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density_estimation.h
#ifndef PROGETTO_DENSITY_ESTIMATION_HPP
#define PROGETTO_DENSITY_ESTIMATION_HPP

#include <Eigen/Dense>
#include <Eigen/Sparse>
#include <iostream>
#include <iterator>
#include <vector>
#include "bspline.h"
#include "sandia_rules.h"
#include "gauss_points_weights.h"

constexpr double tol = 1e-04;

// NOTE: in densityEstimator::solve() there is the following note:
//        NOTE: QR should do this automatically without giving any warning (CHECK)
/*! \file
  @brief Parmeters container class and methods to compute the solution of the problem
*/

/*!
@brief	Parameter class manager
@note These parameters are related to the problem itself, not to each single row.
*/
class parametersManager
{
protected:
  /*! Spline degree */
  unsigned int k;
  /*! order of derivative in penalization term */
  unsigned int l;
  /*! penalization parameter */
  double alpha;
  /*! Number of control points */
  unsigned int n;
  /*! Number of knots - 2 (number of internal ones) */
  unsigned int g;
  /*! Number of knots including additional ones G = g+k+1 */
  unsigned int G;
  /*! spline knots */
  std::vector<double> knots;
  /*! [u,v] support of splines */
  double u, v;
  /*! control points */
  std::vector<double> xcp;

public:
  parametersManager
  (const unsigned int kk, const unsigned int ll, const double opt_param):
    k(kk), l(ll), alpha(opt_param), n(0), g(0), G(0), u(0), v(0) {};

  /*!
	@brief Read knots from C-array style and store them in the std::vector<double> member
  */
  void
  readKnots
  (const double * inputKnots, const unsigned int & size);

  /*!
	@brief Read control points from C-array style and store them in the std::vector<double> member
  @param cancel If cancel = j, it does not consider j-th column.
        Useful for cross-validation. Disabled by default.
  */
  void
  readXcp
  (const double * inputXcp, const unsigned int & size, const int & cancel = -1);


  void
  set_alpha
  (const double & opt_param)
  {
    alpha = opt_param;
  }

  unsigned int
  get_G() const { return G; };

  double
  get_u() const { return u; };

  double
  get_v() const { return v;};

  unsigned int
  get_k() const{ return k;};

  unsigned int
  get_n() const{ return n;};
};

/*!
@brief	Parameter class manager
@note These are the whole set of parameters
*/
class densityEstimator: public parametersManager
{
private:
  /*! Collocation matrix - dimensions nxG */
  Eigen::MatrixXd C;
  /*! dimensions GxG */
  Eigen::MatrixXd M;


  Eigen::SparseMatrix<double> S;
  /*! dimensions GxG */
  Eigen::SparseMatrix<double> DK;
  /*! matrix of the problem to solve - dimensions GxG */
  Eigen::MatrixXd P;

  /*! constant term vector of the problem to solve - dimensions G */
  Eigen::VectorXd p;
  /*! solution of the problem: c = P^(-)p - dimensions G */
  Eigen::VectorXd c;
  /*! B-spline coefficients - dimensions G */
  Eigen::VectorXd b;

  /*! Weights associated to data.
                            More in general they allow to take in account the various data accuracy */
  Eigen::VectorXd weights;
  /*! extended vector of knots - with extra ones
                                 dimension: g + 2k + 2 = G + k + 1 */
  std::vector<double> lambda;
  /*! extended vector of knots of the l-th derivative */
  std::vector<double> lambda_der;

  void
  fill_C
  (const std::vector<double>& cp);

  void
  fill_M
  ();

  void
  fill_DK
  ();

  /*!  Compute the S_l matrix for the penalization term */
  void
  fill_S
  ();

  void
  set_lambda
  (const std::vector<double>& knots);

  void
  set_lambda_der
  (const std::vector<double> & knots);

public:

  densityEstimator
  (const parametersManager & input): parametersManager(input)
  {};

  /*!
  	@brief Compute the matrices of the problem
  */
  void
  set_matrix
  ();

  void
  set_weights
      (const Eigen::Block<Eigen::Map<Eigen::Matrix<double, -1, -1>,0, Eigen::Stride<0, 0> >, 1, -1, false> & row);

  /*!
  	@brief Compute the value of the functional to be minimized.
  	@param ycp Value of data in the control points.
  */
  double
  eval_J
  (const std::vector<double>& ycp);

  /*!
  	@brief Compute the solution of the linear system.
  	@param bspline Vector of Bspline coefficients computed from the solution of the system.
  	@param ycp Value of data in the control points.
  */
  void
  solve
  (Eigen::Block<Eigen::Matrix<double, -1, -1>, 1, -1, false> bspline, const std::vector<double>& ycp);

  void
  print_all
  () const;

  void
  print_sol
  () const;

  std::vector<double>
  get_lambda() const { return lambda; };

};

#endif //PROGETTO_DENSITY_ESTIMATION_HPP
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