class ROOT::Math::GaussIntegrator: public ROOT::Math::VirtualIntegratorOneDim

 Destructor 

 Default Constructor. 

 Static function: set the fgAbsValue flag.
       By default TF1::Integral uses the original function value to compute the integral
       However, TF1::Moment, CentralMoment require to compute the integral
       using the absolute value of the function.

 Implementing VirtualIntegrator Interface
 Set the desired relative Error. 

 This method is not implemented. 

 Returns the result of the last Integral calculation. 

 Return the estimate of the absolute Error of the last Integral calculation. 

 return the status of the last integration - 0 in case of success 

 Implementing VirtualIntegratorOneDim Interface

     Returns Integral of function between a and b.
     Based on original CERNLIB routine DGAUSS by Sigfried Kolbig
     converted to C++ by Rene Brun

     This function computes, to an attempted specified accuracy, the value
     of the integral.

    Method:
       For any interval [a,b] we define g8(a,b) and g16(a,b) to be the 8-point
       and 16-point Gaussian quadrature approximations to


      and define


      Then,


      where, starting with x0 = A and finishing with xk = B,
      the subdivision points xi(i=1,2,...) are given by




      is equal to the first member of the
      sequence 1,1/2,1/4,... for which r(xi-1, xi) < EPS.
      If, at any stage in the process of subdivision, the ratio


      is so small that 1+0.005q is indistinguishable from 1 to
      machine accuracy, an error exit occurs with the function value
      set equal to zero.

   Accuracy:
      The user provides absolute and relative error bounds (epsrel and epsabs) and the
      algorithm will stop when the estimated error is less than the epsabs OR is less
      than |I| * epsrel.
      Unless there is severe cancellation of positive and negative values of
      f(x) over the interval [A,B], the relative error may be considered as
      specifying a bound on the <I>relative</I> error of I in the case
      |I|&gt;1, and a bound on the absolute error in the case |I|&lt;1. More
      precisely, if k is the number of sub-intervals contributing to the
      approximation (see Method), and if


      then the relation


      will nearly always be true, provided the routine terminates without
      printing an error message. For functions f having no singularities in
      the closed interval [A,B] the accuracy will usually be much higher than
      this.

    Error handling:
      The requested accuracy cannot be obtained (see Method).
      The function value is set equal to zero.

    Note 1:
      Values of the function f(x) at the interval end-points A and B are not
      required. The subprogram may therefore be used when these values are
      undefined

 Returns Integral of function on an infinite interval.
      This function computes, to an attempted specified accuracy, the value of the integral:


      Usage:
        In any arithmetic expression, this function has the approximate value
        of the integral I.

      The integral is mapped onto [0,1] using a transformation then integral computation is surrogated to DoIntegral.

 Returns Integral of function on an upper semi-infinite interval.
      This function computes, to an attempted specified accuracy, the value of the integral:


      Usage:
        In any arithmetic expression, this function has the approximate value
        of the integral I.
        - A: lower end-point of integration interval.

      The integral is mapped onto [0,1] using a transformation then integral computation is surrogated to DoIntegral.

 Returns Integral of function on a lower semi-infinite interval.
       This function computes, to an attempted specified accuracy, the value of the integral:


      Usage:
         In any arithmetic expression, this function has the approximate value
         of the integral I.
         - B: upper end-point of integration interval.

      The integral is mapped onto [0,1] using a transformation then integral computation is surrogated to DoIntegral.

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

 This method is not implemented. 

 This method is not implemented. 

 set the options

      Integration surrugate method. Return integral of passed function in  interval [a,b]
      Derived class (like GaussLegendreIntegrator)  can re-implement this method to modify to use
      an improved algorithm