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#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "neumann-laplace-assembly.h"
size_t N;
Float f (const point& x) { return 1; }
Float g (const point& x) { return -0.5/N; }
int main(int argc, char**argv) {
  geo omega (argv[1]);
  N = omega.dimension();
  space Xh (omega, argv[2]);
  form m (Xh, Xh, "mass");
  form a (Xh, Xh, "grad_grad");
  field b = m*field(Xh,1.0);
  csr<Float> A = neumann_laplace_assembly (a.uu, b.u);
  field fh = interpolate(Xh, f);
  space Wh (omega, omega["boundary"], argv[2]);
  field gh = interpolate(Wh, g);
  form mb (Wh, Xh, "mass");
  field lh = m*fh + mb*gh;
  vec<Float> L(lh.u.size()+1, 0.0);
  for (size_t i = 0; i < L.size()-1; i++) L.at(i) = lh.u.at(i);
  L.at(L.size()-1) = 0;
  vec<Float> U (L.size());
  ssk<Float> fact_A = ldlt(A);
  U = fact_A.solve(L);
  field uh(Xh);
  for (size_t i = 0; i < U.size()-1; i++) uh.u.at(i) = U.at(i);
  Float lambda = U.at(U.size()-1);
  cout << setprecision(numeric_limits<Float>::digits10)
       << catchmark("u") << uh 
       << catchmark("lambda") << lambda << endl;
}