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

 * 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   SmartProjectionPoseFactorRollingShutter.h
 * @brief  Smart projection factor on poses modeling rolling shutter effect with given readout time
 * @author Luca Carlone
 */

#pragma once

#include <gtsam/slam/SmartProjectionFactor.h>

namespace gtsam {
/**
 *
 * @addtogroup SLAM
 *
 * If you are using the factor, please cite:
 * L. Carlone, Z. Kira, C. Beall, V. Indelman, F. Dellaert,
 * Eliminating conditionally independent sets in factor graphs:
 * a unifying perspective based on smart factors,
 * Int. Conf. on Robotics and Automation (ICRA), 2014.
 */

/**
 * This factor optimizes two consecutive poses of the body assuming a rolling shutter model of the camera with given readout time.
 * The factor requires that values contain (for each pixel observation) two consecutive camera poses
 * from which the pixel observation pose can be interpolated.
 * @addtogroup SLAM
 */
template<class CALIBRATION>
class SmartProjectionPoseFactorRollingShutter : public SmartProjectionFactor<
PinholePose<CALIBRATION> > {

 protected:
  /// shared pointer to calibration object (one for each observation)
  std::vector<boost::shared_ptr<CALIBRATION> > K_all_;

  /// The keys of the pose of the body (with respect to an external world frame): two consecutive poses for each observation
  std::vector<std::pair<Key, Key>> world_P_body_key_pairs_;

  /// interpolation factor (one for each observation) to interpolate between pair of consecutive poses
  std::vector<double> alphas_;

  /// Pose of the camera in the body frame
  std::vector<Pose3> body_P_sensors_;

 public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW

  /// shorthand for base class type
  typedef SmartProjectionFactor<PinholePose<CALIBRATION> > Base;

  /// shorthand for this class
  typedef SmartProjectionPoseFactorRollingShutter This;

  /// shorthand for a smart pointer to a factor
  typedef boost::shared_ptr<This> shared_ptr;

  static const int DimBlock = 12;  ///< size of the variable stacking 2 poses from which the observation pose is interpolated
  static const int DimPose = 6;  ///< Pose3 dimension
  static const int ZDim = 2;  ///< Measurement dimension (Point2)
  typedef Eigen::Matrix<double, ZDim, DimBlock> MatrixZD;  // F blocks (derivatives wrt block of 2 poses)
  typedef std::vector<MatrixZD, Eigen::aligned_allocator<MatrixZD> > FBlocks;  // vector of F blocks

  /**
   * Constructor
   * @param Isotropic measurement noise
   * @param params internal parameters of the smart factors
   */
  SmartProjectionPoseFactorRollingShutter(
      const SharedNoiseModel& sharedNoiseModel,
      const SmartProjectionParams& params = SmartProjectionParams())
  : Base(sharedNoiseModel, params) {
  }

  /** Virtual destructor */
  ~SmartProjectionPoseFactorRollingShutter() override = default;

  /**
   * add a new measurement, with 2 pose keys, interpolation factor, camera (intrinsic and extrinsic) calibration, and observed pixel.
   * @param measured 2-dimensional location of the projection of a
   * single landmark in a single view (the measurement), interpolated from the 2 poses
   * @param world_P_body_key1 key corresponding to the first body poses (time <= time pixel is acquired)
   * @param world_P_body_key2 key corresponding to the second body poses (time >= time pixel is acquired)
   * @param alpha interpolation factor in [0,1], such that if alpha = 0 the interpolated pose is the same as world_P_body_key1
   * @param K (fixed) camera intrinsic calibration
   * @param body_P_sensor (fixed) camera extrinsic calibration
   */
  void add(const Point2& measured, const Key& world_P_body_key1,
           const Key& world_P_body_key2, const double& alpha,
           const boost::shared_ptr<CALIBRATION>& K, const Pose3 body_P_sensor = Pose3::identity()) {
    // store measurements in base class
    this->measured_.push_back(measured);

