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/* jetfit.cpp - Package to fit multi-Gaussian distributions to histograms
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* Author: David Nisson
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*/
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#include <cstdlib>
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#include <cmath>
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#include <ctime>
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#include <cstdio>
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#include <cstring>
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#include <cctype>
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#include <iostream>
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#include <fstream>
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#include <sstream>
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#include <string>
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#include <vector>
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#include <set>
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#include <map>
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#include <limits>
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#include <exception>
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#include <TMinuit.h>
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#include <TH1.h>
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#include <TH2.h>
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#include <TF2.h>
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#include <TRandom3.h>
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#include <Rtypes.h>
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#include <TFormula.h>
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#include <TSystem.h>
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#include <TMath.h>
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#include "UserCode/JetFitAnalyzer/interface/jetfit.h"
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#define PI 3.141592653
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#define MAX_GAUSS 3
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using namespace std;
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namespace jetfit {
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// configurable options
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bool ignorezero = false; // ignore zero bins when fitting
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model_def *mdef;
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model_def& curr_model_def() {
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return *mdef;
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}
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void set_model_def(model_def *_mdef) {
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mdef = _mdef;
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}
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int model_def::get_ngauss() {
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return ngauss;
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}
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void model_def::set_ngauss(int _ngauss) {
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ngauss = _ngauss;
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}
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// fit function
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double model_def::fit_fcn(double x, double y, double *xval) {
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int npar_indiv = get_formula()->GetNpar();
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double val = 0.0;
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for (int i = 0; i < ngauss; i++) {
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get_formula()->SetParameters(xval + i*npar_indiv);
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val += mdef->get_formula()->Eval(x, y);
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}
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return val;
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}
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// TF2-compatible fit function
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double fit_fcn_TF2(double *x, double *pval) {
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double val = mdef->fit_fcn(x[0], x[1], pval);
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return val;
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}
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// Integral of (model formula)^2 / chisquare sigma
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double model_def::formula_int(double xlo, double xhi, double ylo, double yhi,
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double *pval, double XbinSize, double YbinSize,
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double *xval) {
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double xstep = (xhi - xlo) / static_cast<double>(20);
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double ystep = (yhi - ylo) / static_cast<double>(20);
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double fsum = 0.0;
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double pval_old[256];
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int npar = get_formula()->GetNpar();
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if (npar > 256) {
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cerr << "Parameter overload" << endl;
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return 0.0;
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}
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get_formula()->GetParameters(pval_old);
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get_formula()->SetParameters(pval);
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for (int i = 0; i < 20; i++) {
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for (int j = 0; j < 20; j++) {
