sac_model.h

/*
 * Software License Agreement (BSD License)
 *
 *  Point Cloud Library (PCL) - www.pointclouds.org
 *  Copyright (c) 2010-2011, Willow Garage, Inc.
 *  Copyright (c) 2012-, Open Perception, Inc.
 *  
 *  All rights reserved.
 *
 *  Redistribution and use in source and binary forms, with or without
 *  modification, are permitted provided that the following conditions
 *  are met:
 *
 *   * Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *   * Redistributions in binary form must reproduce the above
 *     copyright notice, this list of conditions and the following
 *     disclaimer in the documentation and/or other materials provided
 *     with the distribution.
 *   * Neither the name of the copyright holder(s) nor the names of its
 *     contributors may be used to endorse or promote products derived
 *     from this software without specific prior written permission.
 *
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 *  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 *  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 *  FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 *  COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 *  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
 *  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 *  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 *  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 *  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 *  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 *  POSSIBILITY OF SUCH DAMAGE.
 *
 * $Id$
 *
 */
 
#pragma once
 
#include <ctime>
#include <limits>
#include <memory>
#include <set>
#include <boost/random/mersenne_twister.hpp> // for mt19937
#include <boost/random/uniform_int.hpp> // for uniform_int
#include <boost/random/variate_generator.hpp> // for variate_generator
#include <random>
#include <numeric> // for iota
 
#include <pcl/memory.h>
#include <pcl/console/print.h>
#include <pcl/point_cloud.h>
#include <pcl/types.h> // for index_t, Indices
#include <pcl/sample_consensus/model_types.h>
 
#include <pcl/search/search.h>
 
namespace pcl
{
  template<class T> class ProgressiveSampleConsensus;
 
  /** \brief @b SampleConsensusModel represents the base model class. All sample consensus models must inherit 
    * from this class.
    * \author Radu B. Rusu
    * \ingroup sample_consensus
    */
  template <typename PointT>
  class SampleConsensusModel
  {
    public:
      using PointCloud = pcl::PointCloud<PointT>;
      using PointCloudConstPtr = typename PointCloud::ConstPtr;
      using PointCloudPtr = typename PointCloud::Ptr;
      using SearchPtr = typename pcl::search::Search<PointT>::Ptr;
 
      using Ptr = shared_ptr<SampleConsensusModel<PointT> >;
      using ConstPtr = shared_ptr<const SampleConsensusModel<PointT> >;
 
    protected:
      /** \brief Empty constructor for base SampleConsensusModel.
        * \param[in] random if true set the random seed to the current time, else set to 12345 (default: false)
        */
      SampleConsensusModel (bool random = false) 
        : input_ ()
        , radius_min_ (-std::numeric_limits<double>::max ())
        , radius_max_ (std::numeric_limits<double>::max ())
        , samples_radius_ (0.)
        , samples_radius_search_ ()
        , rng_dist_ (new boost::uniform_int<> (0, std::numeric_limits<int>::max ()))
        , custom_model_constraints_ ([](auto){return true;})
      {
        // Create a random number generator object
        if (random)
          rng_alg_.seed (std::random_device()());
        else
          rng_alg_.seed (12345u);
 
        rng_gen_.reset (new boost::variate_generator<boost::mt19937&, boost::uniform_int<> > (rng_alg_, *rng_dist_)); 
       }
 
    public:
      /** \brief Constructor for base SampleConsensusModel.
        * \param[in] cloud the input point cloud dataset
        * \param[in] indices a vector of point indices to be used from \a cloud
        * \param[in] random if true set the random seed to the current time, else set to 12345 (default: false)
        */
      SampleConsensusModel (const PointCloudConstPtr &cloud, const Indices &indices, const bool random = false)
        : input_ (cloud)
        , indices_(new Indices(indices))
        , radius_min_ (-std::numeric_limits<double>::max ())
        , radius_max_ (std::numeric_limits<double>::max ())
        , samples_radius_ (0.)
        , samples_radius_search_ ()
        , rng_dist_ (new boost::uniform_int<> (0, std::numeric_limits<int>::max ()))
        , custom_model_constraints_ ([](auto){return true;})
      {
        if (random)
          rng_alg_.seed (std::random_device()());
        else
          rng_alg_.seed (12345u);
 
