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// $Id: Funcs.cc,v 1.3 2009/07/20 04:55:44 loizides Exp $
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#include "MitCommon/MathTools/interface/Funcs.h"
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#include <TF1.h>
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ClassImp(mithep::Funcs)
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using namespace mithep;
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::BreitGaus(Double_t x, Double_t m, Double_t mwidth, Double_t msig,
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Double_t fintf, Double_t xmin, Double_t xmax)
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{
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// Breit-Wigner convoluted with Gaussian.
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// Fit parameters:
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// m: Most probable location) Breit mean
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// mwidth: Width (scale) Breit-Wigner
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// msig: Width (sigma) of convoluted Gaussian function
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// fintf: interference fraction between Z and gamma
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// xmin: minimum x (for normalization)
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// xmax: maximum x (for normalization)
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// Numeric constants
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const Double_t invsq2pi = 0.3989422804014; //(2pi)^(-1/2)
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// Control constants
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const Double_t np = 300; // number of convolution steps
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const Double_t sc = 3.0; // convolution extends to +-sc Gaussian sigmas
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// Range of convolution integral
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const Double_t xlow = x - sc * msig;
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const Double_t xupp = x + sc * msig;
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const Double_t step = (xupp-xlow) / np;
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// Convolution integral of Breit and Gaussian by sum
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Double_t sum0 = 0.0;
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if (fintf<1) {
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for(Double_t i=1.0; i<=np/2; i++) {
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Double_t xx = xlow + (i-0.5) * step;
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Double_t fland = BreitWignerZ(xx,m,mwidth);
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sum0 += fland * TMath::Gaus(x,xx,msig);
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xx = xupp - (i-0.5) * step;
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fland = BreitWignerZ(xx,m,mwidth);
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sum0 += fland * TMath::Gaus(x,xx,msig);
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}
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sum0 = (step * sum0 * invsq2pi / msig);
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}
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Double_t sum1 = 0.0;
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if (fintf>0) {
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for(Double_t i=1.0; i<=np/2; i++) {
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Double_t xx = xlow + (i-0.5) * step;
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Double_t fland = BreitWignerGamma(xx,m,mwidth);
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sum1 += fland * TMath::Gaus(x,xx,msig);
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xx = xupp - (i-0.5) * step;
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fland = BreitWignerGamma(xx,m,mwidth);
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sum1 += fland * TMath::Gaus(x,xx,msig);
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}
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sum1 = (step * sum1 * invsq2pi / msig / (xmax-xmin));
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}
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return ((1.-fintf)*sum0+fintf*sum1);
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::BreitGaus(Double_t *x, Double_t *par)
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{
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// Breit-Wigner convoluted with Gaussian.
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// Fit parameters:
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// norm: Normalization factor
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// m: Most probable location) Breit mean
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// mwidth: Width (scale) Breit-Wigner
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// msig: Width (sigma) of convoluted Gaussian function
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// fintf: interference fraction between Z and gamma
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// xmin: minimum x (for normalization)
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// xmax: maximum x (for normalization)
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Double_t xx = x[0];
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Double_t norm = par[0];
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Double_t m = par[1];
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Double_t mwidth = par[2];
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Double_t msig = par[3];
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Double_t fintf = par[4];
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Double_t xmin = par[5];
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Double_t xmax = par[6];
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Double_t ret = norm * BreitGaus(xx, m, mwidth, msig, fintf, xmin, xmax);
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return ret;
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::BreitWignerZ(Double_t x, Double_t mean, Double_t gamma)
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{
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// Breit-Wigner for Z peak.
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Double_t bw = (gamma*mean*mean)/
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((x*x-mean*mean)*(x*x-mean*mean) + x*x*x*x*(gamma*gamma)/(mean*mean));
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return bw / (TMath::Pi()/2.0);
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::BreitWignerZ(Double_t *x, Double_t *par)
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{
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// Breit-Wigner for Z peak.
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Double_t xx = x[0];
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Double_t norm = par[0];
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Double_t mean = par[1];
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Double_t gamma = par[2];
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Double_t ret = norm * BreitWignerZ(xx,mean,gamma);
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return ret;
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::BreitWignerGamma(Double_t x, Double_t mean, Double_t gamma)
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{
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// Breit-Wigner for gamma interference.
