def _recreate_gMinuit(self):
self.__gMinuit = TMinuit(self.num_pars)
self.__gMinuit.SetPrintLevel(-1)
self.__gMinuit.mncomd("SET STRATEGY {}".format(self._strategy),
ctypes.c_int(0))
self.__gMinuit.SetFCN(self._minuit_fcn)
self.__gMinuit.SetErrorDef(self._err_def)
# set gMinuit parameters
error_code = ctypes.c_int(0)
for _pid, (_pn, _pv, _pe) in enumerate(
zip(self._par_names, self._par_val, self._par_err)):
self.__gMinuit.mnparm(_pid, _pn, _pv, 0.1 * _pe, 0, 0, error_code)
err_code = ctypes.c_int(0)
# set fixed parameters
for _par_id, _pf in enumerate(self._par_fixed):
if _pf:
self.__gMinuit.mnfixp(_par_id, err_code)
# set parameter limits
for _par_id, _pb in enumerate(self._par_bounds):
if _pb is not None:
_lo_lim, _up_lim = _pb
self.__gMinuit.mnexcm(
"SET LIM", arr('d', [_par_id + 1, _lo_lim, _up_lim]), 3,
error_code)
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" )
self.__minuit.SetFCN( fcn )
self.__pars= pars
self.__parerrors= parerrors
self.__parnames= parnames
self.__setParameters()
self.__ndof= ndof
return
def __init__(self, myFCN, params, **kwargs):
from ROOT import TMinuit, Long, Double
self.limits = np.zeros((len(params), 2))
self.steps = .04 * np.ones(
len(params)) # about 10 percent in log10 space
self.tolerance = .001
self.maxcalls = 10000
self.printMode = 0
self.up = 0.5
self.param_names = ['p%i' % i for i in xrange(len(params))]
self.erflag = Long()
self.npars = len(params)
self.args = ()
self.gradient = None
self.force_gradient = 0
self.strategy = 1
self.fixed = np.zeros_like(params)
self.__dict__.update(kwargs)
self.params = np.asarray(params, dtype='float')
self.fixed = np.asarray(self.fixed, dtype=bool)
self.fcn = FCN(myFCN,
self.params,
args=self.args,
gradient=self.gradient)
self.fval = self.fcn.fval
self.minuit = TMinuit(self.npars)
self.minuit.SetPrintLevel(self.printMode)
self.minuit.SetFCN(self.fcn)
if self.gradient:
self.minuit.mncomd('SET GRA %i' % (self.force_gradient),
self.erflag)
self.minuit.mncomd('SET STR %i' % self.strategy, Long())
for i in xrange(self.npars):
if self.limits[i][0] is None: self.limits[i][0] = 0.0
if self.limits[i][1] is None: self.limits[i][1] = 0.0
self.minuit.DefineParameter(i, self.param_names[i], self.params[i],
self.steps[i], self.limits[i][0],
self.limits[i][1])
self.minuit.SetErrorDef(self.up)
for index in np.where(self.fixed)[0]:
self.minuit.FixParameter(int(index))
def fit(self):
numberOfParameters = len(self.samples)
gMinuit = TMinuit(numberOfParameters)
if self.method == "logLikelihood": # set function for minimisation
gMinuit.SetFCN(self.logLikelihood)
gMinuit.SetPrintLevel(-1)
# Error definition: 1 for chi-squared, 0.5 for negative log likelihood
gMinuit.SetErrorDef(1)
# error flag for functions passed as reference.set to as 0 is no error
errorFlag = Long(2)
N_total = self.normalisation[self.data_label] * 2
N_min = 0
param_index = 0
for sample in self.samples: # all samples but data
gMinuit.mnparm(param_index, sample, self.normalisation[sample], 10.0, N_min, N_total, errorFlag)
param_index += 1
# N_signal = self.normalisation['signal']
# gMinuit.mnparm(0, "N_signal(ttbar+single_top)", N_signal, 10.0, N_min, N_total, errorFlag)
# gMinuit.mnparm(1, "bkg1", 10, 10.0, N_min, N_total, errorFlag)
arglist = array("d", 10 * [0.0])
# minimisation strategy: 1 standard, 2 try to improve minimum (a bit slower)
arglist[0] = 2
# minimisation itself
gMinuit.mnexcm("SET STR", arglist, 1, errorFlag)
gMinuit.Migrad()
self.module = gMinuit
self.performedFit = True
if not self.module:
raise Exception("No fit results available. Please run fit method first")
results = {}
param_index = 0
for sample in self.samples:
temp_par = Double(0)
temp_err = Double(0)
self.module.GetParameter(param_index, temp_par, temp_err)
if math.isnan(temp_err):
self.logger.warning("Template fit error is NAN, setting to sqrt(N).")
temp_err = math.sqrt(temp_par)
results[sample] = (temp_par, temp_err)
param_index += 1
self.results = results
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 __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" )
self.__minuit.SetFCN( fcn )
self.__pars= pars
self.__parerrors= parerrors
self.__parnames= parnames
self.__setParameters()
self.__ndof= ndof
return
def __init__(self,myFCN,params,**kwargs):
from ROOT import TMinuit,Long,Double
self.limits = np.zeros((len(params),2))
self.steps = .04*np.ones(len(params)) # about 10 percent in log10 space
self.tolerance = .001
self.maxcalls = 10000
self.printMode = 0
self.up = 0.5
self.param_names = ['p%i'%i for i in xrange(len(params))]
self.erflag = Long()
self.npars = len(params)
self.args = ()
self.gradient = None
self.force_gradient = 0
self.strategy = 1
self.fixed = np.zeros_like(params)
self.__dict__.update(kwargs)
self.params = np.asarray(params,dtype='float')
self.fixed=np.asarray(self.fixed,dtype=bool)
self.fcn = FCN(myFCN,self.params,args=self.args,gradient=self.gradient)
self.fval = self.fcn.fval
self.minuit = TMinuit(self.npars)
self.minuit.SetPrintLevel(self.printMode)
self.minuit.SetFCN(self.fcn)
if self.gradient:
self.minuit.mncomd('SET GRA %i'%(self.force_gradient),self.erflag)
self.minuit.mncomd('SET STR %i'%self.strategy,Long())
for i in xrange(self.npars):
if self.limits[i][0] is None: self.limits[i][0] = 0.0
if self.limits[i][1] is None: self.limits[i][1] = 0.0
self.minuit.DefineParameter(i,self.param_names[i],self.params[i],self.steps[i],self.limits[i][0],self.limits[i][1])
self.minuit.SetErrorDef(self.up)
for index in np.where(self.fixed)[0]:
self.minuit.FixParameter(int(index))
def fit_mu(self, background, signal):
myMinuit = TMinuit(self.npar)
myMinuit.SetFCN(self.fcn)
gMinuit.Command('SET PRINT -1')
ierflg = Long(0)
myMinuit.mnparm(0, 'mu', self.start_value_mu, self.init_step_mu, self.min_mu, self.max_mu, ierflg)
arglist = array('d', (0, 0))
arglist[0] = self.max_iterations
arglist[1] = self.tolerance
myMinuit.mnexcm("MINIMIZE", arglist, 2, ierflg)
# check TMinuit status
amin, edm, errdef = Double(0.), Double(0.), Double(0.)
nvpar, nparx, icstat = Long(0), Long(0), Long(0)
myMinuit.mnstat(amin, edm, errdef, nvpar, nparx, icstat)
# get final results
p, pe = Double(0), Double(0)
myMinuit.GetParameter(0, p, pe)
# finalPar = float(p)
# finalParErr = float(pe)
# print_banner('MINUIT fit completed:')
# print ' fcn@minimum = %.3g' %(amin)," error code =", ierflg, " status =", icstat
# print " Results: \t value error"
# print ' %s: \t%10.3e +/- %.1e '%('mu', finalPar, finalParErr)
return p
# --- fcn -- called by MINUIT repeatedly with varying parameters
# NOTE: the function name is set via TMinuit.SetFCN
def fcn(npar, deriv, f, apar, iflag):
""" meaning of parameters:
npar: # of parameters
deriv: array of derivatives df/dp_i(x), optional
f: value of function to be minimised (typically chi2 or negLogL)
apar: the array of parameters
iflag: internal flag: 1 at first call, 3 at the last, 4 during
minimisation
"""
f[0] = calcChi2(npar, apar)
# --> set up MINUIT
myMinuit = TMinuit(npar) # initialize TMinuit with maximum of npar parameters
myMinuit.setFCN(fcn) # set func to minimize
arglist = arr('d', 2*[0.01])# set error definition
ieflg = Long(0)
arglist[0] = 1. # 1 sigma is Delta chi^2 = 1
myMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
#−−>Set starting values and step sizes for parameters
for i in range(0, npar):
#Define the parameters for the fit
myMinuit.mnparm(i, name[i], vstart[i], step[i], 0, 0, ierflg)
arglist[0] = 6000 # Number of calls to FCN before giving up.
arglist[1] = 0.3 # Tolerance
def run_mass_fit(self, peak_scale_initial, mass=0):
self.gMinuit = TMinuit(30)
self.gMinuit.SetPrintLevel(-1)
self.gMinuit.SetFCN(self.Fitfcn_max_likelihood)
arglist = array("d", [
0,
] * 10)
ierflg = ROOT.Long(0)
arglist[0] = ROOT.Double(1)
# peak_scale_initial = ROOT.Double(peak_scale_initial)
tmp = array("d", [
0,
])
self.gMinuit.mnexcm("SET NOWarnings", tmp, 0, ierflg)
self.gMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
self.gMinuit.mnparm(0, "p1", 5e-6, 1e-7, 0, 0, ierflg)
self.gMinuit.mnparm(1, "p2", 10, 10, 0, 0, ierflg)
self.gMinuit.mnparm(2, "p3", -5.3, 1, 0, 0, ierflg)
self.gMinuit.mnparm(3, "p4", -4e-2, 1e-2, 0, 0, ierflg)
self.gMinuit.mnparm(4, "p5", peak_scale_initial,
peak_scale_initial / 50, 0, 0, ierflg)
self.background_fit_only = [
0,
] * len(self.data)
arglist[0] = ROOT.Double(0)
arglist[1] = ROOT.Double(0)
#self.exclude_regions = ((2.2, 3.3),)
self.gMinuit.FixParameter(2)
self.gMinuit.FixParameter(3)
self.gMinuit.FixParameter(4)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
self.gMinuit.Release(2)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
self.gMinuit.Release(3)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
# Find an actual best fit
#self.exclude_regions = ((0, 2), (3.3, 100),)
self.gMinuit.FixParameter(0)
self.gMinuit.FixParameter(1)
self.gMinuit.FixParameter(2)
self.gMinuit.FixParameter(3)
self.gMinuit.Release(4)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
self.exclude_regions = ()
self.gMinuit.Release(0)
self.gMinuit.Release(1)
self.gMinuit.Release(2)
self.gMinuit.Release(3)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
best_fit_value = ROOT.Double(0)
self.gMinuit.mnstat(best_fit_value, ROOT.Double(0), ROOT.Double(0),
ROOT.Long(0), ROOT.Long(0), ROOT.Long(0))
#print("Best fit value", best_fit_value)
# And prepare for iterating over fit values for N injected events
self.gMinuit.Release(0)
self.gMinuit.Release(1)
self.gMinuit.Release(2)
self.gMinuit.Release(3)
self.exclude_regions = ()
#self.data_fits = no_peak_data_fits
x_values = []
y_values = []
fitted_N = ROOT.Double(0)
self.gMinuit.GetParameter(4, fitted_N, ROOT.Double(0))
best_fit_likelihood = self.calc_likelihood(fitted_N)
step = 5
if int(mass) >= 4000:
step = 1
if int(mass) >= 5000:
step = 0.2
if int(mass) >= 6000:
step = 0.1
if int(mass) >= 6500:
step = 0.05
N = 0
while N < 5000:
start_sum = sum([math.exp(-a) for a in y_values])
fit_likelihood = self.calc_likelihood(N)
x_values.append(N)
y_values.append(fit_likelihood - best_fit_likelihood)
probabilities = [math.exp(-a) for a in y_values]
end_sum = sum(probabilities)
max_prob = max(probabilities)
normalised_probabilities = [a / max_prob for a in probabilities]
if N / step > 50 and all(
[v > 0.99 for v in normalised_probabilities]):
print(
"Probability=1 everywhere, probably something wrong with fit"
)
print(normalised_probabilities)
return None, None
# if new value changes total by less than 0.1%, end loop
if N > 0 and (end_sum - start_sum) / start_sum < 0.0001:
print("Iterated up to {0}".format(N))
break
N += step
self.iflag = int(ierflg)
return x_values, y_values
def main():
#The first part of the script is to input the root files#
canvas = TCanvas("Canvas_d", "Canvas_d", 533, 76, 1383, 852)
input_datafile = TFile(args["input_data"])
EV_data = input_datafile.Get("EventCategorizer subtask 0 stats/ExpecValue")
entries_data = EV_data.GetSize()
print "# of Entries in Data file:", entries_data
print "Experimental Data Inputed"
data_arr = []
canvas = TCanvas("Canvas_mc", "Canvas_mc", 533, 76, 1383, 852)
input_mcfile = TFile(args["input_mc"])
EV_mc = input_mcfile.Get(
"EventCategorizer subtask 0 stats/ExpecValue_Smeared")
entries_mc = EV_mc.GetSize()
print "# of Entries in MC file:", entries_mc
print "MC Data Inputed"
mc_arr = []
bin_arr = []
for x in range(entries_data):
Data_i = EV_data.GetBinContent(x)
MC_i = EV_mc.GetBinContent(x)
data_arr.append(Data_i)
mc_arr.append(MC_i)
Bin_i = EV_data.GetBinCenter(x)
bin_arr.append(Bin_i)
#print Data_i
#print MC_i
#print data_arr
#print mc_arr
#print bin_arr
# --> Set parameters and function to f i t
name = ["c", "d"] #variable names
vstart = arr('d', (1.0, 1.0)) #the initial values
step = arr('d', (0.001, 0.001)) #the initial step size
npar = len(name)
# --> Defining the Chi-Square function to be minimized#
def Chi_Induced(Data, MC, BinCenter, C, D):
chi = 0.
for i in range(0, entries_data):
#num1 = Data[i]
#num2 = D*((1-(C*BinCenter[i]))*MC[i])
#num = (num1 - num2)**2
#num = 0.
#den1 = ((Data[i])**(1/2))**2
#den2 = (D*((1-(C*BinCenter[i])))*((MC[i])**(1/2)))**2
num = 2
den = 2
#den = den1 + den2
chi = chi + num / den
return chi
# --> set up MINUIT
myMinuit = TMinuit(
npar) # initialize TMinuit with maximum of npar parameters
myMinuit.SetFCN(Chi_Induced) # set function to minimize
ierflg = Long(0)
arglist = arr('d', 2 * [0.01]) # set error definition
arglist[0] = 6000 # Number of calls for FCN before gving up
arglist[1] = 0.3 # Toleranceierflg = Long(0)
myMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
for i in range(0, npar):
myMinuit.mnparm(i, name[i], vstart[i], step[i], 0, 0, ierflg)
myMinuit.mnexcm("MIGRAD", arglist, 1, ierflg) # execute the minimisation
# --> check TMinuit status
amin, edm, errdef = Double(0.), Double(0.), Double(0.)
nvpar, nparx, icstat = Long(0), Long(0), Long(0)
myMinuit.mnstat(amin, edm, errdef, nvpar, nparx, icstat)
def signalfit(data_hist, signalfunction, signalname):
binning = HistBinsToList(data_hist)
data_x = HistToList(data_hist)
data_error = HistErrorList(data_hist)
parfunction = signalfunction.GetNumberFreeParameters()
partot = signalfunction.GetNumberFreeParameters()
print partot
### 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):
# continue
bincen = binning[ibin]
mu_x = 0
data = data_x[ibin]
if data_error[ibin] == 0:
continue
#if data<0.1:
# continue
if signalname == "CrystalBall":
if par[3] < 0:
mu_x = 0
else:
t = (bincen - par[2]) / (par[3])
if (par[0] < 0):
t = -t
absAlpha = abs(par[0])
if (t >= -absAlpha):
mu_x = par[4] * exp(-0.5 * t * t)
else:
nDivAlpha = par[1] / absAlpha
AA = exp(-0.5 * absAlpha * absAlpha)
B = nDivAlpha - absAlpha
arg = nDivAlpha / (B - t)
mu_x = par[4] * (arg**par[1])
if signalname == "CrystalBallGaus":
if par[3] < 0:
mu_x = 0
else:
t = (bincen - par[2]) / (par[3])
if (par[0] < 0):
t = -t
absAlpha = abs(par[0])
if (t >= -absAlpha):
mu_x = par[4] * exp(-0.5 * t * t +
exp(-(bincen - par[5])**2 /
(2 * par[6]**2)))
else:
nDivAlpha = par[1] / absAlpha
AA = exp(-0.5 * absAlpha * absAlpha)
B = nDivAlpha - absAlpha
arg = nDivAlpha / (B - t)
mu_x = par[4] * (arg**par[1] +
exp(-(bincen - par[5])**2 /
(2 * par[6]**2)))
#print mu_x, data, data_error[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 = [125.0] * partot
step = [0.1] * partot
upper = [1000000] * partot
lower = [-100] * partot
varname = []
lower[3] = 0
lower[4] = 0
lower[1] = 0
vstart[3] = data_hist.GetRMS()
lower[3] = data_hist.GetRMS() / 3.0
upper[3] = data_hist.GetRMS() * 3.0
vstart[3] = 125
lower[3] = 5
upper[3] = 20
vstart[4] = data_hist.Integral()
vstart[2] = data_hist.GetMean()
lower[2] = data_hist.GetMean() - 10
upper[2] = data_hist.GetMean() + 10
vstart[2] = 125
lower[2] = 110
upper[2] = 130
if len(vstart) > 5:
vstart[5] = data_hist.GetMean()
lower[5] = data_hist.GetMean() - 10
upper[5] = data_hist.GetMean() + 10
vstart[5] = 125
lower[5] = 110
upper[5] = 150
#vstart[6] = data_hist.GetRMS()
#lower[6] = data_hist.GetRMS()/3.0
#upper[6] = data_hist.GetRMS()*3.0
vstart[6] = 10
lower[6] = 5
upper[6] = 20
for i in range(parfunction):
varname.append("p" + str(i))
for i in range(partot):
gMinuit.mnparm(i, varname[i], vstart[i], step[i], lower[i], upper[i],
ierflag)
# 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(signalfunction.GetNumberFreeParameters()):
signalfunction.SetParameter(p, fitval[p])
print "fit uncert", fiterr_p[p]
signalfunction.SetChisquare(fmin_p[0])
print fmin_p[0]
return fitval[partot - 1], fitval[partot - 2]
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]
def runMinuit(numParameters):
minuit = TMinuit(numParameters)
minuit.SetPrintLevel(0)
minuit.SetFCN(fcn)
arglist = np.zeros(numParameters) + 0.01
internalFlag, arglist[0] = Long(0), 0.5
minuit.mnexcm("SET ERR", arglist, 1, internalFlag)
initialValues = np.zeros(numParameters) + 0.01
steps = np.zeros(numParameters) + 0.0001
for i in xrange(numParameters):
name = "epsilon%s" % i
minuit.mnparm(i, name, initialValues[i], steps[i], 0, 1, internalFlag)
# arglist[0] = 2
# minuit.mnexcm("SET STR", arglist, 1, internalFlag)
arglist[0], arglist[1] = 10000, 0.1
minuit.mnexcm("SIMPLEX", arglist, 1, internalFlag)
minuit.mnexcm("MIGRAD", arglist, 1, internalFlag)
print "FIT STATUS is " +str(minuit.GetStatus())
return ratesAndErrors(numParameters, minuit)
class MinimizerROOTTMinuit(MinimizerBase):
def __init__(self,
parameter_names,
parameter_values,
parameter_errors,
function_to_minimize,
tolerance=1e-9,
errordef=MinimizerBase.ERRORDEF_CHI2,
strategy=1):
self._strategy = strategy
self._par_bounds = np.array([None] * len(parameter_names))
self._par_fixed = np.array([False] * len(parameter_names))
self.reset() # sets self.__gMinuit and caches to None
super(MinimizerROOTTMinuit,
self).__init__(parameter_names=parameter_names,
parameter_values=parameter_values,
parameter_errors=parameter_errors,
function_to_minimize=function_to_minimize,
tolerance=tolerance,
errordef=errordef)
# -- private methods
def _save_state(self):
if self._par_val is None:
self._save_state_dict["par_val"] = self._par_val
else:
self._save_state_dict["par_val"] = np.array(self._par_val)
if self._par_err is None:
self._save_state_dict["par_err"] = self._par_err
else:
self._save_state_dict["par_err"] = np.array(self._par_err)
self._save_state_dict['par_fixed'] = np.array(self._par_fixed)
self._save_state_dict['gMinuit'] = self.__gMinuit
super(MinimizerROOTTMinuit, self)._save_state()
def _load_state(self):
self.reset()
self._par_val = self._save_state_dict["par_val"]
if self._par_val is not None:
self._par_val = np.array(self._par_val)
self._par_err = self._save_state_dict["par_err"]
if self._par_err is not None:
self._par_err = np.array(self._par_err)
self._par_fixed = np.array(self._save_state_dict['par_fixed'])
self.__gMinuit = self._save_state_dict['gMinuit']
# call the function to propagate the changes to the nexus:
self._func_handle(*self.parameter_values)
super(MinimizerROOTTMinuit, self)._load_state()
def _recreate_gMinuit(self):
self.__gMinuit = TMinuit(self.num_pars)
self.__gMinuit.SetPrintLevel(-1)
self.__gMinuit.mncomd("SET STRATEGY {}".format(self._strategy),
ctypes.c_int(0))
self.__gMinuit.SetFCN(self._minuit_fcn)
self.__gMinuit.SetErrorDef(self._err_def)
# set gMinuit parameters
error_code = ctypes.c_int(0)
for _pid, (_pn, _pv, _pe) in enumerate(
zip(self._par_names, self._par_val, self._par_err)):
self.__gMinuit.mnparm(_pid, _pn, _pv, 0.1 * _pe, 0, 0, error_code)
err_code = ctypes.c_int(0)
# set fixed parameters
for _par_id, _pf in enumerate(self._par_fixed):
if _pf:
self.__gMinuit.mnfixp(_par_id, err_code)
# set parameter limits
for _par_id, _pb in enumerate(self._par_bounds):
if _pb is not None:
_lo_lim, _up_lim = _pb
self.__gMinuit.mnexcm(
"SET LIM", arr('d', [_par_id + 1, _lo_lim, _up_lim]), 3,
error_code)
def _get_gMinuit(self):
if self.__gMinuit is None:
self._recreate_gMinuit()
return self.__gMinuit
def _migrad(self, max_calls=6000):
# need to set the FCN explicitly before every call
self._get_gMinuit().SetFCN(self._minuit_fcn)
error_code = ctypes.c_int(0)
self._get_gMinuit().mnexcm("MIGRAD",
arr('d', [max_calls, self.tolerance]), 2,
error_code)
def _minuit_fcn(self, number_of_parameters, derivatives, f, parameters,
internal_flag):
"""
This is actually a function called in *ROOT* and acting as a C wrapper
for our `FCN`, which is implemented in Python.
