advection_matrix_sparse.m

   1 function S = advection_matrix_sparse(integerN)
   2   %
   3   % Sparse version of the advection_matrix function. See
   4   % advection_matrix.m for details.
   5   %
   6
   7   if (integerN < 2)
   8     S = NA;
   9     return
  10   end
  11
  12   % The ones directly above the diagonal.
  13   top = [ [zeros(integerN-1, 1), speye(integerN-1)]; ...
  14           zeros(1, integerN)];
  15
  16   % The negative ones directly below the diagonal.
  17   bottom = [ [zeros(1, integerN-1); ...
  18              -speye(integerN-1)    ], zeros(integerN, 1)];
  19
  20   % Combine the top and bottom.
  21   S = top + bottom;
  22
  23   % Fill in the entries in the corner.
  24   S(1, integerN) = -1;
  25   S(integerN, 1) = 1;
  26
  27   % And divide the whole thing by 2.
  28   S = (1/2)*S;
  29 end