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#ifndef PCL_REGISTRATION_NDT_H_
#define PCL_REGISTRATION_NDT_H_

#include <pcl/registration/registration.h>
#include <pcl/filters/voxel_grid_covariance.h>

#include <unsupported/Eigen/NonLinearOptimization>

namespace pcl
{
  /** \brief A 3D Normal Distribution Transform registration implementation for point cloud data.
    * \note For more information please see
    * <b>Magnusson, M. (2009). The Three-Dimensional Normal-Distributions Transform —
    * an Efﬁcient Representation for Registration, Surface Analysis, and Loop Detection.
    * PhD thesis, Orebro University. Orebro Studies in Technology 36.</b>,
    * <b>More, J., and Thuente, D. (1994). Line Search Algorithm with Guaranteed Sufficient Decrease
    * In ACM Transactions on Mathematical Software.</b> and
    * Sun, W. and Yuan, Y, (2006) Optimization Theory and Methods: Nonlinear Programming. 89-100
    * \note Math refactored by Todor Stoyanov.
    * \author Brian Okorn (Space and Naval Warfare Systems Center Pacific)
    */
  template<typename PointSource, typename PointTarget>
  class NormalDistributionsTransform : public Registration<PointSource, PointTarget>
  {
    protected:

      typedef typename Registration<PointSource, PointTarget>::PointCloudSource PointCloudSource;
      typedef typename PointCloudSource::Ptr PointCloudSourcePtr;
      typedef typename PointCloudSource::ConstPtr PointCloudSourceConstPtr;

      typedef typename Registration<PointSource, PointTarget>::PointCloudTarget PointCloudTarget;
      typedef typename PointCloudTarget::Ptr PointCloudTargetPtr;
      typedef typename PointCloudTarget::ConstPtr PointCloudTargetConstPtr;

      typedef PointIndices::Ptr PointIndicesPtr;
      typedef PointIndices::ConstPtr PointIndicesConstPtr;

      /** \brief Typename of searchable voxel grid containing mean and covariance. */
      typedef VoxelGridCovariance<PointTarget> TargetGrid;
      /** \brief Typename of pointer to searchable voxel grid. */
      typedef TargetGrid* TargetGridPtr;
      /** \brief Typename of const pointer to searchable voxel grid. */
      typedef const TargetGrid* TargetGridConstPtr;
      /** \brief Typename of const pointer to searchable voxel grid leaf. */
      typedef typename TargetGrid::LeafConstPtr TargetGridLeafConstPtr;


    public:

      typedef boost::shared_ptr< NormalDistributionsTransform<PointSource, PointTarget> > Ptr;
      typedef boost::shared_ptr< const NormalDistributionsTransform<PointSource, PointTarget> > ConstPtr;


      /** \brief Constructor.
        * Sets \ref outlier_ratio_ to 0.35, \ref step_size_ to 0.05 and \ref resolution_ to 1.0
        */
      NormalDistributionsTransform ();
      
      /** \brief Empty destructor */
      virtual ~NormalDistributionsTransform () {}

      /** \brief Provide a pointer to the input target (e.g., the point cloud that we want to align the input source to).
        * \param[in] cloud the input point cloud target
        */
      inline void
      setInputTarget (const PointCloudTargetConstPtr &cloud)
      {
        Registration<PointSource, PointTarget>::setInputTarget (cloud);
        init ();
      }

      /** \brief Set/change the voxel grid resolution.
        * \param[in] resolution side length of voxels
        */
      inline void
      setResolution (float resolution)
      {
        // Prevents unnessary voxel initiations
        if (resolution_ != resolution)
        {
          resolution_ = resolution;
          if (input_)
            init ();
        }
      }

      /** \brief Get voxel grid resolution.
        * \return side length of voxels
        */
      inline float
      getResolution () const
      {
        return (resolution_);
      }

      /** \brief Get the newton line search maximum step length.
        * \return maximum step length
        */
      inline double
      getStepSize () const
      {
        return (step_size_);
      }

      /** \brief Set/change the newton line search maximum step length.
        * \param[in] step_size maximum step length
        */
      inline void
      setStepSize (double step_size)
      {
        step_size_ = step_size;
      }

