function point_num = levels_index_size_own ( dim_num, level_max )
%*****************************************************************************80
%
%% LEVELS_INDEX_SIZE_OWN sizes a sparse grid made from OWN 1D rules.
%
% Discussion:
%
% The sparse grid is presumed to have been created from products
% of OPEN WEAKLY NESTED 1D quadrature rules.
%
% OWN rules include Gauss Hermite and Gauss Legendre.
%
% The sparse grid is the logical sum of product grids with total LEVEL
% between LEVEL_MIN and LEVEL_MAX.
%
% Oddly enough, in order to count the number of points, we will
% behave as though LEVEL_MIN was zero. This is because our computation
% concentrates on throwing away all points generated at lower levels,
% but, in fact, if we start at a nonzero level, we need to include
% on that level all the points that would have been generated on lower
% levels.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 02 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.
%
% Parameters:
%
% Input, integer DIM_NUM, the spatial dimension.
%
% Input, integer LEVEL_MAX, the maximum value of LEVEL.
%
% Output, integer POINT_NUM, the number of points in the grid.
%
% Special case.
%
if ( level_max == 0 )
point_num = 1;
return
end
%
% The outer loop generates LEVELs from LEVEL_MIN to LEVEL_MAX.
%
% The normal definition of LEVEL_MIN:
%
% level_min = max ( 0, level_max + 1 - dim_num )
%
% Our somewhat artificial temporary local definition of LEVEL_MIN:
%
if ( dim_num == 1 )
level_min = level_max;
point_num = 1;
else
level_min = 0;
point_num = 0;
end
for level = level_min : level_max
%
% The middle loop generates the next partition that adds up to LEVEL.
%
level_1d = [];
more = 0;
h = 0;
t = 0;
while ( 1 )
[ level_1d, more, h, t ] = comp_next ( level, dim_num, level_1d, more, h, t );
%
% Transform each 1D level to a corresponding 1D order.
%
order_1d = level_to_order_open ( dim_num, level_1d );
for dim = 1 : dim_num
%
% Account for the repetition of the center point.
%
if ( 1 < order_1d(dim) )
order_1d(dim) = order_1d(dim) - 1;
end
end
point_num = point_num + prod ( order_1d(1:dim_num) );
if ( ~more )
break
end
end
end
return
end