition at line 41 of file WrappedFunction.h.

◆ FreeParamMultiFunctionPtr

typedef double( * ROOT::Math::FreeParamMultiFunctionPtr) (const double *, const double *)

Definition at line 29 of file WrappedParamFunction.h.

◆ GSLFdfPointer

typedef void( * ROOT::Math::GSLFdfPointer) (double, void *, double *, double *)

Definition at line 46 of file GSLFunctionWrapper.h.

◆ GSLFuncPointer

typedef double(* ROOT::Math::GSLFuncPointer)(double, void *)

Function pointer corresponding to gsl_function signature

Definition at line 45 of file GSLFunctionAdapter.h.

◆ GSLMultiFitDfPointer

typedef void( * ROOT::Math::GSLMultiFitDfPointer) (const gsl_vector *, void *, gsl_matrix *)

Definition at line 48 of file GSLMultiFitFunctionWrapper.h.

◆ GSLMultiFitFdfPointer

typedef void( * ROOT::Math::GSLMultiFitFdfPointer) (const gsl_vector *, void *, gsl_vector *, gsl_matrix *)

Definition at line 49 of file GSLMultiFitFunctionWrapper.h.

◆ GSLMultiFitFPointer

typedef double( * ROOT::Math::GSLMultiFitFPointer) (const gsl_vector *, void *, gsl_vector *)

Definition at line 47 of file GSLMultiFitFunctionWrapper.h.

◆ GSLMultiMinDfPointer

typedef void( * ROOT::Math::GSLMultiMinDfPointer) (const gsl_vector *, void *, gsl_vector *)

Definition at line 47 of file GSLMultiMinFunctionWrapper.h.

◆ GSLMultiMinFdfPointer

typedef void( * ROOT::Math::GSLMultiMinFdfPointer) (const gsl_vector *, void *, double *, gsl_vector *)

Definition at line 48 of file GSLMultiMinFunctionWrapper.h.

◆ GSLMultiMinFuncPointer

typedef double( * ROOT::Math::GSLMultiMinFuncPointer) (const gsl_vector *, void *)

Definition at line 46 of file GSLMultiMinFunctionWrapper.h.

◆ GSLRngRanLux1

typedef GSLRngRanLuxS1 ROOT::Math::GSLRngRanLux1

Definition at line 369 of file GSLRndmEngines.h.

◆ GSLRngRanLux2

typedef GSLRngRanLuxS2 ROOT::Math::GSLRngRanLux2

Definition at line 384 of file GSLRndmEngines.h.

◆ GSLRngRanLux48

typedef GSLRngRanLuxD2 ROOT::Math::GSLRngRanLux48

Definition at line 413 of file GSLRndmEngines.h.

◆ IBaseFunctionMultiDim

using ROOT::Math::IBaseFunctionMultiDim = typedef IBaseFunctionMultiDimTempl<double>

Definition at line 33 of file IFunctionfwd.h.

◆ IGenFunction

typedef IBaseFunctionOneDim ROOT::Math::IGenFunction

Definition at line 39 of file IFunctionfwd.h.

◆ IGradFunction

typedef IGradientFunctionOneDim ROOT::Math::IGradFunction

Definition at line 42 of file IFunctionfwd.h.

◆ IGradientFunctionMultiDim

using ROOT::Math::IGradientFunctionMultiDim = typedef IGradientFunctionMultiDimTempl<double>

Definition at line 36 of file IFunctionfwd.h.

◆ IGradientMultiDim

using ROOT::Math::IGradientMultiDim = typedef IGradientMultiDimTempl<double>

Definition at line 37 of file IFunctionfwd.h.

◆ IMultiGenFunction

typedef IBaseFunctionMultiDim ROOT::Math::IMultiGenFunction

Definition at line 34 of file IFunctionfwd.h.

◆ IMultiGenFunctionTempl

template<class T >

using ROOT::Math::IMultiGenFunctionTempl = typedef IBaseFunctionMultiDimTempl<T>

Definition at line 32 of file IFunctionfwd.h.

◆ IMultiGradFunction

typedef IGradientFunctionMultiDim ROOT::Math::IMultiGradFunction

Definition at line 43 of file IFunctionfwd.h.

◆ IParametricFunctionMultiDim

using ROOT::Math::IParametricFunctionMultiDim = typedef IParametricFunctionMultiDimTempl<double>

Definition at line 26 of file IParamFunctionfwd.h.

◆ IParametricGradFunctionMultiDim

using ROOT::Math::IParametricGradFunctionMultiDim = typedef IParametricGradFunctionMultiDimTempl<double>

Definition at line 29 of file IParamFunctionfwd.h.

◆ IParamFunction

typedef IParametricFunctionOneDim ROOT::Math::IParamFunction

Definition at line 31 of file IParamFunctionfwd.h.

◆ IParamGradFunction

typedef IParametricGradFunctionOneDim ROOT::Math::IParamGradFunction

Definition at line 36 of file IParamFunctionfwd.h.

◆ IParamMultiFunction

typedef IParametricFunctionMultiDim ROOT::Math::IParamMultiFunction

Definition at line 32 of file IParamFunctionfwd.h.

◆ IParamMultiFunctionTempl

template<class T >

using ROOT::Math::IParamMultiFunctionTempl = typedef IParametricFunctionMultiDimTempl<T>

Definition at line 34 of file IParamFunctionfwd.h.

◆ IParamMultiGradFunction

typedef IParametricGradFunctionMultiDim ROOT::Math::IParamMultiGradFunction

Definition at line 37 of file IParamFunctionfwd.h.

