JetFitAnalyzer/src/jetfit.cpp~

/* jetfit.cpp - Package to fit multi-Gaussian distributions to histograms
 * rewrite after accidental deletion 07-24-09
 * Author: David Nisson
 */

#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cstdio>
#include <cstring>
#include <cctype>
#include <iostream>
#include <fstream>
#include <sstream>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <limits>
#include <exception>

#include <TMinuit.h>
#include <TH1.h>
#include <TH2.h>
#include <TF2.h>
#include <TRandom3.h>
#include <Rtypes.h>
#include <TFormula.h>
#include <TSystem.h>

#include "UserCode/JetFitAnalyzer/interface/jetfit.h"

#define PI 3.141592653

#define MAX_GAUSS 3

using namespace std;

namespace jetfit {
  // configurable options
  bool ignorezero = false; // ignore zero bins when fitting
  
  int ngauss; // number of Gaussians in current model
  
  struct histo {
    vector< vector<double> > bins;
    double Xlo, Xhi, Ylo, Yhi;
  } energy;


  model_def *mdef;

  model_def& curr_model_def() {
    return *mdef;
  }

  void set_model_def(model_def *_mdef) {
    mdef = _mdef;
  }

  int get_ngauss() {
    return ngauss;
  }
  
  void set_ngauss(int _ngauss) {
    ngauss = _ngauss;
  }

  // fit function
  double fit_fcn(double x, double y, double *xval) {
    int npar_indiv = mdef->get_formula()->GetNpar();
    double val = 0.0;
    for (int i = 0; i < ngauss; i++) {
      mdef->get_formula()->SetParameters(xval + i*npar_indiv);
      val += mdef->get_formula()->Eval(x, y);
    }
    return val;
  }

  // TF2-compatible fit function
  double fit_fcn_TF2(double *x, double *pval) {
    double val = fit_fcn(x[0], x[1], pval);
    return val;
  }

  // Integral of model formula / chisquare sigma
  double formula_int(double xlo, double xhi, double ylo, double yhi,
                     double *pval, double XbinSize, double YbinSize,
                     double *xval) {
    double xstep = (xhi - xlo) / static_cast<double>(20);
    double ystep = (yhi - ylo) / static_cast<double>(20);

    double fsum = 0.0;
    double pval_old[256];
    int npar = mdef->get_formula()->GetNpar();
    if (npar > 256) {
      cerr << "Parameter overload" << endl;
      return 0.0;
    }
    mdef->get_formula()->GetParameters(pval_old);
    mdef->get_formula()->SetParameters(pval);

    for (int i = 0; i < 20; i++) {
      for (int j = 0; j < 20; j++) {
        double x = (static_cast<double>(i) + 0.5)*xstep + xlo;
        double y = (static_cast<double>(j) + 0.5)*ystep + ylo;
        double sig_cut = 1.0e-5;
        double nu = XbinSize * YbinSize * fit_fcn(x, y, xval);
        double sigma = mdef->chisquare_error(nu) < sig_cut
          ? sig_cut : mdef->chisquare_error(nu);

        fsum += xstep * ystep * mdef->get_formula()->Eval(x, y)
          / sigma / sigma;
      }
    }

    mdef->get_formula()->SetParameters(pval_old);
    return fsum;
  }

  // MINUIT objective function 
  void fcn(int &npar, double *grad, double &fcnval, double *xval, int iflag)
  {
    double chisquare = 0.0;
    double XbinSize = (energy.Xhi - energy.Xlo)
      / static_cast<double>(energy.bins.size());
    double YbinSize = (energy.Yhi - energy.Ylo)
      / static_cast<double>(energy.bins.at(0).size());
    try {
      // add errors in data points in histogram
      for (int i = 0; i < energy.bins.size(); i++) {
        for (int j = 0; j < energy.bins.at(i).size(); j++) {
          double x = (static_cast<double>(i) + 0.5) * (energy.Xhi - energy.Xlo) 
            / static_cast<double>(energy.bins.size()) + energy.Xlo;
          double y = (static_cast<double>(j) + 0.5) * (energy.Yhi - energy.Ylo)
            / static_cast<double>(energy.bins.at(i).size()) + energy.Ylo;
          double nu = fit_fcn(x, y, xval) * XbinSize * YbinSize;
          double sig_cut = 1.0e-5;
          if (mdef->chisquare_error(nu) > sig_cut || !ignorezero)
            chisquare += pow(energy.bins.at(i).at(j) - nu, 2.0) 
              / pow(mdef->chisquare_error(nu), 2.0);
          else
            chisquare += pow(energy.bins.at(i).at(j) - nu, 2.0) 
              / pow(sig_cut, 2.0);
        }
      }

      // add errors due to Gaussians outside histogram
      double eps = 0.1; // accuracy set for this function
      for (int i = 0; i < ngauss; i++) {
        double *pval = xval+i*mdef->get_formula()->GetNpar();
        double par_x = pval[mdef->get_indiv_max_x()];
        double par_y = pval[mdef->get_indiv_max_y()];
        double par_sig = pval[3];
        double cutoff_rad = -log(eps * 2.0 * PI * par_sig * par_sig
          / pval[0]);

        bool left = par_x < energy.Xlo + cutoff_rad;
        bool right = par_x > energy.Xhi - cutoff_rad;
        bool top = par_y > energy.Yhi - cutoff_rad;
        bool bottom = par_y > energy.Ylo + cutoff_rad;

        if (left) {
          double xlo = par_x - cutoff_rad;
          double xhi = energy.Xlo;
          double ylo = energy.Ylo;
          double yhi = energy.Yhi;
          chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
                                   XbinSize, YbinSize, xval);
        }
        if (right) {
          double xlo = energy.Xhi;
          double xhi = par_x + cutoff_rad;
          double ylo = energy.Ylo;
          double yhi = energy.Yhi;
          chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
                                   XbinSize, YbinSize, xval);
        }
        if (top) {
          double xlo = left ? par_x - cutoff_rad : energy.Xlo;
          double xhi = right ? par_x + cutoff_rad : energy.Xhi;
          double ylo = energy.Yhi;
          double yhi = par_y + cutoff_rad;
          chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
                                   XbinSize, YbinSize, xval);
        }
        if (bottom) {
          double xlo = left ? par_x - cutoff_rad : energy.Xlo;
          double xhi = right ? par_x + cutoff_rad : energy.Xhi;
          double ylo = par_y - cutoff_rad;
          double yhi = energy.Ylo;
          chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
                                   XbinSize, YbinSize, xval);
        }
      }

      fcnval = chisquare;
    }
    catch (exception ex) {
      cerr << "Exception in jetfit::fcn" << endl;
    }
  }

  bool get_ignorezero() {
    return ignorezero;
  }

  void set_ignorezero(bool _iz) {
    ignorezero = _iz;
  }

  TFormula * model_def::get_formula() {
    return indiv_formula;
  }

  void model_def::set_formula(TFormula *new_formula) {
    indiv_formula = new_formula;
  }

