function [ a, f ] = assemble_poisson_sparse ( node_num, node_xy, ...
  element_num, element_node, quad_num, nz_num )

%*****************************************************************************80
%
%% ASSEMBLE_POISSON_SPARSE assembles the system for the Poisson equation.
%
%  Discussion:
%
%    The matrix is stored in MATLAB sparse matrix format.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    14 February 2003
%
%  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 ELEMENT_NUM, the number of elements.
%
%    Input, integer ELEMENT_NODE(3,ELEMENT_NUM);
%    element_NODE(I,J) is the global index of local node I in element J.
%
%    Input, integer QUAD_NUM, the number of quadrature points used in assembly.
%
%    Input, integer NZ_NUM, the (maximum) number of nonzeros in the matrix.
%    If set to 0 on input, we hope MATLAB's sparse utility will be able
%    to take over the task of reallocating space as necessary.
%
%    Output, real sparse A, the coefficient matrix, stored in MATLAB
%    sparse matrix format.
%
%    Output, real F(NODE_NUM), the right hand side.
%
%  Local parameters:
%
%    Local, real BI, DBIDX, DBIDY, the value of some basis function
%    and its first derivatives at a quadrature point.
%
%    Local, real BJ, DBJDX, DBJDY, the value of another basis
%    function and its first derivatives at a quadrature point.
%

%
%  Initialize the arrays to zero.
%
  f(1:node_num) = 0.0;

  fprintf ( 1, '\n' );
  fprintf ( 1, 'ASSEMBLE_POISSON_SPARSE:\n' );
  fprintf ( 1, '  Setting up sparse Poisson matrix with NZ_NUM = %d\n', nz_num );

  a = sparse ( [], [], [], node_num, node_num, nz_num );
%
%  Get the quadrature weights and nodes.
%
  [ quad_w, quad_xy ] = quad_rule ( quad_num );
%
%  Add up all quantities associated with the element-th element.
%
  for element = 1 : element_num
%
%  Make a copy of the element.
%
    t3(1:2,1:3) = node_xy(1:2,element_node(1:3,element));
%
%  Map the quadrature points QUAD_XY to points XY in the physical element.
%
    xy(1:2,1:quad_num) = reference_to_physical_t3 ( t3, quad_num, quad_xy );

    area = abs ( triangle_area_2d ( t3 ) );

    w(1:quad_num) = quad_w(1:quad_num) * area;

    quad_rhs = rhs ( quad_num, quad_xy );

    quad_k = k_coef ( quad_num, quad_xy );
%
%  Consider the QUAD-th quadrature point..
%
    for quad = 1 : quad_num
%
%  Consider the TEST-th test function.
%
%  We generate an integral for every node associated with an unknown.
%  But if a node is associated with a boundary condition, we do nothing.
%
      for test = 1 : 3

        i = element_node(test,element);

        [ bi, dbidx, dbidy ] = basis_11_t3 ( t3, test, xy(1:2,quad) );

        f(i) = f(i) + w(quad) * quad_rhs(quad) * bi;
%
%  Consider the BASIS-th basis function, which is used to form the
%  value of the solution function.
%
        for basis = 1 : 3

          j = element_node(basis,element);

          [ bj, dbjdx, dbjdy ] = basis_11_t3 ( t3, basis, xy(1:2,quad) );

          a(i,j) = a(i,j) + w(quad) * ( ...
            dbidx * dbjdx + dbidy * dbjdy + quad_k(quad) * bj * bi );

        end

      end

    end

  end

  return
end