JSimplex.hh

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#ifndef __JFIT__JSIMPLEX__
#define __JFIT__JSIMPLEX__

#include <cmath>
#include <vector>
#include <ostream>
#include <iomanip>

#include "Jeep/JPrint.hh"
#include "Jeep/JMessage.hh"


/**
 * \author mdejong
 */

namespace JFIT {}
namespace JPP { using namespace JFIT; }

namespace JFIT {

  using JEEP::JMessage;


  /**
   * Simple fit method based on Powell's algorithm, see reference:
   * Numerical Recipes in C++, W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery,
   * Cambridge University Press.
   *
   * The template argument refers to the model that should be fitted to the data.
   * This data structure should have arithmetic capabalities.
   *
   * The data member JSimplex::value corresponds to the start, current or final value
   * of the model of the fit procedure.
   * The data member JSimplex::step corresponds to the step directions.
   * Note that the step directions may change during the fit.
   * The template fit function should return the data type JGandalf::result_type
   * which is composed of the values of the chi2 and gradient of a hit.
   * The function operator returns the chi2 of the fit.
   */
  template<class JModel_t>
  class JSimplex :
    public JMessage< JSimplex<JModel_t> >
  {
  public:

    using JMessage< JSimplex<JModel_t> >::debug;


    /**
     * Default constructor.
     */
    JSimplex()
    {}


    /**
     * Multi-dimensional fit.
     *
     * The given fit function should return the equivalent of chi2 for 
     * the current value of the given model and a given data point.
     *
     * \param  fit            fit function
     * \param  __begin        begin of data
     * \param  __end          end   of data
     * \return                chi2
     */
    template<class JFunction_t, class T>
    double operator()(const JFunction_t& fit, T __begin, T __end)
    {
      using namespace std;
      using namespace JPP;

      double chi2_old = evaluate(fit, __begin, __end);

      const int N = step.size();

      if (N != 0) {

        double chi2[N];

        numberOfIterations = 0;

        while (numberOfIterations != MAXIMUM_ITERATIONS) {

          DEBUG("old: " << FIXED(12,5) << chi2_old << endl);

          const JModel_t p0(value);

          for (int i = 0; i != N; ++i) {

            DEBUG("step: " << i << ' ' << setw(5) << numberOfIterations << endl);

            chi2[i] = (*this)(fit, __begin, __end, step[i]);
          }

          // overall step direction of last iteration

          JModel_t wall = value - p0;

          const double chi2_new = (*this)(fit, __begin, __end, wall);

          DEBUG("new: " << FIXED(12,5) << chi2_new << endl);


          if (fabs(chi2_old - chi2_new) < EPSILON*fabs(chi2_old)) {
            return chi2_new;
          }

          // double overall step

          wall   = value - p0;

          value += wall;

          const double fe = evaluate(fit, __begin, __end);

          value -= wall;


          for (int i = N-1; i != 0; --i) {
            chi2[i] = chi2[i-1] - chi2[i];
          }

          chi2[0] = chi2_old - chi2[0];


          double df = 0.0;

          for (int i = 0; i != N; ++i) {
            if (chi2[i] > df) {
              df = chi2[i];
            }
          }

          const double fn = chi2_new;
          const double f0 = chi2_old;
          const double ff = f0 - fn - df;

          // shift step directions

          if (fe < f0 && 2.0*(f0 - 2.0*fn + fe)*ff*ff < (f0-fe)*(f0-fe)*df) {

            for (int i = 0; i != N - 1; ++i) {
              step[i] = step[i+1];
            }

            step[N-1] = wall;
          }

          chi2_old = chi2_new;
        }
      }

      return chi2_old;
    }


    /**
     * 1D fit.
     *
     * The given fit function should return the equivalent of chi2 for 
     * the current value of the given model and a given data point.
     *
     * \param  fit            fit function
     * \param  __begin        begin of data
     * \param  __end          end   of data
     * \param  step           step direction
     */
    template<class JFunction_t, class T>
    double operator()(const JFunction_t& fit, T __begin, T __end, const JModel_t& step)
    {
      using namespace std;
      using namespace JPP;

      double lambda = 0.5;                                     // control parameter
      double factor = 1.0;                                     // multiplication factor

      double chi2_old = evaluate(fit, __begin, __end);

      for (int i = 0; numberOfIterations != MAXIMUM_ITERATIONS; ++numberOfIterations, ++i) {

        value += lambda * step;

        const double chi2_new = evaluate(fit, __begin, __end);

        DEBUG("step: " << setw(3) << i << ' ' << FIXED(12,5) << chi2_old << ' ' << FIXED(12,5) << chi2_new << ' ' << FIXED(5,2) << lambda << endl);

        if (fabs(chi2_old - chi2_new) < EPSILON*fabs(chi2_old)) {

          if (chi2_new > chi2_old) {

            value -= lambda * step;                            // undo last step

            return chi2_old;

          } else {

            return chi2_new;
          }
        }

        if (chi2_new < chi2_old) {

          chi2_old = chi2_new;

        } else {
            
          value  -=  lambda * step;                            // step back
          lambda  = -lambda;                                   // change direction
          
          if (i != 0) {
            factor = 0.5;                                      // reduce step size
          }
        }
        
        lambda = factor * lambda;
      }

      return chi2_old;
    }


    static int     MAXIMUM_ITERATIONS;                         //!< maximal number of iterations
    static double  EPSILON;                                    //!< maximal distance to minimum
 
    JModel_t              value;
    std::vector<JModel_t> step;
    int                   numberOfIterations;

  private:
    /**
     * Evaluate chi2 for given data set.
     *
     * \param  fit            fit function
     * \param  __begin        begin of data
     * \param  __end          end   of data
     */
    template<class JFunction_t, class T>
    inline double evaluate(const JFunction_t& fit, T __begin, T __end) const
    {
      double chi2 = 0.0;

      for (T hit = __begin; hit != __end; ++hit) {
        chi2 += fit(value, *hit);
      }

      return chi2;
    }
  };


  /**
   * maximal number of iterations.
   */
  template<class JModel_t>
  int JSimplex<JModel_t>::MAXIMUM_ITERATIONS = 1000;


  /**
   * maximal distance to minimum.
   */
  template<class JModel_t>
  double JSimplex<JModel_t>::EPSILON = 1.0e-4;
}

#endif