function point_num = gp_s_size ( dim_num, level_max )

%*****************************************************************************80
%
%% gp_s_size(): Gauss Patterson Slow Exponential Growth.
%
%  Discussion:
%
%    The Gauss Patterson Slow Exponential Growth family assumes that, for the 
%    underlying 1D rules, a precision of 2*L+1 is needed at level L.  Therefore, 
%    the lowest possible order Gauss-Patterson rule is chosen that will achieve
%    that precision.  This retains a combination of the advantages of
%    nestedness and high accuracy.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    15 January 2010
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Fabio Nobile, Raul Tempone, Clayton Webster,
%    A Sparse Grid Stochastic Collocation Method for Partial Differential
%    Equations with Random Input Data,
%    SIAM Journal on Numerical Analysis,
%    Volume 46, Number 5, 2008, pages 2309-2345.
%
%  Input:
%
%    integer DIM_NUM, the spatial dimension.
%
%    integer LEVEL_MAX, the maximum value of LEVEL.
%
%  Output:
%
%    integer POINT_NUM, the total number of unique
%    points in the grids.
%

%
%  Special case.
%
  if ( level_max < 0 )
    point_num = 0;
    return
  end

  if ( level_max == 0 )
    point_num = 1;
    return
  end
%
%  Count the points in the 1D rule.
%
  order_1d = zeros ( level_max+1, 1 );

  order_1d(0+1) = 1;
  for level = 1 : level_max
    p = 5;
    o = 3;
    while ( p < 2 * level + 1 )
      p = 2 * p + 1;
      o = 2 * o + 1;
    end
    order_1d(level+1) = o;
  end
%
%  Count the new points in the 1D rule.
%
  new_1d = zeros(level_max+1,1);

  new_1d(0+1) = 1;
  for level = 1 : level_max
    new_1d(level+1) = order_1d(level+1) - order_1d(level-1+1);
  end
%
%  Count the number of points by counting the number of new points
%  associated with each level vector.
%
  level_1d = zeros ( dim_num, 1 );

  point_num = 0;

  for level = 0 : level_max

    level_1d = [];
    more = 0;
    h = 0;
    t = 0;

    while ( true )

      [ level_1d, more, h, t ] = comp_next ( level, dim_num, level_1d, more, h, t );

      point_num = point_num + prod ( new_1d(level_1d(1:dim_num)+1) );

      if ( ~ more )
        break
      end

    end

  end

  return
end
