def bkgfit(data_hist, bkgfunction, bkgname, doFloatZ=False, signal_hist=None, z_hist=None): isBkgPlusZFit = False isSpuriousFit = False binning = HistBinsToList(data_hist) data_x = HistToList(data_hist) data_error = HistErrorList(data_hist) z_x = [] signal_x = [] if z_hist != None: isBkgPlusZFit = True z_x = HistToList(z_hist) if signal_hist != None: isSpuriousFit = True signal_x = HistToList(signal_hist) parfunction = bkgfunction.GetNumberFreeParameters() partot = bkgfunction.GetNumberFreeParameters() + 2 ### the fucntion used for TMinuit def fcn(npar, gin, f, par, ifag): L = 0 # calculate likelihood, input par[0] is the N_B, par[1] is N_C, par[2] is N_L for ibin in range(len(binning)): if (data_x[ibin] < 0.5): continue bincen = binning[ibin] bkg = 0 data = data_x[ibin] if bkgname == "BernsteinO2": bkg = (par[0] * (1 - (bincen - fit_start) / fit_range)**2 + 2 * par[1] * (1 - (bincen - fit_start) / fit_range) * ((bincen - fit_start) / fit_range) + par[2] * ((bincen - fit_start) / fit_range)**2) if bkgname == "BernsteinO3": bkg = par[0] * (1 - ( (bincen - fit_start) / fit_range))**3 + par[1] * ( 3 * ((bincen - fit_start) / fit_range) * (1 - ((bincen - fit_start) / fit_range))**2) + par[2] * ( 3 * ((bincen - fit_start) / fit_range)**2 * (1 - ((bincen - fit_start) / fit_range))) + par[3] * ( (bincen - fit_start) / fit_range)**3 if bkgname == "BernsteinO4": bkg = par[0] * (1 - ( (bincen - fit_start) / fit_range))**4 + par[1] * ( 4 * ((bincen - fit_start) / fit_range) * (1 - ((bincen - fit_start) / fit_range))**3) + par[2] * ( 6 * ((bincen - fit_start) / fit_range)**2 * (1 - ((bincen - fit_start) / fit_range))**2 ) + par[3] * ( 4 * ((bincen - fit_start) / fit_range)**3 * (1 - ((bincen - fit_start) / fit_range))) + par[4] * ( (bincen - fit_start) / fit_range)**4 if bkgname == "BernsteinO5": bkg = par[0] * (1 - ( (bincen - fit_start) / fit_range))**5 + par[1] * (5 * ( (bincen - fit_start) / fit_range) * (1 - ( (bincen - fit_start) / fit_range))**4) + par[2] * ( 10 * ((bincen - fit_start) / fit_range)**2 * (1 - ((bincen - fit_start) / fit_range))**3 ) + par[3] * (10 * ( (bincen - fit_start) / fit_range)**3 * (1 - ( (bincen - fit_start) / fit_range ))**2) + par[4] * (5 * ( (bincen - fit_start) / fit_range)**4 * (1 - ((bincen - fit_start) / fit_range))) + par[5] * ( (bincen - fit_start) / fit_range)**5 if bkgname == "BernsteinO6": bkg = (par[0] * (1 - ((bincen - fit_start) / fit_range))**6 + par[1] * (6 * ((bincen - fit_start) / fit_range)**1 * (1 - ((bincen - fit_start) / fit_range))**5) + par[2] * (15 * ((bincen - fit_start) / fit_range)**2 * (1 - ((bincen - fit_start) / fit_range))**4) + par[3] * (20 * ((bincen - fit_start) / fit_range)**3 * (1 - ((bincen - fit_start) / fit_range))**3) + par[4] * (15 * ((bincen - fit_start) / fit_range)**4 * (1 - ((bincen - fit_start) / fit_range))**2) + par[5] * (6 * ((bincen - fit_start) / fit_range)**5 * (1 - ((bincen - fit_start) / fit_range))**1) + par[6] * ((bincen - fit_start) / fit_range)**6) if bkgname == "ExpoBernsteinO2": try: bkg = exp(par[0] * (bincen - fit_start) / fit_range) * ( par[1] * (1 - (bincen - fit_start) / fit_range)**2 + 2 * par[2] * (1 - (bincen - fit_start) / fit_range) * ((bincen - fit_start) / fit_range) + par[3] * ((bincen - fit_start) / fit_range)**2) except OverflowError: bkg = 0 if bkgname == "ExpoBernsteinO3": try: bkg = exp(par[0] * (bincen - fit_start) / fit_range) * ( par[1] * (1 - ((bincen - fit_start) / fit_range))**3 + par[2] * (3 * ((bincen - fit_start) / fit_range) * (1 - ((bincen - fit_start) / fit_range))**2) + par[3] * (3 * ((bincen - fit_start) / fit_range)**2 * (1 - ((bincen - fit_start) / fit_range))) + par[4] * ((bincen - fit_start) / fit_range)**3) except OverflowError: bkg = 0 if bkgname == "ExpoBernsteinO4": try: bkg = exp(par[0] * (bincen - fit_start) / fit_range) * ( par[1] * (1 - ((bincen - fit_start) / fit_range))**4 + par[2] * (4 * ((bincen - fit_start) / fit_range) * (1 - ((bincen - fit_start) / fit_range))**3) + par[3] * (6 * ((bincen - fit_start) / fit_range)**2 * (1 - ((bincen - fit_start) / fit_range))**2) + par[4] * (4 * ((bincen - fit_start) / fit_range)**3 * (1 - ((bincen - fit_start) / fit_range))) + par[5] * ((bincen - fit_start) / fit_range)**4) except OverflowError: bkg = 0 if bkgname == "ExpoBernsteinO5": try: bkg = exp(par[0] * (bincen - fit_start) / fit_range) * ( par[1] * (1 - ((bincen - fit_start) / fit_range))**5 + par[2] * (5 * ((bincen - fit_start) / fit_range) * (1 - ((bincen - fit_start) / fit_range))**4) + par[3] * (10 * ((bincen - fit_start) / fit_range)**2 * (1 - ((bincen - fit_start) / fit_range))**3) + par[4] * (10 * ((bincen - fit_start) / fit_range)**3 * (1 - ((bincen - fit_start) / fit_range))**2) + par[5] * (5 * ((bincen - fit_start) / fit_range)**4 * (1 - ((bincen - fit_start) / fit_range))) + par[6] * ((bincen - fit_start) / fit_range)**5) except OverflowError: bkg = 0 if bkgname == "ExpoPolO2": bkg = exp(-(par[0] + par[1] * ((bincen - fit_start) / fit_range) + par[2] * ((bincen - fit_start) / fit_range)**2)) if bkgname == "ExpoPolO3": bkg = exp(-(par[0] + par[1] * ((bincen - fit_start) / fit_range) + par[2] * ((bincen - fit_start) / fit_range)**2 + par[3] * ((bincen - fit_start) / fit_range)**3)) if bkgname == "ExpoPolO4": bkg = exp(-(par[0] + par[1] * ((bincen - fit_start) / fit_range) + par[2] * ((bincen - fit_start) / fit_range)**2 + par[3] * ((bincen - fit_start) / fit_range)**3 + par[4] * ((bincen - fit_start) / fit_range)**4)) mu_x = bkg #if isBkgPlusZFit: # mu_x = mu_x + (par[partot-1] *z_x[ibin]) if isSpuriousFit: mu_x = mu_x + par[partot - 2] * signal_x[ibin] #L = L + mu_x - data*log(mu_x) L = L + ((mu_x - data) / data_error[ibin])**2 f[0] = L # initialize the TMinuit object arglist_p = 10 * [0] arglist = array.array('d') arglist.fromlist(arglist_p) ierflag = Long(0) maxiter = 1000000000 arglist_p = [1] gMinuit = TMinuit(partot) gMinuit.mnexcm('SET PRIntout', arglist, 0, ierflag) gMinuit.SetPrintLevel(1) gMinuit.SetErrorDef(1.0) gMinuit.SetFCN(fcn) arglist_p = [2] arglist = array.array('d') arglist.fromlist(arglist_p) gMinuit.mnexcm('SET STRategy', arglist, 1, ierflag) arglist_p = [maxiter, 0.0000001] arglist = array.array('d') arglist.fromlist(arglist_p) gMinuit.mnexcm('MIGrad', arglist, 2, ierflag) gMinuit.SetMaxIterations(maxiter) # initialize fitting the variables vstart = [100.0] * partot # start alpha_z with 1 vstart[partot - 