This function is called by `Minuit` several times during a fitters. It
doesn't return anything but modifies one of its arguments (*f*).
This is *ugly*, but it's how *ROOT*'s ``TMinuit`` works. Its argument
structure is fixed and determined by `Minuit`:
**number_of_parameters** : int
The number of parameters of the current fitters
**derivatives** : C array
If the user chooses to calculate the first derivative of the
function inside the `FCN`, this value should be written here. This
interface to `Minuit` ignores this derivative, however, so
calculating this inside the `FCN` has no effect (yet).
**f** : C array
The desired function value is in f[0] after execution.
**parameters** : C array
A C array of parameters. Is cast to a Python list
**internal_flag** : int
A flag allowing for different behaviour of the function.
Can be any integer from 1 (initial run) to 4(normal run). See
`Minuit`'s specification.
"""
# Retrieve the parameters from the C side of ROOT and
# store them in a Python list -- resource-intensive
# for many calls, but can't be improved (yet?)
parameter_list = np.frombuffer(parameters,
dtype=float,
count=self.num_pars)
# call the Python implementation of FCN.
f[0] = self._func_wrapper(*parameter_list)
def _calculate_asymmetric_parameter_errors(self):
self._get_gMinuit().mnmnos()
_asymm_par_errs = np.zeros(shape=(self.num_pars, 2))
for _n in range(self.num_pars):
_number = Long(_n)
_eplus = ctypes.c_double(0)
_eminus = ctypes.c_double(0)
_eparab = ctypes.c_double(0)
_gcc = ctypes.c_double(0)
self._get_gMinuit().mnerrs(_number, _eplus, _eminus, _eparab, _gcc)
_asymm_par_errs[_n, 0] = _eminus.value
_asymm_par_errs[_n, 1] = _eplus.value
self.minimize()
return _asymm_par_errs
def _get_fit_info(self, info):
'''Retrieves other info from `Minuit`.
**info** : string
Information about the fit to retrieve.
This can be any of the following:
- ``'fcn'``: `FCN` value at minimum,
- ``'edm'``: estimated distance to minimum
- ``'err_def'``: `Minuit` error matrix status code
- ``'status_code'``: `Minuit` general status code
'''
# declare vars in which to retrieve other info
fcn_at_min = ctypes.c_double(0)
edm = ctypes.c_double(0)
err_def = ctypes.c_double(0)
n_var_param = ctypes.c_int(0)
n_tot_param = ctypes.c_int(0)
status_code = ctypes.c_int(0)
# Tell TMinuit to update the variables declared above
self.__gMinuit.mnstat(fcn_at_min, edm, err_def, n_var_param,
n_tot_param, status_code)
if info == 'fcn':
return fcn_at_min.value
elif info == 'edm':
return edm.value
elif info == 'err_def':
return err_def.value
elif info == 'status_code':
return status_code.value
else:
raise ValueError("Unknown fit info: %s" % info)
# -- public properties
@property
def hessian(self):
if not self.did_fit:
return None
if self._hessian is None:
_submat = self._remove_zeroes_for_fixed(self.cov_mat)
_submat_inv = 2.0 * self.errordef * np.linalg.inv(_submat)
self._hessian = self._fill_in_zeroes_for_fixed(_submat_inv)
return self._hessian.copy()
@property
def cov_mat(self):
if not self.did_fit:
return None
if self._par_cov_mat is None:
_n_pars_total = self.num_pars
_tmp_mat_array = arr('d', [0.0] * (_n_pars_total**2))
# get parameter covariance matrix from TMinuit
self._get_gMinuit().mnemat(_tmp_mat_array, _n_pars_total)
# reshape into 2D array
_sub_cov_mat = np.asarray(np.reshape(
_tmp_mat_array, (_n_pars_total, _n_pars_total)),
dtype=np.float)
_num_pars_free = np.sum(np.invert(self._par_fixed))
_sub_cov_mat = _sub_cov_mat[:_num_pars_free, :_num_pars_free]
self._par_cov_mat = self._fill_in_zeroes_for_fixed(_sub_cov_mat)
return self._par_cov_mat.copy()
@property
def hessian_inv(self):
if not self.did_fit:
return None
if self._hessian_inv is None:
self._hessian_inv = self.cov_mat / (2.0 * self.errordef)
return self._hessian_inv.copy()
@property
def parameter_values(self):
return self._par_val.copy()
@parameter_values.setter
def parameter_values(self, new_values):
self._par_val = np.array(new_values)
self.reset()
@property
def parameter_errors(self):
return self._par_err.copy()
@parameter_errors.setter
def parameter_errors(self, new_errors):
_err_array = np.array(new_errors)
if not np.all(_err_array > 0):
raise ValueError("All parameter errors must be > 0! Received: %s" %
new_errors)
self._par_err = _err_array
self.reset()
# -- private "properties"
# -- public methods
def reset(self):
super(MinimizerROOTTMinuit, self).reset()
self.__gMinuit = None
def set(self, parameter_name, parameter_value):
if parameter_name not in self._par_names:
raise ValueError("No parameter named '%s'!" % (parameter_name, ))
_par_id = self.parameter_names.index(parameter_name)
self._par_val[_par_id] = parameter_value
self.reset()
def fix(self, parameter_name):
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if self._par_fixed[_par_id]:
return # par is already fixed
self._par_fixed[_par_id] = True
if self.__gMinuit is not None:
# also update Minuit instance
err_code = ctypes.c_int(0)
self.__gMinuit.mnfixp(_par_id, err_code)
# self.__gMinuit.mnexcm("FIX",
# arr('d', [_par_id+1]), 1, error_code)
self._invalidate_cache()
def is_fixed(self, parameter_name):
_par_id = self.parameter_names.index(parameter_name)
return self._par_fixed[_par_id]
def release(self, parameter_name):
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if not self._par_fixed[_par_id]:
return # par is already released
self._par_fixed[_par_id] = False
if self.__gMinuit is not None:
# also update Minuit instance
self.__gMinuit.mnfree(-_par_id - 1)
# self.__gMinuit.mnexcm("RELEASE",
# arr('d', [_par_id+1]), 1, error_code)
self._invalidate_cache()
def limit(self, parameter_name, parameter_bounds):
assert len(parameter_bounds) == 2
if parameter_bounds[0] is None or parameter_bounds[1] is None:
raise MinimizerROOTTMinuitException(
"Cannot define one-sided parameter limits when using the ROOT TMinuit Minimizer."
)
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if self._par_bounds[_par_id] == parameter_bounds:
return # same limits already set
if self._par_val[_par_id] < parameter_bounds[0]:
self.set(parameter_name, parameter_bounds[0])
elif self._par_val[_par_id] > parameter_bounds[1]:
self.set(parameter_name, parameter_bounds[1])
self._par_bounds[_par_id] = parameter_bounds
if self.__gMinuit is not None:
_lo_lim, _up_lim = self._par_bounds[_par_id]
# also update Minuit instance
error_code = ctypes.c_int(0)
self.__gMinuit.mnexcm("SET LIM",
arr('d', [_par_id + 1, _lo_lim, _up_lim]), 3,
error_code)
self._did_fit = False
self._invalidate_cache()
def unlimit(self, parameter_name):
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if self._par_bounds[_par_id] is None:
return # parameter is already unlimited
self._par_bounds[_par_id] = None
if self.__gMinuit is not None:
# also update Minuit instance
error_code = ctypes.c_int(0)
self.__gMinuit.mnexcm("SET LIM", arr('d', [_par_id + 1]), 1,
error_code)
self._did_fit = False
self._invalidate_cache()
def minimize(self, max_calls=6000):
if np.all(self._par_fixed):
raise MinimizerROOTTMinuitException(
"Cannot perform a fit if all parameters are fixed!")
self._migrad(max_calls=max_calls)
# retrieve fitters parameters
self._par_val = np.zeros(self.num_pars)
self._par_err = np.zeros(self.num_pars)
_pv, _pe = ctypes.c_double(0), ctypes.c_double(0)
for _par_id in six.moves.range(0, self.num_pars):
self.__gMinuit.GetParameter(_par_id, _pv,
_pe) # retrieve fit result
self._par_val[_par_id] = _pv.value
self._par_err[_par_id] = _pe.value
self._did_fit = True
def contour(self,
parameter_name_1,
parameter_name_2,
sigma=1.0,
**minimizer_contour_kwargs):
if not self.did_fit:
raise MinimizerROOTTMinuitException(
"Need to perform a fit before calling contour()!")
_numpoints = minimizer_contour_kwargs.pop("numpoints", 100)
if minimizer_contour_kwargs:
raise MinimizerROOTTMinuitException(
"Unknown parameters: {}".format(minimizer_contour_kwargs))
_id_1 = self.parameter_names.index(parameter_name_1)
_id_2 = self.parameter_names.index(parameter_name_2)
self.__gMinuit.SetErrorDef(sigma**2)
_t_graph = self.__gMinuit.Contour(_numpoints, _id_1, _id_2)
self.__gMinuit.SetErrorDef(self._err_def)
_x_buffer, _y_buffer = _t_graph.GetX(), _t_graph.GetY()
_N = _t_graph.GetN()
_x = np.frombuffer(_x_buffer, dtype=float, count=_N)
_y = np.frombuffer(_y_buffer, dtype=float, count=_N)
self._func_handle(*self.parameter_values)
return ContourFactory.create_xy_contour((_x, _y), sigma)
def profile(self,
parameter_name,
bins=21,
bound=2,
args=None,
subtract_min=False):
if not self.did_fit:
raise MinimizerROOTTMinuitException(
"Need to perform a fit before calling profile()!")
MAX_ITERATIONS = 6000
_error_code = ctypes.c_int(0)
_minuit_id = Long(self.parameter_names.index(parameter_name) + 1)
_par_min = ctypes.c_double(0)
_par_err = ctypes.c_double(0)
self.__gMinuit.GetParameter(_minuit_id - 1, _par_min, _par_err)
_par_min = _par_min.value
_par_err = _par_err.value
_x = np.linspace(start=_par_min - bound * _par_err,
stop=_par_min + bound * _par_err,
num=bins,
endpoint=True)
self.__gMinuit.mnexcm("FIX", arr('d', [_minuit_id]), 1, _error_code)
_y = np.zeros(bins)
for i in range(bins):
self.__gMinuit.mnexcm("SET PAR",
arr('d',
[_minuit_id, Double(_x[i])]), 2,
_error_code)
self.__gMinuit.mnexcm("MIGRAD",
arr('d', [MAX_ITERATIONS, self.tolerance]),
2, _error_code)
_y[i] = self._get_fit_info("fcn")
self.__gMinuit.mnexcm("RELEASE", arr('d', [_minuit_id]), 1,
_error_code)
self._migrad()
self.__gMinuit.mnexcm("SET PAR",
arr('d',
[_minuit_id, Double(_par_min)]), 2,
_error_code)
if subtract_min:
_y -= self.function_value
return np.asarray((_x, _y))
def __init__(self, number_of_parameters, function_to_minimize,
parameter_names, start_parameters, parameter_errors,
quiet=True, verbose=False):
'''
Create a Minuit minimizer for a function `function_to_minimize`.
Necessary arguments are the number of parameters and the function to be
minimized `function_to_minimize`. The function `function_to_minimize`'s
arguments must be numerical values. The same goes for its output.
Another requirement is for every parameter of `function_to_minimize` to
have a default value. These are then used to initialize Minuit.
**number_of_parameters** : int
The number of parameters of the function to minimize.
**function_to_minimize** : function
The function which `Minuit` should minimize. This must be a Python
function with <``number_of_parameters``> arguments.
**parameter_names** : tuple/list of strings
The parameter names. These are used to keep track of the parameters
in `Minuit`'s output.
**start_parameters** : tuple/list of floats
The start values of the parameters. It is important to have a good,
if rough, estimate of the parameters at the minimum before starting
the minimization. Wrong initial parameters can yield a local
minimum instead of a global one.
**parameter_errors** : tuple/list of floats
An initial guess of the parameter errors. These errors are used to
define the initial step size.
*quiet* : boolean (optional, default: ``True``)
If ``True``, suppresses all output from ``TMinuit``.
*verbose* : boolean (optional, default: ``False``)
If ``True``, sets ``TMinuit``'s print level to a high value, so
that all output is logged.
'''
#: the name of this minimizer type
self.name = "ROOT::TMinuit"
#: the actual `FCN` called in ``FCN_wrapper``
self.function_to_minimize = function_to_minimize
#: number of parameters to minimize for
self.number_of_parameters = number_of_parameters
if not quiet:
self.out_file = open(log_file("minuit.log"), 'a')
else:
self.out_file = null_file()
# create a TMinuit instance for that number of parameters
self.__gMinuit = TMinuit(self.number_of_parameters)
# instruct Minuit to use this class's FCN_wrapper method as a FCN
self.__gMinuit.SetFCN(self.FCN_wrapper)
# set print level according to flag
if quiet:
self.set_print_level(-1000) # suppress output
elif verbose:
self.set_print_level(10) # detailed output
else:
self.set_print_level(0) # frugal output
# initialize minimizer
self.set_err()
self.set_strategy()
self.set_parameter_values(start_parameters)
self.set_parameter_errors(parameter_errors)
self.set_parameter_names(parameter_names)
#: maximum number of iterations until ``TMinuit`` gives up
self.max_iterations = M_MAX_ITERATIONS
#: ``TMinuit`` tolerance
self.tolerance = M_TOLERANCE
class Minuit:
'''
A class for communicating with ROOT's function minimizer tool Minuit.
'''
def __init__(self, number_of_parameters, function_to_minimize,
parameter_names, start_parameters, parameter_errors,
quiet=True, verbose=False):
'''
Create a Minuit minimizer for a function `function_to_minimize`.
Necessary arguments are the number of parameters and the function to be
minimized `function_to_minimize`. The function `function_to_minimize`'s
arguments must be numerical values. The same goes for its output.
Another requirement is for every parameter of `function_to_minimize` to
have a default value. These are then used to initialize Minuit.
**number_of_parameters** : int
The number of parameters of the function to minimize.
**function_to_minimize** : function
The function which `Minuit` should minimize. This must be a Python
function with <``number_of_parameters``> arguments.
**parameter_names** : tuple/list of strings
The parameter names. These are used to keep track of the parameters
in `Minuit`'s output.
**start_parameters** : tuple/list of floats
The start values of the parameters. It is important to have a good,
if rough, estimate of the parameters at the minimum before starting
the minimization. Wrong initial parameters can yield a local
minimum instead of a global one.
**parameter_errors** : tuple/list of floats
An initial guess of the parameter errors. These errors are used to
define the initial step size.
*quiet* : boolean (optional, default: ``True``)
If ``True``, suppresses all output from ``TMinuit``.
*verbose* : boolean (optional, default: ``False``)
If ``True``, sets ``TMinuit``'s print level to a high value, so
that all output is logged.
'''
#: the name of this minimizer type
self.name = "ROOT::TMinuit"
#: the actual `FCN` called in ``FCN_wrapper``
self.function_to_minimize = function_to_minimize
#: number of parameters to minimize for
self.number_of_parameters = number_of_parameters
if not quiet:
self.out_file = open(log_file("minuit.log"), 'a')
else:
self.out_file = null_file()
# create a TMinuit instance for that number of parameters
self.__gMinuit = TMinuit(self.number_of_parameters)
# instruct Minuit to use this class's FCN_wrapper method as a FCN
self.__gMinuit.SetFCN(self.FCN_wrapper)
# set print level according to flag
if quiet:
self.set_print_level(-1000) # suppress output
elif verbose:
self.set_print_level(10) # detailed output
else:
self.set_print_level(0) # frugal output
# initialize minimizer
self.set_err()
self.set_strategy()
self.set_parameter_values(start_parameters)
self.set_parameter_errors(parameter_errors)
self.set_parameter_names(parameter_names)
#: maximum number of iterations until ``TMinuit`` gives up
self.max_iterations = M_MAX_ITERATIONS
#: ``TMinuit`` tolerance
self.tolerance = M_TOLERANCE
def update_parameter_data(self, show_warnings=False):
"""
(Re-)Sets the parameter names, values and step size on the
C++ side of Minuit.
"""
error_code = Long(0)
try:
# Set up the starting fit parameters in TMinuit
for i in range(0, self.number_of_parameters):
self.__gMinuit.mnparm(i, self.parameter_names[i],
self.current_parameters[i],
0.1 * self.parameter_errors[i],
0, 0, error_code)
# use 10% of the par. 1-sigma errors as the initial step size
except AttributeError as e:
if show_warnings:
logger.warning("Cannot update Minuit data on the C++ side. "
"AttributeError: %s" % (e, ))
return error_code
# Set methods
##############
def set_print_level(self, print_level=P_DETAIL_LEVEL):
'''Sets the print level for Minuit.
*print_level* : int (optional, default: 1 (frugal output))
Tells ``TMinuit`` how much output to generate. The higher this
value, the more output it generates.
'''
self.__gMinuit.SetPrintLevel(print_level) # set Minuit print level
self.print_level = print_level
def set_strategy(self, strategy_id=1):
'''Sets the strategy Minuit.
*strategy_id* : int (optional, default: 1 (optimized))
Tells ``TMinuit`` to use a certain strategy. Refer to ``TMinuit``'s
documentation for available strategies.
'''
error_code = Long(0)
# execute SET STRATEGY command
self.__gMinuit.mnexcm("SET STRATEGY",
arr('d', [strategy_id]), 1, error_code)
def set_err(self, up_value=1.0):
'''Sets the ``UP`` value for Minuit.
*up_value* : float (optional, default: 1.0)
This is the value by which `FCN` is expected to change.
'''
# Tell TMinuit to use an up-value of 1.0
error_code = Long(0)
# execute SET ERR command
self.__gMinuit.mnexcm("SET ERR", arr('d', [up_value]), 1, error_code)
def set_parameter_values(self, parameter_values):
'''
Sets the fit parameters. If parameter_values=`None`, tries to infer
defaults from the function_to_minimize.