  void model_def::get_indiv_par(int i, string &name, double &start, double &step,
                     double &lo, double &hi) {
    try {
      name = indiv_par_names.at(i);
      start = indiv_par_starts.at(i);
      step = indiv_par_start_steps.at(i);
      lo = indiv_par_lo.at(i);
      hi = indiv_par_hi.at(i);
    } catch (exception ex) {
      cerr << "exception in jetfit::model_def::get_indiv_par" << endl;
    }
  }

  void model_def::set_indiv_par(int i, string name, double start, double step,
                     double lo, double hi) {
    if (indiv_par_names.size() < i+1) {
      indiv_par_names.resize(i+1);
      indiv_par_starts.resize(i+1);
      indiv_par_start_steps.resize(i+1);
      indiv_par_lo.resize(i+1);
      indiv_par_hi.resize(i+1);
    }
    try {
      indiv_par_names.at(i) = name;
      indiv_par_starts.at(i) = start;
      indiv_par_start_steps.at(i) = step;
      indiv_par_lo.at(i) = lo;
      indiv_par_hi.at(i) = hi;
    }
    catch (exception ex) {
      cerr << "exception in jetfit::model_def::set_indiv_par" << endl;
    }
  }

  int model_def::get_indiv_max_E() {
    return indiv_max_E;
  }

  void model_def::set_indiv_max_E(int _new_max_E) {
    indiv_max_E = _new_max_E;
  }

  int model_def::get_indiv_max_x() {
    return indiv_max_x;
  }

  void model_def::set_indiv_max_x(int new_max_x) {
    indiv_max_x = new_max_x;
  }

  int model_def::get_indiv_max_y() {
    return indiv_max_y;
  }

  void model_def::set_indiv_max_y(int new_max_y) {
    indiv_max_y = new_max_y;
  }

  unsigned model_def::get_n_special_par_sets() {
    return special_par_starts.size();
  }

  void model_def::get_special_par(int g, int i, double &pstart,
                                  double &perr, double &plo, double &phi) {
    try {
      pstart = special_par_starts.at(g).at(i);
      perr = special_par_start_steps.at(g).at(i);
      plo = special_par_lo.at(g).at(i);
      phi = special_par_hi.at(g).at(i);
    } catch (exception ex) {
      cerr << "Exception in model_def::get_special_par" << endl;
    }
  }

  void model_def::set_special_par(int g, int i, double pstart,
                                  double perr, double plo, double phi) {
    if (g+1 > special_par_starts.size()) {
      special_par_starts.resize(g+1);
      special_par_start_steps.resize(g+1);
      special_par_lo.resize(g+1);
      special_par_hi.resize(g+1);
    }

    try {
      if (i+1 > special_par_starts.at(g).size()) {
        special_par_starts.at(g).resize(i+1);
        special_par_start_steps.at(g).resize(i+1);
        special_par_lo.at(g).resize(i+1);
        special_par_hi.at(g).resize(i+1);
      }

      special_par_starts.at(g).at(i) = pstart;
      special_par_start_steps.at(g).at(i) = perr;
      special_par_lo.at(g).at(i) = plo;
      special_par_hi.at(g).at(i) = phi;
    }
    catch (exception ex) {
      cerr << "exception in jetfit::model_def::set_special_par" << endl;
    }
  }

  // translation of CERN's ERFC function
  double erfc(double x) {
    bool lef = false;
    double p2[5], q2[5];

    const double z1 = 1.0, hf = z1/2.0, c1 = 0.56418958;
    const double vmax = 7.0;
    const double switch_ = 4.0;

    double p10 = 3.6767877, q10 = 3.2584593, p11 = -9.7970465e-2;
    p2[0] = 7.3738883;
    q2[0] = 7.3739609;
    p2[1] = 6.8650185;
    q2[1] = 1.5184908e1;
    p2[2] = 3.0317993;
    q2[2] = 1.2795530e1;
    p2[3] = 5.6316962e-1;
    q2[3] = 5.3542168;
    p2[4] = 4.3187787e-5;
    q2[4] = 1.0;

    double p30 = -1.2436854e-1, q30 = 4.4091706e-1, p31 = -9.6821036e-2;

    double v = fabs(x);
    double y, h, hc, ap, aq;
    if (v < hf) {
      y = v*v;
      h = x*(p10 + p11*y)/(q10 + y);
      hc = 1.0 - h;
    }
    else {
      if (v < switch_) {
        ap = p2[4];
        aq = q2[4];
        for (int i = 3; i >= 0; i--) {
          ap = p2[i] + v*ap;
          aq = q2[i] + v*aq;
        }
        hc = exp(-v*v)*ap/aq;
        h = 1.0 - hc;
      }
      else if (v < vmax) {
        y = 1/v/v;
        hc = exp(-v*v)*(c1 + y*(p30 + p31*y)/(q30 + y))/v;
        h = 1.0 - hc;
      }
      // for very big values we can save us any calculation
      // and the FP-exceptions from exp
      else {
        h = 1.0;
        hc = 0.0;
      }
      if (x < 0) {
        h = -h;
        hc = 2.0 - hc;
      }
    }
    if (lef) {
      return h;
    }
    else {
      return hc;
    }
  }

  // translation of CERN's PROB function
  double prob(double x, int n) {
    const char *name = "PROB";
    char errtxt[80];

    const double r1 = 1.0,
      hf = r1/2.0, th = r1/3.0, f1 = 2.0*r1/9.0;
    const double c1 = 1.128379167095513;
    const int nmax = 300;
    // maximum chi2 per df for df >= 2., if chi2/df > chipdf prob=0
    const double chipdf = 100.0;
    const double xmax = 174.673, xmax2 = 2.0*xmax;
    const double xlim = 24.0;
    const double eps = 1e-30;

    double y = x;
    double u = hf*y;
    double h, w, s, t, fi, e;
    int m;
    if (n < 0) {
      h = 0.0;
      sprintf(errtxt, "n = %d < 1", n);
      cerr << "PROB: G100.1: "<<errtxt;
    }
    else if (y < 0.0) {
      h = 0.0;
      sprintf(errtxt, "x = %f < 0", n);
      cerr << "PROB: G100.2: "<<errtxt;
    }
    else if (y == 0.0 || n/20 > y) {
      h = 1.0;
    }
    else if (n == 1) {
      w = sqrt(u);
      if (w < xlim) {
        h = erfc(w);
      }
      else {
        h = 0.0;
      }
    }
    else if (n > nmax) {
      s = r1 / ((double)n);
      t = f1 * s;
      w = (pow(y*s, th) - (1.0 - t)) / sqrt(2.0*t);
      if (w < -xlim) {
        h = 1.0;
      }
      else if (w < xlim) {
        h = hf * erfc(w);
      }
      else {
        h = 0.0;
      }
    }
    else {
      m = n/2;
      if (u < xmax2 && (y/n) <= chipdf) {
        s = exp(-hf*u);
        t = s;
        e = s;
        if (2*m == n) {
          fi = 0.0;
          for (int i = 1; i < m; i++) {
            fi += 1.0;
            t = u*t/fi;
            s += t;
          }
          h = s*e;
        }
        else {
          fi = 1.0;
          for (int i = 1; i < m; i++) {
            fi += 2.0;
            t = t*y/fi;
            s += t;
          }
          w = sqrt(u);
          if (w < xlim) {
            h = c1*w*s*e + erfc(w);
          }
          else {
            h = 0.0;
          }
        }
      }
      else {
        h = 0.0;
      }
    }
    if (h > eps) {
      return h;
    }
    else {
      return 0.0;
    }
  }
 
