function a = jacobian_adjust_dirichlet_sparse ( node_num, node_xy, node_p_variable, ...
  node_u_variable, node_v_variable, node_p_condition, ...
  node_u_condition, node_v_condition, variable_num, a )

%% JACOBIAN_ADJUST_DIRICHLET_SPARSE adjusts the jacobian matrix for Dirichlet conditions.
%
%  Modified:
%
%    20 September 2006
%
%  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_P_VARIABLE(NODE_NUM),
%    is the index of the pressure variable associated with the node,
%    or -1 if there is no associated pressure variable.
%
%    Input, integer NODE_U_VARIABLE(NODE_NUM),
%    is the index of the horizontal velocity variable associated with the node.
%
%    Input, integer NODE_V_VARIABLE(NODE_NUM),
%    is the index of the vertical velocity variable associated with the node.
%
%    Input, integer NODE_P_CONDITION(NODE_NUM),
%    indicates the condition used to determine pressure at a node.
%    0, there is no condition at this node.
%    1, a finite element equation is used;
%    2, a Dirichlet condition is used.
%    3, a Neumann condition is used.
%
%    Input, integer NODE_U_CONDITION(NODE_NUM),
%    indicates the condition used to determine horizontal velocity at a node.
%    0, there is no condition at this node.
%    1, a finite element equation is used;
%    2, a Dirichlet condition is used.
%    3, a Neumann condition is used.
%
%    Input, integer NODE_V_CONDITION(NODE_NUM),
%    indicates the condition used to determine vertical velocity at a node.
%    0, there is no condition at this node.
%    1, a finite element equation is used;
%    2, a Dirichlet condition is used.
%    3, a Neumann condition is used.
%
%    Input, integer VARIABLE_NUM, the number of variables.
%
%    Input, real sparse A, the coefficient matrix, 
%    stored as a MATLAB sparse matrix.
%
%    Output, real sparse A, the  coefficient matrix has 
%    been adjusted for Dirichlet boundary conditions.
%
  DIRICHLET = 2;

  for node = 1 : node_num

    iu = node_u_variable(node);
    iv = node_v_variable(node);
    ip = node_p_variable(node);

    if ( node_u_condition(node) == DIRICHLET )

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

    end

    if ( node_v_condition(node) == DIRICHLET )

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

    end

    if ( 0 < ip )

      if ( node_p_condition(node) == DIRICHLET )

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

      end
    end
  end