ROOT::Math::Polynomial Class Reference
[Function Classes and Interfaces]

Parametric Function class describing polynomials of order n. More...

#include <Polynomial.h>

Inheritance diagram for ROOT::Math::Polynomial:

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Collaboration diagram for ROOT::Math::Polynomial:

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List of all members.

Public Member Functions
	Polynomial (unsigned int n=0)
	Construct a Polynomial function of order n.
	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 : a*x**2 + b*x + c.
	Polynomial (double a, double b, double c, double d)
	Construct a Polynomial of degree 3 : a*x**3 + b*x**2 + c*x + d.
	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.
virtual	~Polynomial ()
double	operator() (double x, const double *p)
	Copy constructor.
const std::vector < std::complex < double > > &	FindRoots ()
	Find the polynomial roots.
std::vector< double >	FindRealRoots ()
	Find the only the real polynomial roots.
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" ).
unsigned int	Order () const
	Order of Polynomial.
IGenFunction *	Clone () const
	Clone a function.

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Detailed Description

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.

Definition at line 56 of file Polynomial.h.

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Constructor & Destructor Documentation

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.

Referenced by Clone().

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.

References ROOT::Math::ParamFunction::fParams.

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.

References ROOT::Math::ParamFunction::fParams.

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.

References ROOT::Math::ParamFunction::fParams.

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.

References ROOT::Math::ParamFunction::fParams.

virtual ROOT::Math::Polynomial::~Polynomial

(

)

[inline, virtual]

Definition at line 88 of file Polynomial.h.

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Member Function Documentation

double ROOT::Math::Polynomial::operator()	(	double	x,
		const double *	p
	)			[virtual]

Copy constructor.

Copy operator

Reimplemented from ROOT::Math::IParametricFunctionOneDim.

Definition at line 127 of file Polynomial.cxx.

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 162 of file Polynomial.cxx.

References FindNumRoots(), gsl_poly_complex_solve_quartic(), and ROOT::Math::ParamFunction::Parameters().

Referenced by 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 248 of file Polynomial.cxx.

References FindRoots().

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 258 of file Polynomial.cxx.

References ROOT::Math::ParamFunction::Parameters().

Referenced by FindRoots().

unsigned int ROOT::Math::Polynomial::Order

(

)

const [inline]

Order of Polynomial.

Definition at line 133 of file Polynomial.h.

IGenFunction * ROOT::Math::Polynomial::Clone

(

)

const [virtual]

Clone a function.

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

Implements ROOT::Math::IBaseFunctionOneDim.

Definition at line 154 of file Polynomial.cxx.

References fDerived_params, ROOT::Math::ParamFunction::Parameters(), Polynomial(), and ROOT::Math::ParamFunction::SetParameters().

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

• Polynomial.h
• Polynomial.cxx

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