function ccu_sparse_test ( )

%*****************************************************************************80
%
%% CCU_SPARSE_TEST uses the CCU function to build a sparse grid.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    07 May 2012
%
%  Author:
%
%    Original MATLAB version by Florian Heiss, Viktor Winschel.
%
%  Local parameters:
%
%    Local, integer D, the spatial dimension.
%
%    Local, integer MAXK, the maximum level to check.
%
  d = 10;
  maxk = 7;

  func = 'prod( exp(-(x/2).^2/2)/2/sqrt(2*pi), 2)';

  trueval = fu_integral ( d );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'CCU_SPARSE_TEST:\n' );
  fprintf ( 1, '  CCU sparse grid:\n' );
  fprintf ( 1, '  Sparse Gaussian unweighted quadrature over [0,1].\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '   D  Level   Nodes    SG error    MC error\n' );
  fprintf ( 1, '\n' );

  for k = 2 : maxk
%
%  Compute sparse grid estimate.
%
    [ x, w ] = nwspgr ( 'ccu', d, k );
    g = eval ( func );
    SGappr = g'*w;
    SGerror = sqrt ( ( SGappr - trueval ).^2 ) / trueval;
%
%  Compute 1000 Monte Carlo estimate with same number of points, and average.
%
    numnodes = length(w);
    sim = zeros(1000,1);
    for r = 1 : 1000
      x = rand ( numnodes, d );
      g = eval ( func );
      sim(r) = mean ( g );
    end
    Simerror = sqrt ( mean ( ( sim - trueval ).^2 ) ) / trueval;

    fprintf( '  %2d     %2d  %6d  %10.5g  %10.5g\n', d, k, numnodes, SGerror, Simerror )

  end

  return
end