function [ grid_index, grid_base ] = sparse_grid_herm_index ( dim_num, ...
  level_max, point_num )

%*****************************************************************************80
%
%% sparse_grid_herm_index(): index sparse grid Gauss-Hermite points.
%
%  Discussion:
%
%    The sparse grid is assumed to be formed from 1D Gauss-Hermite rules
%    of ODD order, which have the property that only the central abscissa,
%    X = 0.0, is "nested".
%
%    The necessary dimensions of GRID_INDEX can be determined by
%    calling SPARSE_GRID_HERM_SIZE first.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    05 July 2008
%
%  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.
%
%    integer POINT_NUM, the total number of points in
%    the grids.
%
%  Output:
%
%    integer GRID_INDEX(DIM_NUM,POINT_NUM), a list of
%    point indices, representing a subset of the product grid of level
%    LEVEL_MAX, representing (exactly once) each point that will show up in a
%    sparse grid of level LEVEL_MAX.
%
%    integer GRID_BASE(DIM_NUM,POINT_NUM), a list of
%    the orders of the Gauss-Hermite rules associated with each point
%    and dimension.
%
  grid_base = zeros ( dim_num, point_num );
  grid_index = zeros ( dim_num, point_num );
%
%  The outer loop generates LEVELs from LEVEL_MIN to LEVEL_MAX.
%
  point_num2 = 0;

  level_min = max ( 0, level_max + 1 - dim_num );

  for level = level_min : level_max
%
%  The middle loop generates the next partition LEVEL_1D(1:DIM_NUM)
%  that adds up to LEVEL.
%
    level_1d = [];
    more = false;
    h = 0;
    t = 0;

    while ( true )

      [ level_1d, more, h, t ] = comp_next ( level, dim_num, level_1d, more, h, t );
%
%  Transform each 1D level to a corresponding 1D order.
%  The relationship is the same as for other OPEN rules.
%  The Gauss-Hermite rule differs from the other OPEN rules only in the nesting behavior.
%
      order_1d = level_to_order_open ( dim_num, level_1d );

      grid_base2(1:dim_num) = round ( ( order_1d(1:dim_num) - 1 ) / 2 );
%
%  The product of the 1D orders gives us the number of points in this subgrid.
%
      order_nd = prod ( order_1d(1:dim_num) );
%
%  The inner (hidden) loop generates all points corresponding to given grid.
%  The grid indices will be between -M to +M, where 2*M + 1 = ORDER_1D(DIM).
%
      grid_index2 = multigrid_index_z ( dim_num, order_1d, order_nd );
%
%  Determine the first level of appearance of each of the points.
%  This allows us to flag certain points as being repeats of points
%  generated on a grid of lower level.
%
%  This is SLIGHTLY tricky.
%
      grid_level = index_level_herm ( level, level_max, dim_num, order_nd, ...
        grid_index2, grid_base2 );
%
%  Only keep those points which first appear on this level.
%
      for point = 1 : order_nd

        if ( grid_level(point) == level )

          point_num2 = point_num2 + 1;

          grid_index(1:dim_num,point_num2) = grid_index2(1:dim_num,point);
          grid_base(1:dim_num,point_num2) = grid_base2(1:dim_num);

        end

      end

      if ( ~more )
        break
      end

    end

  end

  return
end
