Parametric Function class describing polynomials of order n.

P(x) = p[0] + p[1]*x + p[2]*x**2 + ....... + p[n]*x**n

The class implements also the derivatives, dP(x)/dx and the dP(x)/dp[i].

The class provides also the method to find the roots of the polynomial. It uses analytical methods up to quartic polynomials.

Implements both the Parameteric function interface and the gradient interface since it provides the analytical gradient with respect to x

Definition at line 64 of file Polynomial.h.

Public Types
typedef ParamFunction< IParamGradFunction >	ParFunc

Public Types inherited from ROOT::Math::ParamFunction< IParamGradFunction >
typedef IPFType::BaseFunc	BaseFunc

typedef IParamGradFunction	BaseParFunc

Public Types inherited from ROOT::Math::IParametricGradFunctionOneDim
typedef IParametricFunctionOneDim::BaseFunc	BaseFunc

typedef IGradientFunctionOneDim	BaseGradFunc

typedef IParametricFunctionOneDim	BaseParamFunc

Public Types inherited from ROOT::Math::IParametricFunctionOneDim
typedef IBaseFunctionOneDim	BaseFunc

Public Types inherited from ROOT::Math::IBaseFunctionOneDim
typedef IBaseFunctionOneDim	BaseFunc

Public Types inherited from ROOT::Math::IGradientFunctionOneDim
typedef IBaseFunctionOneDim	BaseFunc

typedef IGradientFunctionOneDim	BaseGrad

Public Member Functions
	Polynomial (double a, double b)
	Construct a Polynomial of degree 1 : a*x + b.

	Polynomial (double a, double b, double c)
	Construct a Polynomial of degree 2 : ax2 + bx + c.

	Polynomial (double a, double b, double c, double d)
	Construct a Polynomial of degree 3 : ax3 + bx*2 + cx + d.

	Polynomial (double a, double b, double c, double d, double e)
	Construct a Polynomial of degree 4 : ax4 + bx*3 + cx**2 + dx + e.

	Polynomial (unsigned int n=0)
	Construct a Polynomial function of order n.

	~Polynomial () override

IGenFunction *	Clone () const override
	Clone a function.

void	FdF (double x, double &f, double &df) const override
	Optimized method to evaluate at the same time the function value and derivative at a point x.

const std::vector< std::complex< double > > &	FindNumRoots ()
	Find the polynomial roots using always an iterative numerical methods The numerical method used is from GSL (see documentation )

std::vector< double >	FindRealRoots ()
	Find the only the real polynomial roots.

const std::vector< std::complex< double > > &	FindRoots ()
	Find the polynomial roots.

unsigned int	Order () const
	Order of Polynomial.

Public Member Functions inherited from ROOT::Math::ParamFunction< IParamGradFunction >
	ParamFunction (unsigned int npar=0)
	Construct a parameteric function with npar parameters.

virtual	~ParamFunction ()

unsigned int	NPar () const
	Return the number of parameters.

virtual const double *	Parameters () const
	Access the parameter values.

virtual void	SetParameters (const double *p)
	Set the parameter values.

Public Member Functions inherited from ROOT::Math::IParametricGradFunctionOneDim
	~IParametricGradFunctionOneDim () override
	Virtual Destructor (no operations)

double	ParameterDerivative (const double x, const double p, unsigned int ipar=0) const
	Partial derivative with respect a parameter Compatibility interface with multi-dimensional functions.

double	ParameterDerivative (const double *x, unsigned int ipar=0) const
	Evaluate partial derivative using cached parameter values (multi-dim like interface)

double	ParameterDerivative (double x, const double *p, unsigned int ipar=0) const
	Partial derivative with respect a parameter.

double	ParameterDerivative (double x, unsigned int ipar=0) const
	Evaluate partial derivative using cached parameter values.

void	ParameterGradient (const double x, const double p, double *grad) const
	Compatibility interface with multi-dimensional functions.

void	ParameterGradient (const double x, double grad) const
	Evaluate all derivatives using cached parameter values (multi-dim like interface)

virtual void	ParameterGradient (double x, const double p, double grad) const
	Evaluate the derivatives of the function with respect to the parameters at a point x.

void	ParameterGradient (double x, double *grad) const
	Evaluate all derivatives using cached parameter values.

