function neighbor = sandia_sgmgg_neighbor_naive ( dim_num, point_num, ...
sparse_index )
%*****************************************************************************80
%
%% SANDIA_SGMGG_NEIGHBOR_NAIVE returns the immediate forward neighbor vector.
%
% Discussion:
%
% A sparse grid index vector is a list of DIM_NUM nonnegative indices.
%
% An immediate forward L-neighbor of a sparse grid index vector I is a
% sparse grid index vector J with the property that all entries of J
% are equal to those of I except for the L-the entry, which is greater by 1.
%
% A forward neighbor of a sparse grid index vector I is a sparse
% grid index vector K with the property that every entry of K is
% equal to or greater by 1 than the corresponding entry of I.
%
% This function is given a collection of sparse grid index vectors,
% and returns information defining, for every such vector, the entire
% set of its immediate forward neighbors. This is done with a
% "NEIGHBOR" array of dimension DIM_NUM. For sparse grid vector I,
% entry L of NEIGHBOR is 1 if I has an immediate forward L-neighbor,
% and 0 otherwise.
%
% This implementation of the procedure is inefficient, and is provided
% solely for demonstration on small problems.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 23 August 2011
%
% 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.
%
% Fabio Nobile, Raul Tempone, Clayton Webster,
% An Anisotropic Sparse Grid Stochastic Collocation Method for Partial
% Differential Equations with Random Input Data,
% SIAM Journal on Numerical Analysis,
% Volume 46, Number 5, 2008, pages 2411-2442.
%
% Parameters:
%
% Input, integer DIM_NUM, the dimension of the vector.
%
% Input, integer POINT_NUM, the number of points.
%
% Input, integer SPARSE_INDEX(DIM_NUM,POINT_NUM),
% the indices that define the points.
%
% Output, integer NEIGHBOR(DIM_NUM,POINT_NUM), the
% immediate forward neighbor array.
%
neighbor = zeros ( dim_num, point_num );
for j1 = 1 : point_num
for j2 = 1 : point_num
l = - 1;
for i = 1 : dim_num
%
% If the entries are not equal...
%
if ( sparse_index(i,j2) ~= sparse_index(i,j1) )
%
% ...and we haven't already found a difference...
%
if ( l ~= -1 )
l = - 1;
break
end
%
% ...and this difference is +1...
%
if ( sparse_index(i,j2) ~= sparse_index(i,j1) + 1 )
break
end
%
% ...then remember this index.
%
l = i;
end
end
%
% If a single unit difference was found, record the direction.
%
if ( l ~= - 1 )
neighbor(l,j1) = 1;
end
end
end
return
end