class ROOT::Math::Polynomial: public ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>, public ROOT::Math::IGradientOneDim


     Parametric Function class describing polynomials of order n.

     <em>P(x) = p[0] + p[1]*x + p[2]*x**2 + ....... + p[n]*x**n</em>

     The class implements also the derivatives, \a dP(x)/dx and the \a 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


     @ingroup ParamFunc

Function Members (Methods)

public:

virtual	~Polynomial()
virtual ROOT::Math::IGenFunction*	Clone() const
double	ROOT::Math::IGradientOneDim::Derivative(double x) const
double	ROOT::Math::IGradientOneDim::Derivative(const double* x) const
virtual void	FdF(double x, double& f, double& df) const
const vector<complex<double> >&	FindNumRoots()
vector<double>	FindRealRoots()
const vector<complex<double> >&	FindRoots()
void	ROOT::Math::IGradientOneDim::Gradient(const double* x, double* g) const
ROOT::Math::IBaseFunctionOneDim	ROOT::Math::IBaseFunctionOneDim::IBaseFunctionOneDim()
ROOT::Math::IBaseFunctionOneDim	ROOT::Math::IBaseFunctionOneDim::IBaseFunctionOneDim(const ROOT::Math::IBaseFunctionOneDim&)
ROOT::Math::IBaseParam	ROOT::Math::IBaseParam::IBaseParam()
ROOT::Math::IBaseParam	ROOT::Math::IBaseParam::IBaseParam(const ROOT::Math::IBaseParam&)
ROOT::Math::IGradientOneDim	ROOT::Math::IGradientOneDim::IGradientOneDim()
ROOT::Math::IGradientOneDim	ROOT::Math::IGradientOneDim::IGradientOneDim(const ROOT::Math::IGradientOneDim&)
ROOT::Math::IParametricFunctionOneDim	ROOT::Math::IParametricFunctionOneDim::IParametricFunctionOneDim()
ROOT::Math::IParametricFunctionOneDim	ROOT::Math::IParametricFunctionOneDim::IParametricFunctionOneDim(ROOT::Math::IParametricFunctionOneDim&&)
ROOT::Math::IParametricFunctionOneDim	ROOT::Math::IParametricFunctionOneDim::IParametricFunctionOneDim(const ROOT::Math::IParametricFunctionOneDim&)
ROOT::Math::IParametricGradFunctionOneDim	ROOT::Math::IParametricGradFunctionOneDim::IParametricGradFunctionOneDim()
ROOT::Math::IParametricGradFunctionOneDim	ROOT::Math::IParametricGradFunctionOneDim::IParametricGradFunctionOneDim(const ROOT::Math::IParametricGradFunctionOneDim&)
virtual unsigned int	ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>::NPar() const
double	ROOT::Math::IParametricFunctionOneDim::operator()(double x, const double* p) const
double	ROOT::Math::IParametricFunctionOneDim::operator()(const double* x, const double* p) const
ROOT::Math::Polynomial&	operator=(const ROOT::Math::Polynomial&)
unsigned int	Order() const
double	ROOT::Math::IParametricGradFunctionOneDim::ParameterDerivative(double x, unsigned int ipar = 0) const
double	ROOT::Math::IParametricGradFunctionOneDim::ParameterDerivative(const double* x, unsigned int ipar = 0) const
double	ROOT::Math::IParametricGradFunctionOneDim::ParameterDerivative(double x, const double* p, unsigned int ipar = 0) const
double	ROOT::Math::IParametricGradFunctionOneDim::ParameterDerivative(const double* x, const double* p, unsigned int ipar = 0) const
void	ROOT::Math::IParametricGradFunctionOneDim::ParameterGradient(double x, double* grad) const
void	ROOT::Math::IParametricGradFunctionOneDim::ParameterGradient(const double* x, double* grad) const
virtual void	ROOT::Math::IParametricGradFunctionOneDim::ParameterGradient(double x, const double* p, double* grad) const
void	ROOT::Math::IParametricGradFunctionOneDim::ParameterGradient(const double* x, const double* p, double* grad) const
virtual string	ROOT::Math::IBaseParam::ParameterName(unsigned int i) const
virtual const double*	ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>::Parameters() const
ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>	ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>(unsigned int npar = 0)
ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>	ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>(const ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>&)
ROOT::Math::Polynomial	Polynomial(unsigned int n = 0)
ROOT::Math::Polynomial	Polynomial(const ROOT::Math::Polynomial&)
ROOT::Math::Polynomial	Polynomial(double a, double b)
ROOT::Math::Polynomial	Polynomial(double a, double b, double c)
ROOT::Math::Polynomial	Polynomial(double a, double b, double c, double d)
ROOT::Math::Polynomial	Polynomial(double a, double b, double c, double d, double e)
virtual void	ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>::SetParameters(const double* p)

private:

virtual double	DoDerivative(double x) const
virtual double	DoEvalPar(double x, const double* p) const
virtual double	DoParameterDerivative(double x, const double* p, unsigned int ipar) const

Data Members

protected:

vector<double>	ROOT::Math::ParamFunction<ROOT::Math::IParametricGradFunctionOneDim>::fParams

private:

vector<double>	fDerived_params
unsigned int	fOrder
vector<complex<double> >	fRoots

Class Charts

Inheritance Inherited Members Includes Libraries

Function documentation

Polynomial(unsigned int n = 0)

      Construct a Polynomial function of order n.
      The number of Parameters is n+1.

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()

{}

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

 use default copy-ctor and assignment operators
   using ParamFunction::operator();

      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" )

std::vector<double > 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" )

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

{ return fOrder; }

IGenFunction * Clone() const

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

double DoEvalPar(double x, const double* p) const

double DoDerivative(double x) const

double DoParameterDerivative(double x, const double* p, unsigned int ipar) const