  void par_init(TH2 *hist, TMinuit *gMinuit, vector<TString> &pars,
                double *pval, double *perr, double *plo, double *phi,
                int npar, results r) {
    int npar1 = npar - mdef->get_formula()->GetNpar();
    bool init_spec_pars = false;
    if (ngauss <= mdef->get_n_special_par_sets()) {
      init_spec_pars = true;
      for (int k = 0; k < ngauss; k++) {
        int ipar0 = k*mdef->get_formula()->GetNpar(); // index of par 0
        for (int l = 0; l < mdef->get_formula()->GetNpar(); l++) {
          int ipar = ipar0 + l;
          if (ipar < npar)
            mdef->get_special_par(k, l, pval[ipar], perr[ipar], plo[ipar],
                                 phi[ipar]);
          else
            cerr << "WARNING: Attempt to set parameter out of index range!"
                 << endl;
        }
      }
    }
    else {
      double XbinSize = (energy.Xhi - energy.Xlo)
        / static_cast<double>(energy.bins.size());
      double YbinSize = (energy.Xhi - energy.Xlo)
        / static_cast<double>(energy.bins.at(0).size());
      vector< vector<double> > sub_energy(energy.bins.size());
      double max_sub, max_x = 0.0, max_y = 0.0;
      double pval_other[256];
      max_sub = -(numeric_limits<double>::infinity());
      for (int i = 0; i < energy.bins.size(); i++) {
        sub_energy[i].resize(energy.bins[i].size());
        for (int j = 0; j < energy.bins[i].size(); j++) {
          double x = static_cast<double>(i)*(energy.Xhi - energy.Xlo)
            / static_cast<double>(energy.bins.size()) + energy.Xlo;
          double y = static_cast<double>(j)*(energy.Yhi - energy.Ylo)
            / static_cast<double>(energy.bins[i].size()) + energy.Ylo;
          if (ngauss > 1) {
            // subtract 4*sigma plus integral of fit function
            try {
              int npval_other = r.pval.at(r.pval.size()-1).size();
              if (npval_other > 256) {
                cerr << "Parameter overload" << endl;
                return;
              }
              for (int k = 0; k < npval_other; k++) {
                pval_other[k] = r.pval[r.pval.size()-1][k];
              }
              ngauss--;
              double nu = fit_fcn(x, y, pval_other) * XbinSize * YbinSize;
              ngauss++;
              sub_energy[i][j] = energy.bins[i][j] - nu 
                - 4.0*mdef->chisquare_error(nu);
            }
            catch (exception ex) {
              cerr << "Exception in par_init" << endl;
            }
          }
          else {
            sub_energy[i][j] = energy.bins[i][j];
          }
          if (sub_energy[i][j] > max_sub) {
            max_sub = sub_energy[i][j];
            max_x = x;
            max_y = y;
          }
        }
      }

      for (int i = npar1; i < npar; i++) {
        if (mdef->get_indiv_max_E() == i - npar1) {
          double nu = 0.0;
          if (ngauss > 1) {
            nu = fit_fcn(max_x, max_y, pval_other) * XbinSize * YbinSize;
          }
          pval[i] = max_sub + (ngauss > 1 ? 4.0*mdef->chisquare_error(nu)
                               : 0.0);
          perr[i] = mdef->chisquare_error(pval[i])*0.1;
          plo[i] = 0.0;
          phi[i] = 1.0e6;
        }
        else if (mdef->get_indiv_max_x() == i - npar1) {
          pval[i] = max_x;
          perr[i] = (energy.Xhi - energy.Xlo) / static_cast<double>(hist->GetXaxis()->GetNbins());
          plo[i] = 0.0;
          phi[i] = 0.0;
        }
        else if (mdef->get_indiv_max_y() == i - npar1) {
          pval[i] = max_y;
          perr[i] = (energy.Yhi - energy.Ylo) / static_cast<double>(hist->GetYaxis()->GetNbins());
          plo[i] = 0.0;
          phi[i] = 0.0;
        }
        else {
          string dummy;
          mdef->get_indiv_par(i-npar1, dummy, pval[i], perr[i], plo[i], phi[i]);
        }
      }
    }
    int n_pars_to_set = init_spec_pars ? ngauss*mdef->get_formula()->GetNpar()
      : npar - npar1;
    int init_par_to_set = init_spec_pars ? 0 : npar1;
    for (int i = 0; i < n_pars_to_set; i++) {
      double dummy;
      string s;
      int ipar = i + init_par_to_set;
      mdef->get_indiv_par(i % mdef->get_formula()->GetNpar(), s,
                         dummy, dummy, dummy, dummy);
      ostringstream par_oss;
      par_oss << s << ipar / (mdef->get_formula()->GetNpar()) << flush;
      try {
        pars.at(ipar) = TString(par_oss.str());
      }
      catch (exception ex) {
        cerr << "exception 2 in par_init" << endl;
      }
      int error_flag;
      try {
        gMinuit->mnparm(ipar, pars.at(ipar),
                        pval[ipar], perr[ipar], plo[ipar], phi[ipar], error_flag);
      } catch (exception ex) {
        cerr << "exception 3 in par_init" << endl;
      }
    }
  }

  results fit_histo(TH2 *hist, vector<trouble> &t_vec,
                 void (*cc_minuit)(TMinuit *, TH2 *, int),
                 int start_ngauss,
                    int rebinX, int rebinY,
                    double P_cutoff_val) {
    TMinuit *gMinuit = new TMinuit();
    int npar_indiv = mdef->get_formula()->GetNpar();
    int istat, erflg;
    results r;

    gMinuit->SetFCN(fcn);
    gMinuit->mninit(5, 6, 7);

    // set error def and machine accuracy
    double cs_err_def = 1.0;
    double fcn_eps = 0.2;
    gMinuit->mnexcm("SET ERR", &cs_err_def, 1, erflg);
    gMinuit->mnexcm("SET EPS", &fcn_eps, 1, erflg);