'''
if len(parameter_values) == self.number_of_parameters:
self.current_parameters = parameter_values
else:
raise Exception("Cannot get default parameter values from the \
FCN. Not all parameters have default values given.")
self.update_parameter_data()
def set_parameter_names(self, parameter_names):
'''Sets the fit parameters. If parameter_values=`None`, tries to infer
defaults from the function_to_minimize.'''
if len(parameter_names) == self.number_of_parameters:
self.parameter_names = parameter_names
else:
raise Exception("Cannot set param names. Tuple length mismatch.")
self.update_parameter_data()
def set_parameter_errors(self, parameter_errors=None):
'''Sets the fit parameter errors. If parameter_values=`None`, sets the
error to 10% of the parameter value.'''
if parameter_errors is None: # set to 0.1% of the parameter value
if not self.current_parameters is None:
self.parameter_errors = [max(0.1, 0.1 * par)
for par in self.current_parameters]
else:
raise Exception("Cannot set parameter errors. No errors \
provided and no parameters initialized.")
elif len(parameter_errors) != len(self.current_parameters):
raise Exception("Cannot set parameter errors. \
Tuple length mismatch.")
else:
self.parameter_errors = parameter_errors
self.update_parameter_data()
# Get methods
##############
def get_error_matrix(self):
'''Retrieves the parameter error matrix from TMinuit.
return : `numpy.matrix`
'''
# set up an array of type `double' to pass to TMinuit
tmp_array = arr('d', [0.0]*(self.number_of_parameters**2))
# get parameter covariance matrix from TMinuit
self.__gMinuit.mnemat(tmp_array, self.number_of_parameters)
# reshape into 2D array
return np.asmatrix(
np.reshape(
tmp_array,
(self.number_of_parameters, self.number_of_parameters)
)
)
def get_parameter_values(self):
'''Retrieves the parameter values from TMinuit.
return : tuple
Current `Minuit` parameter values
'''
result = []
# retrieve fit parameters
p, pe = Double(0), Double(0)
for i in range(0, self.number_of_parameters):
self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult
result.append(float(p))
return tuple(result)
def get_parameter_errors(self):
'''Retrieves the parameter errors from TMinuit.
return : tuple
Current `Minuit` parameter errors
'''
result = []
# retrieve fit parameters
p, pe = Double(0), Double(0)
for i in range(0, self.number_of_parameters):
self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult
result.append(float(pe))
return tuple(result)
def get_parameter_info(self):
'''Retrieves parameter information from TMinuit.
return : list of tuples
``(parameter_name, parameter_val, parameter_error)``
'''
result = []
# retrieve fit parameters
p, pe = Double(0), Double(0)
for i in range(0, self.number_of_parameters):
self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult
result.append((self.get_parameter_name(i), float(p), float(pe)))
return result
def get_parameter_name(self, parameter_nr):
'''Gets the name of parameter number ``parameter_nr``
**parameter_nr** : int
Number of the parameter whose name to get.
'''
return self.parameter_names[parameter_nr]
def get_fit_info(self, info):
'''Retrieves other info from `Minuit`.
**info** : string
Information about the fit to retrieve.
This can be any of the following:
- ``'fcn'``: `FCN` value at minimum,
- ``'edm'``: estimated distance to minimum
- ``'err_def'``: `Minuit` error matrix status code
- ``'status_code'``: `Minuit` general status code
'''
# declare vars in which to retrieve other info
fcn_at_min = Double(0)
edm = Double(0)
err_def = Double(0)
n_var_param = Long(0)
n_tot_param = Long(0)
status_code = Long(0)
# Tell TMinuit to update the variables declared above
self.__gMinuit.mnstat(fcn_at_min,
edm,
err_def,
n_var_param,
n_tot_param,
status_code)
if info == 'fcn':
return fcn_at_min
elif info == 'edm':
return edm
elif info == 'err_def':
return err_def
elif info == 'status_code':
try:
return D_MATRIX_ERROR[status_code]
except:
return status_code
def get_chi2_probability(self, n_deg_of_freedom):
'''
Returns the probability that an observed :math:`\chi^2` exceeds
the calculated value of :math:`\chi^2` for this fit by chance,
even for a correct model. In other words, returns the probability that
a worse fit of the model to the data exists. If this is a small value
(typically <5%), this means the fit is pretty bad. For values below
this threshold, the model very probably does not fit the data.
n_def_of_freedom : int
The number of degrees of freedom. This is typically
:math:`n_\text{datapoints} - n_\text{parameters}`.
'''
chi2 = Double(self.get_fit_info('fcn'))
ndf = Long(n_deg_of_freedom)
return TMath.Prob(chi2, ndf)
def get_contour(self, parameter1, parameter2, n_points=21):
'''
Returns a list of points (2-tuples) representing a sampling of
the :math:`1\\sigma` contour of the TMinuit fit. The ``FCN`` has
to be minimized before calling this.
**parameter1** : int
ID of the parameter to be displayed on the `x`-axis.
**parameter2** : int
ID of the parameter to be displayed on the `y`-axis.
*n_points* : int (optional)
number of points used to draw the contour. Default is 21.
*returns* : 2-tuple of tuples
a 2-tuple (x, y) containing ``n_points+1`` points sampled
along the contour. The first point is repeated at the end
of the list to generate a closed contour.
'''
self.out_file.write('\n')
# entry in log-file
self.out_file.write('\n')
self.out_file.write('#'*(5+28))
self.out_file.write('\n')
self.out_file.write('# Contour for parameters %2d, %2d #\n'\
%(parameter1, parameter2) )
self.out_file.write('#'*(5+28))
self.out_file.write('\n\n')
self.out_file.flush()
#
# first, make sure we are at minimum
self.minimize(final_fit=True, log_print_level=0)
# get the TGraph object from ROOT
g = self.__gMinuit.Contour(n_points, parameter1, parameter2)
# extract point data into buffers
xbuf, ybuf = g.GetX(), g.GetY()
N = g.GetN()
# generate tuples from buffers
x = np.frombuffer(xbuf, dtype=float, count=N)
y = np.frombuffer(ybuf, dtype=float, count=N)
#
return (x, y)
def get_profile(self, parid, n_points=21):
'''
Returns a list of points (2-tuples) the profile
the :math:`\\chi^2` of the TMinuit fit.
**parid** : int
ID of the parameter to be displayed on the `x`-axis.
*n_points* : int (optional)
number of points used for profile. Default is 21.
*returns* : two arrays, par. values and corresp. :math:`\\chi^2`
containing ``n_points`` sampled profile points.
'''
self.out_file.write('\n')
# entry in log-file
self.out_file.write('\n')
self.out_file.write('#'*(2+26))
self.out_file.write('\n')
self.out_file.write("# Profile for parameter %2d #\n" % (parid))
self.out_file.write('#'*(2+26))
self.out_file.write('\n\n')
self.out_file.flush()
# redirect stdout stream
_redirection_target = None
## -- disable redirection completely, for now
##if log_print_level >= 0:
## _redirection_target = self.out_file
with redirect_stdout_to(_redirection_target):
pv = []
chi2 = []
error_code = Long(0)
self.__gMinuit.mnexcm("SET PRINT",
arr('d', [0.0]), 1, error_code) # no printout
# first, make sure we are at minimum, i.e. re-minimize
self.minimize(final_fit=True, log_print_level=0)
minuit_id = Double(parid + 1) # Minuit parameter numbers start with 1
# retrieve information about parameter with id=parid
pmin = Double(0)
perr = Double(0)
self.__gMinuit.GetParameter(parid, pmin, perr) # retrieve fitresult
# fix parameter parid ...
self.__gMinuit.mnexcm("FIX",
arr('d', [minuit_id]),
1, error_code)
# ... and scan parameter values, minimizing at each point
for v in np.linspace(pmin - 3.*perr, pmin + 3.*perr, n_points):
pv.append(v)
self.__gMinuit.mnexcm("SET PAR",
arr('d', [minuit_id, Double(v)]),
2, error_code)
self.__gMinuit.mnexcm("MIGRAD",
arr('d', [self.max_iterations, self.tolerance]),
2, error_code)
chi2.append(self.get_fit_info('fcn'))
# release parameter to back to initial value and release
self.__gMinuit.mnexcm("SET PAR",
arr('d', [minuit_id, Double(pmin)]),
2, error_code)
self.__gMinuit.mnexcm("RELEASE",
arr('d', [minuit_id]),
1, error_code)
return pv, chi2
# Other methods
################
def fix_parameter(self, parameter_number):
'''
Fix parameter number <`parameter_number`>.
**parameter_number** : int
Number of the parameter to fix.
'''
error_code = Long(0)
logger.info("Fixing parameter %d in Minuit" % (parameter_number,))
# execute FIX command
self.__gMinuit.mnexcm("FIX",
arr('d', [parameter_number+1]), 1, error_code)
def release_parameter(self, parameter_number):
'''
Release parameter number <`parameter_number`>.
**parameter_number** : int
Number of the parameter to release.
'''
error_code = Long(0)
logger.info("Releasing parameter %d in Minuit" % (parameter_number,))
# execute RELEASE command
self.__gMinuit.mnexcm("RELEASE",
arr('d', [parameter_number+1]), 1, error_code)
def reset(self):
'''Execute TMinuit's `mnrset` method.'''
self.__gMinuit.mnrset(0) # reset TMinuit
def FCN_wrapper(self, number_of_parameters, derivatives,
f, parameters, internal_flag):
'''
This is actually a function called in *ROOT* and acting as a C wrapper
for our `FCN`, which is implemented in Python.
This function is called by `Minuit` several times during a fit. It
doesn't return anything but modifies one of its arguments (*f*).
This is *ugly*, but it's how *ROOT*'s ``TMinuit`` works. Its argument
structure is fixed and determined by `Minuit`:
**number_of_parameters** : int
The number of parameters of the current fit
**derivatives** : C array
If the user chooses to calculate the first derivative of the
function inside the `FCN`, this value should be written here. This
interface to `Minuit` ignores this derivative, however, so
calculating this inside the `FCN` has no effect (yet).
**f** : C array
The desired function value is in f[0] after execution.
**parameters** : C array
A C array of parameters. Is cast to a Python list
**internal_flag** : int
A flag allowing for different behaviour of the function.
Can be any integer from 1 (initial run) to 4(normal run). See
`Minuit`'s specification.
'''
# Retrieve the parameters from the C side of ROOT and
# store them in a Python list -- resource-intensive
# for many calls, but can't be improved (yet?)
parameter_list = np.frombuffer(parameters, dtype=float,
count=self.number_of_parameters)
# call the Python implementation of FCN.
f[0] = self.function_to_minimize(*parameter_list)
def minimize(self, final_fit=True, log_print_level=2):
'''Do the minimization. This calls `Minuit`'s algorithms ``MIGRAD``
for minimization and, if `final_fit` is `True`, also ``HESSE``
for computing/checking the parameter error matrix.'''
# Set the FCN again. This HAS to be done EVERY
# time the minimize method is called because of
# the implementation of SetFCN, which is not
# object-oriented but sets a global pointer!!!
logger.debug("Updating current FCN")
self.__gMinuit.SetFCN(self.FCN_wrapper)
# Run minimization algorithm (MIGRAD + HESSE)
error_code = Long(0)
prefix = "Minuit run on" # set the timestamp prefix
# insert timestamp
self.out_file.write('\n')
self.out_file.write('#'*(len(prefix)+4+20))
self.out_file.write('\n')
self.out_file.write("# %s " % (prefix,) +
strftime("%Y-%m-%d %H:%M:%S #\n", gmtime()))
self.out_file.write('#'*(len(prefix)+4+20))
self.out_file.write('\n\n')
self.out_file.flush()
# redirect stdout stream
_redirection_target = None
if log_print_level >= 0:
_redirection_target = self.out_file
with redirect_stdout_to(_redirection_target):
self.__gMinuit.SetPrintLevel(log_print_level) # set Minuit print level
logger.debug("Running MIGRAD")
self.__gMinuit.mnexcm("MIGRAD",
arr('d', [self.max_iterations, self.tolerance]),
2, error_code)
if(final_fit):
logger.debug("Running HESSE")
self.__gMinuit.mnexcm("HESSE", arr('d', [self.max_iterations]), 1, error_code)
# return to normal print level
self.__gMinuit.SetPrintLevel(self.print_level)
def minos_errors(self, log_print_level=1):
'''
Get (asymmetric) parameter uncertainties from MINOS
algorithm. This calls `Minuit`'s algorithms ``MINOS``,
which determines parameter uncertainties using profiling
of the chi2 function.
returns : tuple
A tuple of [err+, err-, parabolic error, global correlation]
'''
# Set the FCN again. This HAS to be done EVERY
# time the minimize method is called because of
# the implementation of SetFCN, which is not
# object-oriented but sets a global pointer!!!
logger.debug("Updating current FCN")
self.__gMinuit.SetFCN(self.FCN_wrapper)
# redirect stdout stream
_redirection_target = None
if log_print_level >= 0:
_redirection_target = self.out_file
with redirect_stdout_to(_redirection_target):
self.__gMinuit.SetPrintLevel(log_print_level)
logger.debug("Running MINOS")
error_code = Long(0)
self.__gMinuit.mnexcm("MINOS", arr('d', [self.max_iterations]), 1, error_code)
# return to normal print level
self.__gMinuit.SetPrintLevel(self.print_level)
output = []
errpos=Double(0) # positive parameter error
errneg=Double(0) # negative parameter error
err=Double(0) # parabolic error
gcor=Double(0) # global correlation coefficient
for i in range(0, self.number_of_parameters):
self.__gMinuit.mnerrs(i, errpos, errneg, err, gcor)
output.append([float(errpos),float(errneg),float(err),float(gcor)])
return output
def __init__(self, number_of_parameters, function_to_minimize,
parameter_names, start_parameters, parameter_errors,
quiet=True, verbose=False):
'''
Create a Minuit minimizer for a function `function_to_minimize`.
Necessary arguments are the number of parameters and the function to be
minimized `function_to_minimize`. The function `function_to_minimize`'s
arguments must be numerical values. The same goes for its output.
Another requirement is for every parameter of `function_to_minimize` to
have a default value. These are then used to initialize Minuit.
**number_of_parameters** : int
The number of parameters of the function to minimize.
**function_to_minimize** : function
The function which `Minuit` should minimize. This must be a Python
function with <``number_of_parameters``> arguments.
**parameter_names** : tuple/list of strings
The parameter names. These are used to keep track of the parameters
in `Minuit`'s output.
**start_parameters** : tuple/list of floats
The start values of the parameters. It is important to have a good,
if rough, estimate of the parameters at the minimum before starting
the minimization. Wrong initial parameters can yield a local
minimum instead of a global one.
**parameter_errors** : tuple/list of floats
An initial guess of the parameter errors. These errors are used to
define the initial step size.
*quiet* : boolean (optional, default: ``True``)
If ``True``, suppresses all output from ``TMinuit``.
*verbose* : boolean (optional, default: ``False``)
If ``True``, sets ``TMinuit``'s print level to a high value, so
that all output is logged.
'''
#: the name of this minimizer type
self.name = "ROOT::TMinuit"
#: the actual `FCN` called in ``FCN_wrapper``
self.function_to_minimize = function_to_minimize
#: number of parameters to minimize for
self.number_of_parameters = number_of_parameters
if not quiet:
self.out_file = open(log_file("minuit.log"), 'a')
else:
self.out_file = null_file()
# create a TMinuit instance for that number of parameters
self.__gMinuit = TMinuit(self.number_of_parameters)
# instruct Minuit to use this class's FCN_wrapper method as a FCN
self.__gMinuit.SetFCN(self.FCN_wrapper)
# set print level according to flag
if quiet:
self.set_print_level(-1000) # suppress output
elif verbose:
self.set_print_level(10) # detailed output
else:
self.set_print_level(0) # frugal output
# initialize minimizer
self.set_err()
self.set_strategy()
self.set_parameter_values(start_parameters)
self.set_parameter_errors(parameter_errors)
self.set_parameter_names(parameter_names)
#: maximum number of iterations until ``TMinuit`` gives up
self.max_iterations = M_MAX_ITERATIONS
#: ``TMinuit`` tolerance
self.tolerance = M_TOLERANCE
class Minuit:
'''
A class for communicating with ROOT's function minimizer tool Minuit.
'''
def __init__(self, number_of_parameters, function_to_minimize,
parameter_names, start_parameters, parameter_errors,
quiet=True, verbose=False):
'''
Create a Minuit minimizer for a function `function_to_minimize`.
Necessary arguments are the number of parameters and the function to be
minimized `function_to_minimize`. The function `function_to_minimize`'s
arguments must be numerical values. The same goes for its output.
Another requirement is for every parameter of `function_to_minimize` to
have a default value. These are then used to initialize Minuit.
**number_of_parameters** : int
The number of parameters of the function to minimize.
**function_to_minimize** : function
The function which `Minuit` should minimize. This must be a Python
function with <``number_of_parameters``> arguments.
**parameter_names** : tuple/list of strings
The parameter names. These are used to keep track of the parameters
in `Minuit`'s output.
**start_parameters** : tuple/list of floats
The start values of the parameters. It is important to have a good,
if rough, estimate of the parameters at the minimum before starting
the minimization. Wrong initial parameters can yield a local
minimum instead of a global one.
**parameter_errors** : tuple/list of floats
An initial guess of the parameter errors. These errors are used to
define the initial step size.
*quiet* : boolean (optional, default: ``True``)
If ``True``, suppresses all output from ``TMinuit``.
*verbose* : boolean (optional, default: ``False``)
If ``True``, sets ``TMinuit``'s print level to a high value, so
that all output is logged.
'''
#: the name of this minimizer type
self.name = "ROOT::TMinuit"
#: the actual `FCN` called in ``FCN_wrapper``
self.function_to_minimize = function_to_minimize
#: number of parameters to minimize for
self.number_of_parameters = number_of_parameters
if not quiet:
self.out_file = open(log_file("minuit.log"), 'a')
else:
self.out_file = null_file()
# create a TMinuit instance for that number of parameters
self.__gMinuit = TMinuit(self.number_of_parameters)
# instruct Minuit to use this class's FCN_wrapper method as a FCN
self.__gMinuit.SetFCN(self.FCN_wrapper)
# set print level according to flag
if quiet:
self.set_print_level(-1000) # suppress output
elif verbose:
self.set_print_level(10) # detailed output
else:
self.set_print_level(0) # frugal output
# initialize minimizer
self.set_err()
self.set_strategy()
self.set_parameter_values(start_parameters)
self.set_parameter_errors(parameter_errors)
self.set_parameter_names(parameter_names)
#: maximum number of iterations until ``TMinuit`` gives up
self.max_iterations = M_MAX_ITERATIONS
#: ``TMinuit`` tolerance
self.tolerance = M_TOLERANCE
def update_parameter_data(self, show_warnings=False):
"""
(Re-)Sets the parameter names, values and step size on the
C++ side of Minuit.
"""
error_code = Long(0)
try:
# Set up the starting fit parameters in TMinuit
for i in range(0, self.number_of_parameters):
self.__gMinuit.mnparm(i, self.parameter_names[i],
self.current_parameters[i],
0.1 * self.parameter_errors[i],
0, 0, error_code)
# use 10% of the par. 1-sigma errors as the initial step size
except AttributeError as e:
if show_warnings:
logger.warn("Cannot update Minuit data on the C++ side. "
"AttributeError: %s" % (e, ))
return error_code
# Set methods
##############
def set_print_level(self, print_level=P_DETAIL_LEVEL):
'''Sets the print level for Minuit.
*print_level* : int (optional, default: 1 (frugal output))
Tells ``TMinuit`` how much output to generate. The higher this
value, the more output it generates.
'''
self.__gMinuit.SetPrintLevel(print_level) # set Minuit print level
self.print_level = print_level
def set_strategy(self, strategy_id=1):
'''Sets the strategy Minuit.
*strategy_id* : int (optional, default: 1 (optimized))
Tells ``TMinuit`` to use a certain strategy. Refer to ``TMinuit``'s
documentation for available strategies.
'''
error_code = Long(0)
# execute SET STRATEGY command
self.__gMinuit.mnexcm("SET STRATEGY",
arr('d', [strategy_id]), 1, error_code)
def set_err(self, up_value=1.0):
'''Sets the ``UP`` value for Minuit.
*up_value* : float (optional, default: 1.0)
This is the value by which `FCN` is expected to change.
'''
# Tell TMinuit to use an up-value of 1.0
error_code = Long(0)
# execute SET ERR command
self.__gMinuit.mnexcm("SET ERR", arr('d', [up_value]), 1, error_code)
def set_parameter_values(self, parameter_values):
'''
Sets the fit parameters. If parameter_values=`None`, tries to infer
defaults from the function_to_minimize.
'''
if len(parameter_values) == self.number_of_parameters:
self.current_parameters = parameter_values
else:
raise Exception("Cannot get default parameter values from the \
FCN. Not all parameters have default values given.")
self.update_parameter_data()
def set_parameter_names(self, parameter_names):
'''Sets the fit parameters. If parameter_values=`None`, tries to infer
defaults from the function_to_minimize.'''
if len(parameter_names) == self.number_of_parameters:
self.parameter_names = parameter_names
else:
raise Exception("Cannot set param names. Tuple length mismatch.")
self.update_parameter_data()
def set_parameter_errors(self, parameter_errors=None):
'''Sets the fit parameter errors. If parameter_values=`None`, sets the
error to 10% of the parameter value.'''
if parameter_errors is None: # set to 0.1% of the parameter value
if not self.current_parameters is None:
self.parameter_errors = [max(0.1, 0.1 * par)
for par in self.current_parameters]
else:
raise Exception("Cannot set parameter errors. No errors \
provided and no parameters initialized.")
elif len(parameter_errors) != len(self.current_parameters):
raise Exception("Cannot set parameter errors. \
Tuple length mismatch.")
else:
self.parameter_errors = parameter_errors
self.update_parameter_data()
# Get methods
##############
def get_error_matrix(self):
'''Retrieves the parameter error matrix from TMinuit.
return : `numpy.matrix`
'''
# set up an array of type `double' to pass to TMinuit
tmp_array = arr('d', [0.0]*(self.number_of_parameters**2))
# get parameter covariance matrix from TMinuit
self.__gMinuit.mnemat(tmp_array, self.number_of_parameters)
# reshape into 2D array
return np.asmatrix(
np.reshape(
tmp_array,
(self.number_of_parameters, self.number_of_parameters)
)
)
def get_parameter_values(self):
'''Retrieves the parameter values from TMinuit.
return : tuple
Current `Minuit` parameter values
'''
result = []
# retrieve fit parameters
p, pe = Double(0), Double(0)
for i in range(0, self.number_of_parameters):
self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult
result.append(float(p))
return tuple(result)
def get_parameter_errors(self):
'''Retrieves the parameter errors from TMinuit.
return : tuple
Current `Minuit` parameter errors
'''
result = []
# retrieve fit parameters
p, pe = Double(0), Double(0)
for i in range(0, self.number_of_parameters):
self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult
result.append(float(pe))
return tuple(result)
def get_parameter_info(self):
'''Retrieves parameter information from TMinuit.
return : list of tuples
``(parameter_name, parameter_val, parameter_error)``
'''
result = []
# retrieve fit parameters
p, pe = Double(0), Double(0)
for i in range(0, self.number_of_parameters):
self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult
result.append((self.get_parameter_name(i), float(p), float(pe)))
return result
def get_parameter_name(self, parameter_nr):
'''Gets the name of parameter number ``parameter_nr``
**parameter_nr** : int
Number of the parameter whose name to get.