      /** \brief Get the point cloud outlier ratio.
        * \return outlier ratio
        */
      inline double
      getOulierRatio () const
      {
        return (outlier_ratio_);
      }

      /** \brief Set/change the point cloud outlier ratio.
        * \param[in] outlier_ratio outlier ratio
        */
      inline void
      setOulierRatio (double outlier_ratio)
      {
        outlier_ratio_ = outlier_ratio;
      }

      /** \brief Get the registration alignment probability.
        * \return transformation probability
        */
      inline double
      getTransformationProbability () const
      {
        return (trans_probability_);
      }

      /** \brief Get the number of iterations required to calculate alignment.
        * \return final number of iterations
        */
      inline int
      getFinalNumIteration () const
      {
        return (nr_iterations_);
      }

      /** \brief Convert 6 element transformation vector to affine transformation.
        * \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
        * \param[out] trans affine transform corresponding to given transfomation vector
        */
      static void
      convertTransform (const Eigen::Matrix<double, 6, 1> &x, Eigen::Affine3f &trans)
      {
        trans = Eigen::Translation<float, 3>(float (x (0)), float (x (1)), float (x (2))) *
                Eigen::AngleAxis<float>(float (x (3)), Eigen::Vector3f::UnitX ()) *
                Eigen::AngleAxis<float>(float (x (4)), Eigen::Vector3f::UnitY ()) *
                Eigen::AngleAxis<float>(float (x (5)), Eigen::Vector3f::UnitZ ());
      }

      /** \brief Convert 6 element transformation vector to transformation matrix.
        * \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
        * \param[out] trans 4x4 transformation matrix corresponding to given transfomation vector
        */
      static void
      convertTransform (const Eigen::Matrix<double, 6, 1> &x, Eigen::Matrix4f &trans)
      {
        Eigen::Affine3f _affine;
        convertTransform (x, _affine);
        trans = _affine.matrix ();
      }

    protected:

      using Registration<PointSource, PointTarget>::reg_name_;
      using Registration<PointSource, PointTarget>::getClassName;
      using Registration<PointSource, PointTarget>::input_;
      using Registration<PointSource, PointTarget>::indices_;
      using Registration<PointSource, PointTarget>::target_;
      using Registration<PointSource, PointTarget>::nr_iterations_;
      using Registration<PointSource, PointTarget>::max_iterations_;
      using Registration<PointSource, PointTarget>::previous_transformation_;
      using Registration<PointSource, PointTarget>::final_transformation_;
      using Registration<PointSource, PointTarget>::transformation_;
      using Registration<PointSource, PointTarget>::transformation_epsilon_;
      using Registration<PointSource, PointTarget>::transformation_rotation_epsilon_;
      using Registration<PointSource, PointTarget>::converged_;
      using Registration<PointSource, PointTarget>::corr_dist_threshold_;
      using Registration<PointSource, PointTarget>::inlier_threshold_;

      using Registration<PointSource, PointTarget>::update_visualizer_;

      /** \brief Estimate the transformation and returns the transformed source (input) as output.
        * \param[out] output the resultant input transformed point cloud dataset
        */
      virtual void
      computeTransformation (PointCloudSource &output)
      {
        computeTransformation (output, Eigen::Matrix4f::Identity ());
      }

      /** \brief Estimate the transformation and returns the transformed source (input) as output.
        * \param[out] output the resultant input transformed point cloud dataset
        * \param[in] guess the initial gross estimation of the transformation
        */
      virtual void
      computeTransformation (PointCloudSource &output, const Eigen::Matrix4f &guess);

      /** \brief Initiate covariance voxel structure. */
      void inline
      init ()
      {
        target_cells_.setLeafSize (resolution_, resolution_, resolution_);
        target_cells_.setInputCloud ( target_ );
        // Initiate voxel structure.
        target_cells_.filter (true);
      }

      /** \brief Compute derivatives of probability function w.r.t. the transformation vector.
        * \note Equation 6.10, 6.12 and 6.13 [Magnusson 2009].
        * \param[out] score_gradient the gradient vector of the probability function w.r.t. the transformation vector
        * \param[out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
        * \param[in] trans_cloud transformed point cloud
        * \param[in] p the current transform vector
        * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
        */
      double
      computeDerivatives (Eigen::Matrix<double, 6, 1> &score_gradient,
                          Eigen::Matrix<double, 6, 6> &hessian,
                          PointCloudSource &trans_cloud,
                          Eigen::Matrix<double, 6, 1> &p,
                          bool compute_hessian = true);