        // If no indices are provided, use all points
        if (indices_->empty())
        {
          indices_->resize(cloud->size());
          std::iota(indices_->begin(), indices_->end(), 0);
        }
 
        if (indices_->size () > input_->size ())
        {
          PCL_ERROR("[pcl::SampleConsensusModel] Invalid index vector given with size "
                    "%zu while the input PointCloud has size %zu!\n",
                    indices_->size(),
                    static_cast<std::size_t>(input_->size()));
          indices_->clear ();
        }
        shuffled_indices_ = *indices_;
 
        // Create a random number generator object
        rng_gen_.reset (new boost::variate_generator<boost::mt19937&, boost::uniform_int<> > (rng_alg_, *rng_dist_)); 
      }
 
      /** \brief Constructor for base SampleConsensusModel.
        * \param[in] cloud the input point cloud dataset
        * \param[in] random if true set the random seed to the current time, else set to 12345 (default: false)
        */
      SampleConsensusModel (const PointCloudConstPtr &cloud, const bool random = false)
        : SampleConsensusModel(cloud, Indices(), random) {};
 
      /** \brief Destructor for base SampleConsensusModel. */
      virtual ~SampleConsensusModel () = default;
 
      /** \brief Get a set of random data samples and return them as point
        * indices.
        * \param[out] iterations the internal number of iterations used by SAC methods
        * \param[out] samples the resultant model samples
        */
      virtual void 
      getSamples (int &iterations, Indices &samples)
      {
        // We're assuming that indices_ have already been set in the constructor
        if (indices_->size () < getSampleSize ())
        {
          PCL_ERROR ("[pcl::SampleConsensusModel::getSamples] Can not select %lu unique points out of %lu!\n",
                     samples.size (), indices_->size ());
          // one of these will make it stop :)
          samples.clear ();
          iterations = std::numeric_limits<int>::max() - 1;
          return;
        }
 
        // Get a second point which is different than the first
        samples.resize (getSampleSize ());
        for (unsigned int iter = 0; iter < max_sample_checks_; ++iter)
        {
          // Choose the random indices
          if (samples_radius_ < std::numeric_limits<double>::epsilon ())
            SampleConsensusModel<PointT>::drawIndexSample (samples);
          else
            SampleConsensusModel<PointT>::drawIndexSampleRadius (samples);
 
          // If it's a good sample, stop here
          if (isSampleGood (samples))
          {
            PCL_DEBUG ("[pcl::SampleConsensusModel::getSamples] Selected %lu samples.\n", samples.size ());
            return;
          }
        }
        PCL_DEBUG ("[pcl::SampleConsensusModel::getSamples] WARNING: Could not select %d sample points in %d iterations!\n", getSampleSize (), max_sample_checks_);
        samples.clear ();
      }
 
      /** \brief Check whether the given index samples can form a valid model,
        * compute the model coefficients from these samples and store them
        * in model_coefficients. Pure virtual.
        * Implementations of this function must be thread-safe.
        * \param[in] samples the point indices found as possible good candidates
        * for creating a valid model 
        * \param[out] model_coefficients the computed model coefficients
        */
      virtual bool
      computeModelCoefficients (const Indices &samples,
                                Eigen::VectorXf &model_coefficients) const = 0;
 
      /** \brief Recompute the model coefficients using the given inlier set
        * and return them to the user. Pure virtual.
        *
        * @note: these are the coefficients of the model after refinement
        * (e.g., after a least-squares optimization)
        *
        * \param[in] inliers the data inliers supporting the model
        * \param[in] model_coefficients the initial guess for the model coefficients
        * \param[out] optimized_coefficients the resultant recomputed coefficients after non-linear optimization
        */
      virtual void
      optimizeModelCoefficients (const Indices &inliers,
                                 const Eigen::VectorXf &model_coefficients,
                                 Eigen::VectorXf &optimized_coefficients) const = 0;
 
      /** \brief Compute all distances from the cloud data to a given model. Pure virtual.
        * 
        * \param[in] model_coefficients the coefficients of a model that we need to compute distances to 
        * \param[out] distances the resultant estimated distances
        */
      virtual void
      getDistancesToModel (const Eigen::VectorXf &model_coefficients,
                           std::vector<double> &distances) const = 0;
 