'''
return self.parameter_names[parameter_nr]
def get_fit_info(self, info):
'''Retrieves other info from `Minuit`.
**info** : string
Information about the fit to retrieve.
This can be any of the following:
- ``'fcn'``: `FCN` value at minimum,
- ``'edm'``: estimated distance to minimum
- ``'err_def'``: `Minuit` error matrix status code
- ``'status_code'``: `Minuit` general status code
'''
# declare vars in which to retrieve other info
fcn_at_min = Double(0)
edm = Double(0)
err_def = Double(0)
n_var_param = Long(0)
n_tot_param = Long(0)
status_code = Long(0)
# Tell TMinuit to update the variables declared above
self.__gMinuit.mnstat(fcn_at_min,
edm,
err_def,
n_var_param,
n_tot_param,
status_code)
if info == 'fcn':
return fcn_at_min
elif info == 'edm':
return edm
elif info == 'err_def':
return err_def
elif info == 'status_code':
try:
return D_MATRIX_ERROR[status_code]
except:
return status_code
def get_chi2_probability(self, n_deg_of_freedom):
'''
Returns the probability that an observed :math:`\chi^2` exceeds
the calculated value of :math:`\chi^2` for this fit by chance,
even for a correct model. In other words, returns the probability that
a worse fit of the model to the data exists. If this is a small value
(typically <5%), this means the fit is pretty bad. For values below
this threshold, the model very probably does not fit the data.
n_def_of_freedom : int
The number of degrees of freedom. This is typically
:math:`n_\text{datapoints} - n_\text{parameters}`.
'''
chi2 = Double(self.get_fit_info('fcn'))
ndf = Long(n_deg_of_freedom)
return TMath.Prob(chi2, ndf)
def get_contour(self, parameter1, parameter2, n_points=21):
'''
Returns a list of points (2-tuples) representing a sampling of
the :math:`1\\sigma` contour of the TMinuit fit. The ``FCN`` has
to be minimized before calling this.
**parameter1** : int
ID of the parameter to be displayed on the `x`-axis.
**parameter2** : int
ID of the parameter to be displayed on the `y`-axis.
*n_points* : int (optional)
number of points used to draw the contour. Default is 21.
*returns* : 2-tuple of tuples
a 2-tuple (x, y) containing ``n_points+1`` points sampled
along the contour. The first point is repeated at the end
of the list to generate a closed contour.
'''
self.out_file.write('\n')
# entry in log-file
self.out_file.write('\n')
self.out_file.write('#'*(5+28))
self.out_file.write('\n')
self.out_file.write('# Contour for parameters %2d, %2d #\n'\
%(parameter1, parameter2) )
self.out_file.write('#'*(5+28))
self.out_file.write('\n\n')
self.out_file.flush()
#
# first, make sure we are at minimum
self.minimize(final_fit=True, log_print_level=0)
# get the TGraph object from ROOT
g = self.__gMinuit.Contour(n_points, parameter1, parameter2)
# extract point data into buffers
xbuf, ybuf = g.GetX(), g.GetY()
N = g.GetN()
# generate tuples from buffers
x = np.frombuffer(xbuf, dtype=float, count=N)
y = np.frombuffer(ybuf, dtype=float, count=N)
#
return (x, y)
def get_profile(self, parid, n_points=21):
'''
Returns a list of points (2-tuples) the profile
the :math:`\\chi^2` of the TMinuit fit.
**parid** : int
ID of the parameter to be displayed on the `x`-axis.
*n_points* : int (optional)
number of points used for profile. Default is 21.
*returns* : two arrays, par. values and corresp. :math:`\\chi^2`
containing ``n_points`` sampled profile points.
'''
self.out_file.write('\n')
# entry in log-file
self.out_file.write('\n')
self.out_file.write('#'*(2+26))
self.out_file.write('\n')
self.out_file.write("# Profile for parameter %2d #\n" % (parid))
self.out_file.write('#'*(2+26))
self.out_file.write('\n\n')
self.out_file.flush()
# redirect stdout stream
_redirection_target = None
## -- disable redirection completely, for now
##if log_print_level >= 0:
## _redirection_target = self.out_file
with redirect_stdout_to(_redirection_target):
pv = []
chi2 = []
error_code = Long(0)
self.__gMinuit.mnexcm("SET PRINT",
arr('d', [0.0]), 1, error_code) # no printout
# first, make sure we are at minimum, i.e. re-minimize
self.minimize(final_fit=True, log_print_level=0)
minuit_id = Double(parid + 1) # Minuit parameter numbers start with 1
# retrieve information about parameter with id=parid
pmin = Double(0)
perr = Double(0)
self.__gMinuit.GetParameter(parid, pmin, perr) # retrieve fitresult
# fix parameter parid ...
self.__gMinuit.mnexcm("FIX",
arr('d', [minuit_id]),
1, error_code)
# ... and scan parameter values, minimizing at each point
for v in np.linspace(pmin - 3.*perr, pmin + 3.*perr, n_points):
pv.append(v)
self.__gMinuit.mnexcm("SET PAR",
arr('d', [minuit_id, Double(v)]),
2, error_code)
self.__gMinuit.mnexcm("MIGRAD",
arr('d', [self.max_iterations, self.tolerance]),
2, error_code)
chi2.append(self.get_fit_info('fcn'))
# release parameter to back to initial value and release
self.__gMinuit.mnexcm("SET PAR",
arr('d', [minuit_id, Double(pmin)]),
2, error_code)
self.__gMinuit.mnexcm("RELEASE",
arr('d', [minuit_id]),
1, error_code)
return pv, chi2
# Other methods
################
def fix_parameter(self, parameter_number):
'''
Fix parameter number <`parameter_number`>.
**parameter_number** : int
Number of the parameter to fix.
'''
error_code = Long(0)
logger.info("Fixing parameter %d in Minuit" % (parameter_number,))
# execute FIX command
self.__gMinuit.mnexcm("FIX",
arr('d', [parameter_number+1]), 1, error_code)
def release_parameter(self, parameter_number):
'''
Release parameter number <`parameter_number`>.
**parameter_number** : int
Number of the parameter to release.
'''
error_code = Long(0)
logger.info("Releasing parameter %d in Minuit" % (parameter_number,))
# execute RELEASE command
self.__gMinuit.mnexcm("RELEASE",
arr('d', [parameter_number+1]), 1, error_code)
def reset(self):
'''Execute TMinuit's `mnrset` method.'''
self.__gMinuit.mnrset(0) # reset TMinuit
def FCN_wrapper(self, number_of_parameters, derivatives,
f, parameters, internal_flag):
'''
This is actually a function called in *ROOT* and acting as a C wrapper
for our `FCN`, which is implemented in Python.
This function is called by `Minuit` several times during a fit. It
doesn't return anything but modifies one of its arguments (*f*).
This is *ugly*, but it's how *ROOT*'s ``TMinuit`` works. Its argument
structure is fixed and determined by `Minuit`:
**number_of_parameters** : int
The number of parameters of the current fit
**derivatives** : C array
If the user chooses to calculate the first derivative of the
function inside the `FCN`, this value should be written here. This
interface to `Minuit` ignores this derivative, however, so
calculating this inside the `FCN` has no effect (yet).
**f** : C array
The desired function value is in f[0] after execution.
**parameters** : C array
A C array of parameters. Is cast to a Python list
**internal_flag** : int
A flag allowing for different behaviour of the function.
Can be any integer from 1 (initial run) to 4(normal run). See
`Minuit`'s specification.
'''
# Retrieve the parameters from the C side of ROOT and
# store them in a Python list -- resource-intensive
# for many calls, but can't be improved (yet?)
parameter_list = np.frombuffer(parameters, dtype=float,
count=self.number_of_parameters)
# call the Python implementation of FCN.
f[0] = self.function_to_minimize(*parameter_list)
def minimize(self, final_fit=True, log_print_level=2):
'''Do the minimization. This calls `Minuit`'s algorithms ``MIGRAD``
for minimization and, if `final_fit` is `True`, also ``HESSE``
for computing/checking the parameter error matrix.'''
# Set the FCN again. This HAS to be done EVERY
# time the minimize method is called because of
# the implementation of SetFCN, which is not
# object-oriented but sets a global pointer!!!
logger.debug("Updating current FCN")
self.__gMinuit.SetFCN(self.FCN_wrapper)
# Run minimization algorithm (MIGRAD + HESSE)
error_code = Long(0)
prefix = "Minuit run on" # set the timestamp prefix
# insert timestamp
self.out_file.write('\n')
self.out_file.write('#'*(len(prefix)+4+20))
self.out_file.write('\n')
self.out_file.write("# %s " % (prefix,) +
strftime("%Y-%m-%d %H:%M:%S #\n", gmtime()))
self.out_file.write('#'*(len(prefix)+4+20))
self.out_file.write('\n\n')
self.out_file.flush()
# redirect stdout stream
_redirection_target = None
if log_print_level >= 0:
_redirection_target = self.out_file
with redirect_stdout_to(_redirection_target):
self.__gMinuit.SetPrintLevel(log_print_level) # set Minuit print level
logger.debug("Running MIGRAD")
self.__gMinuit.mnexcm("MIGRAD",
arr('d', [self.max_iterations, self.tolerance]),
2, error_code)
if(final_fit):
logger.debug("Running HESSE")
self.__gMinuit.mnexcm("HESSE", arr('d', [self.max_iterations]), 1, error_code)
# return to normal print level
self.__gMinuit.SetPrintLevel(self.print_level)
def minos_errors(self, log_print_level=1):
'''
Get (asymmetric) parameter uncertainties from MINOS
algorithm. This calls `Minuit`'s algorithms ``MINOS``,
which determines parameter uncertainties using profiling
of the chi2 function.
returns : tuple
A tuple of [err+, err-, parabolic error, global correlation]
'''
# Set the FCN again. This HAS to be done EVERY
# time the minimize method is called because of
# the implementation of SetFCN, which is not
# object-oriented but sets a global pointer!!!
logger.debug("Updating current FCN")
self.__gMinuit.SetFCN(self.FCN_wrapper)
# redirect stdout stream
_redirection_target = None
if log_print_level >= 0:
_redirection_target = self.out_file
with redirect_stdout_to(_redirection_target):
self.__gMinuit.SetPrintLevel(log_print_level)
logger.debug("Running MINOS")
error_code = Long(0)
self.__gMinuit.mnexcm("MINOS", arr('d', [self.max_iterations]), 1, error_code)
# return to normal print level
self.__gMinuit.SetPrintLevel(self.print_level)
output = []
errpos=Double(0) # positive parameter error
errneg=Double(0) # negative parameter error
err=Double(0) # parabolic error
gcor=Double(0) # global correlation coefficient
for i in range(0, self.number_of_parameters):
self.__gMinuit.mnerrs(i, errpos, errneg, err, gcor)
output.append([float(errpos),float(errneg),float(err),float(gcor)])
return output
class Minuit:
'''
A class for communicating with ROOT's function minimizer tool Minuit.
'''
def __init__(self,
number_of_parameters,
function_to_minimize,
parameter_names,
start_parameters,
parameter_errors,
quiet=True,
verbose=False):
'''
Create a Minuit minimizer for a function `function_to_minimize`.
Necessary arguments are the number of parameters and the function to be
minimized `function_to_minimize`. The function `function_to_minimize`'s
arguments must be numerical values. The same goes for its output.
Another requirement is for every parameter of `function_to_minimize` to
have a default value. These are then used to initialize Minuit.
**number_of_parameters** : int
The number of parameters of the function to minimize.
**function_to_minimize** : function
The function which `Minuit` should minimize. This must be a Python
function with <``number_of_parameters``> arguments.
**parameter_names** : tuple/list of strings
The parameter names. These are used to keep track of the parameters
in `Minuit`'s output.
**start_parameters** : tuple/list of floats
The start values of the parameters. It is important to have a good,
if rough, estimate of the parameters at the minimum before starting
the minimization. Wrong initial parameters can yield a local
minimum instead of a global one.
**parameter_errors** : tuple/list of floats
An initial guess of the parameter errors. These errors are used to
define the initial step size.
*quiet* : boolean (optional, default: ``True``)
If ``True``, suppresses all output from ``TMinuit``.
*verbose* : boolean (optional, default: ``False``)
If ``True``, sets ``TMinuit``'s print level to a high value, so
that all output is logged.
'''
#: the name of this minimizer type
self.name = "ROOT::TMinuit"
#: the actual `FCN` called in ``FCN_wrapper``
self.function_to_minimize = function_to_minimize
#: number of parameters to minimize for
self.number_of_parameters = number_of_parameters
if not quiet:
self.out_file = open(log_file("minuit.log"), 'a')
else:
self.out_file = null_file()
# create a TMinuit instance for that number of parameters
self.__gMinuit = TMinuit(self.number_of_parameters)
# instruct Minuit to use this class's FCN_wrapper method as a FCN
self.__gMinuit.SetFCN(self.FCN_wrapper)
# set print level according to flag
if quiet:
self.set_print_level(-1000) # suppress output
elif verbose:
self.set_print_level(10) # detailed output
else:
self.set_print_level(0) # frugal output
# initialize minimizer
self.set_err()
self.set_strategy()
self.set_parameter_values(start_parameters)
self.set_parameter_errors(parameter_errors)
self.set_parameter_names(parameter_names)
#: maximum number of iterations until ``TMinuit`` gives up
self.max_iterations = M_MAX_ITERATIONS
#: ``TMinuit`` tolerance
self.tolerance = M_TOLERANCE
def update_parameter_data(self, show_warnings=False):
"""
(Re-)Sets the parameter names, values and step size on the
C++ side of Minuit.
"""
error_code = Long(0)
try:
# Set up the starting fit parameters in TMinuit
for i in xrange(0, self.number_of_parameters):
self.__gMinuit.mnparm(i, self.parameter_names[i],
self.current_parameters[i],
0.1 * self.parameter_errors[i], 0, 0,
error_code)
# use 10% of the par. 1-sigma errors as the initial step size
except AttributeError, e:
if show_warnings:
logger.warn("Cannot update Minuit data on the C++ side. "
"AttributeError: %s" % (e, ))
return error_code
def fit(self):
numberOfParameters = len(self.samples)
gMinuit = TMinuit(numberOfParameters)
if self.method == "logLikelihood": # set function for minimisation
gMinuit.SetFCN(self.logLikelihood)
gMinuit.SetMaxIterations(1000000000000)
# set Minuit print level
# printlevel = -1 quiet (also suppress all warnings)
# = 0 normal
# = 1 verbose
# = 2 additional output giving intermediate results.
# = 3 maximum output, showing progress of minimizations.
gMinuit.SetPrintLevel(-1)
# Error definition: 1 for chi-squared, 0.5 for negative log likelihood
# SETERRDEF<up>: Sets the value of UP (default value= 1.), defining parameter errors.
# Minuit defines parameter errors as the change in parameter value required to change the function value by UP.
# Normally, for chisquared fits UP=1, and for negative log likelihood, UP=0.5.
gMinuit.SetErrorDef(0.5)
# error flag for functions passed as reference.set to as 0 is no error
errorFlag = Long(2)
N_min = 0
N_max = self.fit_data_collection.max_n_data() * 2
param_index = 0
# MNPARM
# Implements one parameter definition:
# mnparm(k, cnamj, uk, wk, a, b, ierflg)
# K (external) parameter number
# CNAMK parameter name
# UK starting value
# WK starting step size or uncertainty
# A, B lower and upper physical parameter limits
# and sets up (updates) the parameter lists.
# Output: IERFLG =0 if no problems
# >0 if MNPARM unable to implement definition
for sample in self.samples: # all samples but data
if self.n_distributions > 1:
gMinuit.mnparm(
param_index,
sample,
self.normalisation[self.distributions[0]][sample],
10.0,
N_min,
N_max,
errorFlag,
)
else:
gMinuit.mnparm(param_index, sample, self.normalisation[sample], 10.0, N_min, N_max, errorFlag)
param_index += 1
arglist = array("d", 10 * [0.0])
# minimisation strategy: 1 standard, 2 try to improve minimum (a bit slower)
arglist[0] = 2
# minimisation itself
# SET STRategy<level>: Sets the strategy to be used in calculating first and second derivatives and in certain minimization methods.
# In general, low values of <level> mean fewer function calls and high values mean more reliable minimization.
# Currently allowed values are 0, 1 (default), and 2.
gMinuit.mnexcm("SET STR", arglist, 1, errorFlag)
gMinuit.Migrad()
gMinuit.mnscan() # class for minimization using a scan method to find the minimum; allows for user interaction: set/change parameters, do minimization, change parameters, re-do minimization etc.
gMinuit.mnmatu(1) # prints correlation matrix (always needed)
self.module = gMinuit
self.performedFit = True
if not self.module:
raise Exception("No fit results available. Please run fit method first")
results = {}
param_index = 0
for sample in self.samples:
temp_par = Double(0)
temp_err = Double(0)
self.module.GetParameter(param_index, temp_par, temp_err)
if math.isnan(temp_err):
self.logger.warning("Template fit error is NAN, setting to sqrt(N).")
temp_err = math.sqrt(temp_par)
# gMinuit.Command("SCAn %i %i %i %i" % ( param_index, 100, N_min, N_total ) );
# scan = gMinuit.GetPlot()
# results[sample] = ( temp_par, temp_err, scan )
results[sample] = (temp_par, temp_err)
param_index += 1
# # gMinuit.Command("CONtour 1 2 3 50")
# gMinuit.SetErrorDef(1)
# results['contour'] = [gMinuit.Contour(100, 0, 1)]
# gMinuit.SetErrorDef(4)
# results['contour'].append(gMinuit.Contour(100, 0, 1))
self.results = results
class Minuit:
'''
A class for communicating with ROOT's function minimizer tool Minuit.
'''
def __init__(self, number_of_parameters, function_to_minimize,
parameter_names, start_parameters, parameter_errors,
quiet=True, verbose=False):
'''
Create a Minuit minimizer for a function `function_to_minimize`.
Necessary arguments are the number of parameters and the function to be
minimized `function_to_minimize`. The function `function_to_minimize`'s
arguments must be numerical values. The same goes for its output.
Another requirement is for every parameter of `function_to_minimize` to
have a default value. These are then used to initialize Minuit.
**number_of_parameters** : int
The number of parameters of the function to minimize.
**function_to_minimize** : function
The function which `Minuit` should minimize. This must be a Python
function with <``number_of_parameters``> arguments.
**parameter_names** : tuple/list of strings
The parameter names. These are used to keep track of the parameters
in `Minuit`'s output.
**start_parameters** : tuple/list of floats
The start values of the parameters. It is important to have a good,
if rough, estimate of the parameters at the minimum before starting
the minimization. Wrong initial parameters can yield a local
minimum instead of a global one.
**parameter_errors** : tuple/list of floats
An initial guess of the parameter errors. These errors are used to
define the initial step size.
*quiet* : boolean (optional, default: ``True``)
If ``True``, suppresses all output from ``TMinuit``.
*verbose* : boolean (optional, default: ``False``)
If ``True``, sets ``TMinuit``'s print level to a high value, so
that all output is logged.
'''
#: the name of this minimizer type
self.name = "ROOT::TMinuit"
#: the actual `FCN` called in ``FCN_wrapper``
self.function_to_minimize = function_to_minimize
#: number of parameters to minimize for
self.number_of_parameters = number_of_parameters
self.out_file = open(log_file("minuit.log"), 'a')
# create a TMinuit instance for that number of parameters
self.__gMinuit = TMinuit(self.number_of_parameters)
# instruct Minuit to use this class's FCN_wrapper method as a FCN
self.__gMinuit.SetFCN(self.FCN_wrapper)
# set print level according to flag
if quiet:
self.set_print_level(-1000) # suppress output
elif verbose:
self.set_print_level(10) # detailed output
else:
self.set_print_level(0) # frugal output
# initialize minimizer
self.set_err()
self.set_strategy()
self.set_parameter_values(start_parameters)
self.set_parameter_errors(parameter_errors)
self.set_parameter_names(parameter_names)
#: maximum number of iterations until ``TMinuit`` gives up
self.max_iterations = M_MAX_ITERATIONS
#: ``TMinuit`` tolerance
self.tolerance = M_TOLERANCE
def update_parameter_data(self, show_warnings=False):
"""
(Re-)Sets the parameter names, values and step size on the
C++ side of Minuit.