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double x = (static_cast<double>(i) + 0.5)*xstep + xlo;
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double y = (static_cast<double>(j) + 0.5)*ystep + ylo;
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double sig_cut = 1.0e-5;
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double nu = XbinSize * YbinSize * fit_fcn(x, y, xval);
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double sigma = fabs(chisquare_error(0.0)) < sig_cut
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? sig_cut : chisquare_error(0.0);
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fsum += pow(xstep * ystep * get_formula()->Eval(x, y), 2.0)
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/ sigma / sigma;
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}
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}
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get_formula()->SetParameters(pval_old);
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return fsum;
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}
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// MINUIT objective function
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void fcn(int &npar, double *grad, double &fcnval, double *xval, int iflag)
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{
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double chisquare = 0.0;
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double XbinSize = (energy.Xhi - energy.Xlo)
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/ static_cast<double>(energy.bins.size());
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double YbinSize = (energy.Yhi - energy.Ylo)
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/ static_cast<double>(energy.bins.at(0).size());
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try {
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// add errors in data points in histogram
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for (int i = 0; i < energy.bins.size(); i++) {
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for (int j = 0; j < energy.bins.at(i).size(); j++) {
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double x = (static_cast<double>(i) + 0.5) * (energy.Xhi - energy.Xlo)
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/ static_cast<double>(energy.bins.size()) + energy.Xlo;
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double y = (static_cast<double>(j) + 0.5) * (energy.Yhi - energy.Ylo)
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/ static_cast<double>(energy.bins.at(i).size()) + energy.Ylo;
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double nu = mdef->fit_fcn(x, y, xval) * XbinSize * YbinSize;
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double sig_cut = 1.0e-5;
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if (fabs(mdef->chisquare_error(energy.bins.at(i).at(j))) > sig_cut || !ignorezero) {
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chisquare += pow(energy.bins.at(i).at(j) - nu, 2.0)
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/ pow(mdef->chisquare_error(energy.bins.at(i).at(j)), 2.0);
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}
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else {
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chisquare += pow(energy.bins.at(i).at(j) - nu, 2.0)
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/ pow(sig_cut, 2.0);
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}
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}
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}
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// add errors due to Gaussians outside histogram
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double eps = 0.01; // accuracy set for this function
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for (int i = 0; i < mdef->get_ngauss(); i++) {
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double *pval = xval+i*(mdef->get_formula()->GetNpar());
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double par_x = pval[mdef->get_indiv_max_x()];
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double par_y = pval[mdef->get_indiv_max_y()];
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double par_sig = pval[3];
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double cutoff_rad = sqrt(-log(eps * 2.0 * PI * par_sig * par_sig
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/ pval[0]) * 2.0 * par_sig * par_sig);
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bool left = par_x < energy.Xlo + cutoff_rad;
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bool right = par_x > energy.Xhi - cutoff_rad;
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bool top = par_y > energy.Yhi - cutoff_rad;
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bool bottom = par_y < energy.Ylo + cutoff_rad;
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if (left) {
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double xlo = par_x - cutoff_rad;
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double xhi = energy.Xlo;
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double ylo = energy.Ylo;
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double yhi = energy.Yhi;
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chisquare += 2.0*mdef->formula_int(xlo, xhi, ylo, yhi, pval,
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XbinSize, YbinSize, xval);
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}
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if (right) {
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double xlo = energy.Xhi;
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double xhi = par_x + cutoff_rad;
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double ylo = energy.Ylo;
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double yhi = energy.Yhi;
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chisquare += 2.0*mdef->formula_int(xlo, xhi, ylo, yhi, pval,
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XbinSize, YbinSize, xval);
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}
