/* ----------------------------------------------------------------------------

 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)

 * See LICENSE for the license information

 * -------------------------------------------------------------------------- */

/**
 * @file testGaussianBayesTree.cpp
 * @date Jul 8, 2010
 * @author Kai Ni
 */

#include <iostream>
#include <CppUnitLite/TestHarness.h>

#include <boost/assign/list_of.hpp>
#include <boost/assign/std/list.hpp> // for operator +=
#include <boost/assign/std/set.hpp> // for operator +=
using namespace boost::assign;

#include <gtsam/base/debug.h>
#include <gtsam/base/numericalDerivative.h>
#include <gtsam/geometry/Rot2.h>
#include <gtsam/linear/GaussianJunctionTree.h>
#include <gtsam/linear/GaussianBayesTree.h>
#include <gtsam/linear/GaussianConditional.h>

using namespace std;
using namespace gtsam;

namespace {
  const Key x1=1, x2=2, x3=3, x4=4;
  const SharedDiagonal chainNoise = noiseModel::Isotropic::Sigma(1, 0.5);
  const GaussianFactorGraph chain = list_of
    (JacobianFactor(x2, (Matrix(1, 1) << 1.).finished(), x1, (Matrix(1, 1) << 1.).finished(), (Vector(1) << 1.).finished(),  chainNoise))
    (JacobianFactor(x2, (Matrix(1, 1) << 1.).finished(), x3, (Matrix(1, 1) << 1.).finished(), (Vector(1) << 1.).finished(),  chainNoise))
    (JacobianFactor(x3, (Matrix(1, 1) << 1.).finished(), x4, (Matrix(1, 1) << 1.).finished(), (Vector(1) << 1.).finished(),  chainNoise))
    (JacobianFactor(x4, (Matrix(1, 1) << 1.).finished(), (Vector(1) << 1.).finished(),  chainNoise));
  const Ordering chainOrdering = Ordering(list_of(x2)(x1)(x3)(x4));

  /* ************************************************************************* */
  // Helper functions for below
  GaussianBayesTreeClique::shared_ptr MakeClique(const GaussianConditional& conditional)
  {
    return boost::make_shared<GaussianBayesTreeClique>(
      boost::make_shared<GaussianConditional>(conditional));
  }

  template<typename CHILDREN>
  GaussianBayesTreeClique::shared_ptr MakeClique(
    const GaussianConditional& conditional, const CHILDREN& children)
  {
    GaussianBayesTreeClique::shared_ptr clique =
      boost::make_shared<GaussianBayesTreeClique>(
      boost::make_shared<GaussianConditional>(conditional));
    clique->children.assign(children.begin(), children.end());
    for(typename CHILDREN::const_iterator child = children.begin(); child != children.end(); ++child)
      (*child)->parent_ = clique;
    return clique;
  }
}

/* ************************************************************************* */
/**
 * x1 - x2 - x3 - x4
 * x3 x4
 *    x2 x1 : x3
 *
 * x2 x1 x3 x4  b
 *  1  1        1
 *  1     1     1
 *        1  1  1
 *           1  1
 *
 *  1  0  0  1
 */
TEST( GaussianBayesTree, eliminate )
{
  GaussianBayesTree bt = *chain.eliminateMultifrontal(chainOrdering);

  Scatter scatter(chain);
  EXPECT_LONGS_EQUAL(4, scatter.size());
  EXPECT_LONGS_EQUAL(1, scatter.at(0).key);
  EXPECT_LONGS_EQUAL(2, scatter.at(1).key);
  EXPECT_LONGS_EQUAL(3, scatter.at(2).key);
  EXPECT_LONGS_EQUAL(4, scatter.at(3).key);

  Matrix two = (Matrix(1, 1) << 2.).finished();
  Matrix one = (Matrix(1, 1) << 1.).finished();

  GaussianBayesTree bayesTree_expected;
  bayesTree_expected.insertRoot(
      MakeClique(
          GaussianConditional(
              pair_list_of<Key, Matrix>(x3, (Matrix21() << 2., 0.).finished())(
                  x4, (Matrix21() << 2., 2.).finished()), 2, Vector2(2., 2.)),
          list_of(
              MakeClique(
                  GaussianConditional(
                      pair_list_of<Key, Matrix>(x2,
                          (Matrix21() << -2. * sqrt(2.), 0.).finished())(x1,
                          (Matrix21() << -sqrt(2.), -sqrt(2.)).finished())(x3,
                          (Matrix21() << -sqrt(2.), sqrt(2.)).finished()), 2,
                      (Vector(2) << -2. * sqrt(2.), 0.).finished())))));

  EXPECT(assert_equal(bayesTree_expected, bt));
}

/* ************************************************************************* */
TEST( GaussianBayesTree, optimizeMultiFrontal )
{
  VectorValues expected = pair_list_of<Key, Vector>
    (x1, (Vector(1) << 0.).finished())
    (x2, (Vector(1) << 1.).finished())
    (x3, (Vector(1) << 0.).finished())
    (x4, (Vector(1) << 1.).finished());

