source: src/FunctionApproximation/FunctionApproximation.hpp@ b8f2ea

/*
 * FunctionApproximation.hpp
 *
 *  Created on: 02.10.2012
 *      Author: heber
 */

#ifndef FUNCTIONAPPROXIMATION_HPP_
#define FUNCTIONAPPROXIMATION_HPP_

// include config.h
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <vector>

#include "FunctionApproximation/FunctionModel.hpp"

class TrainingData;

/** This class encapsulates the solution to approximating a high-dimensional
 * function represented by two vectors of tuples, being input variables and
 * output of the function via a model function, manipulated by a set of
 * parameters.
 *
 * \note For this reason the input and output dimension has to be given in
 * the constructor since these are fixed parameters to the problem as a
 * whole and usually: a different input dimension means we have a completely
 * different problem (and hence we may as well construct and new instance of
 * this class).
 *
 * The "training data", i.e. the two sets of input and output values, is
 * given extra.
 *
 * The problem is then that a given high-dimensional function is supplied,
 * the "model", and we have to fit this function via its set of variable
 * parameters. This fitting procedure is executed via a Levenberg-Marquardt
 * algorithm as implemented in the
 * <a href="http://www.ics.forth.gr/~lourakis/levmar/index.html">LevMar</a>
 * package.
 *
 * \section FunctionApproximation-details Details on the inner workings.
 *
 *  FunctionApproximation::operator() is the main function that performs the
 *  non-linear regression. It consists of the following steps:
 *  -# hand given (initial) parameters over to model.
 *  -# convert output vector to format suitable to levmar
 *  -# allocate memory for levmar to work in
 *  -# depending on whether the model is constrained or not and whether we
 *   have a derivative, we make use of various levmar functions with prepared
 *   parameters.
 *  -# memory is free'd and some final infos is given.
 *
 *  levmar needs to evaluate the model. To this end, FunctionApproximation has
 *  two functions whose signatures is such as to match with the one required
 *  by the levmar package. Hence,
 *  -# FunctionApproximation::LevMarCallback()
 *  -# FunctionApproximation::LevMarDerivativeCallback()
 *  are used as callbacks by levmar only.
 *  These hand over the current set of parameters to the model, then both bind
 *  FunctionApproximation::evaluate() and
 *  FunctionApproximation::evaluateDerivative(), respectively, and execute
 *  FunctionModel::operator() or FunctionModel::parameter_derivative(),
 *  respectively.
 *
 */
class FunctionApproximation
{
public:
  //!> typedef for a vector of input arguments
  typedef std::vector<FunctionModel::arguments_t> inputs_t;
  //!> typedef for a vector of input arguments
  typedef std::vector<FunctionModel::list_of_arguments_t> filtered_inputs_t;
  //!> typedef for a vector of output values
  typedef std::vector<FunctionModel::results_t> outputs_t;
public:
  /** Constructor of the class FunctionApproximation.
   *
   * \param _data container with tuple of (input, output) values
   * \param _model FunctionModel to use in approximation
   * \param _precision desired precision of fit
   */
  FunctionApproximation(
      const TrainingData &_data,
      FunctionModel &_model,
      const double _precision);

  /** Constructor of the class FunctionApproximation.
   *
   * \param _input_dimension input dimension for this function approximation
   * \param _output_dimension output dimension for this function approximation
   * \param _model FunctionModel to use in approximation
   */
  FunctionApproximation(
      const size_t &_input_dimension,
      const size_t &_output_dimension,
      FunctionModel &_model,
      const double _precision) :
    input_dimension(_input_dimension),
    output_dimension(_output_dimension),
    model(_model),
    precision(_precision)
  {}
  /** Destructor for class FunctionApproximation.
   *
   */
  ~FunctionApproximation()
  {}

  /** Setter for the training data to be used.
   *
   * \param input vector of input tuples, needs to be of
   *        FunctionApproximation::input_dimension size
   * \param output vector of output tuples, needs to be of
   *        FunctionApproximation::output_dimension size
   */
  void setTrainingData(const filtered_inputs_t &input, const outputs_t &output);

  /** Setter for the model function to be used in the approximation.
   *
   */
  void setModelFunction(FunctionModel &_model);

  /** This enum steers whether we use finite differences or
   * FunctionModel::parameter_derivative to calculate the jacobian.
   *
   */
  enum JacobianMode {
    FiniteDifferences,
    ParameterDerivative,
    MAXMODE
  };

  /** This starts the fitting process, resulting in the parameters to
   * the model function being optimized with respect to the given training
   * data.
   *
   * \param mode whether to use finite differences or the parameter derivative
   *        in calculating the jacobian
   */
  void operator()(const enum JacobianMode mode = FiniteDifferences);

  /** Evaluates the model function for each pair of training tuple and returns
   * the output of the function as a vector.
   *
   * This function as a signature compatible to the one required by the
   * LevMar package (with double precision).
   *
   * \param *p array of parameters for the model function of dimension \a m
   * \param *x array of result values of dimension \a n
   * \param m parameter dimension
   * \param n output dimension
   * \param *data additional data, unused here
   */
  void evaluate(double *p, double *x, int m, int n, void *data);

  /** Evaluates the parameter derivative of the model function for each pair of
   * training tuple and returns the output of the function as vector.
   *
   * This function as a signature compatible to the one required by the
   * LevMar package (with double precision).
   *
   * \param *p array of parameters for the model function of dimension \a m
   * \param *jac on output jacobian matrix of result values of dimension \a n times \a m
   * \param m parameter dimension
   * \param n output dimension times parameter dimension
   * \param *data additional data, unused here
   */
  void evaluateDerivative(double *p, double *jac, int m, int n, void *data);

  /** This functions checks whether the parameter derivative of the FunctionModel
   * has been correctly implemented by validating against finite differences.
   *
   * We use LevMar's dlevmar_chkjac() function.
   *
   * \return true - gradients are ok (>0.5), false - else
   */
  bool checkParameterDerivatives();

private:
  static void LevMarCallback(double *p, double *x, int m, int n, void *data);

  static void LevMarDerivativeCallback(double *p, double *x, int m, int n, void *data);

  void prepareModel(double *p, int m);

  void prepareParameters(double *&p, int &m) const;

  void prepareOutput(double *&x, int &n) const;

private:
  //!> input dimension (is fixed from construction)
  const size_t input_dimension;
  //!> output dimension (is fixed from construction)
  const size_t output_dimension;
  //!> desired precision given to LevMar
  const double precision;

  //!> current input set of training data
  filtered_inputs_t input_data;
  //!> current output set of training data
  outputs_t output_data;

  //!> the model function to be used in the high-dimensional approximation
  FunctionModel &model;
};

#endif /* FUNCTIONAPPROXIMATION_HPP_ */