Public Member Functions inherited from ROOT::Math::IParametricFunctionOneDim
double	operator() (const double x, const double p) const
	multidim-like interface

double	operator() (double x, const double *p) const
	Evaluate function at a point x and for given parameters p.

Public Member Functions inherited from ROOT::Math::IBaseFunctionOneDim
virtual	~IBaseFunctionOneDim ()=default

double	operator() (const double *x) const
	Evaluate the function at a point x[].

double	operator() (double x) const
	Evaluate the function at a point x.

Public Member Functions inherited from ROOT::Math::IBaseParam
virtual	~IBaseParam ()
	Virtual Destructor (no operations)

virtual std::string	ParameterName (unsigned int i) const
	Return the name of the i-th parameter (starting from zero) Overwrite if want to avoid the default name ("Par_0, Par_1, ...")

Public Member Functions inherited from ROOT::Math::IGradientFunctionOneDim
double	Derivative (const double *x) const
	Compatibility method with multi-dimensional interface for partial derivative.

double	Derivative (double x) const
	Return the derivative of the function at a point x Use the private method DoDerivative.

void	FdF (const double x, double &f, double df) const
	Compatibility method with multi-dimensional interface for Gradient and function evaluation.

void	Gradient (const double x, double g) const
	Compatibility method with multi-dimensional interface for Gradient.

bool	HasGradient () const override

Private Member Functions
double	DoDerivative (double x) const override
	Function to evaluate the derivative with respect each coordinate. To be implemented by the derived class.

double	DoEvalPar (double x, const double *p) const override
	Implementation of the evaluation function using the x value and the parameters.

double	DoParameterDerivative (double x, const double *p, unsigned int ipar) const override
	Evaluate the gradient, to be implemented by the derived classes.

Private Attributes
std::vector< double >	fDerived_params

unsigned int	fOrder

std::vector< std::complex< double > >	fRoots

Additional Inherited Members
Protected Attributes inherited from ROOT::Math::ParamFunction< IParamGradFunction >
std::vector< double >	fParams

#include <Math/Polynomial.h>

Inheritance diagram for ROOT::Math::Polynomial:

[legend]

Member Typedef Documentation

◆ ParFunc

typedef ParamFunction<IParamGradFunction> ROOT::Math::Polynomial::ParFunc

Definition at line 71 of file Polynomial.h.

Constructor & Destructor Documentation

◆ Polynomial() [1/5]

ROOT::Math::Polynomial::Polynomial ( unsigned int n = 0 )

Construct a Polynomial function of order n.

The number of Parameters is n+1.

Definition at line 49 of file Polynomial.cxx.

◆ Polynomial() [2/5]

ROOT::Math::Polynomial::Polynomial	(	double	a,
		double	b
	)

Construct a Polynomial of degree 1 : a*x + b.

Definition at line 58 of file Polynomial.cxx.

◆ Polynomial() [3/5]

ROOT::Math::Polynomial::Polynomial	(	double	a,
		double	b,
		double	c
	)

Construct a Polynomial of degree 2 : a*x**2 + b*x + c.

Definition at line 68 of file Polynomial.cxx.

◆ Polynomial() [4/5]

ROOT::Math::Polynomial::Polynomial	(	double	a,
		double	b,
		double	c,
		double	d
	)

Construct a Polynomial of degree 3 : a*x**3 + b*x**2 + c*x + d.

Definition at line 79 of file Polynomial.cxx.

◆ Polynomial() [5/5]

ROOT::Math::Polynomial::Polynomial	(	double	a,
		double	b,
		double	c,
		double	d,
		double	e
	)

Construct a Polynomial of degree 4 : a*x**4 + b*x**3 + c*x**2 + dx + e.

Definition at line 92 of file Polynomial.cxx.

◆ ~Polynomial()

ROOT::Math::Polynomial::~Polynomial ( )

inlineoverride

Definition at line 100 of file Polynomial.h.

Member Function Documentation

◆ Clone()

IGenFunction * ROOT::Math::Polynomial::Clone ( ) const

overridevirtual

Clone a function.

Each derived class will implement their version of the private DoClone method.

Implements ROOT::Math::IBaseFunctionOneDim.

Definition at line 143 of file Polynomial.cxx.