  VectorValues actual = chain.eliminateMultifrontal(chainOrdering)->optimize();
  EXPECT(assert_equal(expected,actual));
}

/* ************************************************************************* */
TEST(GaussianBayesTree, complicatedMarginal) {

  // Create the conditionals to go in the BayesTree
  GaussianBayesTree bt;
  bt.insertRoot(
    MakeClique(GaussianConditional(pair_list_of<Key, Matrix> (11, (Matrix(3,1) << 0.0971, 0, 0).finished()) 
                                                         (12, (Matrix(3,2) << 0.3171, 0.4387,  0.9502, 0.3816,  0, 0.7655).finished()),
                                            2, Vector3(0.2638, 0.1455, 0.1361)), list_of
      (MakeClique(GaussianConditional(pair_list_of<Key, Matrix> (9, (Matrix(3,1) << 0.7952, 0, 0).finished())
                                                            (10, (Matrix(3,2) << 0.4456, 0.7547, 0.6463, 0.2760, 0, 0.6797).finished())
                                                            (11, (Matrix(3,1) << 0.6551, 0.1626, 0.1190).finished())
                                                            (12, (Matrix(3,2) << 0.4984, 0.5853, 0.9597, 0.2238, 0.3404, 0.7513).finished()),
                                               2, Vector3(0.4314, 0.9106, 0.1818))))
      (MakeClique(GaussianConditional(pair_list_of<Key, Matrix> (7, (Matrix(3,1) << 0.2551, 0, 0).finished())
                                                            (8, (Matrix(3,2) << 0.8909, 0.1386, 0.9593, 0.1493, 0, 0.2575).finished())
                                                            (11, (Matrix(3,1) << 0.8407, 0.2543, 0.8143).finished()),
                                               2, Vector3(0.3998, 0.2599, 0.8001)), list_of
          (MakeClique(GaussianConditional(pair_list_of<Key, Matrix> (5, (Matrix(3,1) << 0.2435, 0, 0).finished())
                                                                (6, (Matrix(3,2) << 0.4733, 0.1966, 0.3517, 0.2511, 0.8308,    0.0).finished())
                                                                // NOTE the non-upper-triangular form
                                                                // here since this test was written when we had column permutations
                                                                // from LDL.  The code still works currently (does not enfore
                                                                // upper-triangularity in this case) but this test will need to be
                                                                // redone if this stops working in the future
                                                                (7, (Matrix(3,1) << 0.5853, 0.5497, 0.9172).finished())
                                                                (8, (Matrix(3,2) << 0.2858, 0.3804, 0.7572, 0.5678, 0.7537, 0.0759).finished()),
                                                  2, Vector3(0.8173, 0.8687, 0.0844)), list_of
              (MakeClique(GaussianConditional(pair_list_of<Key, Matrix> (3, (Matrix(3,1) << 0.0540, 0, 0).finished())
                                                                    (4, (Matrix(3,2) << 0.9340, 0.4694, 0.1299, 0.0119, 0, 0.3371).finished())
                                                                    (6, (Matrix(3,2) << 0.1622, 0.5285, 0.7943, 0.1656, 0.3112, 0.6020).finished()),
                                                      2, Vector3(0.9619, 0.0046, 0.7749))))
              (MakeClique(GaussianConditional(pair_list_of<Key, Matrix> (1, (Matrix(3,1) << 0.2630, 0, 0).finished())
                                                                    (2, (Matrix(3,2) << 0.7482, 0.2290, 0.4505, 0.9133, 0, 0.1524).finished())
                                                                    (5, (Matrix(3,1) << 0.8258, 0.5383, 0.9961).finished()),
                                                      2, Vector3(0.0782, 0.4427, 0.1067))))))))));

  // Marginal on 5
  Matrix expectedCov = (Matrix(1,1) << 236.5166).finished();
  //GaussianConditional actualJacobianChol = *bt.marginalFactor(5, EliminateCholesky);
  GaussianConditional actualJacobianQR = *bt.marginalFactor(5, EliminateQR);
  //EXPECT(assert_equal(actualJacobianChol, actualJacobianQR)); // Check that Chol and QR obtained marginals are the same
  LONGS_EQUAL(1, (long)actualJacobianQR.rows());
  LONGS_EQUAL(1, (long)actualJacobianQR.size());
  LONGS_EQUAL(5, (long)actualJacobianQR.keys()[0]);
  Matrix actualA = actualJacobianQR.getA(actualJacobianQR.begin());
  Matrix actualCov = (actualA.transpose() * actualA).inverse();
  EXPECT(assert_equal(expectedCov, actualCov, 1e-1));

