function [ o, x, w ] = en_r2_11_1 ( n, option ) %*****************************************************************************80 % %% EN_R2_11_1 implements the Stroud rule 11.1 for region EN_R2. % % Discussion: % % The rule has order % % O = ( 4 * N^5 - 20 * N^4 + 140 * N^3 - 130 * N^2 + 96 * N + 15 ) / 15. % % The rule has precision P = 11. % % EN_R2 is the entire N-dimensional space with weight function % % w(x) = exp ( - x1^2 - x2^2 ... - xn^2 ) % % There are two versions of each rule, chosen by setting the % OPTION variable to 1 or 2. % % The rule as tabulated by Stenger is available for N = 2 through 20. % This function accepts N = 3 through 5. % % N O % __ ___ % 3 151 % 4 417 % 5 983 % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 21 January 2010 % % Author: % % John Burkardt % % Reference: % % Arthur Stroud, % Approximate Calculation of Multiple Integrals, % Prentice Hall, 1971, % ISBN: 0130438936, % LC: QA311.S85. % % Parameters: % % Input, integer N, the spatial dimension. % 3 <= N <= 5. % % Input, integer OPTION, chooses rule option 1 or 2. % % Output, integer O, the order. % % Output, real X(N,O), the abscissas. % % Output, real W(O), the weights. % if ( n < 3 | 5 < n ) fprintf ( 1, '\n' ); fprintf ( 1, 'EN_R2_11_1 - Fatal error!\n' ); fprintf ( 1, ' 3 <= N <= 5 required.\n' ); error ( 'EN_R2_11_1 - Fatal error!' ) end if ( nargin < 2 ) option = 1; end if ( option < 1 | 2 < option ) fprintf ( 1, '\n' ); fprintf ( 1, 'EN_R2_11_1 - Fatal error!\n' ); fprintf ( 1, ' 1 <= OPTION <= 2 required.\n' ); error ( 'EN_R2_11_1 - Fatal error!' ) end o = ( 4 * n^5 - 20 * n^4 + 140 * n^3 - 130 * n^2 + 96 * n + 15 ) / 15; volume = sqrt ( pi^n ); if ( n == 3 & option == 1 ) u = 0.235060497367449E+01; v = 0.436077411927617E+00; w2 = 0.133584907401370E+01; b0 = - 0.881591029957858E+01; b1 = - 0.751996143360650E-01; b2 = 0.621743189471515E+01; b3 = 0.241426451456494E+00; b4 = - 0.120709739276065E-02; b5 = - 0.427751221210138E+01; b6 = 0.550169924840163E-01; b7 = 0.237084999634707E-01; b8 = - 0.169791992887741E-02; b9 = - 0.252266276123350E-04; b10 = 0.326777873717691E+01; b11 = 0.968469949206802E-02; b12 = 0.789754514877422E-03; b13 = 0.000000000000000E+00; b14 = 0.000000000000000E+00; b15 = 0.000000000000000E+00; elseif ( n == 3 & option == 2 ) u = 0.235060497367449E+01; v = 0.133584907401370E+01; w2 = 0.436077411927617E+00; b0 = - 0.141214037032900E+02; b1 = - 0.803730274707282E-01; b2 = 0.235546545595906E+00; b3 = 0.888123191556611E+01; b4 = 0.142467131155533E-03; b5 = 0.582993124006494E-01; b6 = - 0.561099173155661E+01; b7 = - 0.204028691521686E-02; b8 = 0.252880089932256E-01; b9 = - 0.814378678627283E-04; b10 = 0.804353953375146E-02; b11 = 0.393451849690453E+01; b12 = 0.171183493169724E-03; b13 = 0.000000000000000E+00; b14 = 0.000000000000000E+00; b15 = 0.000000000000000E+00; elseif ( n == 4 & option == 1 ) u = 0.235060497367449E+01; v = 0.436077411927617E+00; w2 = 0.133584907401370E+01; b0 = 0.241502736147339E+03; b1 = - 0.196095938531478E+00; b2 = - 0.128675737999280E+03; b3 = 0.307568784278696E+00; b4 = - 0.480908422319460E-02; b5 = 0.698087019367085E+02; b6 = 0.631837143743771E-01; b7 = 0.392226151971179E-01; b8 = - 0.300948471646799E-02; b9 = - 0.650235306755170E-04; b10 = - 0.386951974646715E+02; b11 = 0.171656829095787E-01; b12 = 0.139980343116450E-02; b13 = 0.101552487093372E-04; b14 = 0.222435922356439E+02; b15 = 0.000000000000000E+00; elseif ( n == 4 & option == 2 ) u = 0.235060497367449E+01; v = 0.133584907401370E+01; w2 = 0.436077411927617E+00; b0 = - 0.151944464736584E+03; b1 = - 0.223498438689039E+00; b2 = 0.243574919068010E+00; b3 = 0.634373877008693E+02; b4 = - 0.782065187814018E-04; b5 = 0.911833754536616E-01; b6 = - 0.238927288245914E+02; b7 = - 0.422314408318853E-02; b8 = 0.448218289217760E-01; b9 = - 0.138053374667391E-03; b10 = 0.607473265800655E-02; b11 = 0.697375246129742E+01; b12 = 0.303414841680135E-03; b13 = - 0.314574391771792E-05; b14 = 0.409103498175100E-02; b15 = 0.000000000000000E+00; elseif ( n == 5 & option == 1 ) u = 0.235060497367449E+01; v = 0.436077411927617E+00; w2 = 0.133584907401370E+01; b0 = 0.255885269311763E+04; b1 = - 0.439598677491526E+00; b2 = - 0.106541406144610E+04; b3 = 0.453540909054264E+00; b4 = - 0.132100905623778E-01; b5 = 0.418606568954203E+03; b6 = 0.511394563043680E-01; b7 = 0.645581013845604E-01; b8 = - 0.533417277494500E-02; b9 = - 0.137981626254496E-03; b10 = - 0.147436933189884E+03; b11 = 0.304253807765057E-01; b12 = 0.248108698207828E-02; b13 = 0.113652094546015E-04; b14 = 0.394257407160391E+02; b15 = 0.331725011358320E-05; elseif ( n == 5 & option == 2 ) u = 0.235060497367449E+01; v = 0.133584907401370E+01; w2 = 0.436077411927617E+00; b0 = - 0.761305347548192E+03; b1 = - 0.536360805019297E+00; b2 = 0.110669832078736E+00; b3 = 0.246421088923968E+03; b4 = - 0.773649327968607E-03; b5 = 0.169088641205970E+00; b6 = - 0.670700680243651E+02; b7 = - 0.856090560229205E-02; b8 = 0.794446232770302E-01; b9 = - 0.220272863263544E-03; b10 = - 0.373515812228225E-02; b11 = 0.123606544052884E+02; b12 = 0.537788804557843E-03; b13 = - 0.122101861480881E-04; b14 = 0.725117070759373E-02; b15 = 0.331725011358320E-05; end x = zeros(n,o); w = zeros(o,1); k = 0; % % 1 point. % k = k + 1; % x(1:n,k) = 0.0; w(k) = b0; % % 2 * N points. % for i = 1 : n k = k + 1; x(i,k) = - u; w(k) = b1; k = k + 1; x(i,k) = + u; w(k) = b1; end % % 2 * N points. % for i = 1 : n k = k + 1; x(i,k) = - v; w(k) = b2; k = k + 1; x(i,k) = + v; w(k) = b2; end % % 2 * N points. % for i = 1 : n k = k + 1; x(i,k) = - w2; w(k) = b3; k = k + 1; x(i,k) = + w2; w(k) = b3; end % % 4 * ( N * ( N - 1 ) / 2 ) points. % for i = 1 : n - 1 for j = i + 1 : n k = k + 1; x(i,k) = - u; x(j,k) = - u; w(k) = b4; k = k + 1; x(i,k) = - u; x(j,k) = + u; w(k) = b4; k = k + 1; x(i,k) = + u; x(j,k) = - u; w(k) = b4; k = k + 1; x(i,k) = + u; x(j,k) = + u; w(k) = b4; end end % % 4 * ( N * ( N - 1 ) / 2 ) points. % for i = 1 : n - 1 for j = i + 1 : n k = k + 1; x(i,k) = - v; x(j,k) = - v; w(k) = b5; k = k + 1; x(i,k) = - v; x(j,k) = + v; w(k) = b5; k = k + 1; x(i,k) = + v; x(j,k) = - v; w(k) = b5; k = k + 1; x(i,k) = + v; x(j,k) = + v; w(k) = b5; end end % % 4 * ( N * ( N - 1 ) / 2 ) points. % for i = 1 : n - 1 for j = i + 1 : n k = k + 1; x(i,k) = - w2; x(j,k) = - w2; w(k) = b6; k = k + 1; x(i,k) = - w2; x(j,k) = + w2; w(k) = b6; k = k + 1; x(i,k) = + w2; x(j,k) = - w2; w(k) = b6; k = k + 1; x(i,k) = + w2; x(j,k) = + w2; w(k) = b6; end end % % 4 * ( N * ( N - 1 ) ) points. % for i = 1 : n - 1 for j = i + 1 : n k = k + 1; x(i,k) = - u; x(j,k) = - v; w(k) = b7; k = k + 1; x(i,k) = - u; x(j,k) = + v; w(k) = b7; k = k + 1; x(i,k) = + u; x(j,k) = - v; w(k) = b7; k = k + 1; x(i,k) = + u; x(j,k) = + v; w(k) = b7; k = k + 1; x(i,k) = - v; x(j,k) = - u; w(k) = b7; k = k + 1; x(i,k) = - v; x(j,k) = + u; w(k) = b7; k = k + 1; x(i,k) = + v; x(j,k) = - u; w(k) = b7; k = k + 1; x(i,k) = + v; x(j,k) = + u; w(k) = b7; end end % % 4 * ( N * ( N - 1 ) ) points. % for i = 1 : n - 1 for j = i + 1 : n k = k + 1; x(i,k) = - u; x(j,k) = - w2; w(k) = b8; k = k + 1; x(i,k) = - u; x(j,k) = + w2; w(k) = b8; k = k + 1; x(i,k) = + u; x(j,k) = - w2; w(k) = b8; k = k + 1; x(i,k) = + u; x(j,k) = + w2; w(k) = b8; k = k + 1; x(i,k) = - w2; x(j,k) = - u; w(k) = b8; k = k + 1; x(i,k) = - w2; x(j,k) = + u; w(k) = b8; k = k + 1; x(i,k) = + w2; x(j,k) = - u; w(k) = b8; k = k + 1; x(i,k) = + w2; x(j,k) = + u; w(k) = b8; end end % % 8 * ( N * ( N - 1 ) * ( N - 2 ) / 6 ) points. % for i = 1 : n - 2 for j = i + 1 : n - 1 for l = j + 1 : n k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = - u; w(k) = b9; k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = + u; w(k) = b9; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = - u; w(k) = b9; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = + u; w(k) = b9; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = - u; w(k) = b9; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = + u; w(k) = b9; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = - u; w(k) = b9; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = + u; w(k) = b9; end end end % % 8 * ( N * ( N - 1 ) * ( N - 2 ) / 6 ) points. % for i = 1 : n - 2 for j = i + 1 : n - 1 for l = j + 1 : n k = k + 1; x(i,k) = - v; x(j,k) = - v; x(l,k) = - v; w(k) = b10; k = k + 1; x(i,k) = - v; x(j,k) = - v; x(l,k) = + v; w(k) = b10; k = k + 1; x(i,k) = - v; x(j,k) = + v; x(l,k) = - v; w(k) = b10; k = k + 1; x(i,k) = - v; x(j,k) = + v; x(l,k) = + v; w(k) = b10; k = k + 1; x(i,k) = + v; x(j,k) = - v; x(l,k) = - v; w(k) = b10; k = k + 1; x(i,k) = + v; x(j,k) = - v; x(l,k) = + v; w(k) = b10; k = k + 1; x(i,k) = + v; x(j,k) = + v; x(l,k) = - v; w(k) = b10; k = k + 1; x(i,k) = + v; x(j,k) = + v; x(l,k) = + v; w(k) = b10; end end end % % 8 * ( N * ( N - 1 ) * ( N - 2 ) / 6 ) points. % for i = 1 : n - 2 for j = i + 1 : n - 1 for l = j + 1 : n k = k + 1; x(i,k) = - w2; x(j,k) = - w2; x(l,k) = - w2; w(k) = b11; k = k + 1; x(i,k) = - w2; x(j,k) = - w2; x(l,k) = + w2; w(k) = b11; k = k + 1; x(i,k) = - w2; x(j,k) = + w2; x(l,k) = - w2; w(k) = b11; k = k + 1; x(i,k) = - w2; x(j,k) = + w2; x(l,k) = + w2; w(k) = b11; k = k + 1; x(i,k) = + w2; x(j,k) = - w2; x(l,k) = - w2; w(k) = b11; k = k + 1; x(i,k) = + w2; x(j,k) = - w2; x(l,k) = + w2; w(k) = b11; k = k + 1; x(i,k) = + w2; x(j,k) = + w2; x(l,k) = - w2; w(k) = b11; k = k + 1; x(i,k) = + w2; x(j,k) = + w2; x(l,k) = + w2; w(k) = b11; end end end % % 8 * ( N * ( N - 1 ) * ( N - 2 ) / 2 ) points. % for i = 1 : n - 2 for j = i + 1 : n - 1 for l = j + 1 : n k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = - v; w(k) = b12; k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = + v; w(k) = b12; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = - v; w(k) = b12; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = + v; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = - v; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = + v; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = - v; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = + v; w(k) = b12; k = k + 1; x(i,k) = - u; x(j,k) = - v; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = - u; x(j,k) = - v; x(l,k) = + u; w(k) = b12; k = k + 1; x(i,k) = - u; x(j,k) = + v; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = - u; x(j,k) = + v; x(l,k) = + u; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = - v; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = - v; x(l,k) = + u; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = + v; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = + u; x(j,k) = + v; x(l,k) = + u; w(k) = b12; k = k + 1; x(i,k) = - v; x(j,k) = - u; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = - v; x(j,k) = - u; x(l,k) = + u; w(k) = b12; k = k + 1; x(i,k) = - v; x(j,k) = + u; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = - v; x(j,k) = + u; x(l,k) = + u; w(k) = b12; k = k + 