    // store the pair of keys for each measurement, in the same order
    world_P_body_key_pairs_.push_back(
        std::make_pair(world_P_body_key1, world_P_body_key2));

    //  also store keys in the keys_ vector: these keys are assumed to be unique, so we avoid duplicates here
    if (std::find(this->keys_.begin(), this->keys_.end(), world_P_body_key1) == this->keys_.end())
      this->keys_.push_back(world_P_body_key1);  // add only unique keys
    if (std::find(this->keys_.begin(), this->keys_.end(), world_P_body_key2) == this->keys_.end())
      this->keys_.push_back(world_P_body_key2);  // add only unique keys

    // store interpolation factor
    alphas_.push_back(alpha);

    // store fixed intrinsic calibration
    K_all_.push_back(K);

    // store fixed extrinsics of the camera
    body_P_sensors_.push_back(body_P_sensor);
  }

  /**
   * Variant of the previous "add" function in which we include multiple measurements
   * @param measurements vector of the 2m dimensional location of the projection
   * of a single landmark in the m views (the measurements)
   * @param world_P_body_key_pairs vector where the i-th element contains a pair of keys corresponding
   * to the pair of poses from which the observation pose for the i0-th measurement can be interpolated
   * @param alphas vector of interpolation params (in [0,1]), one for each measurement (in the same order)
   * @param Ks vector of (fixed) intrinsic calibration objects
   * @param body_P_sensors vector of (fixed) extrinsic calibration objects
   */
  void add(const Point2Vector& measurements,
           const std::vector<std::pair<Key, Key>>& world_P_body_key_pairs,
           const std::vector<double>& alphas,
           const std::vector<boost::shared_ptr<CALIBRATION>>& Ks,
           const std::vector<Pose3> body_P_sensors) {
    assert(world_P_body_key_pairs.size() == measurements.size());
    assert(world_P_body_key_pairs.size() == alphas.size());
    assert(world_P_body_key_pairs.size() == Ks.size());
    for (size_t i = 0; i < measurements.size(); i++) {
      add(measurements[i], world_P_body_key_pairs[i].first,
          world_P_body_key_pairs[i].second, alphas[i], Ks[i],
          body_P_sensors[i]);
    }
  }

  /**
   * Variant of the previous "add" function in which we include multiple measurements
   * with the same (intrinsic and extrinsic) calibration
   * @param measurements vector of the 2m dimensional location of the projection
   * of a single landmark in the m views (the measurements)
   * @param world_P_body_key_pairs vector where the i-th element contains a pair of keys corresponding
   * to the pair of poses from which the observation pose for the i0-th measurement can be interpolated
   * @param alphas vector of interpolation params (in [0,1]), one for each measurement (in the same order)
   * @param K (fixed) camera intrinsic calibration (same for all measurements)
   * @param body_P_sensor (fixed) camera extrinsic calibration (same for all measurements)
   */
  void add(const Point2Vector& measurements,
           const std::vector<std::pair<Key, Key>>& world_P_body_key_pairs,
           const std::vector<double>& alphas,
           const boost::shared_ptr<CALIBRATION>& K, const Pose3 body_P_sensor = Pose3::identity()) {
    assert(world_P_body_key_pairs.size() == measurements.size());
    assert(world_P_body_key_pairs.size() == alphas.size());
    for (size_t i = 0; i < measurements.size(); i++) {
      add(measurements[i], world_P_body_key_pairs[i].first,
          world_P_body_key_pairs[i].second, alphas[i], K, body_P_sensor);
    }
  }

  /// return the calibration object
  inline std::vector<boost::shared_ptr<CALIBRATION>> calibration() const {
    return K_all_;
  }

  /// return (for each observation) the keys of the pair of poses from which we interpolate
  const std::vector<std::pair<Key, Key>> world_P_body_key_pairs() const {
    return world_P_body_key_pairs_;
  }

