// Create a Kalman smoother for t=1:T and optimize
double timeKalmanSmoother(int T) {
  GaussianFactorGraph smoother = createSmoother(T);
  clock_t start = clock();
  // Keys will come out sorted since keys() returns a set
  smoother.optimize(Ordering(smoother.keys()));
  clock_t end = clock ();
  double dif = (double)(end - start) / CLOCKS_PER_SEC;
  return dif;
}
/* ************************************************************************* */
TEST(GaussianBayesTree, shortcut_overlapping_separator)
{
  // Test computing shortcuts when the separator overlaps.  This previously
  // would have highlighted a problem where information was duplicated.

  // Create factor graph:
  // f(1,2,5)
  // f(3,4,5)
  // f(5,6)
  // f(6,7)
  GaussianFactorGraph fg;
  noiseModel::Diagonal::shared_ptr model = noiseModel::Unit::Create(1);
  fg.add(1, (Matrix(1, 1) <<  1.0).finished(), 3, (Matrix(1, 1) <<  2.0).finished(), 5, (Matrix(1, 1) <<  3.0).finished(), (Vector(1) << 4.0).finished(), model);
  fg.add(1, (Matrix(1, 1) <<  5.0).finished(), (Vector(1) << 6.0).finished(), model);
  fg.add(2, (Matrix(1, 1) <<  7.0).finished(), 4, (Matrix(1, 1) <<  8.0).finished(), 5, (Matrix(1, 1) <<  9.0).finished(), (Vector(1) << 10.0).finished(), model);
  fg.add(2, (Matrix(1, 1) <<  11.0).finished(), (Vector(1) << 12.0).finished(), model);
  fg.add(5, (Matrix(1, 1) <<  13.0).finished(), 6, (Matrix(1, 1) <<  14.0).finished(), (Vector(1) << 15.0).finished(), model);
  fg.add(6, (Matrix(1, 1) <<  17.0).finished(), 7, (Matrix(1, 1) <<  18.0).finished(), (Vector(1) << 19.0).finished(), model);
  fg.add(7, (Matrix(1, 1) <<  20.0).finished(), (Vector(1) << 21.0).finished(), model);

  // Eliminate into BayesTree
  // c(6,7)
  // c(5|6)
  //   c(1,2|5)
  //   c(3,4|5)
  Ordering ordering(fg.keys());
  GaussianBayesTree bt = *fg.eliminateMultifrontal(ordering); // eliminate in increasing key order, fg.keys() is sorted.

  GaussianFactorGraph joint = *bt.joint(1,2, EliminateQR);

  Matrix expectedJointJ = (Matrix(2,3) <<
    5, 0, 6,
    0, -11, -12
    ).finished();
  Matrix actualJointJ = joint.augmentedJacobian();

  EXPECT(assert_equal(expectedJointJ, actualJointJ));
}