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if (top) {
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double xlo = left ? par_x - cutoff_rad : energy.Xlo;
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double xhi = right ? par_x + cutoff_rad : energy.Xhi;
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double ylo = energy.Yhi;
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double yhi = par_y + cutoff_rad;
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chisquare += 2.0*mdef->formula_int(xlo, xhi, ylo, yhi, pval,
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XbinSize, YbinSize, xval);
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}
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if (bottom) {
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double xlo = left ? par_x - cutoff_rad : energy.Xlo;
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double xhi = right ? par_x + cutoff_rad : energy.Xhi;
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double ylo = par_y - cutoff_rad;
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double yhi = energy.Ylo;
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chisquare += 2.0*mdef->formula_int(xlo, xhi, ylo, yhi, pval,
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XbinSize, YbinSize, xval);
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}
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}
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fcnval = chisquare;
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}
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catch (exception ex) {
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cerr << "Exception in jetfit::fcn" << endl;
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}
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}
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bool get_ignorezero() {
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return ignorezero;
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}
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void set_ignorezero(bool _iz) {
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ignorezero = _iz;
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}
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TFormula * model_def::get_formula() {
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return indiv_formula;
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}
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void model_def::set_formula(TFormula *new_formula) {
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indiv_formula = new_formula;
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}
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void model_def::get_indiv_par(int i, string &name, double &start, double &step,
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double &lo, double &hi) {
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try {
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name = indiv_par_names.at(i);
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start = indiv_par_starts.at(i);
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step = indiv_par_start_steps.at(i);
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lo = indiv_par_lo.at(i);
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hi = indiv_par_hi.at(i);
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} catch (exception ex) {
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cerr << "exception in jetfit::model_def::get_indiv_par" << endl;
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}
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}
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void model_def::set_indiv_par(int i, string name, double start, double step,
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double lo, double hi) {
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if (indiv_par_names.size() < i+1) {
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indiv_par_names.resize(i+1);
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indiv_par_starts.resize(i+1);
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indiv_par_start_steps.resize(i+1);
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indiv_par_lo.resize(i+1);
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indiv_par_hi.resize(i+1);
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}
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try {
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indiv_par_names.at(i) = name;
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indiv_par_starts.at(i) = start;
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indiv_par_start_steps.at(i) = step;
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indiv_par_lo.at(i) = lo;
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indiv_par_hi.at(i) = hi;
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}
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catch (exception ex) {
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cerr << "exception in jetfit::model_def::set_indiv_par" << endl;
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}
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}
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int model_def::get_indiv_max_E() {
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return indiv_max_E;
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}
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void model_def::set_indiv_max_E(int _new_max_E) {
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indiv_max_E = _new_max_E;
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}
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int model_def::get_indiv_max_x() {
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return indiv_max_x;
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}
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void model_def::set_indiv_max_x(int new_max_x) {
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indiv_max_x = new_max_x;
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}
