function [ o, x, w ] = cn_geg_01_1 ( n, alpha ) %*****************************************************************************80 % %% CN_GEG_01_1 implements a precision 1 rule for region CN_GEG. % % Discussion: % % The rule has order O = 1. % % The rule has precision P = 1. % % CN_GEG is the cube [-1,+1]^N with the Gegenbauer weight function % % w(alpha;x) = product ( 1 <= i <= n ) (1-x(i)^2)^alpha. % % with -1.0 < alpha. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 30 January 2010 % % Author: % % John Burkardt % % Parameters: % % Input, integer N, the spatial dimension. % % Input, real ALPHA, the parameter. % -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, 'CN_GEG_01_1 - Fatal error!\n' ); fprintf ( 1, ' ALPHA <= -1.0\n' ); error ( 'CN_GEG_01_1 - Fatal error!' ); end o = 1; x = zeros ( n, o ); w = zeros ( o, 1 ); expon = 0; value1 = c1_geg_monomial_integral ( alpha, expon ); volume = value1 ^ n; expon = 1; value2 = c1_geg_monomial_integral ( alpha, expon ); k = 0; % % 1 point. % k = k + 1; x(1:n,k) = value2 / value1; w(k) = volume; return end