      /** \brief Select all the points which respect the given model
        * coefficients as inliers. Pure virtual.
        * 
        * \param[in] model_coefficients the coefficients of a model that we need to compute distances to
        * \param[in] threshold a maximum admissible distance threshold for determining the inliers from 
        * the outliers
        * \param[out] inliers the resultant model inliers
        */
      virtual void 
      selectWithinDistance (const Eigen::VectorXf &model_coefficients, 
                            const double threshold,
                            Indices &inliers) = 0;
 
      /** \brief Count all the points which respect the given model
        * coefficients as inliers. Pure virtual.
        * Implementations of this function must be thread-safe.
        * \param[in] model_coefficients the coefficients of a model that we need to
        * compute distances to
        * \param[in] threshold a maximum admissible distance threshold for
        * determining the inliers from the outliers
        * \return the resultant number of inliers
        */
      virtual std::size_t
      countWithinDistance (const Eigen::VectorXf &model_coefficients,
                           const double threshold) const = 0;
 
      /** \brief Create a new point cloud with inliers projected onto the model. Pure virtual.
        * \param[in] inliers the data inliers that we want to project on the model
        * \param[in] model_coefficients the coefficients of a model
        * \param[out] projected_points the resultant projected points
        * \param[in] copy_data_fields set to true (default) if we want the \a
        * projected_points cloud to be an exact copy of the input dataset minus
        * the point projections on the plane model
        */
      virtual void
      projectPoints (const Indices &inliers,
                     const Eigen::VectorXf &model_coefficients,
                     PointCloud &projected_points,
                     bool copy_data_fields = true) const = 0;
 
      /** \brief Verify whether a subset of indices verifies a given set of
        * model coefficients. Pure virtual.
        *
        * \param[in] indices the data indices that need to be tested against the model
        * \param[in] model_coefficients the set of model coefficients
        * \param[in] threshold a maximum admissible distance threshold for
        * determining the inliers from the outliers
        */
      virtual bool 
      doSamplesVerifyModel (const std::set<index_t> &indices,
                            const Eigen::VectorXf &model_coefficients,
                            const double threshold) const = 0;
 
      /** \brief Provide a pointer to the input dataset
        * \param[in] cloud the const boost shared pointer to a PointCloud message
        */
      inline virtual void
      setInputCloud (const PointCloudConstPtr &cloud)
      {
        input_ = cloud;
        if (!indices_)
          indices_.reset (new Indices ());
        if (indices_->empty ())
        {
          // Prepare a set of indices to be used (entire cloud)
          indices_->resize (cloud->size ());
          for (std::size_t i = 0; i < cloud->size (); ++i) 
            (*indices_)[i] = static_cast<index_t> (i);
        }
        shuffled_indices_ = *indices_;
       }
 
      /** \brief Get a pointer to the input point cloud dataset. */
      inline PointCloudConstPtr 
      getInputCloud () const { return (input_); }
 
      /** \brief Provide a pointer to the vector of indices that represents the input data.
        * \param[in] indices a pointer to the vector of indices that represents the input data.
        */
      inline void 
      setIndices (const IndicesPtr &indices)
      { 
        indices_ = indices; 
        shuffled_indices_ = *indices_;
       }
 
      /** \brief Provide the vector of indices that represents the input data.
        * \param[out] indices the vector of indices that represents the input data.
        */
      inline void 
      setIndices (const Indices &indices)
      { 
        indices_.reset (new Indices (indices));
        shuffled_indices_ = indices;
       }
 
      /** \brief Get a pointer to the vector of indices used. */
      inline IndicesPtr
      getIndices () const { return (indices_); }
 
      /** \brief Return a unique id for each type of model employed. */
      virtual SacModel 
      getModelType () const = 0;
 
      /** \brief Get a string representation of the name of this class. */
      inline const std::string&
      getClassName () const
      {
        return (model_name_);
      }
 
      /** \brief Return the size of a sample from which the model is computed. */
      inline unsigned int
      getSampleSize () const
      {
        return sample_size_;
      }
 
      /** \brief Return the number of coefficients in the model. */
      inline unsigned int
      getModelSize () const
      {
        return model_size_;
      }
 
