class ROOT::Math::GaussLegendreIntegrator: public ROOT::Math::VirtualIntegratorOneDim


   User class for performing function integration.

   It will use the Gauss-Legendre Method for function integration in a given interval.
   This class is implemented from TF1::Integral().

   @ingroup Integration

Function Members (Methods)

public:

virtual	~GaussLegendreIntegrator()
virtual double	Error() const
ROOT::Math::GaussLegendreIntegrator	GaussLegendreIntegrator(const ROOT::Math::GaussLegendreIntegrator&)
ROOT::Math::GaussLegendreIntegrator	GaussLegendreIntegrator(int num = 10, double eps = 1e-12)
void	GetWeightVectors(double* x, double* w)
virtual double	Integral()
virtual double	Integral(const vector<double>& pts)
virtual double	Integral(double a, double b)
virtual double	IntegralCauchy(double a, double b, double c)
virtual double	IntegralLow(double b)
virtual double	IntegralUp(double a)
ROOT::Math::VirtualIntegratorOneDim&	ROOT::Math::VirtualIntegratorOneDim::operator=(const ROOT::Math::VirtualIntegratorOneDim&)
virtual double	Result() const
virtual void	SetAbsTolerance(double)
virtual void	SetFunction(const ROOT::Math::IGenFunction&, bool copy = false)
void	SetNumberPoints(int num)
virtual void	SetRelTolerance(double)
virtual int	Status() const

private:

void	CalcGaussLegendreSamplingPoints()

Data Members

protected:

double	fEpsilon	Desired relative error.
const ROOT::Math::IGenFunction*	fFunction	Pointer to function used.
bool	fFunctionCopied	Bool value to check if the function was copied when set.
double	fLastError	Error from the last stimation.
double	fLastResult	Result from the last stimation.
int	fNum	Number of points used in the stimation of the integral.
bool	fUsedOnce	Bool value to check if the function was at least called once.
double*	fW	Weights of the points used.
double*	fX	Abscisa of the points used.

Class Charts

Function documentation

GaussLegendreIntegrator(int num = 10, double eps = 1e-12)

 Basic contructor of GaussLegendreIntegrator.
       \@param num Number of desired points to calculate the integration.
       \@param eps Desired relative error.

void GetWeightVectors(double* x, double* w)

 Returns the arrays x and w containing the abscissa and weight of
       the Gauss-Legendre n-point quadrature formula.

       Gauss-Legendre: W(x)=1 -1<x<1
                       (j+1)P_{j+1} = (2j+1)xP_j-jP_{j-1}

double Integral(double a, double b)

 Implementing VirtualIntegratorOneDim Interface
 Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints.

void SetFunction(const ROOT::Math::IGenFunction& , bool copy = false)

 Set integration function (flag control if function must be copied inside).
       \@param f Function to be used in the calculations.
       \@param copy Indicates whether the function has to be copied.

void CalcGaussLegendreSamplingPoints()

 Middle functions

      Type: unsafe but fast interface filling the arrays x and w (static method)

      Given the number of sampling points this routine fills the arrays x and w
      of length num, containing the abscissa and weight of the Gauss-Legendre
      n-point quadrature formula.

      Gauss-Legendre: W(x)=1  -1<x<1
                      (j+1)P_{j+1} = (2j+1)xP_j-jP_{j-1}

      num is the number of sampling points (>0)
      x and w are arrays of size num
      eps is the relative precision

      If num<=0 or eps<=0 no action is done.

      Reference: Numerical Recipes in C, Second Edition