1] = 1.0 vstart[partot - 2] = 0 step = [0.1] * partot upper = [100000] * partot lower = [0.1] * partot varname = [] if "ExpoPol" in bkgname: upper = [1000] * partot lower = [-1000] * partot if "ExpoBernstein" in bkgname: vstart[0] = -1 upper[0] = 0 lower[0] = -10 for i in range(parfunction): varname.append("p" + str(i)) varname.append("alpha_sig") varname.append("alpha_z") if doFloatZ: vstart[partot - 1] = 1.0 upper[partot - 1] = 2 lower[partot - 1] = 0 step[partot - 1] = 0.01 if isSpuriousFit: upper[partot - 2] = 10.0 lower[partot - 2] = -10.0 step[partot - 2] = 0.1 vstart[partot - 2] = 1 for i in range(partot): gMinuit.mnparm(i, varname[i], vstart[i], step[i], lower[i], upper[i], ierflag) if not isSpuriousFit: vstart[partot - 2] = 0 gMinuit.FixParameter(partot - 2) if not doFloatZ: lower[partot - 1] = 1 upper[partot - 1] = 1 gMinuit.FixParameter(partot - 1) if not isBkgPlusZFit: vstart[partot - 1] = 0.0 gMinuit.FixParameter(partot - 1) # fitting procedure migradstat = gMinuit.Command('MIGrad ' + str(maxiter) + ' ' + str(0.001)) improvestat = gMinuit.Command('IMProve ' + str(maxiter) + ' ' + str(0.01)) for i in range(partot): arglist_p.append(i + 1) arglist = array.array('d') arglist.fromlist(arglist_p) #gMinuit.mnmnos() # get fitting parameters fitval_p = [Double(0)] * partot fiterr_p = [Double(0)] * partot errup_p = [Double(0)] * partot errdown_p = [Double(0)] * partot eparab_p = [Double(0)] * partot gcc_p = [Double(0)] * partot fmin_p = [Double(0)] fedm_p = [Double(0)] errdef_p = [Double(0)] npari_p = Long(0) nparx_p = Long(0) istat_p = Long(0) fitval = array.array('d') fiterr = array.array('d') errup = array.array('d') errdown = array.array('d') eparab = array.array('d') gcc = array.array('d') for i in range(partot): gMinuit.GetParameter(i, fitval_p[i], fiterr_p[i]) fitval.append(fitval_p[i]) fiterr.append(fiterr_p[i]) errup.append(errup_p[i]) errdown.append(errdown_p[i]) eparab.append(eparab_p[i]) gcc.append(gcc_p[i]) gMinuit.mnstat(fmin_p[0], fedm_p[0], errdef_p[0], npari_p, nparx_p, istat_p) for p in range(bkgfunction.GetNumberFreeParameters()): bkgfunction.SetParameter(p, fitval[p]) print "fit uncert", fiterr_p[p] bkgfunction.SetChisquare(fmin_p[0]) return fitval[partot - 1], fitval[partot - 2]
class minuitSolver(): def __init__(self, fcn, pars, parerrors, parnames, ndof, maxpars=50): if len(pars) > maxpars: raise MinuitError("More than 50 parameters, increase maxpars") self.__minuit = TMinuit(maxpars) self.minuitCommand("SET PRI -1") # Hold on to fcn or python will kill it after passing to TMinuit self.__fcn = fcn self.__minuit.SetFCN(fcn) self.__pars = pars self.__parerrors = parerrors self.__parnames = parnames self.__setParameters() self.__ndof = ndof return def __setParameters(self): for par, parerror, parname, i in zip(self.__pars, self.__parerrors, self.__parnames, range(len(self.__pars))): ierflg = self.__minuit.DefineParameter(i, parname, par, parerror, 0.0, 0.0) if ierflg != 0: message = "Minuit define parameter error: " + str(ierflg) raise MinuitError(message) return def minuitCommand(self, command): errorcode = self.__minuit.Command(command) if errorcode != 0: message = "Minuit command " + command + " failed: " + str( errorcode) raise MinuitError(message) return def solve(self, lBlobel=True): self.