      /** \brief Set the minimum and maximum allowable radius limits for the
        * model (applicable to models that estimate a radius)
        * \param[in] min_radius the minimum radius model
        * \param[in] max_radius the maximum radius model
        * \todo change this to set limits on the entire model
        */
      inline void
      setRadiusLimits (const double &min_radius, const double &max_radius)
      {
        radius_min_ = min_radius;
        radius_max_ = max_radius;
      }
 
      /** \brief Get the minimum and maximum allowable radius limits for the
        * model as set by the user.
        *
        * \param[out] min_radius the resultant minimum radius model
        * \param[out] max_radius the resultant maximum radius model
        */
      inline void
      getRadiusLimits (double &min_radius, double &max_radius) const
      {
        min_radius = radius_min_;
        max_radius = radius_max_;
      }
 
      /** \brief This can be used to impose any kind of constraint on the model,
        * e.g. that it has a specific direction, size, or anything else.
        * \param[in] function A function that gets model coefficients and returns whether the model is acceptable or not.
        */
      inline void
      setModelConstraints (std::function<bool(const Eigen::VectorXf &)> function)
      {
        if (!function)
        {
          PCL_ERROR ("[pcl::SampleConsensusModel::setModelConstraints] The given function is empty (i.e. does not contain a callable target)!\n");
          return;
        }
        custom_model_constraints_ = std::move (function);
      }
 
      /** \brief Set the maximum distance allowed when drawing random samples
        * \param[in] radius the maximum distance (L2 norm)
        * \param search
        */
      inline void
      setSamplesMaxDist (const double &radius, SearchPtr search)
      {
        samples_radius_ = radius;
        samples_radius_search_ = search;
      }
 
      /** \brief Get maximum distance allowed when drawing random samples
        *
        * \param[out] radius the maximum distance (L2 norm)
        */
      inline void
      getSamplesMaxDist (double &radius) const
      {
        radius = samples_radius_;
      }
 
      friend class ProgressiveSampleConsensus<PointT>;
 
      /** \brief Compute the variance of the errors to the model.
        * \param[in] error_sqr_dists a vector holding the distances
        */
      inline double
      computeVariance (const std::vector<double> &error_sqr_dists) const
      {
        std::vector<double> dists (error_sqr_dists);
        const std::size_t medIdx = dists.size () >> 1;
        std::nth_element (dists.begin (), dists.begin () + medIdx, dists.end ());
        double median_error_sqr = dists[medIdx];
        return (2.1981 * median_error_sqr);
      }
 
      /** \brief Compute the variance of the errors to the model from the internally
        * estimated vector of distances. The model must be computed first (or at least
        * selectWithinDistance must be called).
        */
      inline double
      computeVariance () const
      {
        if (error_sqr_dists_.empty ())
        {
          PCL_ERROR ("[pcl::SampleConsensusModel::computeVariance] The variance of the Sample Consensus model distances cannot be estimated, as the model has not been computed yet. Please compute the model first or at least run selectWithinDistance before continuing. Returning NAN!\n");
          return (std::numeric_limits<double>::quiet_NaN ());
        }
        return (computeVariance (error_sqr_dists_));
      }
 
    protected:
 
      /** \brief Fills a sample array with random samples from the indices_ vector
        * \param[out] sample the set of indices of target_ to analyze
        */
      inline void
      drawIndexSample (Indices &sample)
      {
        std::size_t sample_size = sample.size ();
        std::size_t index_size = shuffled_indices_.size ();
        for (std::size_t i = 0; i < sample_size; ++i)
          // The 1/(RAND_MAX+1.0) trick is when the random numbers are not uniformly distributed and for small modulo
          // elements, that does not matter (and nowadays, random number generators are good)
          //std::swap (shuffled_indices_[i], shuffled_indices_[i + (rand () % (index_size - i))]);
          std::swap (shuffled_indices_[i], shuffled_indices_[i + (rnd () % (index_size - i))]);
        std::copy (shuffled_indices_.cbegin (), shuffled_indices_.cbegin () + sample_size, sample.begin ());
      }
 