"""
error_code = Long(0)
try:
# Set up the starting fit parameters in TMinuit
for i in xrange(0, self.number_of_parameters):
self.__gMinuit.mnparm(i, self.parameter_names[i],
self.current_parameters[i],
0.1 * self.parameter_errors[i],
0, 0, error_code)
# use 10% of the par. 1-sigma errors as the initial step size
except AttributeError, e:
if show_warnings:
logger.warn("Cannot update Minuit data on the C++ side. "
"AttributeError: %s" % (e, ))
return error_code
def test1MinuitFit(self):
"""Test minuit callback and fit"""
# setup minuit and callback
gMinuit = TMinuit(5)
gMinuit.SetPrintLevel(-1) # quiet
gMinuit.SetGraphicsMode(ROOT.kFALSE)
gMinuit.SetFCN(fcn)
arglist = array('d', 10 * [0.])
if not exp_pyroot and sys.hexversion < 0x3000000:
ierflg = ROOT.Long()
else:
ierflg = ctypes.c_int()
arglist[0] = 1
gMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
# set starting values and step sizes for parameters
vstart = array('d', [3, 1, 0.1, 0.01])
step = array('d', [0.1, 0.1, 0.01, 0.001])
gMinuit.mnparm(0, "a1", vstart[0], step[0], 0, 0, ierflg)
gMinuit.mnparm(1, "a2", vstart[1], step[1], 0, 0, ierflg)
gMinuit.mnparm(2, "a3", vstart[2], step[2], 0, 0, ierflg)
gMinuit.mnparm(3, "a4", vstart[3], step[3], 0, 0, ierflg)
# now ready for minimization step
arglist[0] = 500
arglist[1] = 1.
gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
# verify results
if exp_pyroot:
Double = ctypes.c_double
else:
Double = ROOT.Double
amin, edm, errdef = Double(), Double(), Double()
if not exp_pyroot and sys.hexversion < 0x3000000:
Long = ROOT.Long
nvpar, nparx, icstat = Long(), Long(), Long()
else:
nvpar, nparx, icstat = ctypes.c_int(), ctypes.c_int(
), ctypes.c_int()
gMinuit.mnstat(amin, edm, errdef, nvpar, nparx, icstat)
# gMinuit.mnprin( 3, amin )
if exp_pyroot or sys.hexversion >= 0x3000000:
nvpar, nparx, icstat = map(lambda x: x.value,
[nvpar, nparx, icstat])
self.assertEqual(nvpar, 4)
self.assertEqual(nparx, 4)
# success means that full covariance matrix is available (icstat==3)
self.assertEqual(icstat, 3)
# check results (somewhat debatable ... )
par, err = Double(), Double()
if exp_pyroot:
# ctypes.c_double requires the explicit retrieval of the inner value
gMinuit.GetParameter(0, par, err)
self.assertEqual(round(par.value - 2.15, 2), 0.)
self.assertEqual(round(err.value - 0.10, 2), 0.)
gMinuit.GetParameter(1, par, err)
self.assertEqual(round(par.value - 0.81, 2), 0.)
self.assertEqual(round(err.value - 0.25, 2), 0.)
gMinuit.GetParameter(2, par, err)
self.assertEqual(round(par.value - 0.17, 2), 0.)
self.assertEqual(round(err.value - 0.40, 2), 0.)
gMinuit.GetParameter(3, par, err)
self.assertEqual(round(par.value - 0.10, 2), 0.)
self.assertEqual(round(err.value - 0.16, 2), 0.)
else:
gMinuit.GetParameter(0, par, err)
self.assertEqual(round(par - 2.15, 2), 0.)
self.assertEqual(round(err - 0.10, 2), 0.)
gMinuit.GetParameter(1, par, err)
self.assertEqual(round(par - 0.81, 2), 0.)
self.assertEqual(round(err - 0.25, 2), 0.)
gMinuit.GetParameter(2, par, err)
self.assertEqual(round(par - 0.17, 2), 0.)
self.assertEqual(round(err - 0.40, 2), 0.)
gMinuit.GetParameter(3, par, err)
self.assertEqual(round(par - 0.10, 2), 0.)
self.assertEqual(round(err - 0.16, 2), 0.)
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
def prepareAndRunOptimizer(self,
xValues,
yValues,
erryValues,
fixParams,
optFunction,
parValues,
parNames,
printOutLevel=0):
self.xValues = xValues
self.yValues = yValues
self.erryValues = erryValues
self.fixParams = fixParams
initialError = 0.1
nBins = len(self.xValues)
gMinuit = TMinuit(nBins)
gMinuit.SetFCN(optFunction)
arglist = array('d', nBins * [0])
ierflg = c_int(0)
arglist[0] = 1 # 1 for chi2, 0.5 for likelihood
gMinuit.mnexcm('SET ERR', arglist, 1, ierflg)
# Set starting values and step sizes for parameters
vStart = parValues
vStep = [initialError for i in range(len(parValues))]
for i, name in enumerate(parNames):
gMinuit.mnparm(i, name, vStart[i], vStep[i], 0, 0, ierflg)
# Fix parameters (counting from 1)
for i, fix in enumerate(self.fixParams):
arglist[i] = fix + 1
gMinuit.mnexcm('FIX', arglist, len(self.fixParams), ierflg)
# Define printout level
arglist[0] = printOutLevel
# -1 = no output except from SHOW
# 0 = minimum output (no starting values or intermediate results) default value, normal output
# 1 = additional output giving intermediate results.
# 2 = maximum output, showing progress of minimizations.
gMinuit.mnexcm('SET PRI', arglist, 1, ierflg)
# Now ready for minimization step
arglist[0] = 5000 # Max calls
arglist[1] = 0.1 # Tolerance
gMinuit.mnexcm('MIGRAD', arglist, 2, ierflg)
# Print results
self.dof = self.nMeas - len(parValues) + len(self.fixParams)
fmin, fedm, errdef = c_double(0.), c_double(0.), c_double(0.)
npari, nparx, istat = c_int(0), c_int(0), c_int(0)
gMinuit.mnstat(fmin, fedm, errdef, npari, nparx, istat)
print('\nFMIN:', round(fmin.value,
2), '\tFEDM:', '{:.1e}'.format(fedm.value),
'\tERRDEF:', errdef.value, '\tNPARI:', npari.value, '\tNPARX:',
nparx.value, '\tISTAT:', istat.value)
print('chi-2:', round(self.chi2, 2), '\td.o.f.:', self.dof,
'\tchi-2/d.o.f.:', round(self.chi2 / self.dof, 2), '\n')
return gMinuit, istat
def test1MinuitFit(self):
"""Test minuit callback and fit"""
# setup minuit and callback
gMinuit = TMinuit(5)
gMinuit.SetPrintLevel(-1) # quiet
gMinuit.SetGraphicsMode(ROOT.kFALSE)
gMinuit.SetFCN(fcn)
arglist = array('d', 10 * [0.])
ierflg = Long()
arglist[0] = 1
gMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
# set starting values and step sizes for parameters
vstart = array('d', [3, 1, 0.1, 0.01])
step = array('d', [0.1, 0.1, 0.01, 0.001])
gMinuit.mnparm(0, "a1", vstart[0], step[0], 0, 0, ierflg)
gMinuit.mnparm(1, "a2", vstart[1], step[1], 0, 0, ierflg)
gMinuit.mnparm(2, "a3", vstart[2], step[2], 0, 0, ierflg)
gMinuit.mnparm(3, "a4", vstart[3], step[3], 0, 0, ierflg)
# now ready for minimization step
arglist[0] = 500
arglist[1] = 1.
gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
# verify results
amin, edm, errdef = Double(), Double(), Double()
nvpar, nparx, icstat = Long(), Long(), Long()
gMinuit.mnstat(amin, edm, errdef, nvpar, nparx, icstat)
# gMinuit.mnprin( 3, amin )
self.assertEqual(nvpar, 4)
self.assertEqual(nparx, 4)
# success means that full covariance matrix is available (icstat==3)
self.assertEqual(icstat, 3)
# check results (somewhat debatable ... )
par, err = Double(), Double()
gMinuit.GetParameter(0, par, err)
self.assertEqual(round(par - 2.15, 2), 0.)
self.assertEqual(round(err - 0.10, 2), 0.)
gMinuit.GetParameter(1, par, err)
self.assertEqual(round(par - 0.81, 2), 0.)
self.assertEqual(round(err - 0.25, 2), 0.)
gMinuit.GetParameter(2, par, err)
self.assertEqual(round(par - 0.17, 2), 0.)
self.assertEqual(round(err - 0.40, 2), 0.)
gMinuit.GetParameter(3, par, err)
self.assertEqual(round(par - 0.10, 2), 0.)
self.assertEqual(round(err - 0.16, 2), 0.)
def dofit(self) :
#print 'starting fit for hypothesis index %d'%(self.fitindex)#DEBUG
#set up the minuit object, etc.
parNames = ['fitindex','pZv','scalelep','scaleblep','scalehad1','scalehad2','scalehad3']
parinivals = [self.fitindex,0.,1.,1.,1.,1.,1.]
parerrs = [0.0,0.0,0.0,0.0,0.0,0.0,0.0]
bestParValues = []
nPars = 6 if self.topology==1 else 7
for i in range(1,nPars) :
bestParValues.append(parinivals[i])
ierflag = Long(1)
arglist = array( 'd', [-1.0] )
minuit = TMinuit(nPars)
minuit.mnexcm('SET PRINT', arglist, 1,ierflag)
minuit.mnexcm('SET NOWARNINGS',arglist,1,ierflag)
arglist[0] = 100000.
#add parameters to the fitter
for i in range(nPars) :
minuit.mnparm(i,parNames[i],parinivals[i],1.0,0.,0.,ierflag)
#fix the first 'fit index' parameter
minuit.mnfixp(0,ierflag)
#set the minimization function to use
if self.topology==1 : minuit.SetFCN(fcnt1)
elif self.topology==2 : minuit.SetFCN(fcnt2)
elif self.topology==3 : minuit.SetFCN(fcnt3)
#minimize and get the error flag
minuit.mnexcm('MIGRAD', arglist, 1, ierflag)
#print 'index = %d, errflag = %s'%(self.fitindex,ierflag) #DEBUG
errflag = int(ierflag)
#Check fit Chi2
tmp1 = Double(1.0); tmp2 = Double(1.0); tmp3 = Double(1.0)
minuit.mnstat(tmp1,tmp2,tmp3,Long(1),Long(1),Long(1))
#print 'chi2 = %.4f'%(tmp1) #DEBUG
chi2value = float(tmp1)
#Get the bestfit parameters back from minuit
for j in range(1,nPars) :
tmp = Double(1.0)
minuit.GetParameter(j,tmp,Double(parerrs[j]))
bestParValues[j-1] = float(tmp)
return errflag, chi2value, bestParValues
class Minuit(object):
"""A wrapper class to initialize a minuit object with a numpy array.
Positional args:
myFCN : A python callable
params : An array (or other python sequence) of parameters
Keyword args:
limits [None] : a nested sequence of (lower_limit,upper_limit) for each parameter.
steps [[.1]*npars] : Estimated errors for the parameters, used as an initial step size.
tolerance [.001] : Tolerance to test for convergence. Minuit considers convergence to be
when the estimated distance to the minimum (edm) is <= .001*up*tolerance,
or 5e-7 by default.
up [.5] : Change in the objective function that determines 1-sigma error. .5 if
the objective function is -log(Likelihood), 1 for chi-squared.
max_calls [10000] : Maximum number of calls to the objective function.
param_names ['p0','p1',...] : a list of names for the parameters
args [()] : a tuple of extra arguments to pass to myFCN and gradient.
gradient [None] : a function that takes a list of parameters and returns a list of
first derivatives of myFCN. Assumed to take the same args as myFCN.
force_gradient [0] : Set to 1 to force Minuit to use the user-provided gradient function.
strategy[1] : Strategy for minuit to use, from 0 (fast) to 2 (safe)
fixed [False, False, ...] : If passed, an array of all the parameters to fix
"""
def __init__(self,myFCN,params,**kwargs):
from ROOT import TMinuit,Long,Double
self.limits = np.zeros((len(params),2))
self.steps = .04*np.ones(len(params)) # about 10 percent in log10 space
self.tolerance = .001
self.maxcalls = 10000
self.printMode = 0
self.up = 0.5
self.param_names = ['p%i'%i for i in xrange(len(params))]
self.erflag = Long()
self.npars = len(params)
self.args = ()
self.gradient = None
self.force_gradient = 0
self.strategy = 1
self.fixed = np.zeros_like(params)
self.__dict__.update(kwargs)
self.params = np.asarray(params,dtype='float')
self.fixed=np.asarray(self.fixed,dtype=bool)
self.fcn = FCN(myFCN,self.params,args=self.args,gradient=self.gradient)
self.fval = self.fcn.fval
self.minuit = TMinuit(self.npars)
self.minuit.SetPrintLevel(self.printMode)
self.minuit.SetFCN(self.fcn)
if self.gradient:
self.minuit.mncomd('SET GRA %i'%(self.force_gradient),self.erflag)
self.minuit.mncomd('SET STR %i'%self.strategy,Long())
for i in xrange(self.npars):
if self.limits[i][0] is None: self.limits[i][0] = 0.0
if self.limits[i][1] is None: self.limits[i][1] = 0.0
self.minuit.DefineParameter(i,self.param_names[i],self.params[i],self.steps[i],self.limits[i][0],self.limits[i][1])
self.minuit.SetErrorDef(self.up)
for index in np.where(self.fixed)[0]:
self.minuit.FixParameter(int(index))
def minimize(self,method='MIGRAD'):
from ROOT import TMinuit,Long,Double
self.minuit.mncomd('%s %i %f'%(method, self.maxcalls,self.tolerance),self.erflag)
for i in xrange(self.npars):
val,err = Double(),Double()
self.minuit.GetParameter(i,val,err)
self.params[i] = val
self.fval = self.fcn.fcn(self.params)
return (self.params,self.fval)
def errors(self,method='HESSE'):
"""method ['HESSE'] : how to calculate the errors; Currently, only 'HESSE' works."""
if not np.any(self.fixed):
mat = np.zeros(self.npars**2)
if method == 'HESSE':
self.minuit.mnhess()
else:
raise Exception("Method %s not recognized." % method)
self.minuit.mnemat(mat,self.npars)
return mat.reshape((self.npars,self.npars))
else:
# Kind of ugly, but for fixed parameters, you need to expand out the covariance matrix.
nf=int(np.sum(~self.fixed))
mat = np.zeros(nf**2)
if method == 'HESSE':
self.minuit.mnhess()
else:
raise Exception("Method %s not recognized." % method)
self.minuit.mnemat(mat,nf)
# Expand out the covariance matrix.
cov = np.zeros((self.npars,self.npars))
cov[np.outer(~self.fixed,~self.fixed)] = np.ravel(mat)
return cov
def uncorrelated_minos_error(self):
""" Kind of a kludge, but a compromise between the speed of
HESSE errors and the accuracy of MINOS errors. It accounts
for non-linearities in the likelihood by varying each function
until the value has fallen by the desired amount using hte
MINOS code. But does not account for correlations between
the parameters by fixing all other parameters during the
minimzation.
Again kludgy, but what is returned is an effective covariance
matrix. The diagonal errors are calcualted by averaging the
upper and lower errors and the off diagonal terms are set
to 0. """
cov = np.zeros((self.npars,self.npars))
# fix all parameters
for i in range(self.npars):
self.minuit.FixParameter(int(i))
# loop over free paramters getting error
for i in np.where(self.fixed==False)[0]:
self.minuit.Release(int(i))
# compute error
self.minuit.mnmnos()
low,hi,parab,gcc=ROOT.Double(),ROOT.Double(),ROOT.Double(),ROOT.Double()
# get error
self.minuit.mnerrs(int(i),low,hi,parab,gcc)
cov[i,i]=((abs(low)+abs(hi))/2.0)**2
self.minuit.FixParameter(int(i))
for i,fixed in enumerate(self.fixed):
if fixed:
self.minuit.FixParameter(int(i))
else:
self.minuit.Release(int(i))
return cov
def test1MinuitFit( self ):
"""Test minuit callback and fit"""
# setup minuit and callback
gMinuit = TMinuit(5)
gMinuit.SetPrintLevel( -1 ) # quiet
gMinuit.SetGraphicsMode( ROOT.kFALSE )
gMinuit.SetFCN( fcn )
arglist = array( 'd', 10*[0.] )
ierflg = Long()
arglist[0] = 1
gMinuit.mnexcm( "SET ERR", arglist, 1, ierflg )
# set starting values and step sizes for parameters
vstart = array( 'd', [ 3, 1, 0.1, 0.01 ] )
step = array( 'd', [ 0.1, 0.1, 0.01, 0.001 ] )
gMinuit.mnparm( 0, "a1", vstart[0], step[0], 0, 0, ierflg )
gMinuit.mnparm( 1, "a2", vstart[1], step[1], 0, 0, ierflg )
gMinuit.mnparm( 2, "a3", vstart[2], step[2], 0, 0, ierflg )
gMinuit.mnparm( 3, "a4", vstart[3], step[3], 0, 0, ierflg )
# now ready for minimization step
arglist[0] = 500
arglist[1] = 1.
gMinuit.mnexcm( "MIGRAD", arglist, 2, ierflg )
# verify results
amin, edm, errdef = Double(), Double(), Double()
nvpar, nparx, icstat = Long(), Long(), Long()
gMinuit.mnstat( amin, edm, errdef, nvpar, nparx, icstat )
# gMinuit.mnprin( 3, amin )
self.assertEqual( nvpar, 4 )
self.assertEqual( nparx, 4 )
# success means that full covariance matrix is available (icstat==3)
self.assertEqual( icstat, 3 )
# check results (somewhat debatable ... )
par, err = Double(), Double()
gMinuit.GetParameter( 0, par, err )
self.assertEqual( round( par - 2.15, 2 ), 0. )
self.assertEqual( round( err - 0.10, 2 ), 0. )
gMinuit.GetParameter( 1, par, err )
self.assertEqual( round( par - 0.81, 2 ), 0. )
self.assertEqual( round( err - 0.25, 2 ), 0. )
gMinuit.GetParameter( 2, par, err )
self.assertEqual( round( par - 0.17, 2 ), 0. )
self.assertEqual( round( err - 0.40, 2 ), 0. )
gMinuit.GetParameter( 3, par, err )
self.assertEqual( round( par - 0.10, 2 ), 0. )
self.assertEqual( round( err - 0.16, 2 ), 0. )
g1 = 0.
g2 = 0.
for i in range(len(error_w1)):
g1 += error_w1[i]**2
g2 += error_w2[i]**2
s = error_w1[3]*error_w2[3]
t = error_w1[4]*error_w2[4]
global kor_matirx
kor_matirx = np.array([[g1, s+t], [ s+t, g2]])
kor_matirx_inv = inv(kor_matirx)
print kor_matirx
# --> set up MINUIT
myMinuit = TMinuit(npar) # initialize TMinuit with maximum of npar parameters
myMinuit.SetFCN(fcn) # set function to minimize
arglist = arr('d', 2*[0.01]) # set error definition
ierflg = Long(0)
arglist[0] = 1. # 1 sigma is Delta chi^2 = 1
myMinuit.mnexcm("SET ERR", arglist ,1,ierflg)
# --> Set starting values and step sizes for parameters
# Define the parameters for the fit
myMinuit.mnparm(1, "mean", 400, 0.001, 0,0,ierflg)
arglist[0] = 6000 # Number of calls to FCN before giving up.
arglist[1] = 0.3 # Tolerance
myMinuit.mnexcm("MIGRAD", arglist ,2,ierflg) # execute the minimisation
outTag =outTag_name+str(q)
loaded_model = joblib.load(os.path.expanduser('~/HHbbgg_ETH_devel/bregression/output_files/regression_heppy_'+outTag+'.pkl'))
X_pred_data = loaded_model.predict(X_test_features).astype(np.float64)
X_predicted_all.append(X_pred_data)
n_evt = len(X_predicted_all[0])
X_predictions_for_fit = np.column_stack([x for x in X_predicted_all])
mpvs=[]
print 'here'
fit_quantile=[]
gMinuit = TMinuit(4)
gMinuit.SetPrintLevel(-1)
gMinuit.SetFCN( fcn )
arglist = np.array( 10*[0.] )
ierflg = 0
arglist[0] = 1
gMinuit.mnexcm( "SET ERR", arglist, 1, Long(ierflg) )
arglist[0] = 0
gMinuit.mnexcm("SET PRINT", arglist ,0,Long(ierflg));
vstart = np.array( [ -2 , 4,-1, 0.5] )
step = np.array( [ 0.001, 0.001, 0.01, 0.01 ] )
gMinuit.mnparm( 0, "a1", vstart[0], step[0], 0, 0, Long(ierflg) )
gMinuit.mnparm( 1, "a2", vstart[1], step[1], 0, 0, Long(ierflg) )
gMinuit.mnparm( 2, "a3", vstart[2], step[2], 0, 0, Long(ierflg) )
gMinuit.mnparm( 3, "a4", vstart[3], step[3], 0, 0, Long(ierflg) )
arglist[0] = 500
g1 = 0.