    // rebin histogram
    TH2 *hist_rebinned;
    if (rebinX > 1 && rebinY > 1)
      hist_rebinned = hist->Rebin2D(rebinX, rebinY);
    else
      hist_rebinned = hist;

    r.hist_rebinned = hist_rebinned;
    // load histogram into energies vector
    energy.bins.resize(hist_rebinned->GetXaxis()->GetNbins());
    for (int i = 0; i < energy.bins.size(); i++) {
      energy.bins[i].resize(hist_rebinned->GetYaxis()->GetNbins());
      for (int j = 0; j < energy.bins[i].size(); j++) {
        energy.bins[i][j] = hist_rebinned->GetBinContent(i+1, j+1);
      }
    }

    energy.Xlo = hist->GetXaxis()->GetXmin();
    energy.Xhi = hist->GetXaxis()->GetXmax();
    energy.Ylo = hist->GetYaxis()->GetXmin();
    energy.Yhi = hist->GetYaxis()->GetXmax();
    
    if (start_ngauss < 1) {
      start_ngauss = 1;
    }

    for (ngauss = start_ngauss;
         ngauss <= (MAX_GAUSS > start_ngauss ? MAX_GAUSS : start_ngauss);
         ngauss++) {
      t_vec.resize(t_vec.size() + 1);
      int npar = npar_indiv*ngauss;
      double pval[256], perr[256], plo[256], phi[256];
      if (npar > 256) {
        cerr << "Parameter overload" << endl;
        return r;
      }
      vector<TString> pars(npar);

      // initialize parameters
      par_init(hist, gMinuit, pars, pval, perr, plo, phi, npar, r);
  
      // minimize
      double chisquare, edm, errdef;
      int nvpar, nparx;
      trouble t;
      t.occ = T_NULL;
      t.istat = 3;
      // fix the N values and sigmas of the Gaussians
      for (int i = 0; i < ngauss; i++) {
        double parno[2];
        parno[0] = i*npar_indiv + 1;
        parno[1] = i*npar_indiv + 4;
        gMinuit->mnexcm("FIX", parno, 2, erflg);
      }
      gMinuit->mnexcm("SIMPLEX", 0, 0, erflg);
      gMinuit->mnexcm("MIGRAD", 0, 0, erflg);
      // release N values and sigmas, fix mu_x and mu_y
      for (int i = 0; i < ngauss; i++) {
        double parno[4];
        parno[0] = i*npar_indiv + 1;
        parno[1] = i*npar_indiv + 2;
        parno[2] = i*npar_indiv + 3;
        parno[3] = i*npar_indiv + 4;
        gMinuit->mnexcm("RELEASE", parno, 1, erflg);
        gMinuit->mnexcm("RELEASE", parno+3, 1, erflg);
        gMinuit->mnexcm("FIX", parno+1, 2, erflg);
      }
      gMinuit->mnexcm("MIGRAD", 0, 0, erflg);
      // release mu_x and mu_y
      for (int i = 0; i < ngauss; i++) {
        double parno[4];
        parno[0] = i*npar_indiv + 1;
        parno[1] = i*npar_indiv + 2;
        parno[2] = i*npar_indiv + 3;
        parno[3] = i*npar_indiv + 4;
        gMinuit->mnexcm("RELEASE", parno+1, 2, erflg);
      }
      gMinuit->mnexcm("MIGRAD", 0, 0, erflg);
      gMinuit->mnstat(chisquare, edm, errdef, nvpar, nparx, istat);
      if (istat == 3) {
        /* we're not concerned about MINOS errors right now
        gMinuit->mnexcm("MINOS", 0, 0, erflg);
        gMinuit->mnstat(chisquare, edm, errdef, nvpar, nparx, istat);
        if (istat != 3) {
          t.occ = T_MINOS;
          t.istat = istat;
        }
        */
      }
      else {
        t.occ = T_MIGRAD;
        t.istat = istat;
      }

      try {
        if (t_vec.size() < ngauss) {
          t_vec.resize(ngauss);
        }
        t_vec.at(ngauss-1) = t;
      }
      catch (exception ex) {
        cerr << "exception in fit_histo" << endl;
      }

      // put parameters in map
      for (int i = 0; i < npar && i < 256; i++) {
        int iuint; // internal parameter number
        gMinuit->mnpout(i, pars[i], pval[i], perr[i], plo[i], phi[i], iuint);
      }
      vector<double> pval_copy(npar);
      vector<double> perr_copy(npar);
      vector<double> plo_copy(npar);
      vector<double> phi_copy(npar);
      for (int i = 0; i < npar && i < 256; i++) {
        pval_copy[i] = pval[i];
        perr_copy[i] = perr[i];
        plo_copy[i] = plo[i];
        phi_copy[i] = phi[i];
      }
      r.pars.push_back(pars);
      r.pval.push_back(pval_copy);
      r.perr.push_back(perr_copy);
      r.plo.push_back(plo_copy);
      r.phi.push_back(phi_copy);

      // execute user minuit code
      if (cc_minuit != 0)
        (*cc_minuit)(gMinuit, hist_rebinned, ngauss);

      int ndof = 0;
      if (!ignorezero)
        ndof = energy.bins.size() * energy.bins[0].size();
      else {
        for (int i = 0; i < energy.bins.size(); i++) {
          for (int j = 0; j < energy.bins[i].size(); j++) {
            if (energy.bins[i][j] > 1.0e-30)
              ndof++;
          }
        }
      }
      ndof -= npar;

      double P = prob(chisquare, ndof);
      cout << "P = "<<P << endl;
      if (P > P_cutoff_val) {
        break;
      }
    }