__setParameters() self.minuitCommand("MIGRAD") return def getChisq(self): hstat = self.__getStat() return hstat["min"] def getNdof(self): return self.__ndof def __printPars(self, par, parerrors, parnames, ffmt=".4f"): for ipar in range(len(par)): name = parnames[ipar] print("{0:>15s}:".format(name), end=" ") fmtstr = "{0:10" + ffmt + "} +/- {1:10" + ffmt + "}" print(fmtstr.format(par[ipar], parerrors[ipar])) return def printResults(self, ffmt=".4f", cov=False, corr=False): print("\nMinuit least squares") print("\nResults after minuit fit") hstat = self.__getStat() chisq = hstat["min"] ndof = self.__ndof fmtstr = "\nChi^2= {0:" + ffmt + "} for {1:d} d.o.f, Chi^2/d.o.f= {2:" + ffmt + "}, P-value= {3:" + ffmt + "}" print( fmtstr.format(chisq, ndof, chisq / float(ndof), TMath.Prob(chisq, ndof))) fmtstr = "Est. dist. to min: {0:.3e}, minuit status: {1}" print(fmtstr.format(hstat["edm"], hstat["status"])) print("\nFitted parameters and errors") print(" Name Value Error") pars = self.getPars() parerrors = self.getParErrors() self.__printPars(pars, parerrors, self.__parnames, ffmt=ffmt) if cov: self.printCovariances() if corr: self.printCorrelations() return def __printMatrix(self, m, ffmt): mshape = m.shape print("{0:>10s}".format(""), end=" ") for i in range(mshape[0]): print("{0:>10s}".format(self.__parnames[i]), end=" ") print() for i in range(mshape[0]): print("{0:>10s}".format(self.__parnames[i]), end=" ") for j in range(mshape[1]): fmtstr = "{0:10" + ffmt + "}" print(fmtstr.format(m[i, j]), end=" ") print() return def printCovariances(self): print("\nCovariance matrix:") self.__printMatrix(self.getCovariancematrix(), ".3e") return def printCorrelations(self): print("\nCorrelation matrix:") self.__printMatrix(self.getCorrelationmatrix(), ".3f") return def getPars(self): pars, parerrors = self.__getPars() return pars def getUparv(self): pars = self.getPars() parv = matrix(pars) parv.shape = (len(pars), 1) return parv def getParErrors(self): pars, parerrors = self.__getPars() return parerrors def __getPars(self): pars = [] parerrors = [] for ipar in range(len(self.__pars)): par = c_double() pare = c_double() ivarbl = self.__minuit.GetParameter(ipar, par, pare) if ivarbl < 0: message = "Parameter " + str(ipar) + " not defined" raise MinuitError(message) pars.append(par.value) parerrors.append(pare.value) return pars, parerrors def getCovariancematrix(self): npar = len(self.__pars) covm = array(npar**2 * [0.0], dtype="double") self.__minuit.mnemat(covm, npar) covm.shape = (npar, npar) return covm def getCorrelationmatrix(self): covm = self.getCovariancematrix() corrm = covm.copy() npar = len(self.__pars) for i in range(npar): for j in range(npar): corrm[i, j] = covm[i, j] / sqrt(covm[i, i] * covm[j, j]) return corrm def __getStat(self): fmin = c_double() fedm = c_double() errdef = c_double() npari = c_int() nparx = c_int() istat = c_int() self.__minuit.mnstat(fmin, fedm, errdef, npari, nparx, istat) hstat = { "min": fmin.value, "edm": fedm.value, "errdef": errdef.value, "npari": npari.value, "nparx": nparx.value, "status": istat.value } return hstat