      /** \brief Fills a sample array with one random sample from the indices_ vector
        *        and other random samples that are closer than samples_radius_
        * \param[out] sample the set of indices of target_ to analyze
        */
      inline void
      drawIndexSampleRadius (Indices &sample)
      {
        std::size_t sample_size = sample.size ();
        std::size_t index_size = shuffled_indices_.size ();
 
        std::swap (shuffled_indices_[0], shuffled_indices_[0 + (rnd () % (index_size - 0))]);
        //const PointT& pt0 = (*input_)[shuffled_indices_[0]];
 
        Indices indices;
        std::vector<float> sqr_dists;
 
        // If indices have been set when the search object was constructed,
        // radiusSearch() expects an index into the indices vector as its
        // first parameter. This can't be determined efficiently, so we use
        // the point instead of the index.
        // Returned indices are converted automatically.
        samples_radius_search_->radiusSearch (input_->at(shuffled_indices_[0]),
                                              samples_radius_, indices, sqr_dists );
 
        if (indices.size () < sample_size - 1)
        {
          // radius search failed, make an invalid model
          for(std::size_t i = 1; i < sample_size; ++i)
            shuffled_indices_[i] = shuffled_indices_[0];
        }
        else
        {
          for (std::size_t i = 0; i < sample_size-1; ++i)
            std::swap (indices[i], indices[i + (rnd () % (indices.size () - i))]);
          for (std::size_t i = 1; i < sample_size; ++i)
            shuffled_indices_[i] = indices[i-1];
        }
 
        std::copy (shuffled_indices_.cbegin (), shuffled_indices_.cbegin () + sample_size, sample.begin ());
      }
 
      /** \brief Check whether a model is valid given the user constraints.
        *
        * Default implementation verifies that the number of coefficients in the supplied model is as expected for this
        * SAC model type. Specific SAC models should extend this function by checking the user constraints (if any).
        *
        * \param[in] model_coefficients the set of model coefficients
        */
      virtual bool
      isModelValid (const Eigen::VectorXf &model_coefficients) const
      {
        if (model_coefficients.size () != model_size_)
        {
          PCL_ERROR ("[pcl::%s::isModelValid] Invalid number of model coefficients given (is %lu, should be %lu)!\n", getClassName ().c_str (), model_coefficients.size (), model_size_);
          return (false);
        }
        if (!custom_model_constraints_(model_coefficients))
        {
          PCL_DEBUG ("[pcl::%s::isModelValid] The user defined isModelValid function returned false.\n", getClassName ().c_str ());
          return (false);
        }
        return (true);
      }
 
      /** \brief Check if a sample of indices results in a good sample of points
        * indices. Pure virtual.
        * \param[in] samples the resultant index samples
        */
      virtual bool
      isSampleGood (const Indices &samples) const = 0;
 
      /** \brief The model name. */
      std::string model_name_;
 
      /** \brief A boost shared pointer to the point cloud data array. */
      PointCloudConstPtr input_;
 
      /** \brief A pointer to the vector of point indices to use. */
      IndicesPtr indices_;
 
      /** The maximum number of samples to try until we get a good one */
      static const unsigned int max_sample_checks_ = 1000;
 
      /** \brief The minimum and maximum radius limits for the model.
        * Applicable to all models that estimate a radius. 
        */
      double radius_min_, radius_max_;
 
      /** \brief The maximum distance of subsequent samples from the first (radius search) */
      double samples_radius_;
 
      /** \brief The search object for picking subsequent samples using radius search */
      SearchPtr samples_radius_search_;
 
      /** Data containing a shuffled version of the indices. This is used and modified when drawing samples. */
      Indices shuffled_indices_;
 
      /** \brief Boost-based random number generator algorithm. */
      boost::mt19937 rng_alg_;
 
      /** \brief Boost-based random number generator distribution. */
      std::shared_ptr<boost::uniform_int<> > rng_dist_;
 
      /** \brief Boost-based random number generator. */
      std::shared_ptr<boost::variate_generator< boost::mt19937&, boost::uniform_int<> > > rng_gen_;
 
      /** \brief A vector holding the distances to the computed model. Used internally. */
      std::vector<double> error_sqr_dists_;
 
      /** \brief The size of a sample from which the model is computed. Every subclass should initialize this appropriately. */
      unsigned int sample_size_;
 
      /** \brief The number of coefficients in the model. Every subclass should initialize this appropriately. */
      unsigned int model_size_;
 
