function value = cyclic8_f ( m, n, x )

%*****************************************************************************80
%
%% CYCLIC8_F returns the function in the cyclic8 problem.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    25 January 2016
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Sashwati Ray, PSV Nataraj,
%    An efficient algorithm for range computation of polynomials using the
%    Bernstein form,
%    Journal of Global Optimization,
%    Volume 45, 2009, pages 403-426.
%
%  Parameters:
%
%    Input, integer M, the number of variables.
%
%    Input, integer N, the number of points.
%
%    Input, real X(M,N), the points.
%
%    Output, real VALUE(N), the value of the function at X.
%
  value(1:n) = ( ...
      x(1,1:n) .* x(2,1:n) .* x(3,1:n) .* x(4,1:n) .* x(5,1:n) .* x(6,1:n) .* x(7,1:n)             ...
    + x(1,1:n) .* x(2,1:n) .* x(3,1:n) .* x(4,1:n) .* x(5,1:n) .* x(6,1:n)             .* x(8,1:n) ...
    + x(1,1:n) .* x(2,1:n) .* x(3,1:n) .* x(4,1:n) .* x(5,1:n)             .* x(7,1:n) .* x(8,1:n) ...
    + x(1,1:n) .* x(2,1:n) .* x(3,1:n) .* x(4,1:n)             .* x(6,1:n) .* x(7,1:n) .* x(8,1:n) ...
    + x(1,1:n) .* x(2,1:n) .* x(3,1:n)             .* x(5,1:n) .* x(6,1:n) .* x(7,1:n) .* x(8,1:n) ...
    + x(1,1:n) .* x(2,1:n)             .* x(4,1:n) .* x(5,1:n) .* x(6,1:n) .* x(7,1:n) .* x(8,1:n) ...
    + x(1,1:n)             .* x(3,1:n) .* x(4,1:n) .* x(5,1:n) .* x(6,1:n) .* x(7,1:n) .* x(8,1:n) ...
    +             x(2,1:n) .* x(3,1:n) .* x(4,1:n) .* x(5,1:n) .* x(6,1:n) .* x(7,1:n) .* x(8,1:n) )';

  return
end