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int model_def::get_indiv_max_y() {
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return indiv_max_y;
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}
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void model_def::set_indiv_max_y(int new_max_y) {
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indiv_max_y = new_max_y;
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}
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unsigned model_def::get_n_special_par_sets() {
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return special_par_starts.size();
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}
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void model_def::get_special_par(int g, int i, double &pstart,
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double &perr, double &plo, double &phi) {
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try {
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pstart = special_par_starts.at(g).at(i);
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perr = special_par_start_steps.at(g).at(i);
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plo = special_par_lo.at(g).at(i);
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phi = special_par_hi.at(g).at(i);
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} catch (exception ex) {
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cerr << "Exception in model_def::get_special_par" << endl;
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}
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}
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void model_def::set_special_par(int g, int i, double pstart,
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double perr, double plo, double phi) {
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if (g+1 > special_par_starts.size()) {
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special_par_starts.resize(g+1);
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special_par_start_steps.resize(g+1);
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special_par_lo.resize(g+1);
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special_par_hi.resize(g+1);
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}
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try {
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if (i+1 > special_par_starts.at(g).size()) {
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special_par_starts.at(g).resize(i+1);
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special_par_start_steps.at(g).resize(i+1);
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special_par_lo.at(g).resize(i+1);
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special_par_hi.at(g).resize(i+1);
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}
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special_par_starts.at(g).at(i) = pstart;
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special_par_start_steps.at(g).at(i) = perr;
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special_par_lo.at(g).at(i) = plo;
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special_par_hi.at(g).at(i) = phi;
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}
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catch (exception ex) {
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cerr << "exception in jetfit::model_def::set_special_par" << endl;
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}
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}
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void fill_histo_with_vec(TH2 *hist, vector< vector<double> > &vec) {
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for (int i = 0; i < vec.size(); i++) {
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for (int j = 0; j < vec[i].size(); j++) {
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hist->SetBinContent(i+1, j+1, vec[i][j]);
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}
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}
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}
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void model_def::par_init(TH2 *hist, TMinuit *gMinuit, vector<TString> &pars,
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double *pval, double *perr, double *plo, double *phi,
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int npar, FitResults r) {
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int npar1 = npar - get_formula()->GetNpar();
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bool init_spec_pars = false;
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if (ngauss <= get_n_special_par_sets()) {
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init_spec_pars = true;
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for (int k = 0; k < ngauss; k++) {
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int ipar0 = k*get_formula()->GetNpar(); // index of indiv par 0
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for (int l = 0; l < get_formula()->GetNpar(); l++) {
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int ipar = ipar0 + l;
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if (ipar < npar)
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get_special_par(k, l, pval[ipar], perr[ipar], plo[ipar],
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phi[ipar]);
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else
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cerr << "WARNING: Attempt to set parameter out of index range!"
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<< endl;
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}
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}
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}
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else {
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double XbinSize = (energy.Xhi - energy.Xlo)
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/ static_cast<double>(energy.bins.size());
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double YbinSize = (energy.Xhi - energy.Xlo)
