function [ a, f ] = dirichlet_apply_sparse ( node_num, node_xy, ...
  node_condition, a, f )

%% DIRICHLET_APPLY_SPARSE accounts for Dirichlet boundary conditions.
%
%  Modified:
%
%    07 January 2007
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer NODE_NUM, the number of nodes.
%
%    Input, real NODE_XY(2,NODE_NUM), the coordinates of nodes.
%
%    Input, integer NODE_CONDITION(NODE_NUM), reports the condition
%    used to set the unknown associated with the node.
%    0, unknown.
%    1, finite element equation.
%    2, Dirichlet condition;
%    3, Neumann condition.
%
%    Input, real sparse A, the coefficient matrix.
%
%    Input, real F(NODE_NUM), the right hand side.
%
%    Output, real sparse A, the coefficient matrix,
%    adjusted for Dirichlet boundary conditions.
%
%    Output, real F(NODE_NUM), the right hand side, adjusted for
%    Dirichlet boundary conditions.
%
  node_bc = dirichlet_condition ( node_num, node_xy );

  DIRICHLET = 2;

  for node = 1 : node_num

    if ( node_condition(node) == DIRICHLET )

      a(node,:) = 0.0;
      a(node,node) = 1.0;

      f(node) = node_bc(node);

    end

  end