◆ IParamMultiGradFunctionTempl

template<class T >

using ROOT::Math::IParamMultiGradFunctionTempl = typedef IParametricGradFunctionMultiDimTempl<T>

Definition at line 39 of file IParamFunctionfwd.h.

◆ MixMaxEngine17

typedef MixMaxEngine<17,0> ROOT::Math::MixMaxEngine17

Definition at line 188 of file MixMaxEngine.h.

◆ MixMaxEngine240

typedef MixMaxEngine<240,0> ROOT::Math::MixMaxEngine240

Definition at line 186 of file MixMaxEngine.h.

◆ MixMaxEngine256

typedef MixMaxEngine<256,2> ROOT::Math::MixMaxEngine256

Definition at line 187 of file MixMaxEngine.h.

Enumeration Type Documentation

◆ EMinimVariableType

enum ROOT::Math::EMinimVariableType

Enumeration describing the status of the variable The enumeration are used in the minimizer classes to categorize the variables

Enumerator
kDefault
kFix
kBounds
kLowBound
kUpBound

Definition at line 27 of file MinimTransformVariable.h.

                               {
          kDefault,    // free variable (unlimited)
          kFix,        // fixed variable
          kBounds,     //  variable has two bounds
          kLowBound,   // variable has a lower bound
          kUpBound     // variable has an upper bounds
       };

Function Documentation

◆ expm1()

double ROOT::Math::expm1 ( double x )

inline

exp(x) -1 with error cancellation when x is small

Definition at line 112 of file Math.h.

                                {
 #ifndef HAVE_NO_EXPM1
    return ::expm1(x);
 #else
    // compute using taylor expansion until difference is less than epsilon
    // use for values smaller than 0.5 (for larger (exp(x)-1 is fine
    if (std::abs(x) < 0.5)
    {
        // taylor series S = x + (1/2!) x^2 + (1/3!) x^3 + ...
  
       double i = 1.0;
       double sum = x;
       double term = x / 1.0;
       do {
          i++ ;
          term *= x/i;
          sum += term;
       }
       while (std::abs(term) > std::abs(sum) * std::numeric_limits<double>::epsilon() ) ;
  
       return sum ;
    }
    else
    {
       return std::exp(x) - 1;
    }
 #endif
 }

◆ gaussian_cdf()

double ROOT::Math::gaussian_cdf	(	double	x,
		double	sigma = `1`,
		double	x0 = `0`
	)

inline

Alternative name for same function.

Definition at line 485 of file ProbFuncMathCore.h.

                                                                          {
       return normal_cdf(x,sigma,x0);
    }

References normal_cdf().

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◆ gaussian_cdf_c()

double ROOT::Math::gaussian_cdf_c	(	double	x,
		double	sigma = `1`,
		double	x0 = `0`
	)

inline

Alternative name for same function.

Definition at line 463 of file ProbFuncMathCore.h.

                                                                            {
       return normal_cdf_c(x,sigma,x0);
    }

References normal_cdf_c().

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◆ log1p()

double ROOT::Math::log1p ( double x )

inline

log(1+x) with error cancelatio when x is small

declarations for functions which are not implemented by some compilers

Definition at line 100 of file Math.h.

    {
 #ifndef HAVE_NO_LOG1P
    return ::log1p(x);
 #else
    // if log1p is not in c math library
   volatile double y;
   y = 1 + x;
   return std::log(y) - ((y-1)-x)/y ;  /* cancels errors with IEEE arithmetic */
 #endif
 }

◆ Pi()

double ROOT::Math::Pi ( )

inline

Mathematical constants

Definition at line 90 of file Math.h.

 {
    return M_PI;
    }

References M_PI.

◆ Polynomial1eval()

double ROOT::Math::Polynomial1eval	(	double	x,
		double *	a,
		unsigned int	N
	)

◆ Polynomialeval()

double ROOT::Math::Polynomialeval	(	double	x,
		double *	a,
		unsigned int	N
	)

Namespaces

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ DefaultEngineType

◆ FitMethodFunction

◆ FitMethodGradFunction

◆ FreeFunctionPtr

◆ FreeMultiFunctionPtr

◆ FreeParamMultiFunctionPtr

◆ GSLFdfPointer

◆ GSLFuncPointer

◆ GSLMultiFitDfPointer

◆ GSLMultiFitFdfPointer

◆ GSLMultiFitFPointer

◆ GSLMultiMinDfPointer

◆ GSLMultiMinFdfPointer

◆ GSLMultiMinFuncPointer

◆ GSLRngRanLux1

◆ GSLRngRanLux2

◆ GSLRngRanLux48

◆ IBaseFunctionMultiDim

◆ IGenFunction

◆ IGradFunction

◆ IGradientFunctionMultiDim

◆ IGradientMultiDim

◆ IMultiGenFunction

◆ IMultiGenFunctionTempl

◆ IMultiGradFunction

◆ IParametricFunctionMultiDim

◆ IParametricGradFunctionMultiDim

◆ IParamFunction

◆ IParamGradFunction

◆ IParamMultiFunction

◆ IParamMultiFunctionTempl

◆ IParamMultiGradFunction

◆ IParamMultiGradFunctionTempl

◆ MixMaxEngine17

◆ MixMaxEngine240

◆ MixMaxEngine256

Enumeration Type Documentation

◆ EMinimVariableType

Function Documentation

◆ expm1()

◆ gaussian_cdf()

◆ gaussian_cdf_c()

◆ log1p()

◆ Pi()

◆ Polynomial1eval()

◆ Polynomialeval()