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

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

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

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

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

virtual	~Polynomial ()

IGenFunction *	Clone () const
	Clone a function. More...

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

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 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_6.html#SEC53" ) More...

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

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

unsigned int	Order () const
	Order of Polynomial. More...

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

virtual	~ParamFunction ()

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

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

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

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

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. More...

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

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

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

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

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

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. More...

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

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

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

Public Member Functions inherited from ROOT::Math::IBaseFunctionOneDim
	IBaseFunctionOneDim ()

virtual	~IBaseFunctionOneDim ()
	virtual destructor More...

virtual IBaseFunctionOneDim *	Clone () const =0
	Clone a function. More...

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

double	operator() (double x) const
	Evaluate the function at a point x Use the a pure virtual private method DoEval which must be implemented by sub-classes. More...

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

virtual unsigned int	NPar () const =0
	Return the number of Parameters. More...

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, ...") More...

virtual const double *	Parameters () const =0
	Access the parameter values. More...

virtual void	SetParameters (const double *p)=0
	Set the parameter values. More...

Public Member Functions inherited from ROOT::Math::IGradientOneDim
virtual	~IGradientOneDim ()
	virtual destructor More...

double	Derivative (const double *x) const
	Compatibility method with multi-dimensional interface for partial derivative. More...

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

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

virtual void	FdF (double x, double &f, double &df) const =0
	Optimized method to evaluate at the same time the function value and derivative at a point x. More...

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

Private Member Functions
double	DoDerivative (double x) const
	function to evaluate the derivative with respect each coordinate. More...

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

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

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 70 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 50 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 59 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 69 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 80 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 93 of file Polynomial.cxx.

◆ ~Polynomial()

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

inlinevirtual

Definition at line 99 of file Polynomial.h.

Member Function Documentation

◆ Clone()

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

virtual

Clone a function.

Each derived class will implement their version of the provate DoClone method

Implements ROOT::Math::IBaseFunctionOneDim.

Definition at line 144 of file Polynomial.cxx.

◆ DoDerivative()

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

privatevirtual

function to evaluate the derivative with respect each coordinate.

To be implemented by the derived class

Implements ROOT::Math::IGradientOneDim.

Definition at line 128 of file Polynomial.cxx.

◆ DoEvalPar()

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

privatevirtual

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 120 of file Polynomial.cxx.

◆ DoParameterDerivative()

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

privatevirtual

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

Implements ROOT::Math::IParametricGradFunctionOneDim.

Definition at line 137 of file Polynomial.cxx.

◆ FdF()

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

inlinevirtual

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

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

Implements ROOT::Math::IGradientOneDim.

Definition at line 143 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 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_6.html#SEC53" )

Definition at line 248 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 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_6.html#SEC53" )

Definition at line 238 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 <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_6.html#SEC53" )

Definition at line 152 of file Polynomial.cxx.

◆ Order()

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

inline

Order of Polynomial.

Definition at line 133 of file Polynomial.h.

Member Data Documentation

◆ fDerived_params

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

mutableprivate

Definition at line 162 of file Polynomial.h.

◆ fOrder

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

private

Definition at line 159 of file Polynomial.h.

◆ fRoots

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

private

Definition at line 166 of file Polynomial.h.

Libraries for ROOT::Math::Polynomial:

[legend]

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