g2 = 0.
for i in range(len(error_w1)):
g1 += error_w1[i]**2
g2 += error_w2[i]**2
s = error_w1[3] * error_w2[3]
t = error_w1[4] * error_w2[4]
global kor_matirx
kor_matirx = np.array([[g1, s + t], [s + t, g2]])
kor_matirx_inv = inv(kor_matirx)
print kor_matirx
# --> set up MINUIT
myMinuit = TMinuit(npar) # initialize TMinuit with maximum of npar parameters
myMinuit.SetFCN(fcn) # set function to minimize
arglist = arr('d', 2 * [0.01]) # set error definition
ierflg = Long(0)
arglist[0] = 1. # 1 sigma is Delta chi^2 = 1
myMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
# --> Set starting values and step sizes for parameters
# Define the parameters for the fit
myMinuit.mnparm(1, "mean", 400, 0.001, 0, 0, ierflg)
arglist[0] = 6000 # Number of calls to FCN before giving up.
arglist[1] = 0.3 # Tolerance
myMinuit.mnexcm("MIGRAD", arglist, 2, ierflg) # execute the minimisation
# --> check TMinuit status
class Fits:
def __init__(self):
self.p_n = [
0,
] * 100
self.e_n = [
0,
] * 100
self.stored_parameters = [
0,
] * 100
self.num_bins = 0
self.xmins = []
self.xmaxes = []
self.data = []
self.errors = []
self.data_fits = []
self.model_scale_values = []
self.final = False
self.exclude_regions = ((0, 0), )
self.col1 = 1
self.col2 = TColor.GetColor(27, 158, 119)
self.col3 = TColor.GetColor(217, 95, 2)
self.col4 = TColor.GetColor(117, 112, 179)
def run_mass_fit(self, peak_scale_initial, mass=0):
self.gMinuit = TMinuit(30)
self.gMinuit.SetPrintLevel(-1)
self.gMinuit.SetFCN(self.Fitfcn_max_likelihood)
arglist = array("d", [
0,
] * 10)
ierflg = ROOT.Long(0)
arglist[0] = ROOT.Double(1)
# peak_scale_initial = ROOT.Double(peak_scale_initial)
tmp = array("d", [
0,
])
self.gMinuit.mnexcm("SET NOWarnings", tmp, 0, ierflg)
self.gMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
self.gMinuit.mnparm(0, "p1", 5e-6, 1e-7, 0, 0, ierflg)
self.gMinuit.mnparm(1, "p2", 10, 10, 0, 0, ierflg)
self.gMinuit.mnparm(2, "p3", -5.3, 1, 0, 0, ierflg)
self.gMinuit.mnparm(3, "p4", -4e-2, 1e-2, 0, 0, ierflg)
self.gMinuit.mnparm(4, "p5", peak_scale_initial,
peak_scale_initial / 50, 0, 0, ierflg)
self.background_fit_only = [
0,
] * len(self.data)
arglist[0] = ROOT.Double(0)
arglist[1] = ROOT.Double(0)
#self.exclude_regions = ((2.2, 3.3),)
self.gMinuit.FixParameter(2)
self.gMinuit.FixParameter(3)
self.gMinuit.FixParameter(4)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
self.gMinuit.Release(2)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
self.gMinuit.Release(3)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
# Find an actual best fit
#self.exclude_regions = ((0, 2), (3.3, 100),)
self.gMinuit.FixParameter(0)
self.gMinuit.FixParameter(1)
self.gMinuit.FixParameter(2)
self.gMinuit.FixParameter(3)
self.gMinuit.Release(4)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
self.exclude_regions = ()
self.gMinuit.Release(0)
self.gMinuit.Release(1)
self.gMinuit.Release(2)
self.gMinuit.Release(3)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
best_fit_value = ROOT.Double(0)
self.gMinuit.mnstat(best_fit_value, ROOT.Double(0), ROOT.Double(0),
ROOT.Long(0), ROOT.Long(0), ROOT.Long(0))
#print("Best fit value", best_fit_value)
# And prepare for iterating over fit values for N injected events
self.gMinuit.Release(0)
self.gMinuit.Release(1)
self.gMinuit.Release(2)
self.gMinuit.Release(3)
self.exclude_regions = ()
#self.data_fits = no_peak_data_fits
x_values = []
y_values = []
fitted_N = ROOT.Double(0)
self.gMinuit.GetParameter(4, fitted_N, ROOT.Double(0))
best_fit_likelihood = self.calc_likelihood(fitted_N)
step = 5
if int(mass) >= 4000:
step = 1
if int(mass) >= 5000:
step = 0.2
if int(mass) >= 6000:
step = 0.1
if int(mass) >= 6500:
step = 0.05
N = 0
while N < 5000:
start_sum = sum([math.exp(-a) for a in y_values])
fit_likelihood = self.calc_likelihood(N)
x_values.append(N)
y_values.append(fit_likelihood - best_fit_likelihood)
probabilities = [math.exp(-a) for a in y_values]
end_sum = sum(probabilities)
max_prob = max(probabilities)
normalised_probabilities = [a / max_prob for a in probabilities]
if N / step > 50 and all(
[v > 0.99 for v in normalised_probabilities]):
print(
"Probability=1 everywhere, probably something wrong with fit"
)
print(normalised_probabilities)
return None, None
# if new value changes total by less than 0.1%, end loop
if N > 0 and (end_sum - start_sum) / start_sum < 0.0001:
print("Iterated up to {0}".format(N))
break
N += step
self.iflag = int(ierflg)
return x_values, y_values
def Fitfcn_max_likelihood(self, npar, gin, fcnVal, par, iflag):
likelihood = 0
mf = ROOT.MyMassSpectrum()
mf.SetParameters(par)
ig = GaussIntegrator()
ig.SetFunction(mf)
ig.SetRelTolerance(0.00001)
for i in range(0, self.num_bins):
for lower, higher in self.exclude_regions:
if lower < self.xmins[i] < higher:
continue
model_val = ig.Integral(self.xmins[i], self.xmaxes[i]) / (
self.xmaxes[i] - self.xmins[i])
self.background_fit_only[i] = model_val
model_val += self.model_scale_values[i] * par[4]
self.data_fits[i] = model_val
likelihood += model_val - self.data[i]
if self.data[i] > 0 and model_val > 0:
likelihood += self.data[i] * (math.log(self.data[i]) -
math.log(model_val))
fcnVal[0] = likelihood
def calc_likelihood(self, peak_scale):
like = 0
for i in range(0, self.num_bins):
if self.data_fits[i] <= 0:
continue
p = peak_scale * self.model_scale_values[i]
tmp = ROOT.TMath.PoissonI(self.data[i],
self.background_fit_only[i] + p)
#if peak_scale == 40000:
# print(i, "\txmin", self.xmins[i], "\tdata", self.data[i], "\tdata_fit", self.data_fits[i], "\tp", p, "\tdata_fit+p", self.data_fits[i]+p)
if tmp == 0:
print("tmp == 0 here")
logtmp = math.log(sys.float_info.min)
else:
logtmp = math.log(tmp)
like += logtmp
return -like
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" )
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 ),
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( "" ),
for i in range(mshape[0]):
print "{0:>10s}".format( self.__parnames[i] ),
print
for i in range(mshape[0]):
print "{0:>10s}".format( self.__parnames[i] ),
for j in range(mshape[1]):
fmtstr= "{0:10"+ffmt+"}"
print fmtstr.format( m[i,j] ),
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= Double()
pare= Double()
ivarbl= self.__minuit.GetParameter( ipar, par, pare )
if ivarbl < 0:
message= "Parameter " + str(ipar) + " not defined"
raise MinuitError( message )
pars.append( par )
parerrors.append( pare )
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= Double()
fedm= Double()
errdef= Double()
npari= Long()
nparx= Long()
istat= Long()
self.__minuit.mnstat( fmin, fedm, errdef, npari, nparx, istat )
hstat= { "min": fmin,
"edm": fedm,
"errdef": errdef,
"npari": npari,
"nparx": nparx,
"status": istat }
return hstat
def fit(self):
numberOfParameters = len(self.samples)
gMinuit = TMinuit(numberOfParameters)
if self.method == 'logLikelihood': # set function for minimisation
gMinuit.SetFCN(self.logLikelihood)
gMinuit.SetMaxIterations(1000000000000)
# set Minuit print level
# printlevel = -1 quiet (also suppress all warnings)
# = 0 normal
# = 1 verbose
# = 2 additional output giving intermediate results.
# = 3 maximum output, showing progress of minimizations.
gMinuit.SetPrintLevel(-1)
# Error definition: 1 for chi-squared, 0.5 for negative log likelihood
# SETERRDEF<up>: Sets the value of UP (default value= 1.), defining parameter errors.
# Minuit defines parameter errors as the change in parameter value required to change the function value by UP.
# Normally, for chisquared fits UP=1, and for negative log likelihood, UP=0.5.
gMinuit.SetErrorDef(0.5)
# error flag for functions passed as reference.set to as 0 is no error
errorFlag = Long(2)
N_min = 0
N_max = self.fit_data_collection.max_n_data() * 2
param_index = 0
# MNPARM
# Implements one parameter definition:
# mnparm(k, cnamj, uk, wk, a, b, ierflg)
# K (external) parameter number
# CNAMK parameter name
# UK starting value
# WK starting step size or uncertainty
# A, B lower and upper physical parameter limits
# and sets up (updates) the parameter lists.
# Output: IERFLG =0 if no problems
# >0 if MNPARM unable to implement definition
for sample in self.samples: # all samples but data
if self.n_distributions > 1:
gMinuit.mnparm(
param_index, sample,
self.normalisation[self.distributions[0]][sample], 10.0,
N_min, N_max, errorFlag)
else:
gMinuit.mnparm(param_index, sample, self.normalisation[sample],
10.0, N_min, N_max, errorFlag)
param_index += 1
arglist = array('d', 10 * [0.])
# minimisation strategy: 1 standard, 2 try to improve minimum (a bit slower)
arglist[0] = 2
# minimisation itself
# SET STRategy<level>: Sets the strategy to be used in calculating first and second derivatives and in certain minimization methods.
# In general, low values of <level> mean fewer function calls and high values mean more reliable minimization.
# Currently allowed values are 0, 1 (default), and 2.
gMinuit.mnexcm("SET STR", arglist, 1, errorFlag)
gMinuit.Migrad()
gMinuit.mnscan(
) # class for minimization using a scan method to find the minimum; allows for user interaction: set/change parameters, do minimization, change parameters, re-do minimization etc.
gMinuit.mnmatu(1) # prints correlation matrix (always needed)
self.module = gMinuit
self.performedFit = True
if not self.module:
raise Exception(
'No fit results available. Please run fit method first')
results = {}
param_index = 0
for sample in self.samples:
temp_par = Double(0)
temp_err = Double(0)
self.module.GetParameter(param_index, temp_par, temp_err)
if (math.isnan(temp_err)):
self.logger.warning(
'Template fit error is NAN, setting to sqrt(N).')
temp_err = math.sqrt(temp_par)
# gMinuit.Command("SCAn %i %i %i %i" % ( param_index, 100, N_min, N_total ) );
# scan = gMinuit.GetPlot()
# results[sample] = ( temp_par, temp_err, scan )
results[sample] = (temp_par, temp_err)
param_index += 1
# # gMinuit.Command("CONtour 1 2 3 50")
# gMinuit.SetErrorDef(1)
# results['contour'] = [gMinuit.Contour(100, 0, 1)]
# gMinuit.SetErrorDef(4)
# results['contour'].append(gMinuit.Contour(100, 0, 1))
self.results = results
class Fits:
def __init__(self):
self.p_n = [
0,
] * 100
self.e_n = [
0,
] * 100
self.stored_parameters = [
0,
] * 100
self.num_bins = 0
self.xmins = []
self.xmaxes = []
self.data = []
self.errors = []
self.data_fits = []
self.model_scale_values = []
self.final = False
self.exclude_regions = ((0, 0), )
self.col1 = 1
self.col2 = TColor.GetColor(27, 158, 119)
self.col3 = TColor.GetColor(217, 95, 2)
self.col4 = TColor.GetColor(117, 112, 179)
def run_mass_fit(self, peak_scale_initial):
self.gMinuit = TMinuit(30)
self.gMinuit.SetPrintLevel(-1)
self.gMinuit.SetFCN(self.Fitfcn_max_likelihood)
self.fit_failed = False
arglist = array("d", [
0,
] * 10)
ierflg = ROOT.Long(0)
arglist[0] = ROOT.Double(1)
# peak_scale_initial = ROOT.Double(peak_scale_initial)
tmp = array("d", [
0,
])
self.gMinuit.mnexcm("SET NOWarnings", tmp, 0, ierflg)
self.gMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
self.gMinuit.mnparm(0, "p1", 30, 20, 0, 100, ierflg)
self.gMinuit.mnparm(1, "p2", 10, 1, 0, 0, ierflg)
self.gMinuit.mnparm(2, "p3", -5.3, 1, 0, 0, ierflg)
self.gMinuit.mnparm(3, "p4", -4e-2, 1e-2, 0, 0, ierflg)
self.gMinuit.mnparm(4, "p5", peak_scale_initial, 1, 0, 10000, ierflg)
self.background_fit_only = [
0,
] * len(self.data)
arglist[0] = ROOT.Double(0)
arglist[1] = ROOT.Double(0)
#self.exclude_regions = ((2.2, 3.3),)
self.gMinuit.FixParameter(1)
self.gMinuit.FixParameter(2)
self.gMinuit.FixParameter(3)
self.gMinuit.FixParameter(4)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
print("Run fit 0")
if self.fit_failed:
print("Fit failed, returning")
return None, None
self.gMinuit.Release(1)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
print("Run fit 1")
if self.fit_failed:
print("Fit failed, returning")
return None, None
self.gMinuit.Release(2)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
print("Run fit 2")
if self.fit_failed:
print("Fit failed, returning")
return None, None
self.gMinuit.Release(3)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
print("Run fit 3")
if self.fit_failed:
print("Fit failed, returning")
return None, None
# Find an actual best fit
#self.exclude_regions = ((0, 2), (3.3, 100),)
self.gMinuit.FixParameter(0)
self.gMinuit.FixParameter(1)
self.gMinuit.FixParameter(2)
self.gMinuit.FixParameter(3)
self.gMinuit.Release(4)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
print("Run fit 4")
if self.fit_failed:
print("Fit failed, returning")
return None, None
self.exclude_regions = ()
self.gMinuit.Release(0)
self.gMinuit.Release(1)
self.gMinuit.Release(2)
self.gMinuit.Release(3)
self.gMinuit.mnexcm("simplex", arglist, 2, ierflg)
self.gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
print("Run last fitting stage")
if self.fit_failed:
print("Fit failed, returning")
return None, None
best_fit_value = ROOT.Double(0)
self.gMinuit.mnstat(best_fit_value, ROOT.Double(0), ROOT.Double(0),
ROOT.Long(0), ROOT.Long(0), ROOT.Long(0))
#print("Best fit value", best_fit_value)
# And prepare for iterating over fit values for N injected events
self.gMinuit.Release(0)
self.gMinuit.Release(1)
self.gMinuit.Release(2)
self.gMinuit.Release(3)
self.exclude_regions = ()
#self.data_fits = no_peak_data_fits
x_values = []
y_values = []
for i in range(0, 5):
p = ROOT.Double(0)
self.gMinuit.GetParameter(i, p, ROOT.Double(0))
print("Parameter", i, p)
fitted_N = ROOT.Double(0)
self.gMinuit.GetParameter(4, fitted_N, ROOT.Double(0))
best_fit_likelihood = self.calc_likelihood(fitted_N)
self.iflag = int(ierflg)
print("iflag:", self.iflag)
step = 5
if int(MASS_FILE) >= 4000:
step = 1
if int(MASS_FILE) >= 5000:
step = 0.2
if int(MASS_FILE) >= 6000:
step = 0.1
if int(MASS_FILE) >= 6500:
step = 0.1
N = 0
print("About to start likelihood testing loop")
while N < 10000:
start_sum = sum([math.exp(-a) for a in y_values])
fit_likelihood = self.calc_likelihood(N)
if fit_likelihood is None:
print("Bad fit_likelihood")
return None, None
x_values.append(N)
y_values.append(fit_likelihood - best_fit_likelihood)
probabilities = [math.exp(-a) for a in y_values]
end_sum = sum(probabilities)
max_prob = max(probabilities)
if max_prob == 0:
print("max_prob == 0")
return None, None
normalised_probabilities = [a / max_prob for a in probabilities]
if N / step > 50 and all(
[v > 0.99 for v in normalised_probabilities]):
print(
"Probability=1 everywhere, probably something wrong with fit"
)
print(normalised_probabilities)
return None, None
# if new value changes total by less than 0.1%, end loop
if N > 0 and (end_sum - start_sum) / start_sum < 0.0001:
print("Iterated up to {0}".format(N))
break
N += step
self.iflag = int(ierflg)
return x_values, y_values
def Fitfcn_max_likelihood(self, npar, gin, fcnVal, par, iflag):
likelihood = 0
mf = ROOT.MyMassSpectrum()
mf.SetParameters(par)
ig = GaussIntegrator()
ig.SetFunction(mf)
ig.SetRelTolerance(0.00001)
for i in range(0, self.num_bins):
for lower, higher in self.exclude_regions:
if lower < self.xmins[i] < higher:
continue
model_val = ig.Integral(self.xmins[i], self.xmaxes[i]) / (
self.xmaxes[i] - self.xmins[i])
self.background_fit_only[i] = model_val
model_val += self.model_scale_values[i] * par[4]
self.data_fits[i] = model_val
mv = model_val
di = self.data[i]
#print("mv", mv, "di", di)
#sys.stdout.flush()
if di > 1e10 or math.isinf(mv) or math.isnan(mv):
self.fit_failed = True
return
likelihood += mv - di
if di > 0 and mv > 0:
likelihood += di * (TMath.Log(di) - TMath.Log(mv))
#sys.stderr.flush()
fcnVal[0] = likelihood
def calc_likelihood(self, peak_scale):
like = 0
for i in range(0, self.num_bins):
if self.data_fits[i] <= 0:
continue
p = peak_scale * self.model_scale_values[i]
tmp = ROOT.TMath.PoissonI(self.data[i],
self.background_fit_only[i] + p)
if tmp == 0:
return None
print("tmp == 0 here")
logtmp = math.log(sys.float_info.min)
else:
logtmp = math.log(tmp)
like += logtmp
return -like
def ifit():
gMinuit = TMinuit(npars)
gMinuit.SetFCN(fcn)
arglist = array('d', 10*[0.])
ierflg = Long(1982)
arglist[0] = 1 # 1 for chisquared fits, 0.5 for negative log likelihood
gMinuit.mnexcm("SET ERR", arglist, 1, ierflg)
arglist[0] = 0.00001 # floating point precision
gMinuit.mnexcm("SET EPS", arglist, 1, ierflg)
arglist[0] = 2 # 1 mean fewer function calls, 2 mean more reliable minimization
gMinuit.mnexcm("SET STR", arglist, 1, ierflg)
# Set starting values and step sizes for parameters
vstart = array('d', npars*[1.0])
#vstart = array('d', [0.909, 1.341, 0.942, 1.300, 1.003])
step = array('d', npars*[0.001])
gMinuit.mnparm(0, "ZjLF", vstart[0], step[0], 0, 0, ierflg)
gMinuit.mnparm(1, "ZjHF", vstart[1], step[1], 0, 0, ierflg)
gMinuit.mnparm(2, "WjLF", vstart[2], step[2], 0, 0, ierflg)
gMinuit.mnparm(3, "WjHF", vstart[3], step[3], 1.3, 2.0, ierflg)
gMinuit.mnparm(4, "TT" , vstart[4], step[4], 0, 0, ierflg)
# Fix parameter
#arglist[0] = 1
#gMinuit.mnexcm("FIX", arglist, 1, ierflg)
#arglist[0] = 2
#gMinuit.mnexcm("FIX", arglist, 1, ierflg)
#arglist[0] = 3
#gMinuit.mnexcm("FIX", arglist, 1, ierflg)
#arglist[0] = 4
#gMinuit.mnexcm("FIX", arglist, 1, ierflg)
#arglist[0] = 5
#gMinuit.mnexcm("FIX", arglist, 1, ierflg)
# Scan for best parameter values
#arglist[0] = 1
#gMinuit.mnexcm("SCAN", arglist, 0, ierflg)
# Now ready for minimization step
arglist[0] = 500
arglist[1] = 1. # default: 0.1
gMinuit.mnexcm("SIMPLEX", arglist, 2, ierflg)
#gMinuit.mnexcm("MIGRAD", arglist, 2, ierflg)
# Search for additional distinct local minima
#arglist[0] = 10000
#gMinuit.mnexcm("IMP", arglist, 1, ierflg)
# Do error analysis
gMinuit.mnexcm("HESSE", arglist, 0, ierflg)
#arglist[0] = 10000
#gMinuit.mnexcm("MINOS", arglist, 1, ierflg)
# Print results
amin, edm, errdef = Double(0.18), Double(0.19), Double(0.20) # passing doubles by reference is allowed, as long as on the python side doubles are unique (init them with different values, for example).
nvpar, nparx, icstat = Long(1986), Long(1987), Long(1988)
gMinuit.mnstat(amin, edm, errdef, nvpar, nparx, icstat)
gMinuit.mnprin(5, amin)
ndf = 0
for i in xrange(len(data[0])): # loop over all bins
mc_ = [m[i] for m in mc]
if sum(mc_) < tolerance:
continue
if data[0][i] < tolerance:
continue
ndf += 1
print "chi^2 = ", amin, ", NDF = ", ndf, ", chi^2/NDF = ", amin/ndf, ", prob = ", TMath.Prob(amin,ndf)
print "amin: ", amin, ", edm: ", edm, ", errdef: ", errdef, ", nvpar: ", nvpar, ", nparx: ", nparx, ", icstat: ", icstat
print "c0: ", vstart[0], ", c1: ", vstart[1], ", c2: ", vstart[2], ", c3: ", vstart[3], ", c4: ", vstart[4]
def fit_model(self, country, time_range):
s_data = self.data_sir["susceptible"]
i_data = self.data_sir["infected"]
r_data = self.data_sir["recovered"]
def fcn(nPar, gin, f, par, flag):
tr = par[0]
rec = par[1]
chi2 = 0.
n_bins = s_data.GetNbinsX()
s_model, i_model, r_model = solve_SIR(tr, rec, time_range)
for i in range(1, n_bins + 1):
dif = (i_data.GetBinContent(i) -
i_model.GetBinContent(i)) / i_data.GetBinError(i)
chi2 += dif**2
dif = (r_data.GetBinContent(i) -
r_model.GetBinContent(i)) / r_data.GetBinError(i)
chi2 += dif**2
f[0] = chi2
return
minuit = TMinuit(3)
minuit.SetFCN(fcn)
vstep = [1e-10, 1e-10]
vinit = [1e-10, 1e-10]
# vinit = [1e-3, 1e-3]
vmin = [1e-15, 1e-15]
vmax = [1e0, 1e0]
from ctypes import c_int, c_double
import array as c_arr
arglist = c_arr.array('d', 10 * [0.])
ierflag = 0
arglist[0] = 1
minuit.mnexcm("SET ERR", arglist, 1, c_int(ierflag))
minuit.mnparm(0, "transition rate", vinit[0], vstep[0], vmin[0],
vmax[0], c_int(ierflag))
minuit.mnparm(1, "recovery rate", vinit[1], vstep[1], vmin[1], vmax[1],
c_int(ierflag))
# minuit.SetErrorDef(1.)
# minuit.SetMaxIteration(500)
# minuit.Migrad()
arglist[0] = 500
arglist[1] = 1.