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Double_t bw = ((x*x-mean*mean)*(x*x-mean*mean))/
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((x*x-mean*mean)*(x*x-mean*mean) + x*x*x*x*(gamma*gamma)/(mean*mean));
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return bw;
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::BreitWignerGamma(Double_t *x, Double_t *par)
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{
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// Breit-Wigner for gamma interference.
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Double_t xx = x[0];
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Double_t norm = par[0];
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Double_t mean = par[1];
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Double_t gamma = par[2];
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Double_t ret = norm * BreitWignerGamma(xx,mean,gamma);
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return ret;
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::ExpRange(Double_t mass, Double_t lambda, Double_t xmin, Double_t xmax)
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{
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// Probability of an exponential in a given interval.
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if (mass < xmin || mass > xmax)
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return 0.0;
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if (lambda == 0.0)
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return 1.0/(xmax-xmin);
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Double_t xmed = 0.5*(xmin+xmax);
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Double_t integ = lambda * TMath::Exp(-lambda*xmed) /
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(TMath::Exp(-lambda*xmin)-TMath::Exp(-lambda*xmax));
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return integ*TMath::Exp(-lambda*(mass-xmed));
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::ExpRange(Double_t *x, Double_t *par)
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{
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// Probability of an exponential in a given interval.
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Double_t xx = x[0];
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Double_t norm = par[0];
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Double_t lambda = par[1];
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Double_t xmin = par[2];
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Double_t xmax = par[3];
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Double_t ret = norm * ExpRange(xx,lambda,xmin,xmax);
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return ret;
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}
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//--------------------------------------------------------------------------------------------------
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Double_t Funcs::ZLineShapePlusBkg(Double_t *x, Double_t *par)
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{
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// Z line shape (BreitGaus) plus background (ExpRange).
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// Parameters:
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// 0: overall norm
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// 1: relative fraction of signal and background
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// 2: relative fraction of exponential and polynomial
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// 3: most probable location) Breit mean
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// 4: width (scale) Breit-Wigner
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// 5: width (sigma) of convoluted Gaussian function
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// 6: interference fraction between Z and gamma
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// 7: lambda of exponential
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// 8: minimum x (for normalization)
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// 9: maximum x (for normalization)
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Double_t xmin=par[8];
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Double_t xmax=par[9];
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Double_t s = (1.0 - par[1]) * BreitGaus(x[0], par[3], par[4], par[5], par[6], xmin, xmax);
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Double_t b = par[1] * ((1.0 - par[2]) * ExpRange(x[0], par[7], xmin, xmax) + par[2]/(xmax-xmin));
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return (s+b)*par[0];
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}
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//--------------------------------------------------------------------------------------------------
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TF1 *Funcs::CreateZLineShapePlusBkg(Double_t norm, Double_t xmin, Double_t xmax, const char *n)
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{
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// Create TF1 for Z line shape and background.
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TF1 *f = new TF1(n,mithep::Funcs::ZLineShapePlusBkg,xmin,xmax,10);
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f->SetParName(0,"norm");
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f->SetParName(1,"f_sb");
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f->SetParName(2,"f_eb");
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f->SetParName(3,"mass");
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f->SetParName(4,"width");
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f->SetParName(5,"gsig");
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f->SetParName(6,"f_int");
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f->SetParName(7,"lambda");
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f->SetParName(8,"min");
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f->SetParName(9,"max");
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f->SetParameters(norm,0.5,0.5,91,1,1,0.1,0.1,xmin,xmax);
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f->SetParLimits(0,0,1e6);
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f->SetParLimits(1,0,1);
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f->SetParLimits(2,0,1);
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f->SetParLimits(3,xmin,xmax);
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f->SetParLimits(4,0.1,5);
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f->SetParLimits(5,0.1,5);
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f->SetParLimits(6,0,1);
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f->SetParLimits(7,0,10);
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f->FixParameter(8,xmin);
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f->FixParameter(9,xmax);
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return f;
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}
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