  /// return the interpolation factors alphas
  const std::vector<double> alphas() const {
    return alphas_;
  }

  /// return the extrinsic camera calibration body_P_sensors
  const std::vector<Pose3> body_P_sensors() const {
    return body_P_sensors_;
  }

  /**
   * print
   * @param s optional string naming the factor
   * @param keyFormatter optional formatter useful for printing Symbols
   */
  void print(const std::string& s = "", const KeyFormatter& keyFormatter =
      DefaultKeyFormatter) const override {
    std::cout << s << "SmartProjectionPoseFactorRollingShutter: \n ";
    for (size_t i = 0; i < K_all_.size(); i++) {
      std::cout << "-- Measurement nr " << i << std::endl;
      std::cout << " pose1 key: "
          << keyFormatter(world_P_body_key_pairs_[i].first) << std::endl;
      std::cout << " pose2 key: "
          << keyFormatter(world_P_body_key_pairs_[i].second) << std::endl;
      std::cout << " alpha: " << alphas_[i] << std::endl;
      body_P_sensors_[i].print("extrinsic calibration:\n");
      K_all_[i]->print("intrinsic calibration = ");
    }
    Base::print("", keyFormatter);
  }

  /// equals
  bool equals(const NonlinearFactor& p, double tol = 1e-9) const override {
    const SmartProjectionPoseFactorRollingShutter<CALIBRATION>* e =
        dynamic_cast<const SmartProjectionPoseFactorRollingShutter<CALIBRATION>*>(&p);

    double keyPairsEqual = true;
    if(this->world_P_body_key_pairs_.size() == e->world_P_body_key_pairs().size()){
      for(size_t k=0; k< this->world_P_body_key_pairs_.size(); k++){
        const Key key1own = world_P_body_key_pairs_[k].first;
        const Key key1e = e->world_P_body_key_pairs()[k].first;
        const Key key2own = world_P_body_key_pairs_[k].second;
        const Key key2e = e->world_P_body_key_pairs()[k].second;
        if ( !(key1own == key1e) || !(key2own == key2e) ){
          keyPairsEqual = false; break;
        }
      }
    }else{ keyPairsEqual = false; }

    double extrinsicCalibrationEqual = true;
    if(this->body_P_sensors_.size() == e->body_P_sensors().size()){
      for(size_t i=0; i< this->body_P_sensors_.size(); i++){
        if (!body_P_sensors_[i].equals(e->body_P_sensors()[i])){
          extrinsicCalibrationEqual = false; break;
        }
      }
    }else{ extrinsicCalibrationEqual = false; }

    return e && Base::equals(p, tol) && K_all_ == e->calibration()
        && alphas_ == e->alphas() && keyPairsEqual && extrinsicCalibrationEqual;
  }

  /**
   * Compute jacobian F, E and error vector at a given linearization point
   * @param values Values structure which must contain camera poses
   * corresponding to keys involved in this factor
   * @return Return arguments are the camera jacobians Fs (including the jacobian with
   * respect to both body poses we interpolate from), the point Jacobian E,
   * and the error vector b. Note that the jacobians are computed for a given point.
   */
  void computeJacobiansWithTriangulatedPoint(FBlocks& Fs, Matrix& E, Vector& b,
                                             const Values& values) const {
    if (!this->result_) {
      throw("computeJacobiansWithTriangulatedPoint");
    } else {  // valid result: compute jacobians
      size_t numViews = this->measured_.size();
      E = Matrix::Zero(2 * numViews, 3);  // a Point2 for each view (point jacobian)
      b = Vector::Zero(2 * numViews);  // a Point2 for each view
      // intermediate Jacobians
      Eigen::Matrix<double, ZDim, DimPose> dProject_dPoseCam;
      Eigen::Matrix<double, DimPose, DimPose> dInterpPose_dPoseBody1,
      dInterpPose_dPoseBody2, dPoseCam_dInterpPose;
      Eigen::Matrix<double, ZDim, 3> Ei;