# minuit.mnexcm( "MIGRAD", arglist, 2, c_int(ierflag) )
res_trans = c_double(0.)
res_rec = c_double(0.)
err_trans = c_double(0.)
err_rec = c_double(0.)
minuit.GetParameter(0, res_trans, err_trans)
minuit.GetParameter(1, res_rec, err_rec)
# return res_trans.value, res_rec.value
hists = self.solve_SIR(res_trans.value, res_rec.value, time_range)
self.hists = {
"susceptible": hists[0],
"infected": hists[1],
"recovered": hists[2]
}
self.draw()
class Minuit(object):
"""A wrapper class to initialize a minuit object with a numpy array.
Positional args:
myFCN : A python callable
params : An array (or other python sequence) of parameters
Keyword args:
limits [None] : a nested sequence of (lower_limit,upper_limit) for each parameter.
steps [[.1]*npars] : Estimated errors for the parameters, used as an initial step size.
tolerance [.001] : Tolerance to test for convergence. Minuit considers convergence to be
when the estimated distance to the minimum (edm) is <= .001*up*tolerance,
or 5e-7 by default.
up [.5] : Change in the objective function that determines 1-sigma error. .5 if
the objective function is -log(Likelihood), 1 for chi-squared.
max_calls [10000] : Maximum number of calls to the objective function.
param_names ['p0','p1',...] : a list of names for the parameters
args [()] : a tuple of extra arguments to pass to myFCN and gradient.
gradient [None] : a function that takes a list of parameters and returns a list of
first derivatives of myFCN. Assumed to take the same args as myFCN.
force_gradient [0] : Set to 1 to force Minuit to use the user-provided gradient function.
strategy[1] : Strategy for minuit to use, from 0 (fast) to 2 (safe)
fixed [False, False, ...] : If passed, an array of all the parameters to fix
"""
def __init__(self, myFCN, params, **kwargs):
from ROOT import TMinuit, Long, Double
self.limits = np.zeros((len(params), 2))
self.steps = .04 * np.ones(
len(params)) # about 10 percent in log10 space
self.tolerance = .001
self.maxcalls = 10000
self.printMode = 0
self.up = 0.5
self.param_names = ['p%i' % i for i in xrange(len(params))]
self.erflag = Long()
self.npars = len(params)
self.args = ()
self.gradient = None
self.force_gradient = 0
self.strategy = 1
self.fixed = np.zeros_like(params)
self.__dict__.update(kwargs)
self.params = np.asarray(params, dtype='float')
self.fixed = np.asarray(self.fixed, dtype=bool)
self.fcn = FCN(myFCN,
self.params,
args=self.args,
gradient=self.gradient)
self.fval = self.fcn.fval
self.minuit = TMinuit(self.npars)
self.minuit.SetPrintLevel(self.printMode)
self.minuit.SetFCN(self.fcn)
if self.gradient:
self.minuit.mncomd('SET GRA %i' % (self.force_gradient),
self.erflag)
self.minuit.mncomd('SET STR %i' % self.strategy, Long())
for i in xrange(self.npars):
if self.limits[i][0] is None: self.limits[i][0] = 0.0
if self.limits[i][1] is None: self.limits[i][1] = 0.0
self.minuit.DefineParameter(i, self.param_names[i], self.params[i],
self.steps[i], self.limits[i][0],
self.limits[i][1])
self.minuit.SetErrorDef(self.up)
for index in np.where(self.fixed)[0]:
self.minuit.FixParameter(int(index))
def minimize(self, method='MIGRAD'):
from ROOT import TMinuit, Long, Double
self.minuit.mncomd(
'%s %i %f' % (method, self.maxcalls, self.tolerance), self.erflag)
for i in xrange(self.npars):
val, err = Double(), Double()
self.minuit.GetParameter(i, val, err)
self.params[i] = val
self.fval = self.fcn.fcn(self.params)
return (self.params, self.fval)
def errors(self, method='HESSE'):
"""method ['HESSE'] : how to calculate the errors; Currently, only 'HESSE' works."""
if not np.any(self.fixed):
mat = np.zeros(self.npars**2)
if method == 'HESSE':
self.minuit.mnhess()
else:
raise Exception("Method %s not recognized." % method)
self.minuit.mnemat(mat, self.npars)
return mat.reshape((self.npars, self.npars))
else:
# Kind of ugly, but for fixed parameters, you need to expand out the covariance matrix.
nf = int(np.sum(~self.fixed))
mat = np.zeros(nf**2)
if method == 'HESSE':
self.minuit.mnhess()
else:
raise Exception("Method %s not recognized." % method)
self.minuit.mnemat(mat, nf)
# Expand out the covariance matrix.
cov = np.zeros((self.npars, self.npars))
cov[np.outer(~self.fixed, ~self.fixed)] = np.ravel(mat)
return cov
def uncorrelated_minos_error(self):
""" Kind of a kludge, but a compromise between the speed of
HESSE errors and the accuracy of MINOS errors. It accounts
for non-linearities in the likelihood by varying each function
until the value has fallen by the desired amount using hte
MINOS code. But does not account for correlations between
the parameters by fixing all other parameters during the
minimzation.
Again kludgy, but what is returned is an effective covariance
matrix. The diagonal errors are calcualted by averaging the
upper and lower errors and the off diagonal terms are set
to 0. """
cov = np.zeros((self.npars, self.npars))
# fix all parameters
for i in range(self.npars):
self.minuit.FixParameter(int(i))
# loop over free paramters getting error
for i in np.where(self.fixed == False)[0]:
self.minuit.Release(int(i))
# compute error
self.minuit.mnmnos()
low, hi, parab, gcc = ROOT.Double(), ROOT.Double(), ROOT.Double(
), ROOT.Double()
# get error
self.minuit.mnerrs(int(i), low, hi, parab, gcc)
cov[i, i] = ((abs(low) + abs(hi)) / 2.0)**2
self.minuit.FixParameter(int(i))
for i, fixed in enumerate(self.fixed):
if fixed:
self.minuit.FixParameter(int(i))
else:
self.minuit.Release(int(i))
return cov
def make_renormalization_dict(name,alpha,epsilon,muRup,muRdown,muFup,muFdown,scup,scdown,pdfas,pdfasup,pdfasdown,topptrwhist) :
global qq_global_hist_projection
global gg_global_hist_projection
returndict = {}
#start with the simple values
returndict['muRup']=muRup.GetMean()
returndict['muRdown']=muRdown.GetMean()
returndict['muFup']=muFup.GetMean()
returndict['muFdown']=muFdown.GetMean()
returndict['scup']=scup.GetMean()
returndict['scdown']=scdown.GetMean()
returndict['pdfas']=pdfas.GetMean()
returndict['pdfasup']=pdfasup.GetMean()
returndict['pdfasdown']=pdfasdown.GetMean()
returndict['topptrwmean']=topptrwhist.GetMean()
printlines = []
if alpha==1.0 and epsilon==1.0 and (name.find('_TT')!=-1 or name.find('_TTJets')!=-1) :
#now we've got to do the fits for the "deweighting" alpha and epsilon values
print 'fitting for alpha/epsilon values... '
#Define the Minuit instance we'll use
alpha_minuit = TMinuit(1); alpha_minuit.SetFCN(alpha_fcn)
epsilon_minuit = TMinuit(1); epsilon_minuit.SetFCN(epsilon_fcn)
#miscellaneous minuit stuff
ierflag = Long(1); arglist = array('d',[-1])
alpha_minuit.mnexcm('SET PRINT', arglist, 1,ierflag); alpha_minuit.mnexcm('SET NOWARNINGS',arglist,1,ierflag)
epsilon_minuit.mnexcm('SET PRINT', arglist, 1,ierflag); epsilon_minuit.mnexcm('SET NOWARNINGS',arglist,1,ierflag)
arglist[0]=100000.
#for each bin in beta
for i in range(1,csvb_qq_global_hist.GetXaxis().GetNbins()+1) :
BETA[0] = csvb_qq_global_hist.GetXaxis().GetBinCenter(i)
#qq_global_hist_projection = symmetrize(csvb_qq_global_hist.ProjectionY('qq_proj_'+str(i),i,i))
qq_global_hist_projection = csvb_qq_global_hist.ProjectionY('qq_proj_'+str(i),i,i)
#add parameter
alpha_minuit.mnparm(0,'alpha',0.1,0.5,0.,0.,ierflag)
#minimize
alpha_minuit.mnexcm('MIGRAD',arglist,1,ierflag)
#get back the fitted alpha value
fitted_alpha=Double(0.0); fitted_alpha_err=Double(0.0)
alpha_minuit.GetParameter(0,fitted_alpha,fitted_alpha_err)
#print 'NEW NAME = alpha_'+str(csvb_qq_global_hist.GetXaxis().GetBinLowEdge(i))
returndict['alpha_'+str(csvb_qq_global_hist.GetXaxis().GetBinLowEdge(i))]=fitted_alpha
printlines.append('fitted alpha value in bin %d = %.4f +/- %.4f'%(i,fitted_alpha,fitted_alpha_err))
#epsilon stuff
for i in range(1,csvb_gg_global_hist.GetXaxis().GetNbins()+1) :
BETA[0] = csvb_gg_global_hist.GetXaxis().GetBinCenter(i)
#gg_global_hist_projection = symmetrize(csvb_gg_global_hist.ProjectionY('gg_proj_'+str(i),i,i))
gg_global_hist_projection = csvb_gg_global_hist.ProjectionY('gg_proj_'+str(i),i,i)
epsilon_minuit.mnparm(0,'epsilon',0.1,0.5,0.,0.,ierflag)
epsilon_minuit.mnexcm('MIGRAD',arglist,1,ierflag)
fitted_epsilon=Double(0.0); fitted_epsilon_err=Double(0.0)
epsilon_minuit.GetParameter(0,fitted_epsilon,fitted_epsilon_err)
returndict['epsilon_'+str(csvb_gg_global_hist.GetXaxis().GetBinLowEdge(i))]=fitted_epsilon
printlines.append('fitted epsilon value in bin %d = %.4f +/- %.4f'%(i,fitted_epsilon,fitted_epsilon_err))
else :
returndict['alpha']=alpha; returndict['epsilon']=epsilon
fitted_alpha_err = 1.0; fitted_epsilon_err = 1.0
#print the values
print 'muRup value = %.4f'%(returndict['muRup'])
print 'muRdown value = %.4f'%(returndict['muRdown'])
print 'muFup value = %.4f'%(returndict['muFup'])
print 'muFdown value = %.4f'%(returndict['muFdown'])
print 'scup value = %.4f'%(returndict['scup'])
print 'scdown value = %.4f'%(returndict['scdown'])
print 'pdfas value = %.4f'%(returndict['pdfas'])
print 'pdfasup value = %.4f'%(returndict['pdfasup'])
print 'pdfasdown value = %.4f'%(returndict['pdfasdown'])
print 'top pT reweight (v1) mean value = %.4f'%(returndict['topptrwmean'])
for line in printlines :
print line
#return the dictionary
return returndict
def Minuit(fun,
x0,
args=(),
bounds=None,
verbose=0,
step_size=0.01,
n_iterations=500,
delta_one_sigma=0.5,
**options):
"""
Interface to ROOT Minuit
@param bounds list of tuple with limits for each variable
@param verbose -1 (silent) 0 (normal) 1 (verbose)
@param step_size float or Sequence
@param n_iterations maximum number of iterations
@param delta_one_sigma delta in loss function which corresponds to one sigma errors
"""
from ROOT import TMinuit, Double, Long
n_parameters = len(x0)
def to_minimize(npar, deriv, f, apar, iflag):
f[0] = fun(np.array([apar[i] for i in range(n_parameters)]), *args)
minuit = TMinuit(n_parameters)
minuit.SetFCN(to_minimize)
minuit.SetPrintLevel(verbose)
ierflg = np.array(0, dtype=np.int32)
minuit.mnexcm("SET ERR", np.array([delta_one_sigma]), 1, ierflg)
if ierflg > 0:
raise RuntimeError("Error during \"SET ERR\" call")
for i in range(n_parameters):
low, high = 0.0, 0.0 # Zero seems to mean no limit
if bounds is not None:
low, high = bounds[i]
minuit.mnparm(
i, 'Parameter_{}'.format(i), x0[i], step_size[i] if isinstance(
step_size, collections.Sequence) else step_size, low, high,
ierflg)
if ierflg > 0:
raise RuntimeError(
"Error during \"nmparm\" call for parmameter {}".format(i))
minuit.mnexcm("MIGRAD", np.array([n_iterations, 0.01], dtype=np.float64),
2, ierflg)
if ierflg > 0:
raise RuntimeError("Error during \"MIGRAD\" call")
xbest = np.zeros(n_parameters)
xbest_error = np.zeros(n_parameters)
p, pe = Double(0), Double(0)
for i in range(n_parameters):
minuit.GetParameter(i, p, pe)
xbest[i] = p
xbest_error[i] = pe
buf = array.array('d', [0.] * (n_parameters**2))
minuit.mnemat(buf, n_parameters) # retrieve error matrix
hessian = np.array(buf).reshape(n_parameters, n_parameters)
amin = Double(0.) # value of fcn at minimum
edm = Double(0.) # estimated distance to mimimum
errdef = Double(0.) # delta_fcn used to define 1 sigma errors
nvpar = np.array(0, dtype=np.int32) # number of variable parameters
nparx = np.array(0, dtype=np.int32) # total number of parameters
icstat = np.array(
0, dtype=np.int32
) # status of error matrix: 3=accurate 2=forced pos. def 1= approximative 0=not calculated
minuit.mnstat(amin, edm, errdef, nvpar, nparx, icstat)
return scipy.optimize.OptimizeResult(x=xbest,
fun=amin,
hessian=hessian,
success=(ierflg == 0),
status=ierflg)
def fit( p , perr ):
global val, err, nBins
val = p
err = perr
nBins=len(val)
#name=['q0','q1','q2','q3','q4']
#name=['q0','q1','q2','q3']
#name=['q0','q1','q2']
name = [ 'q0' , 'q1' ]
npar=len(name)
# the initial values
vstart = arr( 'd' , npar*[0.1] )
# the initial step size
step = arr( 'd' , npar*[0.000001] )
# --> set up MINUIT
gMinuit = TMinuit ( npar ) # initialize TMinuit with maximum of npar parameters
gMinuit.SetFCN( fcn ) # set function to minimize
arglist = arr( 'd' , npar*[0.01] ) # set error definition
ierflg = c_int(0)
arglist[0] = 1. # 1 sigma is Delta chi2 = 1
gMinuit.mnexcm("SET ERR", arglist, 1, ierflg )
# --> set starting values and step size for parameters
# Define the parameters for the fit
for i in range(0,npar): gMinuit.mnparm( i, name[i] , vstart[i] , step[i] , 0, 0, ierflg )
# now ready for minimization step
arglist [0] = 500 # Number of calls for FCN before giving up
arglist [1] = 1. # Tolerance
gMinuit.mnexcm("MIGRAD" , arglist , 2 , ierflg) # execute the minimisation
# --> check TMinuit status
amin , edm , errdef = c_double(0.) , c_double(0.) , c_double(0.)
nvpar , nparx , icstat = c_int(0) , c_int(0) , c_int(0)
gMinuit.mnstat (amin , edm , errdef , nvpar , nparx , icstat )
gMinuit.mnprin(3,amin) # print-out by Minuit
# meaning of parameters:
# amin: value of fcn distance at minimum (=chi^2)
# edm: estimated distance to minimum
# errdef: delta_fcn used to define 1 sigam errors
# nvpar: total number of parameters
# icstat: status of error matrix:
# 3 = accurate
# 2 = forced pos. def
# 1 = approximative
# 0 = not calculated
#
# --> get results from MINUIT
finalPar = []
finalParErr = []
p, pe = c_double(0.) , c_double(0.)
for i in range(0,npar):
gMinuit.GetParameter(i, p, pe) # retrieve parameters and errors
finalPar.append( float(p.value) )
finalParErr.append( float(pe.value) )
# get covariance matrix
buf = arr('d' , npar*npar*[0.])
gMinuit.mnemat( buf , npar ) # retrieve error matrix
emat = np.array( buf ).reshape( npar , npar )
# --> provide formatted output of results
print "\n"
print "*==* MINUIT fit completed:"
print'fcn@minimum = %.3g'%( amin.value ) , " error code =" , ierflg.value , " status =" , icstat.value , " (if its 3, mean accurate)"
print " Results: \t value error corr. mat."