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/ static_cast<double>(energy.bins.at(0).size());
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vector< vector<double> > sub_energy(energy.bins.size());
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double max_sub, max_x = 0.0, max_y = 0.0;
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double pval_other[256];
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max_sub = -(numeric_limits<double>::max());
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for (int i = 0; i < energy.bins.size(); i++) {
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sub_energy[i].resize(energy.bins[i].size());
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for (int j = 0; j < energy.bins[i].size(); j++) {
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double x = static_cast<double>(i)*(energy.Xhi - energy.Xlo)
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| 356 |
/ static_cast<double>(energy.bins.size()) + energy.Xlo;
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| 357 |
double y = static_cast<double>(j)*(energy.Yhi - energy.Ylo)
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| 358 |
/ static_cast<double>(energy.bins[i].size()) + energy.Ylo;
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| 359 |
if (ngauss > 1) {
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// subtract integral of fit function
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| 361 |
try {
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| 362 |
int npval_other = r.pval.at(r.pval.size()-1).size();
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| 363 |
if (npval_other > 256) {
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| 364 |
cerr << "Parameter overload" << endl;
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| 365 |
return;
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| 366 |
}
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| 367 |
for (int k = 0; k < npval_other; k++) {
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| 368 |
pval_other[k] = r.pval[r.pval.size()-1][k];
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}
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| 370 |
ngauss--;
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| 371 |
double nu = fit_fcn(x, y, pval_other) * XbinSize * YbinSize;
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| 372 |
ngauss++;
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| 373 |
sub_energy[i][j] = energy.bins[i][j] - nu;
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}
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| 375 |
catch (exception ex) {
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| 376 |
cerr << "Exception in par_init" << endl;
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}
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}
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else {
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| 380 |
sub_energy[i][j] = energy.bins[i][j];
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}
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}
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}
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| 384 |
TH2D *hist_sub = new TH2D("hist_sub", "Subtracted histo",
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sub_energy.size(), energy.Xlo,
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energy.Xhi,
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sub_energy[0].size(), energy.Ylo,
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energy.Yhi);
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fill_histo_with_vec(hist_sub, sub_energy);
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| 390 |
max_sub = 0.0;
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| 391 |
max_x = 0.0;
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| 392 |
max_y = 0.0;
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| 393 |
for (int i = 1; i <= hist_sub->GetXaxis()->GetNbins(); i++) {
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| 394 |
for (int j = 1; j <= hist_sub->GetYaxis()->GetNbins(); j++) {
|
| 395 |
double nu = energy.bins[i-1][j-1] - sub_energy[i-1][j-1];
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| 396 |
if (hist_sub->GetBinContent(i, j)
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| 397 |
- 3.0*pow(chisquare_error(nu), 2.0) > max_sub) {
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| 398 |
max_sub = hist_sub->GetBinContent(i, j);
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| 399 |
max_x = static_cast<double>(i-1)*XbinSize
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| 400 |
+ hist_sub->GetXaxis()->GetXmin();
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| 401 |
max_y = static_cast<double>(j-1)*YbinSize
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| 402 |
+ hist_sub->GetYaxis()->GetXmin();
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| 403 |
}
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| 404 |
}
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| 405 |
}
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| 406 |
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| 407 |
for (int i = npar1; i < npar; i++) {
|
| 408 |
if (get_indiv_max_E() == i - npar1) {
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| 409 |
pval[i] = max_sub / XbinSize / YbinSize;
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| 410 |
perr[i] = mdef->chisquare_error(pval[i])*0.5;
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| 411 |
plo[i] = 0.0;
|
| 412 |
phi[i] = 1.0e6;
|
| 413 |
}
|
| 414 |
else if (get_indiv_max_x() == i - npar1) {
|
| 415 |
pval[i] = max_x;
|
| 416 |
perr[i] = (energy.Xhi - energy.Xlo) / static_cast<double>(hist->GetXaxis()->GetNbins());
|
| 417 |
plo[i] = 0.0;
|
| 418 |
phi[i] = 0.0;
|
| 419 |
}
|
| 420 |
else if (get_indiv_max_y() == i - npar1) {
|
| 421 |
pval[i] = max_y;
|
| 422 |
perr[i] = (energy.Yhi - energy.Ylo) / static_cast<double>(hist->GetYaxis()->GetNbins());
|
| 423 |
plo[i] = 0.0;
|
| 424 |
phi[i] = 0.0;
|
| 425 |
}
|
| 426 |
else {
|
| 427 |