      /** \brief Compute individual point contirbutions to derivatives of probability function w.r.t. the transformation vector.
        * \note Equation 6.10, 6.12 and 6.13 [Magnusson 2009].
        * \param[in,out] score_gradient the gradient vector of the probability function w.r.t. the transformation vector
        * \param[in,out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
        * \param[in] x_trans transformed point minus mean of occupied covariance voxel
        * \param[in] c_inv covariance of occupied covariance voxel
        * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
        */
      double
      updateDerivatives (Eigen::Matrix<double, 6, 1> &score_gradient,
                         Eigen::Matrix<double, 6, 6> &hessian,
                         Eigen::Vector3d &x_trans, Eigen::Matrix3d &c_inv,
                         bool compute_hessian = true);

      /** \brief Precompute anglular components of derivatives.
        * \note Equation 6.19 and 6.21 [Magnusson 2009].
        * \param[in] p the current transform vector
        * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
        */
      void
      computeAngleDerivatives (Eigen::Matrix<double, 6, 1> &p, bool compute_hessian = true);

      /** \brief Compute point derivatives.
        * \note Equation 6.18-21 [Magnusson 2009].
        * \param[in] x point from the input cloud
        * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
        */
      void
      computePointDerivatives (Eigen::Vector3d &x, bool compute_hessian = true);

      /** \brief Compute hessian of probability function w.r.t. the transformation vector.
        * \note Equation 6.13 [Magnusson 2009].
        * \param[out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
        * \param[in] trans_cloud transformed point cloud
        * \param[in] p the current transform vector
        */
      void
      computeHessian (Eigen::Matrix<double, 6, 6> &hessian,
                      PointCloudSource &trans_cloud,
                      Eigen::Matrix<double, 6, 1> &p);

      /** \brief Compute individual point contirbutions to hessian of probability function w.r.t. the transformation vector.
        * \note Equation 6.13 [Magnusson 2009].
        * \param[in,out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
        * \param[in] x_trans transformed point minus mean of occupied covariance voxel
        * \param[in] c_inv covariance of occupied covariance voxel
        */
      void
      updateHessian (Eigen::Matrix<double, 6, 6> &hessian,
                     Eigen::Vector3d &x_trans, Eigen::Matrix3d &c_inv);

      /** \brief Compute line search step length and update transform and probability derivatives using More-Thuente method.
        * \note Search Algorithm [More, Thuente 1994]
        * \param[in] x initial transformation vector, \f$ x \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ \vec{p} \f$ in Algorithm 2 [Magnusson 2009]
        * \param[in] step_dir descent direction, \f$ p \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ \delta \vec{p} \f$ normalized in Algorithm 2 [Magnusson 2009]
        * \param[in] step_init initial step length estimate, \f$ \alpha_0 \f$ in Moore-Thuente (1994) and the noramal of \f$ \delta \vec{p} \f$ in Algorithm 2 [Magnusson 2009]
        * \param[in] step_max maximum step length, \f$ \alpha_max \f$ in Moore-Thuente (1994)
        * \param[in] step_min minimum step length, \f$ \alpha_min \f$ in Moore-Thuente (1994)
        * \param[out] score final score function value, \f$ f(x + \alpha p) \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ score \f$ in Algorithm 2 [Magnusson 2009]
        * \param[in,out] score_gradient gradient of score function w.r.t. transformation vector, \f$ f'(x + \alpha p) \f$ in Moore-Thuente (1994) and \f$ \vec{g} \f$ in Algorithm 2 [Magnusson 2009]
        * \param[out] hessian hessian of score function w.r.t. transformation vector, \f$ f''(x + \alpha p) \f$ in Moore-Thuente (1994) and \f$ H \f$ in Algorithm 2 [Magnusson 2009]
        * \param[in,out] trans_cloud transformed point cloud, \f$ X \f$ transformed by \f$ T(\vec{p},\vec{x}) \f$ in Algorithm 2 [Magnusson 2009]
        * \return final step length
        */
      double
      computeStepLengthMT (const Eigen::Matrix<double, 6, 1> &x,
                           Eigen::Matrix<double, 6, 1> &step_dir,
                           double step_init,
                           double step_max, double step_min,
                           double &score,
                           Eigen::Matrix<double, 6, 1> &score_gradient,
                           Eigen::Matrix<double, 6, 6> &hessian,
                           PointCloudSource &trans_cloud);