  // Marginal on 6
//  expectedCov = (Matrix(2,2) <<
//      8471.2, 2886.2,
//      2886.2, 1015.8);
  expectedCov = (Matrix(2,2) <<
      1015.8,    2886.2,
      2886.2,    8471.2).finished();
  //actualJacobianChol = bt.marginalFactor(6, EliminateCholesky);
  actualJacobianQR = *bt.marginalFactor(6, EliminateQR);
  //EXPECT(assert_equal(actualJacobianChol, actualJacobianQR)); // Check that Chol and QR obtained marginals are the same
  LONGS_EQUAL(2, (long)actualJacobianQR.rows());
  LONGS_EQUAL(1, (long)actualJacobianQR.size());
  LONGS_EQUAL(6, (long)actualJacobianQR.keys()[0]);
  actualA = actualJacobianQR.getA(actualJacobianQR.begin());
  actualCov = (actualA.transpose() * actualA).inverse();
  EXPECT(assert_equal(expectedCov, actualCov, 1e1));
}

/* ************************************************************************* */
namespace {
double computeError(const GaussianBayesTree& gbt, const Vector10& values) {
  pair<Matrix, Vector> Rd = GaussianFactorGraph(gbt).jacobian();
  return 0.5 * (Rd.first * values - Rd.second).squaredNorm();
}
}

/* ************************************************************************* */
TEST(GaussianBayesTree, ComputeSteepestDescentPointBT) {

  // Create an arbitrary Bayes Tree
  GaussianBayesTree bt;
  bt.insertRoot(MakeClique(GaussianConditional(
    pair_list_of<Key, Matrix>
    (2, (Matrix(6, 2) <<
    31.0,32.0,
    0.0,34.0,
    0.0,0.0,
    0.0,0.0,
    0.0,0.0,
    0.0,0.0).finished())
    (3, (Matrix(6, 2) <<
    35.0,36.0,
    37.0,38.0,
    41.0,42.0,
    0.0,44.0,
    0.0,0.0,
    0.0,0.0).finished())
    (4, (Matrix(6, 2) <<
    0.0,0.0,
    0.0,0.0,
    45.0,46.0,
    47.0,48.0,
    51.0,52.0,
    0.0,54.0).finished()),
    3, (Vector(6) << 29.0,30.0,39.0,40.0,49.0,50.0).finished()), list_of
      (MakeClique(GaussianConditional(
      pair_list_of<Key, Matrix>
      (0, (Matrix(4, 2) <<
      3.0,4.0,
      0.0,6.0,
      0.0,0.0,
      0.0,0.0).finished())
      (1, (Matrix(4, 2) <<
      0.0,0.0,
      0.0,0.0,
      17.0,18.0,
      0.0,20.0).finished())
      (2, (Matrix(4, 2) <<
      0.0,0.0,
      0.0,0.0,
      21.0,22.0,
      23.0,24.0).finished())
      (3, (Matrix(4, 2) <<
      7.0,8.0,
      9.0,10.0,
      0.0,0.0,
      0.0,0.0).finished())
      (4, (Matrix(4, 2) <<
      11.0,12.0,
      13.0,14.0,
      25.0,26.0,
      27.0,28.0).finished()),
      2, (Vector(4) << 1.0,2.0,15.0,16.0).finished())))));

  // Compute the Hessian numerically
  Matrix hessian = numericalHessian<Vector10>(
      boost::bind(&computeError, bt, _1), Vector10::Zero());

  // Compute the gradient numerically
  Vector gradient = numericalGradient<Vector10>(
      boost::bind(&computeError, bt, _1), Vector10::Zero());

  // Compute the gradient using dense matrices
  Matrix augmentedHessian = GaussianFactorGraph(bt).augmentedHessian();
  LONGS_EQUAL(11, (long)augmentedHessian.cols());
  Vector denseMatrixGradient = -augmentedHessian.col(10).segment(0,10);
  EXPECT(assert_equal(gradient, denseMatrixGradient, 1e-5));

  // Compute the steepest descent point
  double step = -gradient.squaredNorm() / (gradient.transpose() * hessian * gradient)(0);
  Vector expected = gradient * step;

  // Known steepest descent point from Bayes' net version
  VectorValues expectedFromBN = pair_list_of<Key, Vector>
    (0, Vector2(0.000129034, 0.000688183))
    (1, Vector2(0.0109679, 0.0253767))
    (2, Vector2(0.0680441, 0.114496))
    (3, Vector2(0.16125, 0.241294))
    (4, Vector2(0.300134, 0.423233));

  // Compute the steepest descent point with the dogleg function
  VectorValues actual = bt.optimizeGradientSearch();

  // Check that points agree
  FastVector<Key> keys = list_of(0)(1)(2)(3)(4);
  EXPECT(assert_equal(expected, actual.vector(keys), 1e-5));
  EXPECT(assert_equal(expectedFromBN, actual, 1e-5));

  // Check that point causes a decrease in error
  double origError = GaussianFactorGraph(bt).error(VectorValues::Zero(actual));
  double newError = GaussianFactorGraph(bt).error(actual);
  EXPECT(newError < origError);
}


/* ************************************************************************* */
int main() { TestResult tr; return TestRegistry::runAllTests(tr);}
/* ************************************************************************* */