string dummy;
|
| 428 |
get_indiv_par(i-npar1, dummy, pval[i], perr[i], plo[i], phi[i]);
|
| 429 |
}
|
| 430 |
}
|
| 431 |
}
|
| 432 |
int n_pars_to_set = init_spec_pars ? ngauss*get_formula()->GetNpar()
|
| 433 |
: npar - npar1;
|
| 434 |
int init_par_to_set = init_spec_pars ? 0 : npar1;
|
| 435 |
for (int i = 0; i < n_pars_to_set; i++) {
|
| 436 |
double dummy;
|
| 437 |
string s;
|
| 438 |
int ipar = i + init_par_to_set;
|
| 439 |
get_indiv_par(i % get_formula()->GetNpar(), s,
|
| 440 |
dummy, dummy, dummy, dummy);
|
| 441 |
ostringstream par_oss;
|
| 442 |
par_oss << s << ipar / (get_formula()->GetNpar()) << flush;
|
| 443 |
try {
|
| 444 |
pars.at(ipar) = TString(par_oss.str());
|
| 445 |
}
|
| 446 |
catch (exception ex) {
|
| 447 |
cerr << "exception 2 in par_init" << endl;
|
| 448 |
}
|
| 449 |
int error_flag;
|
| 450 |
try {
|
| 451 |
gMinuit->mnparm(ipar, pars.at(ipar),
|
| 452 |
pval[ipar], perr[ipar], plo[ipar], phi[ipar], error_flag);
|
| 453 |
} catch (exception ex) {
|
| 454 |
cerr << "exception 3 in par_init" << endl;
|
| 455 |
}
|
| 456 |
}
|
| 457 |
}
|
| 458 |
|
| 459 |
FitResults fit_histo(TH2 *hist, vector<trouble> &t_vec,
|
| 460 |
void (*cc_minuit)(TMinuit *, TH2 *, int),
|
| 461 |
int start_ngauss,
|
| 462 |
int rebinX, int rebinY,
|
| 463 |
double P_cutoff_val) {
|
| 464 |
TMinuit *gMinuit = new TMinuit();
|
| 465 |
int npar_indiv = mdef->get_formula()->GetNpar();
|
| 466 |
int istat, erflg;
|
| 467 |
FitResults r;
|
| 468 |
|
| 469 |
gMinuit->SetFCN(fcn);
|
| 470 |
gMinuit->mninit(5, 6, 7);
|
| 471 |
|
| 472 |
// set error def and machine accuracy
|
| 473 |
double cs_err_def = 1.0;
|
| 474 |
double fcn_eps = 0.2;
|
| 475 |
gMinuit->mnexcm("SET ERR", &cs_err_def, 1, erflg);
|
| 476 |
gMinuit->mnexcm("SET EPS", &fcn_eps, 1, erflg);
|
| 477 |
|
| 478 |
// rebin histogram
|
| 479 |
TH2 *hist_rebinned;
|
| 480 |
if (rebinX > 1 && rebinY > 1)
|
| 481 |
hist_rebinned = hist->Rebin2D(rebinX, rebinY);
|
| 482 |
else
|
| 483 |
hist_rebinned = hist;
|
| 484 |
|
| 485 |
r.hist_rebinned = hist_rebinned;
|
| 486 |
// load histogram into energies vector
|
| 487 |
energy.bins.resize(hist_rebinned->GetXaxis()->GetNbins());
|
| 488 |
for (int i = 0; i < energy.bins.size(); i++) {
|
| 489 |
energy.bins[i].resize(hist_rebinned->GetYaxis()->GetNbins());
|
| 490 |
for (int j = 0; j < energy.bins[i].size(); j++) {
|
| 491 |
energy.bins[i][j] = hist_rebinned->GetBinContent(i+1, j+1);
|
| 492 |
}
|
| 493 |
}
|
| 494 |
|
| 495 |
energy.Xlo = hist->GetXaxis()->GetXmin();
|
| 496 |
energy.Xhi = hist->GetXaxis()->GetXmax();
|
| 497 |
energy.Ylo = hist->GetYaxis()->GetXmin();
|
| 498 |
energy.Yhi = hist->GetYaxis()->GetXmax();
|
| 499 |
|
| 500 |
if (start_ngauss < 1) {
|
| 501 |
start_ngauss = 1;
|
| 502 |
}
|
| 503 |
|
| 504 |
for (mdef->set_ngauss(start_ngauss);
|
| 505 |
mdef->get_ngauss() <=
|
| 506 |
(MAX_GAUSS > start_ngauss ? MAX_GAUSS : start_ngauss);
|
| 507 |
mdef->set_ngauss(mdef->get_ngauss()+1)) {
|
| 508 |
|
| 509 |
int ngauss = mdef->get_ngauss();
|
| 510 |
t_vec.resize(t_vec.size() + 1);
|
| 511 |
int npar = npar_indiv*mdef->get_ngauss();
|
| 512 |
double pval[256], perr[256], plo[256], phi[256];
|
| 513 |
if (npar > 256) {
|
| 514 |
cerr << "Parameter overload" << endl;
|
| 515 |
return r;
|
| 516 |
}
|
| 517 |
vector<TString> pars(npar);
|
| 518 |
|
| 519 |
// initialize parameters
|
| 520 |
mdef->par_init(hist, gMinuit, pars, pval, perr, plo, phi, npar, r);
|
| 521 |
|
| 522 |
// minimize
|
| 523 |
double chisquare, edm, errdef;
|
| 524 |
int nvpar, nparx;
|
| 525 |
trouble t;
|
| 526 |
t.occ = T_NULL;
|
| 527 |
t.istat = 3;
|
| 528 |
// fix sigmas of the Gaussians
|
| 529 |
for (int i = 0; i < ngauss; i++) {
|
| 530 |
double parno[2];
|
| 531 |
parno[0] = i*npar_indiv + 4;
|
| 532 |
gMinuit->mnexcm("FIX", parno, 1, erflg);
|
| 533 |
}
|
| 534 |
gMinuit->mnexcm("SIMPLEX", 0, 0, erflg);
|
| 535 |
gMinuit->mnexcm("MIGRAD", 0, 0, erflg);
|
| 536 |
gMinuit->mnstat(chisquare, edm, errdef, nvpar, nparx, istat);
|
| 537 |
if (istat == 3) {
|
| 538 |
/* we're not concerned about MINOS errors right now
|
| 539 |
gMinuit->mnexcm("MINOS", 0, 0, erflg);
|
| 540 |
gMinuit->mnstat(chisquare, edm, errdef, nvpar, nparx, istat);
|
| 541 |
if (istat != 3) {
|
| 542 |
t.occ = T_MINOS;
|
| 543 |
t.istat = istat;
|
| 544 |
}
|
| 545 |
*/
|
| 546 |
}
|
| 547 |
else {
|
| 548 |
t.occ = T_MIGRAD;
|
| 549 |
t.istat = istat;
|
| 550 |
}
|
| 551 |
|
| 552 |
try {
|
| 553 |
if (t_vec.size() < ngauss) {
|
| 554 |
t_vec.resize(ngauss);
|
| 555 |
}
|
| 556 |
t_vec.at(ngauss-1) = t;
|
| 557 |
}
|
| 558 |
catch (exception ex) {
|
| 559 |
cerr << "exception in fit_histo" << endl;
|
| 560 |
}
|
| 561 |
|
| 562 |
// put parameters in map
|
| 563 |
for (int i = 0; i < npar && i < 256; i++) {
|
| 564 |
int iuint; // internal parameter number
|
| 565 |
gMinuit->mnpout(i, pars[i], pval[i], perr[i], plo[i], phi[i], iuint);
|
| 566 |
}
|
| 567 |
vector<double> pval_copy(npar);
|
| 568 |
vector<double> perr_copy(npar);
|
| 569 |
vector<double> plo_copy(npar);
|
| 570 |
vector<double> phi_copy(npar);
|
| 571 |
for (int i = 0; i < npar && i < 256; i++) {
|
| 572 |
pval_copy[i] = pval[i];
|
| 573 |
perr_copy[i] = perr[i];
|
| 574 |
plo_copy[i] = plo[i];
|
| 575 |
phi_copy[i] = phi[i];
|
| 576 |
}
|
| 577 |
r.pars.push_back(pars);
|
| 578 |
r.pval.push_back(pval_copy);
|
| 579 |
r.perr.push_back(perr_copy);
|
| 580 |
r.plo.push_back(plo_copy);
|
| 581 |
r.phi.push_back(phi_copy);
|
| 582 |
|
| 583 |
// execute user minuit code
|
| 584 |
if (cc_minuit != 0)
|
| 585 |
(*cc_minuit)(gMinuit, hist_rebinned, ngauss);
|
| 586 |
|
| 587 |
int ndof = 0;
|
| 588 |
if (!ignorezero)
|
| 589 |
ndof = energy.bins.size() * energy.bins[0].size();
|
| 590 |
else {
|
| 591 |
for (int i = 0; i < energy.bins.size(); i++) {
|
| 592 |
for (int j = 0; j < energy.bins[i].size(); j++) {
|
| 593 |
if (energy.bins[i][j] > 1.0e-30)
|
| 594 |
ndof++;
|
| 595 |
}
|
| 596 |
}
|
| 597 |
}
|
| 598 |
ndof -= npar;
|
| 599 |
|
| 600 |
r.chisquare.push_back(chisquare);
|
| 601 |
double P = TMath::Prob(chisquare, ndof);
|
| 602 |
if (P > P_cutoff_val) {
|
| 603 |
break;
|
| 604 |
}
|
| 605 |
}
|
| 606 |
|
| 607 |
delete gMinuit;
|
| 608 |
return r;
|
| 609 |
}
|
| 610 |
}
|