      /** \brief Update interval of possible step lengths for More-Thuente method, \f$ I \f$ in More-Thuente (1994)
        * \note Updating Algorithm until some value satisfies \f$ \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$
        * and Modified Updating Algorithm from then on [More, Thuente 1994].
        * \param[in,out] a_l first endpoint of interval \f$ I \f$, \f$ \alpha_l \f$ in Moore-Thuente (1994)
        * \param[in,out] f_l value at first endpoint, \f$ f_l \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_l) \f$ for Update Algorithm and \f$ \phi(\alpha_l) \f$ for Modified Update Algorithm
        * \param[in,out] g_l derivative at first endpoint, \f$ g_l \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_l) \f$ for Update Algorithm and \f$ \phi'(\alpha_l) \f$ for Modified Update Algorithm
        * \param[in,out] a_u second endpoint of interval \f$ I \f$, \f$ \alpha_u \f$ in Moore-Thuente (1994)
        * \param[in,out] f_u value at second endpoint, \f$ f_u \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_u) \f$ for Update Algorithm and \f$ \phi(\alpha_u) \f$ for Modified Update Algorithm
        * \param[in,out] g_u derivative at second endpoint, \f$ g_u \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_u) \f$ for Update Algorithm and \f$ \phi'(\alpha_u) \f$ for Modified Update Algorithm
        * \param[in] a_t trial value, \f$ \alpha_t \f$ in Moore-Thuente (1994)
        * \param[in] f_t value at trial value, \f$ f_t \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_t) \f$ for Update Algorithm and \f$ \phi(\alpha_t) \f$ for Modified Update Algorithm
        * \param[in] g_t derivative at trial value, \f$ g_t \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_t) \f$ for Update Algorithm and \f$ \phi'(\alpha_t) \f$ for Modified Update Algorithm
        * \return if interval converges
        */
      bool
      updateIntervalMT (double &a_l, double &f_l, double &g_l,
                        double &a_u, double &f_u, double &g_u,
                        double a_t, double f_t, double g_t);

      /** \brief Select new trial value for More-Thuente method.
        * \note Trial Value Selection [More, Thuente 1994], \f$ \psi(\alpha_k) \f$ is used for \f$ f_k \f$ and \f$ g_k \f$
        * until some value satisfies the test \f$ \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$
        * then \f$ \phi(\alpha_k) \f$ is used from then on.
        * \note Interpolation Minimizer equations from Optimization Theory and Methods: Nonlinear Programming By Wenyu Sun, Ya-xiang Yuan (89-100).
        * \param[in] a_l first endpoint of interval \f$ I \f$, \f$ \alpha_l \f$ in Moore-Thuente (1994)
        * \param[in] f_l value at first endpoint, \f$ f_l \f$ in Moore-Thuente (1994)
        * \param[in] g_l derivative at first endpoint, \f$ g_l \f$ in Moore-Thuente (1994)
        * \param[in] a_u second endpoint of interval \f$ I \f$, \f$ \alpha_u \f$ in Moore-Thuente (1994)
        * \param[in] f_u value at second endpoint, \f$ f_u \f$ in Moore-Thuente (1994)
        * \param[in] g_u derivative at second endpoint, \f$ g_u \f$ in Moore-Thuente (1994)
        * \param[in] a_t previous trial value, \f$ \alpha_t \f$ in Moore-Thuente (1994)
        * \param[in] f_t value at previous trial value, \f$ f_t \f$ in Moore-Thuente (1994)
        * \param[in] g_t derivative at previous trial value, \f$ g_t \f$ in Moore-Thuente (1994)
        * \return new trial value
        */
      double
      trialValueSelectionMT (double a_l, double f_l, double g_l,
                             double a_u, double f_u, double g_u,
                             double a_t, double f_t, double g_t);