    delete gMinuit;
    return r;
  }
}
Revision:	1.2
Committed:	Fri Sep 4 20:09:16 2009 UTC (15 years, 7 months ago) by dnisson
Branch:	MAIN
CVS Tags:	HEAD
Changes since 1.1:	+0 -0 lines
State:	*FILE REMOVED*
Log Message:	Deleting ~ clutter.
#	User	Rev	Content
1	dnisson	1.1	/* jetfit.cpp - Package to fit multi-Gaussian distributions to histograms
2			* rewrite after accidental deletion 07-24-09
3			* Author: David Nisson
4			*/
5
6			#include <cstdlib>
7			#include <cmath>
8			#include <ctime>
9			#include <cstdio>
10			#include <cstring>
11			#include <cctype>
12			#include <iostream>
13			#include <fstream>
14			#include <sstream>
15			#include <string>
16			#include <vector>
17			#include <set>
18			#include <map>
19			#include <limits>
20			#include <exception>
21
22			#include <TMinuit.h>
23			#include <TH1.h>
24			#include <TH2.h>
25			#include <TF2.h>
26			#include <TRandom3.h>
27			#include <Rtypes.h>
28			#include <TFormula.h>
29			#include <TSystem.h>
30
31			#include "UserCode/JetFitAnalyzer/interface/jetfit.h"
32
33			#define PI 3.141592653
34
35			#define MAX_GAUSS 3
36
37			using namespace std;
38
39			namespace jetfit {
40			// configurable options
41			bool ignorezero = false; // ignore zero bins when fitting
42
43			int ngauss; // number of Gaussians in current model
44
45			struct histo {
46			vector< vector<double> > bins;
47			double Xlo, Xhi, Ylo, Yhi;
48			} energy;
49
50
51			model_def *mdef;
52
53			model_def& curr_model_def() {
54			return *mdef;
55			}
56
57			void set_model_def(model_def *_mdef) {
58			mdef = _mdef;
59			}
60
61			int get_ngauss() {
62			return ngauss;
63			}
64
65			void set_ngauss(int _ngauss) {
66			ngauss = _ngauss;
67			}
68
69			// fit function
70			double fit_fcn(double x, double y, double *xval) {
71			int npar_indiv = mdef->get_formula()->GetNpar();
72			double val = 0.0;
73			for (int i = 0; i < ngauss; i++) {
74			mdef->get_formula()->SetParameters(xval + i*npar_indiv);
75			val += mdef->get_formula()->Eval(x, y);
76			}
77			return val;
78			}
79
80			// TF2-compatible fit function
81			double fit_fcn_TF2(double x, double pval) {
82			double val = fit_fcn(x[0], x[1], pval);
83			return val;
84			}
85
86			// Integral of model formula / chisquare sigma
87			double formula_int(double xlo, double xhi, double ylo, double yhi,
88			double *pval, double XbinSize, double YbinSize,
89			double *xval) {
90			double xstep = (xhi - xlo) / static_cast<double>(20);
91			double ystep = (yhi - ylo) / static_cast<double>(20);
92
93			double fsum = 0.0;
94			double pval_old[256];
95			int npar = mdef->get_formula()->GetNpar();
96			if (npar > 256) {
97			cerr << "Parameter overload" << endl;
98			return 0.0;
99			}
100			mdef->get_formula()->GetParameters(pval_old);
101			mdef->get_formula()->SetParameters(pval);
102
103			for (int i = 0; i < 20; i++) {
104			for (int j = 0; j < 20; j++) {
105			double x = (static_cast<double>(i) + 0.5)*xstep + xlo;
106			double y = (static_cast<double>(j) + 0.5)*ystep + ylo;
107			double sig_cut = 1.0e-5;
108			double nu = XbinSize * YbinSize * fit_fcn(x, y, xval);
109			double sigma = mdef->chisquare_error(nu) < sig_cut
110			? sig_cut : mdef->chisquare_error(nu);
111
112			fsum += xstep * ystep * mdef->get_formula()->Eval(x, y)
113			/ sigma / sigma;
114			}
115			}
116
117			mdef->get_formula()->SetParameters(pval_old);
118			return fsum;
119			}
120
121			// MINUIT objective function
122			void fcn(int &npar, double grad, double &fcnval, double xval, int iflag)
123			{
124			double chisquare = 0.0;
125			double XbinSize = (energy.Xhi - energy.Xlo)
126			/ static_cast<double>(energy.bins.size());
127			double YbinSize = (energy.Yhi - energy.Ylo)
128			/ static_cast<double>(energy.bins.at(0).size());
129			try {
130			// add errors in data points in histogram
131			for (int i = 0; i < energy.bins.size(); i++) {
132			for (int j = 0; j < energy.bins.at(i).size(); j++) {
133			double x = (static_cast<double>(i) + 0.5) * (energy.Xhi - energy.Xlo)
134			/ static_cast<double>(energy.bins.size()) + energy.Xlo;
135			double y = (static_cast<double>(j) + 0.5) * (energy.Yhi - energy.Ylo)
136			/ static_cast<double>(energy.bins.at(i).size()) + energy.Ylo;
137			double nu = fit_fcn(x, y, xval) * XbinSize * YbinSize;
138			double sig_cut = 1.0e-5;
139			if (mdef->chisquare_error(nu) > sig_cut \|\| !ignorezero)
140			chisquare += pow(energy.bins.at(i).at(j) - nu, 2.0)
141			/ pow(mdef->chisquare_error(nu), 2.0);
142			else
143			chisquare += pow(energy.bins.at(i).at(j) - nu, 2.0)
144			/ pow(sig_cut, 2.0);
145			}
146			}
147
148			// add errors due to Gaussians outside histogram
149			double eps = 0.1; // accuracy set for this function
150			for (int i = 0; i < ngauss; i++) {
151			double pval = xval+imdef->get_formula()->GetNpar();
152			double par_x = pval[mdef->get_indiv_max_x()];
153			double par_y = pval[mdef->get_indiv_max_y()];
154			double par_sig = pval[3];
155			double cutoff_rad = -log(eps * 2.0 * PI * par_sig * par_sig
156			/ pval[0]);
157
158			bool left = par_x < energy.Xlo + cutoff_rad;
159			bool right = par_x > energy.Xhi - cutoff_rad;
160			bool top = par_y > energy.Yhi - cutoff_rad;
161			bool bottom = par_y > energy.Ylo + cutoff_rad;
162
163			if (left) {
164			double xlo = par_x - cutoff_rad;
165			double xhi = energy.Xlo;
166			double ylo = energy.Ylo;
167			double yhi = energy.Yhi;
168			chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
169			XbinSize, YbinSize, xval);
170			}
171			if (right) {
172			double xlo = energy.Xhi;
173			double xhi = par_x + cutoff_rad;
174			double ylo = energy.Ylo;
175			double yhi = energy.Yhi;
176			chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
177			XbinSize, YbinSize, xval);
