GaussQuadrature            package:tdist            R Documentation

_G_a_u_s_s_i_a_n _q_u_a_d_r_a_t_u_r_e _w_e_i_g_h_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     The 'grule' computes Gauss base points and weight factors for
     Gaussian quadrature on interval [0 1] and the 'gweights' is the
     generator of points and weight factors for the Gaussian quadrature
     on several different subintervals.

_U_s_a_g_e:

     grule(n)
     gweights(limits, ms, bp, wf)

_A_r_g_u_m_e_n_t_s:

       n: number of base points and weight factors

  limits: borders of subintervals.

      ms: number of base points in particular subinterval.

      bp: base points of the Gaussian quadrature genterated by 'grule'
          on  interval [0 1].

      wf: weight factors of the Gaussian quadrature genterated by
          'grule' on interval [0 1].

_D_e_t_a_i_l_s:

     The 'gweights' divides the whole interval into 'ms[i]'
     subintervals given by 'limits[i]' and 'limits[i + 1]' and the
     integration over each subinterval is done with an 'nquad' point
     Gauss formula which involves base points BP and weight factors WF.
     The normalized interval of integration for the BP and WF constants
     is 0 to 1. The base points and weight factors must first be
     generated by a call to grule.

_V_a_l_u_e:

     The 'grule' generates a list of 

      bp: base points on interval [0 1].

      wf: weight factors on interval [0 1].

      tt: base points of all subintervals.

       w: weight factors of all subintervals.

_A_u_t_h_o_r(_s):

     Gordon K Smyth, STATBOX 4.1 smyth@wehi.edu.au. Rewritten from
     Matlab algorithm to R by Alexander Savin savin@savba.sk.

_R_e_f_e_r_e_n_c_e_s:

     Davis, Rabinowitz (1975), _Methods of Numerical Integration_.
     Academic Press, page 365.

