function [ o, x, w ] = epn_glg_00_1 ( n, alpha ) %*****************************************************************************80 % %% EPN_GLG_00_1 implements the "midpoint rule" for region EPN_GLG. % % Discussion: % % The rule has order O = 1. % % The rule has precision P = 0. % % EPN_GLG is the N-dimensional positive space [0,+oo)^N with generalized % Laguerre weight function: % % w(alpha;x) = product ( 1 <= i <= n ) x(i)^alpha exp ( - x(i) ) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 29 January 2010 % % Author: % % John Burkardt % % Parameters: % % Input, integer N, the spatial dimension. % % Input, real ALPHA, the exponent of X in the weight function. % -1.0 < ALPHA. % % Input, integer O, the order. % % Output, real X(N,O), the abscissas. % % Output, real W(O), the weights. % if ( alpha <= -1.0 ) fprintf ( 1, '\n' ); fprintf ( 1, 'EPN_GLG_00_1 - Fatal error!\n' ); fprintf ( 1, ' ALPHA <= -1.0\n' ); error ( 'EPN_GLG_00_1 - Fatal error!' ); end expon = 0; volume = ep1_glg_monomial_integral ( expon, alpha ); volume = volume ^ n; o = 1; x = zeros ( n, o ); w = zeros ( o, 1 ); k = 0; % % 1 point. % k = k + 1; x(1:n,k) = 1.0; w(k) = volume; return end