      for (size_t i = 0; i < numViews; i++) {  // for each camera/measurement
        const Pose3& w_P_body1 = values.at<Pose3>(world_P_body_key_pairs_[i].first);
        const Pose3& w_P_body2 = values.at<Pose3>(world_P_body_key_pairs_[i].second);
        double interpolationFactor = alphas_[i];
        // get interpolated pose:
        const Pose3& w_P_body = interpolate<Pose3>(w_P_body1, w_P_body2,interpolationFactor, dInterpPose_dPoseBody1, dInterpPose_dPoseBody2);
        const Pose3& body_P_cam = body_P_sensors_[i];
        const Pose3& w_P_cam = w_P_body.compose(body_P_cam, dPoseCam_dInterpPose);
        PinholeCamera<CALIBRATION> camera(w_P_cam, *K_all_[i]);

        // get jacobians and error vector for current measurement
        Point2 reprojectionError_i = Point2(
            camera.project(*this->result_, dProject_dPoseCam, Ei)
            - this->measured_.at(i));
        Eigen::Matrix<double, ZDim, DimBlock> J;  // 2 x 12
        J.block(0, 0, ZDim, 6) = dProject_dPoseCam * dPoseCam_dInterpPose
            * dInterpPose_dPoseBody1;  // (2x6) * (6x6) * (6x6)
        J.block(0, 6, ZDim, 6) = dProject_dPoseCam * dPoseCam_dInterpPose
            * dInterpPose_dPoseBody2;  // (2x6) * (6x6) * (6x6)

        // fit into the output structures
        Fs.push_back(J);
        size_t row = 2 * i;
        b.segment<ZDim>(row) = -reprojectionError_i;
        E.block<ZDim, 3>(row, 0) = Ei;
      }
    }
  }

  /// linearize and return a Hessianfactor that is an approximation of error(p)
  boost::shared_ptr<RegularHessianFactor<DimPose> > createHessianFactor(
      const Values& values, const double lambda = 0.0, bool diagonalDamping =
          false) const {

    // we may have multiple observation sharing the same keys (due to the rolling shutter interpolation),
    // hence the number of unique keys may be smaller than 2 * nrMeasurements
    size_t nrUniqueKeys = this->keys_.size(); // note: by construction, keys_ only contains unique keys

    // Create structures for Hessian Factors
    KeyVector js;
    std::vector < Matrix > Gs(nrUniqueKeys * (nrUniqueKeys + 1) / 2);
    std::vector < Vector > gs(nrUniqueKeys);

    if (this->measured_.size() != this->cameras(values).size()) // 1 observation per interpolated camera
      throw std::runtime_error("SmartProjectionPoseFactorRollingShutter: "
                               "measured_.size() inconsistent with input");

    // triangulate 3D point at given linearization point
    this->triangulateSafe(this->cameras(values));

    if (!this->result_) {  // failed: return "empty/zero" Hessian
      if (this->params_.degeneracyMode == ZERO_ON_DEGENERACY) {
        for (Matrix& m : Gs)
          m = Matrix::Zero(DimPose, DimPose);
        for (Vector& v : gs)
          v = Vector::Zero(DimPose);
        return boost::make_shared < RegularHessianFactor<DimPose>
            > (this->keys_, Gs, gs, 0.0);
      } else {
        throw std::runtime_error("SmartProjectionPoseFactorRollingShutter: "
                                       "only supported degeneracy mode is ZERO_ON_DEGENERACY");
      }
    }
    // compute Jacobian given triangulated 3D Point
    FBlocks Fs;
    Matrix E;
    Vector b;
    this->computeJacobiansWithTriangulatedPoint(Fs, E, b, values);