178			}
179			if (top) {
180			double xlo = left ? par_x - cutoff_rad : energy.Xlo;
181			double xhi = right ? par_x + cutoff_rad : energy.Xhi;
182			double ylo = energy.Yhi;
183			double yhi = par_y + cutoff_rad;
184			chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
185			XbinSize, YbinSize, xval);
186			}
187			if (bottom) {
188			double xlo = left ? par_x - cutoff_rad : energy.Xlo;
189			double xhi = right ? par_x + cutoff_rad : energy.Xhi;
190			double ylo = par_y - cutoff_rad;
191			double yhi = energy.Ylo;
192			chisquare += formula_int(xlo, xhi, ylo, yhi, pval,
193			XbinSize, YbinSize, xval);
194			}
195			}
196
197			fcnval = chisquare;
198			}
199			catch (exception ex) {
200			cerr << "Exception in jetfit::fcn" << endl;
201			}
202			}
203
204			bool get_ignorezero() {
205			return ignorezero;
206			}
207
208			void set_ignorezero(bool _iz) {
209			ignorezero = _iz;
210			}
211
212			TFormula * model_def::get_formula() {
213			return indiv_formula;
214			}
215
216			void model_def::set_formula(TFormula *new_formula) {
217			indiv_formula = new_formula;
218			}
219
220			void model_def::get_indiv_par(int i, string &name, double &start, double &step,
221			double &lo, double &hi) {
222			try {
223			name = indiv_par_names.at(i);
224			start = indiv_par_starts.at(i);
225			step = indiv_par_start_steps.at(i);
226			lo = indiv_par_lo.at(i);
227			hi = indiv_par_hi.at(i);
228			} catch (exception ex) {
229			cerr << "exception in jetfit::model_def::get_indiv_par" << endl;
230			}
231			}
232
233			void model_def::set_indiv_par(int i, string name, double start, double step,
234			double lo, double hi) {
235			if (indiv_par_names.size() < i+1) {
236			indiv_par_names.resize(i+1);
237			indiv_par_starts.resize(i+1);
238			indiv_par_start_steps.resize(i+1);
239			indiv_par_lo.resize(i+1);
240			indiv_par_hi.resize(i+1);
241			}
242			try {
243			indiv_par_names.at(i) = name;
244			indiv_par_starts.at(i) = start;
245			indiv_par_start_steps.at(i) = step;
246			indiv_par_lo.at(i) = lo;
247			indiv_par_hi.at(i) = hi;
248			}
249			catch (exception ex) {
250			cerr << "exception in jetfit::model_def::set_indiv_par" << endl;
251			}
252			}
253
254			int model_def::get_indiv_max_E() {
255			return indiv_max_E;
256			}
257
258			void model_def::set_indiv_max_E(int _new_max_E) {
259			indiv_max_E = _new_max_E;
260			}
261
262			int model_def::get_indiv_max_x() {
263			return indiv_max_x;
264			}
265
266			void model_def::set_indiv_max_x(int new_max_x) {
267			indiv_max_x = new_max_x;
268			}
269
270			int model_def::get_indiv_max_y() {
271			return indiv_max_y;
272			}
273
274			void model_def::set_indiv_max_y(int new_max_y) {
275			indiv_max_y = new_max_y;
276			}
277
278			unsigned model_def::get_n_special_par_sets() {
279			return special_par_starts.size();
280			}
281
282			void model_def::get_special_par(int g, int i, double &pstart,
283			double &perr, double &plo, double &phi) {
284			try {
285			pstart = special_par_starts.at(g).at(i);
286			perr = special_par_start_steps.at(g).at(i);
287			plo = special_par_lo.at(g).at(i);
288			phi = special_par_hi.at(g).at(i);
289			} catch (exception ex) {
290			cerr << "Exception in model_def::get_special_par" << endl;
291			}
292			}
293
294			void model_def::set_special_par(int g, int i, double pstart,
295			double perr, double plo, double phi) {
296			if (g+1 > special_par_starts.size()) {
297			special_par_starts.resize(g+1);
298			special_par_start_steps.resize(g+1);
299			special_par_lo.resize(g+1);
300			special_par_hi.resize(g+1);
301			}
302
303			try {
304			if (i+1 > special_par_starts.at(g).size()) {
305			special_par_starts.at(g).resize(i+1);
306			special_par_start_steps.at(g).resize(i+1);
307			special_par_lo.at(g).resize(i+1);
308			special_par_hi.at(g).resize(i+1);
309			}
310
311			special_par_starts.at(g).at(i) = pstart;
312			special_par_start_steps.at(g).at(i) = perr;
313			special_par_lo.at(g).at(i) = plo;
314			special_par_hi.at(g).at(i) = phi;
315			}
316			catch (exception ex) {
317			cerr << "exception in jetfit::model_def::set_special_par" << endl;
318			}
319			}
320
321			// translation of CERN's ERFC function
322			double erfc(double x) {
323			bool lef = false;
324			double p2[5], q2[5];
325
326			const double z1 = 1.0, hf = z1/2.0, c1 = 0.56418958;
327			const double vmax = 7.0;
328			const double switch_ = 4.0;
329
330			double p10 = 3.6767877, q10 = 3.2584593, p11 = -9.7970465e-2;
331			p2[0] = 7.3738883;
332			q2[0] = 7.3739609;
333			p2[1] = 6.8650185;
334			q2[1] = 1.5184908e1;
335			p2[2] = 3.0317993;
336			q2[2] = 1.2795530e1;
337			p2[3] = 5.6316962e-1;
338			q2[3] = 5.3542168;
339			p2[4] = 4.3187787e-5;
340			q2[4] = 1.0;
341
342			double p30 = -1.2436854e-1, q30 = 4.4091706e-1, p31 = -9.6821036e-2;
343
344			double v = fabs(x);
345			double y, h, hc, ap, aq;
346			if (v < hf) {
347			y = v*v;
348			h = x(p10 + p11y)/(q10 + y);
349			hc = 1.0 - h;
350			}
351			else {
352			if (v < switch_) {
353			ap = p2[4];
354			aq = q2[4];
355			for (int i = 3; i >= 0; i--) {
356			ap = p2[i] + v*ap;
357			aq = q2[i] + v*aq;
358			}
359			hc = exp(-vv)ap/aq;
360			h = 1.0 - hc;
361			}
362			else if (v < vmax) {
363			y = 1/v/v;
364			hc = exp(-vv)(c1 + y(p30 + p31y)/(q30 + y))/v;
365			h = 1.0 - hc;
366			}
367			// for very big values we can save us any calculation
368			// and the FP-exceptions from exp
369			else {
370			h = 1.0;
371			hc = 0.0;
372			}
373			if (x < 0) {
374			h = -h;
375			hc = 2.0 - hc;
376			}
377			}
378			if (lef) {
379			return h;
380			}
381			else {
382			return hc;
383			}
384			}
385
386			// translation of CERN's PROB function
387			double prob(double x, int n) {