1; x(i,k) = + v; x(j,k) = - u; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = + v; x(j,k) = - u; x(l,k) = + u; w(k) = b12; k = k + 1; x(i,k) = + v; x(j,k) = + u; x(l,k) = - u; w(k) = b12; k = k + 1; x(i,k) = + v; x(j,k) = + u; x(l,k) = + u; w(k) = b12; end end end % % 16 * ( N * ( N - 1 ) * ( N - 2 ) * ( N - 3 ) / 24 ) points. % for i = 1 : n - 3 for j = i + 1 : n - 2 for l = j + 1 : n - 1 for m = l + 1 : n k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = - u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = - u; x(m,k) = + u; w(k) = b13; k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = + u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = - u; x(j,k) = - u; x(l,k) = + u; x(m,k) = + u; w(k) = b13; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = - u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = - u; x(m,k) = + u; w(k) = b13; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = + u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = - u; x(j,k) = + u; x(l,k) = + u; x(m,k) = + u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = - u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = - u; x(m,k) = + u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = + u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = - u; x(l,k) = + u; x(m,k) = + u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = - u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = - u; x(m,k) = + u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = + u; x(m,k) = - u; w(k) = b13; k = k + 1; x(i,k) = + u; x(j,k) = + u; x(l,k) = + u; x(m,k) = + u; w(k) = b13; end end end end % % 16 * ( N * ( N - 1 ) * ( N - 2 ) * ( N - 3 ) / 24 ) points. % for i = 1 : n - 3 for j = i + 1 : n - 2 for l = j + 1 : n - 1 for m = l + 1 : n k = k + 1; x(i,k) = - v; x(j,k) = - v; x(l,k) = - v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = - v; x(j,k) = - v; x(l,k) = - v; x(m,k) = + v; w(k) = b14; k = k + 1; x(i,k) = - v; x(j,k) = - v; x(l,k) = + v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = - v; x(j,k) = - v; x(l,k) = + v; x(m,k) = + v; w(k) = b14; k = k + 1; x(i,k) = - v; x(j,k) = + v; x(l,k) = - v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = - v; x(j,k) = + v; x(l,k) = - v; x(m,k) = + v; w(k) = b14; k = k + 1; x(i,k) = - v; x(j,k) = + v; x(l,k) = + v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = - v; x(j,k) = + v; x(l,k) = + v; x(m,k) = + v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = - v; x(l,k) = - v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = - v; x(l,k) = - v; x(m,k) = + v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = - v; x(l,k) = + v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = - v; x(l,k) = + v; x(m,k) = + v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = + v; x(l,k) = - v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = + v; x(l,k) = - v; x(m,k) = + v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = + v; x(l,k) = + v; x(m,k) = - v; w(k) = b14; k = k + 1; x(i,k) = + v; x(j,k) = + v; x(l,k) = + v; x(m,k) = + v; w(k) = b14; end end end end % % All quintuples UUUUU with 32 sign combinations. % for i1 = 1 : n - 4 for i2 = i1 + 1 : n - 3 for i3 = i2 + 1 : n - 2 for i4 = i3 + 1 : n - 1 for i5 = i4 + 1 : n k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = - u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = - u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = - u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = - u; x(i5,k) = + u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = - u; w(k) = b15; k = k + 1; x(i1,k) = + u; x(i2,k) = + u; x(i3,k) = + u; x(i4,k) = + u; x(i5,k) = + u; w(k) = b15; end end end end end return end