◆ DoDerivative()

double ROOT::Math::Polynomial::DoDerivative ( double x ) const

overrideprivatevirtual

Function to evaluate the derivative with respect each coordinate. To be implemented by the derived class.

Implements ROOT::Math::IGradientFunctionOneDim.

Definition at line 127 of file Polynomial.cxx.

◆ DoEvalPar()

double ROOT::Math::Polynomial::DoEvalPar	(	double	x,
		const double *	p
	)		const

overrideprivatevirtual

Implementation of the evaluation function using the x value and the parameters.

Must be implemented by derived classes

Implements ROOT::Math::IParametricFunctionOneDim.

Definition at line 119 of file Polynomial.cxx.

◆ DoParameterDerivative()

double ROOT::Math::Polynomial::DoParameterDerivative	(	double	x,
		const double *	p,
		unsigned int	ipar
	)		const

overrideprivatevirtual

Evaluate the gradient, to be implemented by the derived classes.

Implements ROOT::Math::IParametricGradFunctionOneDim.

Definition at line 136 of file Polynomial.cxx.

◆ FdF()

void ROOT::Math::Polynomial::FdF	(	double	x,
		double &	f,
		double &	df
	)		const

inlineoverridevirtual

Optimized method to evaluate at the same time the function value and derivative at a point x.

Implement the interface specified by ROOT::Math::IGradientOneDim. In the case of polynomial there is no advantage to compute both at the same time

Reimplemented from ROOT::Math::IGradientFunctionOneDim.

Definition at line 147 of file Polynomial.h.

◆ FindNumRoots()

const std::vector< std::complex< double > > & ROOT::Math::Polynomial::FindNumRoots ( )

Find the polynomial roots using always an iterative numerical methods The numerical method used is from GSL (see documentation )

Definition at line 247 of file Polynomial.cxx.

◆ FindRealRoots()

std::vector< double > ROOT::Math::Polynomial::FindRealRoots ( )

Find the only the real polynomial roots.

For n <= 4, the roots are found analytically while for larger order an iterative numerical method is used The numerical method used is from GSL (see documentation )

Definition at line 237 of file Polynomial.cxx.

◆ FindRoots()

const std::vector< std::complex< double > > & ROOT::Math::Polynomial::FindRoots ( )

Find the polynomial roots.

For n <= 4, the roots are found analytically while for larger order an iterative numerical method is used The numerical method used is from GSL (see documentation ) For the case of n = 4 by default an analytical algorithm is used from an implementation by Andrew W. Steiner and Andy Buckley which is a translation from the original Cenrlib routine (< HREF="https://cds.cern.ch/record/2050876/files/c208.html">RRTEQ4 ). Note that depending on the coefficients the result could be not very accurate if the discriminant of the resolvent cubic equation is very small. In that case it might be more robust to use the numerical method, by calling directly FindNumRoots()

Definition at line 151 of file Polynomial.cxx.

◆ Order()

unsigned int ROOT::Math::Polynomial::Order ( ) const

inline

Order of Polynomial.

Definition at line 137 of file Polynomial.h.

Member Data Documentation

◆ fDerived_params

std::vector<double> ROOT::Math::Polynomial::fDerived_params

mutableprivate

Definition at line 166 of file Polynomial.h.

◆ fOrder

unsigned int ROOT::Math::Polynomial::fOrder

private

Definition at line 163 of file Polynomial.h.

◆ fRoots

std::vector< std::complex < double > > ROOT::Math::Polynomial::fRoots

private

Definition at line 170 of file Polynomial.h.

Libraries for ROOT::Math::Polynomial:

[legend]

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

math/mathmore/inc/Math/Polynomial.h
math/mathmore/src/Polynomial.cxx

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ ParFunc

Constructor & Destructor Documentation

◆ Polynomial() [1/5]

◆ Polynomial() [2/5]

◆ Polynomial() [3/5]

◆ Polynomial() [4/5]

◆ Polynomial() [5/5]

◆ ~Polynomial()

Member Function Documentation

◆ Clone()

◆ DoDerivative()

◆ DoEvalPar()

◆ DoParameterDerivative()

◆ FdF()

◆ FindNumRoots()

◆ FindRealRoots()

◆ FindRoots()

◆ Order()

Member Data Documentation

◆ fDerived_params

◆ fOrder

◆ fRoots