388			const char *name = "PROB";
389			char errtxt[80];
390
391			const double r1 = 1.0,
392			hf = r1/2.0, th = r1/3.0, f1 = 2.0*r1/9.0;
393			const double c1 = 1.128379167095513;
394			const int nmax = 300;
395			// maximum chi2 per df for df >= 2., if chi2/df > chipdf prob=0
396			const double chipdf = 100.0;
397			const double xmax = 174.673, xmax2 = 2.0*xmax;
398			const double xlim = 24.0;
399			const double eps = 1e-30;
400
401			double y = x;
402			double u = hf*y;
403			double h, w, s, t, fi, e;
404			int m;
405			if (n < 0) {
406			h = 0.0;
407			sprintf(errtxt, "n = %d < 1", n);
408			cerr << "PROB: G100.1: "<<errtxt;
409			}
410			else if (y < 0.0) {
411			h = 0.0;
412			sprintf(errtxt, "x = %f < 0", n);
413			cerr << "PROB: G100.2: "<<errtxt;
414			}
415			else if (y == 0.0 \|\| n/20 > y) {
416			h = 1.0;
417			}
418			else if (n == 1) {
419			w = sqrt(u);
420			if (w < xlim) {
421			h = erfc(w);
422			}
423			else {
424			h = 0.0;
425			}
426			}
427			else if (n > nmax) {
428			s = r1 / ((double)n);
429			t = f1 * s;
430			w = (pow(ys, th) - (1.0 - t)) / sqrt(2.0t);
431			if (w < -xlim) {
432			h = 1.0;
433			}
434			else if (w < xlim) {
435			h = hf * erfc(w);
436			}
437			else {
438			h = 0.0;
439			}
440			}
441			else {
442			m = n/2;
443			if (u < xmax2 && (y/n) <= chipdf) {
444			s = exp(-hf*u);
445			t = s;
446			e = s;
447			if (2*m == n) {
448			fi = 0.0;
449			for (int i = 1; i < m; i++) {
450			fi += 1.0;
451			t = u*t/fi;
452			s += t;
453			}
454			h = s*e;
455			}
456			else {
457			fi = 1.0;
458			for (int i = 1; i < m; i++) {
459			fi += 2.0;
460			t = t*y/fi;
461			s += t;
462			}
463			w = sqrt(u);
464			if (w < xlim) {
465			h = c1ws*e + erfc(w);
466			}
467			else {
468			h = 0.0;
469			}
470			}
471			}
472			else {
473			h = 0.0;
474			}
475			}
476			if (h > eps) {
477			return h;
478			}
479			else {
480			return 0.0;
481			}
482			}
483
484			void par_init(TH2 hist, TMinuit gMinuit, vector<TString> &pars,
485			double pval, double perr, double plo, double phi,
486			int npar, results r) {
487			int npar1 = npar - mdef->get_formula()->GetNpar();
488			bool init_spec_pars = false;
489			if (ngauss <= mdef->get_n_special_par_sets()) {
490			init_spec_pars = true;
491			for (int k = 0; k < ngauss; k++) {
492			int ipar0 = k*mdef->get_formula()->GetNpar(); // index of par 0
493			for (int l = 0; l < mdef->get_formula()->GetNpar(); l++) {
494			int ipar = ipar0 + l;
495			if (ipar < npar)
496			mdef->get_special_par(k, l, pval[ipar], perr[ipar], plo[ipar],
497			phi[ipar]);
498			else
499			cerr << "WARNING: Attempt to set parameter out of index range!"
500			<< endl;
501			}
502			}
503			}
504			else {
505			double XbinSize = (energy.Xhi - energy.Xlo)
506			/ static_cast<double>(energy.bins.size());
507			double YbinSize = (energy.Xhi - energy.Xlo)
508			/ static_cast<double>(energy.bins.at(0).size());
509			vector< vector<double> > sub_energy(energy.bins.size());
510			double max_sub, max_x = 0.0, max_y = 0.0;
511			double pval_other[256];
512			max_sub = -(numeric_limits<double>::infinity());
513			for (int i = 0; i < energy.bins.size(); i++) {
514			sub_energy[i].resize(energy.bins[i].size());
515			for (int j = 0; j < energy.bins[i].size(); j++) {
516			double x = static_cast<double>(i)*(energy.Xhi - energy.Xlo)
517			/ static_cast<double>(energy.bins.size()) + energy.Xlo;
518			double y = static_cast<double>(j)*(energy.Yhi - energy.Ylo)
519			/ static_cast<double>(energy.bins[i].size()) + energy.Ylo;
520			if (ngauss > 1) {
521			// subtract 4*sigma plus integral of fit function
522			try {
523			int npval_other = r.pval.at(r.pval.size()-1).size();
524			if (npval_other > 256) {
525			cerr << "Parameter overload" << endl;
526			return;
527			}
528			for (int k = 0; k < npval_other; k++) {
529			pval_other[k] = r.pval[r.pval.size()-1][k];
530			}
531			ngauss--;
532			double nu = fit_fcn(x, y, pval_other) * XbinSize * YbinSize;
533			ngauss++;
534			sub_energy[i][j] = energy.bins[i][j] - nu
535			- 4.0*mdef->chisquare_error(nu);
536			}
537			catch (exception ex) {
538			cerr << "Exception in par_init" << endl;
539			}
540			}
541			else {
542			sub_energy[i][j] = energy.bins[i][j];
543			}
544			if (sub_energy[i][j] > max_sub) {
545			max_sub = sub_energy[i][j];
546			max_x = x;
547			max_y = y;
548			}
549			}
550			}
551
552			for (int i = npar1; i < npar; i++) {
553			if (mdef->get_indiv_max_E() == i - npar1) {
554			double nu = 0.0;
555			if (ngauss > 1) {
556			nu = fit_fcn(max_x, max_y, pval_other) * XbinSize * YbinSize;
557			}
558			pval[i] = max_sub + (ngauss > 1 ? 4.0*mdef->chisquare_error(nu)
559			: 0.0);
560			perr[i] = mdef->chisquare_error(pval[i])*0.1;
561			plo[i] = 0.0;
562			phi[i] = 1.0e6;
563			}
564			else if (mdef->get_indiv_max_x() == i - npar1) {
565			pval[i] = max_x;
566			perr[i] = (energy.Xhi - energy.Xlo) / static_cast<double>(hist->GetXaxis()->GetNbins());
567			plo[i] = 0.0;
568			phi[i] = 0.0;
569			}
570			else if (mdef->get_indiv_max_y() == i - npar1) {
571			pval[i] = max_y;
572			perr[i] = (energy.Yhi - energy.Ylo) / static_cast<double>(hist->GetYaxis()->GetNbins());
573			plo[i] = 0.0;
574			phi[i] = 0.0;
575			}
576			else {
577			string dummy;
578			mdef->get_indiv_par(i-npar1, dummy, pval[i], perr[i], plo[i], phi[i]);
579			}
580			}
581			}
582			int n_pars_to_set = init_spec_pars ? ngauss*mdef->get_formula()->GetNpar()
583			: npar - npar1;
584			int init_par_to_set = init_spec_pars ? 0 : npar1;
585			for (int i = 0; i < n_pars_to_set; i++) {
586			double dummy;
587			string s;
588			int ipar = i + init_par_to_set;
589			mdef->get_indiv_par(i % mdef->get_formula()->GetNpar(), s,
590			dummy, dummy, dummy, dummy);