      /** \brief Auxiliary function used to determine endpoints of More-Thuente interval.
        * \note \f$ \psi(\alpha) \f$ in Equation 1.6 (Moore, Thuente 1994)
        * \param[in] a the step length, \f$ \alpha \f$ in More-Thuente (1994)
        * \param[in] f_a function value at step length a, \f$ \phi(\alpha) \f$ in More-Thuente (1994)
        * \param[in] f_0 initial function value, \f$ \phi(0) \f$ in Moore-Thuente (1994)
        * \param[in] g_0 initial function gradiant, \f$ \phi'(0) \f$ in More-Thuente (1994)
        * \param[in] mu the step length, constant \f$ \mu \f$ in Equation 1.1 [More, Thuente 1994]
        * \return sufficient decrease value
        */
      inline double
      auxilaryFunction_PsiMT (double a, double f_a, double f_0, double g_0, double mu = 1.e-4)
      {
        return (f_a - f_0 - mu * g_0 * a);
      }

      /** \brief Auxiliary function derivative used to determine endpoints of More-Thuente interval.
        * \note \f$ \psi'(\alpha) \f$, derivative of Equation 1.6 (Moore, Thuente 1994)
        * \param[in] g_a function gradient at step length a, \f$ \phi'(\alpha) \f$ in More-Thuente (1994)
        * \param[in] g_0 initial function gradiant, \f$ \phi'(0) \f$ in More-Thuente (1994)
        * \param[in] mu the step length, constant \f$ \mu \f$ in Equation 1.1 [More, Thuente 1994]
        * \return sufficient decrease derivative
        */
      inline double
      auxilaryFunction_dPsiMT (double g_a, double g_0, double mu = 1.e-4)
      {
        return (g_a - mu * g_0);
      }

      /** \brief The voxel grid generated from target cloud containing point means and covariances. */
      TargetGrid target_cells_;

      //double fitness_epsilon_;

      /** \brief The side length of voxels. */
      float resolution_;

      /** \brief The maximum step length. */
      double step_size_;

      /** \brief The ratio of outliers of points w.r.t. a normal distribution, Equation 6.7 [Magnusson 2009]. */
      double outlier_ratio_;

      /** \brief The normalization constants used fit the point distribution to a normal distribution, Equation 6.8 [Magnusson 2009]. */
      double gauss_d1_, gauss_d2_;

      /** \brief The probability score of the transform applied to the input cloud, Equation 6.9 and 6.10 [Magnusson 2009]. */
      double trans_probability_;

      /** \brief Precomputed Angular Gradient
        *
        * The precomputed angular derivatives for the jacobian of a transformation vector, Equation 6.19 [Magnusson 2009]. 
        */
      Eigen::Vector3d j_ang_a_, j_ang_b_, j_ang_c_, j_ang_d_, j_ang_e_, j_ang_f_, j_ang_g_, j_ang_h_;

      /** \brief Precomputed Angular Hessian
        *
        * The precomputed angular derivatives for the hessian of a transformation vector, Equation 6.19 [Magnusson 2009].
        */
      Eigen::Vector3d h_ang_a2_, h_ang_a3_,
                      h_ang_b2_, h_ang_b3_,
                      h_ang_c2_, h_ang_c3_,
                      h_ang_d1_, h_ang_d2_, h_ang_d3_,
                      h_ang_e1_, h_ang_e2_, h_ang_e3_,
                      h_ang_f1_, h_ang_f2_, h_ang_f3_;

      /** \brief The first order derivative of the transformation of a point w.r.t. the transform vector, \f$ J_E \f$ in Equation 6.18 [Magnusson 2009]. */
      Eigen::Matrix<double, 3, 6> point_gradient_;

      /** \brief The second order derivative of the transformation of a point w.r.t. the transform vector, \f$ H_E \f$ in Equation 6.20 [Magnusson 2009]. */
      Eigen::Matrix<double, 18, 6> point_hessian_;

    public:
      EIGEN_MAKE_ALIGNED_OPERATOR_NEW

  };

}

#include <pcl/registration/impl/ndt.hpp>

#endif // PCL_REGISTRATION_NDT_H_