      /** \brief Boost-based random number generator. */
      inline int
      rnd ()
      {
        return ((*rng_gen_) ());
      }
 
      /** \brief A user defined function that takes model coefficients and returns whether the model is acceptable or not. */
      std::function<bool(const Eigen::VectorXf &)> custom_model_constraints_;
    public:
      PCL_MAKE_ALIGNED_OPERATOR_NEW
 };
 
  /** \brief @b SampleConsensusModelFromNormals represents the base model class
    * for models that require the use of surface normals for estimation.
    * \ingroup sample_consensus
    */
  template <typename PointT, typename PointNT>
  class SampleConsensusModelFromNormals //: public SampleConsensusModel<PointT>
  {
    public:
      using PointCloudNConstPtr = typename pcl::PointCloud<PointNT>::ConstPtr;
      using PointCloudNPtr = typename pcl::PointCloud<PointNT>::Ptr;
 
      using Ptr = shared_ptr<SampleConsensusModelFromNormals<PointT, PointNT> >;
      using ConstPtr = shared_ptr<const SampleConsensusModelFromNormals<PointT, PointNT> >;
 
      /** \brief Empty constructor for base SampleConsensusModelFromNormals. */
      SampleConsensusModelFromNormals () :  normals_ () {};
 
      /** \brief Destructor. */
      virtual ~SampleConsensusModelFromNormals () = default;
 
      /** \brief Set the normal angular distance weight.
        * \param[in] w the relative weight (between 0 and 1) to give to the angular
        * distance (0 to pi/2) between point normals and the plane normal.
        * (The Euclidean distance will have weight 1-w.)
        */
      inline void 
      setNormalDistanceWeight (const double w) 
      { 
        if (w < 0.0 || w > 1.0)
        {
          PCL_ERROR ("[pcl::SampleConsensusModel::setNormalDistanceWeight] w is %g, but should be in [0; 1]. Weight will not be set.", w);
          return;
        }
        normal_distance_weight_ = w; 
      }
 
      /** \brief Get the normal angular distance weight. */
      inline double 
      getNormalDistanceWeight () const { return (normal_distance_weight_); }
 
      /** \brief Provide a pointer to the input dataset that contains the point
        * normals of the XYZ dataset.
        *
        * \param[in] normals the const boost shared pointer to a PointCloud message
        */
      inline void 
      setInputNormals (const PointCloudNConstPtr &normals) 
      { 
        normals_ = normals; 
      }
 
      /** \brief Get a pointer to the normals of the input XYZ point cloud dataset. */
      inline PointCloudNConstPtr 
      getInputNormals () const { return (normals_); }
 
    protected:
      /** \brief The relative weight (between 0 and 1) to give to the angular
        * distance (0 to pi/2) between point normals and the plane normal. 
        */
      double normal_distance_weight_{0.0};
 
      /** \brief A pointer to the input dataset that contains the point normals
        * of the XYZ dataset. 
        */
      PointCloudNConstPtr normals_;
  };
 
  /** Base functor all the models that need non linear optimization must
    * define their own one and implement operator() (const Eigen::VectorXd& x, Eigen::VectorXd& fvec)
    * or operator() (const Eigen::VectorXf& x, Eigen::VectorXf& fvec) depending on the chosen _Scalar
    */
  template<typename _Scalar, int NX=Eigen::Dynamic, int NY=Eigen::Dynamic>
  struct Functor
  {
    using Scalar = _Scalar;
    enum 
    {
      InputsAtCompileTime = NX,
      ValuesAtCompileTime = NY
    };
 
    using ValueType = Eigen::Matrix<Scalar,ValuesAtCompileTime,1>;
    using InputType = Eigen::Matrix<Scalar,InputsAtCompileTime,1>;
    using JacobianType = Eigen::Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime>;
 
    /** \brief Empty Constructor. */
    Functor () : m_data_points_ (ValuesAtCompileTime) {}
 
    /** \brief Constructor
      * \param[in] m_data_points number of data points to evaluate.
      */
    Functor (int m_data_points) : m_data_points_ (m_data_points) {}
  
    virtual ~Functor () = default;
 
    /** \brief Get the number of values. */ 
    int
    values () const { return (m_data_points_); }
 
    private:
      const int m_data_points_;
  };
}