591			ostringstream par_oss;
592			par_oss << s << ipar / (mdef->get_formula()->GetNpar()) << flush;
593			try {
594			pars.at(ipar) = TString(par_oss.str());
595			}
596			catch (exception ex) {
597			cerr << "exception 2 in par_init" << endl;
598			}
599			int error_flag;
600			try {
601			gMinuit->mnparm(ipar, pars.at(ipar),
602			pval[ipar], perr[ipar], plo[ipar], phi[ipar], error_flag);
603			} catch (exception ex) {
604			cerr << "exception 3 in par_init" << endl;
605			}
606			}
607			}
608
609			results fit_histo(TH2 *hist, vector<trouble> &t_vec,
610			void (cc_minuit)(TMinuit , TH2 *, int),
611			int start_ngauss,
612			int rebinX, int rebinY,
613			double P_cutoff_val) {
614			TMinuit *gMinuit = new TMinuit();
615			int npar_indiv = mdef->get_formula()->GetNpar();
616			int istat, erflg;
617			results r;
618
619			gMinuit->SetFCN(fcn);
620			gMinuit->mninit(5, 6, 7);
621
622			// set error def and machine accuracy
623			double cs_err_def = 1.0;
624			double fcn_eps = 0.2;
625			gMinuit->mnexcm("SET ERR", &cs_err_def, 1, erflg);
626			gMinuit->mnexcm("SET EPS", &fcn_eps, 1, erflg);
627
628			// rebin histogram
629			TH2 *hist_rebinned;
630			if (rebinX > 1 && rebinY > 1)
631			hist_rebinned = hist->Rebin2D(rebinX, rebinY);
632			else
633			hist_rebinned = hist;
634
635			r.hist_rebinned = hist_rebinned;
636			// load histogram into energies vector
637			energy.bins.resize(hist_rebinned->GetXaxis()->GetNbins());
638			for (int i = 0; i < energy.bins.size(); i++) {
639			energy.bins[i].resize(hist_rebinned->GetYaxis()->GetNbins());
640			for (int j = 0; j < energy.bins[i].size(); j++) {
641			energy.bins[i][j] = hist_rebinned->GetBinContent(i+1, j+1);
642			}
643			}
644
645			energy.Xlo = hist->GetXaxis()->GetXmin();
646			energy.Xhi = hist->GetXaxis()->GetXmax();
647			energy.Ylo = hist->GetYaxis()->GetXmin();
648			energy.Yhi = hist->GetYaxis()->GetXmax();
649
650			if (start_ngauss < 1) {
651			start_ngauss = 1;
652			}
653
654			for (ngauss = start_ngauss;
655			ngauss <= (MAX_GAUSS > start_ngauss ? MAX_GAUSS : start_ngauss);
656			ngauss++) {
657			t_vec.resize(t_vec.size() + 1);
658			int npar = npar_indiv*ngauss;
659			double pval[256], perr[256], plo[256], phi[256];
660			if (npar > 256) {
661			cerr << "Parameter overload" << endl;
662			return r;
663			}
664			vector<TString> pars(npar);
665
666			// initialize parameters
667			par_init(hist, gMinuit, pars, pval, perr, plo, phi, npar, r);
668
669			// minimize
670			double chisquare, edm, errdef;
671			int nvpar, nparx;
672			trouble t;
673			t.occ = T_NULL;
674			t.istat = 3;
675			// fix the N values and sigmas of the Gaussians
676			for (int i = 0; i < ngauss; i++) {
677			double parno[2];
678			parno[0] = i*npar_indiv + 1;
679			parno[1] = i*npar_indiv + 4;
680			gMinuit->mnexcm("FIX", parno, 2, erflg);
681			}
682			gMinuit->mnexcm("SIMPLEX", 0, 0, erflg);
683			gMinuit->mnexcm("MIGRAD", 0, 0, erflg);
684			// release N values and sigmas, fix mu_x and mu_y
685			for (int i = 0; i < ngauss; i++) {
686			double parno[4];
687			parno[0] = i*npar_indiv + 1;
688			parno[1] = i*npar_indiv + 2;
689			parno[2] = i*npar_indiv + 3;
690			parno[3] = i*npar_indiv + 4;
691			gMinuit->mnexcm("RELEASE", parno, 1, erflg);
692			gMinuit->mnexcm("RELEASE", parno+3, 1, erflg);
693			gMinuit->mnexcm("FIX", parno+1, 2, erflg);
694			}
695			gMinuit->mnexcm("MIGRAD", 0, 0, erflg);
696			// release mu_x and mu_y
697			for (int i = 0; i < ngauss; i++) {
698			double parno[4];
699			parno[0] = i*npar_indiv + 1;
700			parno[1] = i*npar_indiv + 2;
701			parno[2] = i*npar_indiv + 3;
702			parno[3] = i*npar_indiv + 4;
703			gMinuit->mnexcm("RELEASE", parno+1, 2, erflg);
704			}
705			gMinuit->mnexcm("MIGRAD", 0, 0, erflg);
706			gMinuit->mnstat(chisquare, edm, errdef, nvpar, nparx, istat);
707			if (istat == 3) {
708			/* we're not concerned about MINOS errors right now
709			gMinuit->mnexcm("MINOS", 0, 0, erflg);
710			gMinuit->mnstat(chisquare, edm, errdef, nvpar, nparx, istat);
711			if (istat != 3) {
712			t.occ = T_MINOS;
713			t.istat = istat;
714			}
715			*/
716			}
717			else {
718			t.occ = T_MIGRAD;
719			t.istat = istat;
720			}
721
722			try {
723			if (t_vec.size() < ngauss) {
724			t_vec.resize(ngauss);
725			}
726			t_vec.at(ngauss-1) = t;
727			}
728			catch (exception ex) {
729			cerr << "exception in fit_histo" << endl;
730			}
731
732			// put parameters in map
733			for (int i = 0; i < npar && i < 256; i++) {
734			int iuint; // internal parameter number
735			gMinuit->mnpout(i, pars[i], pval[i], perr[i], plo[i], phi[i], iuint);
736			}
737			vector<double> pval_copy(npar);
738			vector<double> perr_copy(npar);
739			vector<double> plo_copy(npar);
740			vector<double> phi_copy(npar);
741			for (int i = 0; i < npar && i < 256; i++) {
742			pval_copy[i] = pval[i];
743			perr_copy[i] = perr[i];
744			plo_copy[i] = plo[i];
745			phi_copy[i] = phi[i];
746			}
747			r.pars.push_back(pars);
748			r.pval.push_back(pval_copy);
749			r.perr.push_back(perr_copy);
750			r.plo.push_back(plo_copy);
751			r.phi.push_back(phi_copy);
752
753			// execute user minuit code
754			if (cc_minuit != 0)
755			(*cc_minuit)(gMinuit, hist_rebinned, ngauss);
756
757			int ndof = 0;
758			if (!ignorezero)
759			ndof = energy.bins.size() * energy.bins[0].size();
760			else {
761			for (int i = 0; i < energy.bins.size(); i++) {
762			for (int j = 0; j < energy.bins[i].size(); j++) {
763			if (energy.bins[i][j] > 1.0e-30)
764			ndof++;
765			}
766			}
767			}
768			ndof -= npar;
769
770			double P = prob(chisquare, ndof);
771			cout << "P = "<<P << endl;
772			if (P > P_cutoff_val) {
773			break;
774			}
775			}
776
777			delete gMinuit;
778			return r;
779			}
780			}