    // Whiten using noise model
    this->noiseModel_->WhitenSystem(E, b);
    for (size_t i = 0; i < Fs.size(); i++)
      Fs[i] = this->noiseModel_->Whiten(Fs[i]);

    Matrix3 P = Base::Cameras::PointCov(E, lambda, diagonalDamping);

    // Collect all the key pairs: these are the keys that correspond to the blocks in Fs (on which we apply the Schur Complement)
    KeyVector nonuniqueKeys;
    for (size_t i = 0; i < world_P_body_key_pairs_.size(); i++) {
      nonuniqueKeys.push_back(world_P_body_key_pairs_.at(i).first);
      nonuniqueKeys.push_back(world_P_body_key_pairs_.at(i).second);
    }

    // Build augmented Hessian (with last row/column being the information vector)
    // Note: we need to get the augumented hessian wrt the unique keys in key_
    SymmetricBlockMatrix augmentedHessianUniqueKeys =
        Base::Cameras::SchurComplementAndRearrangeBlocks_3_12_6(
            Fs, E, P, b, nonuniqueKeys, this->keys_);

    return boost::make_shared < RegularHessianFactor<DimPose>
        > (this->keys_, augmentedHessianUniqueKeys);
  }

  /**
   * error calculates the error of the factor.
   */
  double error(const Values& values) const override {
    if (this->active(values)) {
      return this->totalReprojectionError(this->cameras(values));
    } else { // else of active flag
      return 0.0;
    }
  }

  /**
   * Collect all cameras involved in this factor
   * @param values Values structure which must contain camera poses
   * corresponding to keys involved in this factor
   * @return Cameras
   */
  typename Base::Cameras cameras(const Values& values) const override {
    size_t numViews = this->measured_.size();
    assert(numViews == K_all_.size());
    assert(numViews == alphas_.size());
    assert(numViews == body_P_sensors_.size());
    assert(numViews == world_P_body_key_pairs_.size());

    typename Base::Cameras cameras;
    for (size_t i = 0; i < numViews; i++) {  // for each measurement
      const Pose3& w_P_body1 = values.at<Pose3>(world_P_body_key_pairs_[i].first);
      const Pose3& w_P_body2 = values.at<Pose3>(world_P_body_key_pairs_[i].second);
      double interpolationFactor = alphas_[i];
      const Pose3& w_P_body = interpolate<Pose3>(w_P_body1, w_P_body2, interpolationFactor);
      const Pose3& body_P_cam = body_P_sensors_[i];
      const Pose3& w_P_cam = w_P_body.compose(body_P_cam);
      cameras.emplace_back(w_P_cam, K_all_[i]);
    }
    return cameras;
  }

  /**
   * Linearize to Gaussian Factor (possibly adding a damping factor Lambda for LM)
   * @param values Values structure which must contain camera poses and extrinsic pose for this factor
   * @return a Gaussian factor
   */
  boost::shared_ptr<GaussianFactor> linearizeDamped(
      const Values& values, const double lambda = 0.0) const {
    // depending on flag set on construction we may linearize to different linear factors
    switch (this->params_.linearizationMode) {
      case HESSIAN:
        return this->createHessianFactor(values, lambda);
      default:
        throw std::runtime_error(
            "SmartProjectionPoseFactorRollingShutter: unknown linearization mode");
    }
  }

  /// linearize
  boost::shared_ptr<GaussianFactor> linearize(const Values& values) const
          override {
    return this->linearizeDamped(values);
  }

 private:
  /// Serialization function
  friend class boost::serialization::access;
  template<class ARCHIVE>
  void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
    ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
    ar & BOOST_SERIALIZATION_NVP(K_all_);
  }

};
// end of class declaration

/// traits
template<class CALIBRATION>
struct traits<SmartProjectionPoseFactorRollingShutter<CALIBRATION> > :
public Testable<SmartProjectionPoseFactorRollingShutter<CALIBRATION> > {
};

}  // namespace gtsam