for i in range(0,npar):
print'%s: \t%10.3e +/- %.1e'%( name[i] , finalPar[i] , finalParErr[i] ) ,
for j in range (0,i): print'%+.3g'%( emat[i][j]/np.sqrt(emat[i][i])/np.sqrt(emat[j][j]) ),
print "\n"
return [ [i,j] for i,j in zip(finalPar , finalParErr) ]
def main():
global freqs_hz, pv, sigq, sigu
parser = OptionParser(usage)
parser.add_option("-r", "--rm", type="float", dest="rm", default=0.,
help="Estimate of the RM")
parser.add_option("-n", "--norm", action="store_true", dest="norm",
default=False, help="Verbose mode")
parser.add_option("-b", "--baseline", action="store_true", dest="baseline",
default=False, help="Fit for a baseline")
parser.add_option("-f", "--nofit", action="store_true", dest="nofit",
default=False, help="Don't fit for the RM with Minuit")
parser.add_option("-c", "--clean", action="store_true", dest="clean",
default=False, help="Clean the baseline")
(opts, args) = parser.parse_args()
#if opts.help:
# print full_usage
arch = psrchive.Archive_load(sys.argv[1])
arch.tscrunch()
arch.bscrunch(2)
#arch.fscrunch(2)
arch.dedisperse()
arch.remove_baseline()
arch.convert_state('Stokes')
arch.centre_max_bin()
#arch.rotate(0.5)
data = arch.get_data()
MJD = arch.get_first_Integration().get_epoch().strtempo()
w = arch.get_weights().sum(0)
I = data[:,0,:,:].mean(0)
Q = data[:,1,:,:].mean(0)
U = data[:,2,:,:].mean(0)
#V = data[:,3,:,:].mean(0)
I = ma.masked_array(I)
Q = ma.masked_array(Q)
U = ma.masked_array(U)
#V = ma.masked_array(V)
I[w==0] = np.ma.masked
Q[w==0] = np.ma.masked
U[w==0] = np.ma.masked
# Get Freqs
nchan = arch.get_nchan()
freqs = np.zeros(nchan)
for i in range(nchan):
freqs[i] = arch.get_Profile(0,0,i).get_centre_frequency()
## Determine phase range
arch.fscrunch()
arch.tscrunch()
arch.pscrunch()
prof = arch.get_Profile(0,0,0)
#print prof.get_amps()
lowbin, hibin = get_pulse_range(arch)
#lowbin, hibin = 458,531
#lowbin, hibin = 20,120
if opts.clean:
for n in range(nchan):
if n%20: continue
baseline_idx = np.append(np.arange(0, lowbin), np.arange(hibin, arch.get_nbin()))
baseline_dat = I[n][baseline_idx]
print n, baseline_idx, baseline_dat
poly = np.polyfit(baseline_idx, baseline_dat, 1)
p = np.poly1d(poly)
pylab.plot(I[n])
I[n] = I[n] - p(np.arange(0, arch.get_nbin()))
pylab.plot(I[n])
pylab.show()
for ii, wx in enumerate(w):
I[ii] *= wx/np.max(w)
Q[ii] *= wx/np.max(w)
U[ii] *= wx/np.max(w)
#V[ii] *= wx
if opts.norm:
print "Will normalize by the rms of the noise"
scale = np.std(I, axis=1) / np.max(np.std(I, axis=1))
for ii, s in enumerate(scale):
I[ii,:] /= s
Q[ii,:] /= s
U[ii,:] /= s
#Q = Q / scale
#U = U / scale
freq_lo = freqs[0]
freq_hi = freqs[-1]
lowphase = lowbin / float(arch.get_nbin())
hiphase = hibin / float(arch.get_nbin())
#lowphase= 0.48
#hiphase = 0.515
#lowphase = 0.515
#hiphase = 0.54
print "Pulse phase window: ", lowphase, hiphase
#pylab.plot(np.sum(I), axis)
#pylab.show()
# 2D plot
f = pylab.figure()
pylab.subplot(321)
#print np.sum(I,axis=0)
#pylab.plot(np.sum(I, axis=0))
pylab.plot(prof.get_amps())
pylab.xlim([0, arch.get_nbin()])
f.text( .5, 0.95, r'%s'%os.path.split(sys.argv[1])[1], horizontalalignment='center')
pylab.subplot(323)
pylab.axis([0,1,freq_lo,freq_hi])
pylab.imshow(I,extent=(0,1,freq_lo,freq_hi), origin='lower', aspect='auto', vmax=I.max()/1.5, vmin=I.min()/1.5)
pylab.xlabel('Pulse phase')
pylab.ylabel('Frequency (MHz)')
# Compute errors of Q and U
sigq = np.std(Q[:,lowbin:hibin], axis=1) / np.sqrt(hibin-lowbin)
sigu = np.std(U[:,lowbin:hibin], axis=1) / np.sqrt(hibin-lowbin)
#sigq = np.std(Q[:,:], axis=1)
#sigu = np.std(U[:,:], axis=1)
pylab.plot([lowphase,lowphase], [freq_lo, freq_hi], 'r--')
pylab.plot([hiphase,hiphase], [freq_lo, freq_hi], 'r--')
freqs_hz = freqs * 1e6
# Select phase range
lowbin = int(lowphase * arch.get_nbin())
hibin = int(hiphase * arch.get_nbin())
dat = Q + 1j * U
pv = dat[:,lowbin:hibin].mean(1) # Select phase range and average
#rhos = np.arange(-90000, 90000, 10)
rhos = np.arange(-2000, 2000, 1)
res = np.absolute(getL(rhos, pv))
# Plot I f(RM)
pylab.subplot(324)
pylab.plot(rhos, res, 'b-')
pylab.xlabel('RM')
pylab.ylabel('I')
# Plot Q
pylab.subplot(325)
pylab.errorbar(freqs, np.real(pv), yerr=sigq, ls='None')
pylab.plot(freqs, np.real(pv), 'bo')
pylab.xlabel('Frequency (MHz)')
pylab.ylabel('Q')
# Plot U
pylab.subplot(326)
pylab.errorbar(freqs, np.imag(pv), yerr=sigu, ls='None')
pylab.plot(freqs, np.imag(pv), 'bo')
pylab.xlabel('Frequency (MHz)')
pylab.ylabel('U')
# Should get the initial RM
if opts.rm:
initial_RM = -opts.rm
else:
initial_RM = -rhos[np.argmax(res)]
print "Will use initial RM", initial_RM
initial_L = getL(np.array([initial_RM]), pv) / (hibin-lowbin)
if not opts.nofit:
# Minuit part
gMinuit = TMinuit(5)
#gMinuit.SetErrorDef(1) # 1-Sigma Error
gMinuit.SetErrorDef(4) # 2-Sigma Error
gMinuit.SetFCN(fcn)
arglist = arr('d', 2*[0.01])
ierflg = Long(0)
#arglist[0] = 1
#gMinuit.mnexcm("SET ERR", arglist ,1,ierflg)
# Set initial parameter values for fit
vstart = arr( 'd', (np.real(initial_L), np.imag(initial_L), initial_RM) )
#vstart = arr( 'd', (2*np.real(initial_L), 2*np.imag(initial_L), initial_RM) )
# Set step size for fit
step = arr( 'd', (0.001, 0.001, 0.001) )
# Define the parameters for the fit
gMinuit.mnparm(0, "Qf", vstart[0], step[0], 0,0,ierflg)
gMinuit.mnparm(1, "Uf", vstart[1], step[1], 0,0,ierflg)
gMinuit.mnparm(2, "RM", vstart[2], step[2], 0,0,ierflg)
gMinuit.mnparm(3, "a", 0.0, step[2], 0,0,ierflg)
gMinuit.mnparm(4, "b", 0.0, step[2], 0,0,ierflg)
#gMinuit.FixParameter(2)
if not opts.baseline:
gMinuit.FixParameter(3)
gMinuit.FixParameter(4)
arglist[0] = 6000 # Number of calls to FCN before giving up.
arglist[1] = 0.1 # Tolerance
gMinuit.mnexcm("MIGRAD", arglist ,2,ierflg)
amin, edm, errdef = Double(0.18), Double(0.19), Double(1.0)
nvpar, nparx, icstat = Long(1), Long(2), Long(3)
gMinuit.mnstat(amin,edm,errdef,nvpar,nparx,icstat);
gMinuit.mnmnos();
gMinuit.mnprin(3,amin);
finalQ, finalQ_err = Double(0), Double(0)
finalU, finalU_err = Double(0), Double(0)
finalRM, finalRM_err = Double(0), Double(0)
A, A_err = Double(0), Double(0)
B, B_err = Double(0), Double(0)
print "\n\n"
gMinuit.GetParameter(0, finalQ, finalQ_err)
gMinuit.GetParameter(1, finalU, finalU_err)
gMinuit.GetParameter(2, finalRM, finalRM_err)
gMinuit.GetParameter(3, A, A_err)
gMinuit.GetParameter(4, B, B_err)
finalRM *= -1.
print finalQ, finalU
line1 = "Final RM: %.1f"%(finalRM) + "(+/-) %.1f "%(finalRM_err) + " (2-sig) "
line2 = "Chi**2r = %.2f"%(get_chi2((finalQ,finalU,-finalRM,A,B)) / ( 2*pv.size - 3 - 1 -2))
print line1
print line2
f.text( .5, 0.92, line1 + line2, horizontalalignment='center')
print MJD, np.mean(freqs), finalRM, finalRM_err, get_chi2((finalQ,finalU,finalRM,A,B)), 2*pv.count()
# Plot best fit model
finalRM *= -1.
pylab.subplot(325)
pylab.plot(freqs, np.real( -A+getPV(finalQ+1j*finalU, finalRM) ))
pylab.subplot(326)
pylab.plot(freqs, np.imag( -B+getPV(finalQ+1j*finalU, finalRM) ))
pylab.show()
class MinimizerROOTTMinuit(MinimizerBase):
def __init__(self,
parameter_names, parameter_values, parameter_errors,
function_to_minimize, strategy = 1):
self._par_names = parameter_names
self._strategy = strategy
self._func_handle = function_to_minimize
self._err_def = 1.0
self._tol = 0.001
# initialize the minimizer parameter specification
self._minimizer_param_dict = {}
assert len(parameter_names) == len(parameter_values) == len(parameter_errors)
self._par_val = []
self._par_err = []
self._par_fixed_mask = []
self._par_limits = []
for _pn, _pv, _pe in zip(parameter_names, parameter_values, parameter_errors):
self._par_val.append(_pv)
self._par_err.append(_pe)
self._par_fixed_mask.append(False)
self._par_limits.append(None)
# TODO: limits/fixed parameters
self.__gMinuit = None
# cache for calculations
self._hessian = None
self._hessian_inv = None
self._fval = None
self._par_cov_mat = None
self._par_cor_mat = None
self._par_asymm_err = None
self._fmin_struct = None
self._pars_contour = None
self._min_result_stale = True
self._printed_inf_cost_warning = False
# -- private methods
# def _invalidate_cache(self):
# self._par_val = None
# self._par_err = None
# self._hessian = None
# self._hessian_inv = None
# self._fval = None
# self._par_cov_mat = None
# self._par_cor_mat = None
# self._par_asymm_err_dn = None
# self._par_asymm_err_up = None
# self._fmin_struct = None
# self._pars_contour = None
def _recreate_gMinuit(self):
self.__gMinuit = TMinuit(self.n_pars)
self.__gMinuit.SetPrintLevel(-1)
self.__gMinuit.mncomd("SET STRATEGY {}".format(self._strategy), Long(0))
self.__gMinuit.SetFCN(self._minuit_fcn)
self.__gMinuit.SetErrorDef(self._err_def)
# set gMinuit parameters
error_code = Long(0)
for _pid, (_pn, _pv, _pe) in enumerate(zip(self._par_names, self._par_val, self._par_err)):
self.__gMinuit.mnparm(_pid,
_pn,
_pv,
0.1 * _pe,
0, 0, error_code)
err_code = Long(0)
# set fixed parameters
for _par_id, _pf in enumerate(self._par_fixed_mask):
if _pf:
self.__gMinuit.mnfixp(_par_id, err_code)
# set parameter limits
for _par_id, _pl in enumerate(self._par_limits):
if _pl is not None:
_lo_lim, _up_lim = _pl
self.__gMinuit.mnexcm("SET LIM",
arr('d', [_par_id + 1, _lo_lim, _up_lim]), 3, error_code)
def _get_gMinuit(self):
if self.__gMinuit is None:
self._recreate_gMinuit()
return self.__gMinuit
def _migrad(self, max_calls=6000):
# need to set the FCN explicitly before every call
self._get_gMinuit().SetFCN(self._minuit_fcn)
error_code = Long(0)
self._get_gMinuit().mnexcm("MIGRAD",
arr('d', [max_calls, self.tolerance]),
2, error_code)
def _hesse(self, max_calls=6000):
# need to set the FCN explicitly before every call
self._get_gMinuit().SetFCN(self._minuit_fcn)
error_code = Long(0)
self._get_gMinuit().mnexcm("HESSE", arr('d', [max_calls]), 1, error_code)
def _minuit_fcn(self,
number_of_parameters, derivatives, f, parameters, internal_flag):
"""
This is actually a function called in *ROOT* and acting as a C wrapper
for our `FCN`, which is implemented in Python.
This function is called by `Minuit` several times during a fitters. It
doesn't return anything but modifies one of its arguments (*f*).
This is *ugly*, but it's how *ROOT*'s ``TMinuit`` works. Its argument
structure is fixed and determined by `Minuit`:
**number_of_parameters** : int
The number of parameters of the current fitters
**derivatives** : C array
If the user chooses to calculate the first derivative of the
function inside the `FCN`, this value should be written here. This
interface to `Minuit` ignores this derivative, however, so
calculating this inside the `FCN` has no effect (yet).
**f** : C array
The desired function value is in f[0] after execution.
**parameters** : C array
A C array of parameters. Is cast to a Python list
**internal_flag** : int
A flag allowing for different behaviour of the function.
Can be any integer from 1 (initial run) to 4(normal run). See
`Minuit`'s specification.
"""
# Retrieve the parameters from the C side of ROOT and
# store them in a Python list -- resource-intensive
# for many calls, but can't be improved (yet?)
parameter_list = np.frombuffer(parameters,
dtype=float,
count=self.n_pars)
# call the Python implementation of FCN.
f[0] = self._func_wrapper(*parameter_list)
def _insert_zeros_for_fixed(self, submatrix):
"""
Takes the partial error matrix (submatrix) and adds
rows and columns with 0.0 where the fixed
parameters should go.
"""
_mat = submatrix
# reduce the matrix before inserting zeros
_n_pars_free = self.n_pars_free
_mat = _mat[0:_n_pars_free,0:_n_pars_free]
_fparam_ids = [_par_id for _par_id, _p in enumerate(self._par_fixed_mask) if _p]
for _id in _fparam_ids:
_mat = np.insert(np.insert(_mat, _id, 0., axis=0), _id, 0., axis=1)
return _mat
# -- public properties
def get_fit_info(self, info):
'''Retrieves other info from `Minuit`.
**info** : string
Information about the fit to retrieve.
This can be any of the following:
- ``'fcn'``: `FCN` value at minimum,
- ``'edm'``: estimated distance to minimum
- ``'err_def'``: `Minuit` error matrix status code
- ``'status_code'``: `Minuit` general status code
'''
# declare vars in which to retrieve other info
fcn_at_min = Double(0)
edm = Double(0)
err_def = Double(0)
n_var_param = Long(0)
n_tot_param = Long(0)
status_code = Long(0)
# Tell TMinuit to update the variables declared above
self.__gMinuit.mnstat(fcn_at_min,
edm,
err_def,
n_var_param,
n_tot_param,
status_code)
if info == 'fcn':
return fcn_at_min
elif info == 'edm':
return edm
elif info == 'err_def':
return err_def
elif info == 'status_code':
try:
return D_MATRIX_ERROR[status_code]
except:
return status_code
@property
def n_pars(self):
return len(self.parameter_names)
@property
def n_pars_free(self):
return len([_p for _p in self._par_fixed_mask if not _p])
@property
def errordef(self):
return self._err_def
@errordef.setter
def errordef(self, err_def):
assert err_def > 0
self._err_def = err_def
if self.__gMinuit is not None:
self.__gMinuit.set_errordef(err_def)
self._min_result_stale = True
@property
def tolerance(self):
return self._tol
@tolerance.setter
def tolerance(self, tolerance):
assert tolerance > 0
self._tol = tolerance
self._min_result_stale = True
@property
def hessian(self):
# TODO: cache this
return 2.0 * self.errordef * np.linalg.inv(self.cov_mat)
@property
def cov_mat(self):
if self._min_result_stale:
raise MinimizerROOTTMinuitException("Cannot get cov_mat: Minimizer result is outdated.")
if self._par_cov_mat is None:
_n_pars_total = self.n_pars
_n_pars_free = self.n_pars_free
_tmp_mat_array = arr('d', [0.0]*(_n_pars_total**2))
# get parameter covariance matrix from TMinuit
self.__gMinuit.mnemat(_tmp_mat_array, _n_pars_total)
# reshape into 2D array
_sub_cov_mat = np.asarray(
np.reshape(
_tmp_mat_array,
(_n_pars_total, _n_pars_total)
)
)
self._par_cov_mat = self._insert_zeros_for_fixed(_sub_cov_mat)
return self._par_cov_mat
@property
def cor_mat(self):
if self._min_result_stale:
raise MinimizerROOTTMinuitException("Cannot get cor_mat: Minimizer result is outdated.")
if self._par_cor_mat is None:
_cov_mat = self.cov_mat
# TODO: use CovMat object!
# Note: for zeros on cov_mat diagonals (which occur for fixed parameters) -> overwrite with 1.0
_sqrt_diag = np.array([_err if _err>0 else 1.0 for _err in np.sqrt(np.diag(_cov_mat))])
self._par_cor_mat = np.asarray(_cov_mat) / np.outer(_sqrt_diag, _sqrt_diag)
return self._par_cor_mat
@property
def hessian_inv(self):
return self.cov_mat / 2.0 / self.errordef
@property
def parameter_values(self):
return self._par_val
@property
def parameter_errors(self):
return self._par_err
@property
def parameter_names(self):
return self._par_names
# -- private "properties"
# -- public methods
def fix(self, parameter_name):
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if self._par_fixed_mask[_par_id]:
return # par is already fixed
self._par_fixed_mask[_par_id] = True
if self.__gMinuit is not None:
# also update Minuit instance
err_code = Long(0)
self.__gMinuit.mnfixp(_par_id, err_code)
# self.__gMinuit.mnexcm("FIX",
# arr('d', [_par_id+1]), 1, error_code)
self._min_result_stale = True
def fix_several(self, parameter_names):
for _pn in parameter_names:
self.fix(_pn)
def release(self, parameter_name):
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if not self._par_fixed_mask[_par_id]:
return # par is already released
self._par_fixed_mask[_par_id] = False
if self.__gMinuit is not None:
# also update Minuit instance
self.__gMinuit.mnfree(-_par_id-1)
# self.__gMinuit.mnexcm("RELEASE",
# arr('d', [_par_id+1]), 1, error_code)
self._min_result_stale = True
def release_several(self, parameter_names):
for _pn in parameter_names:
self.release(_pn)
def limit(self, parameter_name, parameter_bounds):
assert len(parameter_bounds) == 2
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if self._par_limits[_par_id] == parameter_bounds:
return # same limits already set
self._par_limits[_par_id] = parameter_bounds
if self.__gMinuit is not None:
_lo_lim, _up_lim = self._par_limits[_par_id]
# also update Minuit instance
error_code = Long(0)
self.__gMinuit.mnexcm("SET LIM",
arr('d', [_par_id+1, _lo_lim, _up_lim]), 3, error_code)
self._min_result_stale = True
def unlimit(self, parameter_name):
# set local flag
_par_id = self.parameter_names.index(parameter_name)
if self._par_limits[_par_id] is None:
return # parameter is already unlimited
self._par_limits[_par_id] = None
if self.__gMinuit is not None:
# also update Minuit instance
error_code = Long(0)
self.__gMinuit.mnexcm("SET LIM",
arr('d', [_par_id+1]), 1, error_code)
self._min_result_stale = True
def minimize(self, max_calls=6000):
self._migrad(max_calls=max_calls)
# retrieve fitters parameters
self._par_val = []
self._par_err = []
_pv, _pe = Double(0), Double(0)
for _par_id in six.moves.range(0, self.n_pars):
self.__gMinuit.GetParameter(_par_id, _pv, _pe) # retrieve fitresult
self._par_val.append(float(_pv))
self._par_err.append(float(_pe))
self._min_result_stale = False
def contour(self, parameter_name_1, parameter_name_2, sigma=1.0, **minimizer_contour_kwargs):
if self.__gMinuit is None:
raise MinimizerROOTTMinuitException("Need to perform a fit before calling contour()!")
_numpoints = minimizer_contour_kwargs.pop("numpoints", 100)
if minimizer_contour_kwargs:
raise MinimizerROOTTMinuitException("Unknown parameters: {}".format(minimizer_contour_kwargs))
_id_1 = self.parameter_names.index(parameter_name_1)
_id_2 = self.parameter_names.index(parameter_name_2)
self.__gMinuit.SetErrorDef(sigma ** 2)
_t_graph = self.__gMinuit.Contour(_numpoints, _id_1, _id_2)
self.__gMinuit.SetErrorDef(self._err_def)
_x_buffer, _y_buffer = _t_graph.GetX(), _t_graph.GetY()
_N = _t_graph.GetN()
_x = np.frombuffer(_x_buffer, dtype=float, count=_N)
_y = np.frombuffer(_y_buffer, dtype=float, count=_N)
self._func_handle(*self.parameter_values)
return ContourFactory.create_xy_contour((_x, _y), sigma)
def profile(self, parameter_name, bins=21, bound=2, args=None, subtract_min=False):
if self.__gMinuit is None:
raise MinimizerROOTTMinuitException("Need to perform a fit before calling profile()!")
MAX_ITERATIONS = 6000
_error_code = Long(0)
_minuit_id = Long(self.parameter_names.index(parameter_name) + 1)
_par_min = Double(0)
_par_err = Double(0)
self.__gMinuit.GetParameter(_minuit_id - 1, _par_min, _par_err)
_x = np.linspace(start=_par_min - bound * _par_err, stop=_par_min + bound * _par_err, num=bins, endpoint=True)
self.__gMinuit.mnexcm("FIX", arr('d', [_minuit_id]), 1, _error_code)
_y = np.zeros(bins)
for i in range(bins):
self.__gMinuit.mnexcm("SET PAR", arr('d', [_minuit_id, Double(_x[i])]), 2, _error_code)
self.__gMinuit.mnexcm("MIGRAD", arr('d', [MAX_ITERATIONS, self.tolerance]), 2, _error_code)
_y[i] = self.get_fit_info("fcn")
self.__gMinuit.mnexcm("RELEASE", arr('d', [_minuit_id]), 1, _error_code)
self._migrad()
self.__gMinuit.mnexcm("SET PAR", arr('d', [_minuit_id, Double(_par_min)]), 2, _error_code)
return np.asarray((_x, _y))
