''' Simple fit without fit error estimation.
For correct fit errors check the advanced example.
Bound should be defined. Eta has to be > 1.
'''
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import numpy as np
import pylandau
# Create fake data with possion error
mpv, eta, sigma, A = 30, 5, 4, 1000
x = np.arange(0, 100, 0.5)
y = pylandau.langau(x, mpv, eta, sigma, A)
yerr = np.random.normal(np.zeros_like(x), np.sqrt(y))
yerr[y < 1] = 1
y += yerr
# Fit with constrains
coeff, pcov = curve_fit(pylandau.langau, x, y,
sigma=yerr,
absolute_sigma=True,
p0=(mpv, eta, sigma, A),
bounds=(1, 10000))
# Plot
plt.errorbar(x, y, np.sqrt(pylandau.langau(x, *coeff)), fmt=".")
plt.plot(x, pylandau.langau(x, *coeff), "-")
plt.show()
# Plot the Landau Gauss convolution (Langau) and cross check with convolution with scipy import numpy as np import pylandau import matplotlib.pyplot as plt from scipy.ndimage.filters import gaussian_filter1d mpv, eta, sigma, A = 10, 1, 3, 1 x = np.arange(0, 50, 0.01) y = pylandau.landau(x, mpv=mpv, eta=eta, A=A) y_gconv = gaussian_filter1d(y, sigma=sigma / 0.01) # Scaled means that the resulting Landau*Gauss function maximum is A at mpv # Otherwise the underlying Landau function before convolution has the # function maximum A at mpv y_gconv_2 = pylandau.langau(x, mpv, eta, sigma, A, scale_langau=False) y_gconv_3 = pylandau.langau(x, mpv, eta, sigma, A, scale_langau=True) plt.plot(x, y, label='Landau') plt.plot(x, y_gconv_2, label='Langau') plt.plot(x, y_gconv, '--', label='Langau Scipy') plt.plot(x, y_gconv_3, label='Langau scaled') plt.legend(loc=0) plt.show()
# Plot the functions using matplotlib
import numpy as np
import pylandau
import matplotlib.pyplot as plt
x = np.arange(0, 100, 0.01)
for A, eta, mpv in ((1, 1, 10), (1, 2, 30), (0.5, 5, 50)):
# Use the function that calculates y values when given array
plt.plot(x, pylandau.landau(x, mpv, eta, A), '-', label='mu=%1.1f, eta=%1.1f, A=%1.1f' % (mpv, eta, A))
# Use the function that calculates the y value given a x value, (e.g. needed for minimizers)
y = np.array([pylandau.get_landau(x_value, mpv, eta, A) for x_value in x])
plt.plot(x, y, 'r--', label='mu=%1.1f, eta=%1.1f, A=%1.1f' % (mpv, eta, A))
# Use the function that calculates the y value given a x value, (e.g. needed for minimizers)
sigma = 10
plt.plot(x, pylandau.langau(x, mpv, eta, sigma, A), '--', label='mu=%1.1f, eta=%1.1f, sigma=%1.1f, A=%1.1f' % (A, eta, sigma, mpv))
plt.legend(loc=0)
plt.show()
def test_negative_amplitude(self):
''' Check exception for negative amplitude '''
x = np.linspace(0, 100)
with self.assertRaises(ValueError):
pylandau.landau(x, A=-1)
x = np.linspace(0, 100)
with self.assertRaises(ValueError):
pylandau.langau(x, A=-1)
def test_langau_stability(self, mpv, eta, sigma, A):
''' Check Langau outputs for same input parameters '''
# Correct input to avoid oscillations
if sigma > 100 * eta:
sigma = eta
assume(sigma * eta < constrains.LANGAU_MAX_ETA_SIGMA)
x = np.linspace(mpv - 5 * sigma * eta, mpv + 5 * sigma * eta, 1000)
y_1 = pylandau.langau(x, mpv=mpv, eta=eta, sigma=sigma, A=A)
y_2 = pylandau.langau(x, mpv=mpv, eta=eta, sigma=sigma, A=A)
self.assertTrue(np.all(y_1 == y_2))
def test_langau_stability(self, mpv, eta, sigma, A):
''' Check Langau outputs for same input parameters '''
# Correct input to avoid oscillations
if sigma > 100 * eta:
sigma = eta
assume(sigma * eta < constraints.LANGAU_MAX_ETA_SIGMA)
x = np.linspace(mpv - 5 * sigma * eta, mpv + 5 * sigma * eta, 1000)
y_1 = pylandau.langau(x, mpv=mpv, eta=eta, sigma=sigma, A=A)
y_2 = pylandau.langau(x, mpv=mpv, eta=eta, sigma=sigma, A=A)
self.assertTrue(np.all(y_1 == y_2))
def test_landau_fallback(self, pars):
''' Check if langau is landau for sigma = 0 '''
(mpv, eta, A) = pars
x = np.linspace(mpv - 5 * eta, mpv + 5 * eta, 1000)
y_1 = pylandau.landau(x, mpv=mpv, eta=eta, A=A)
y_2 = pylandau.langau(x, mpv=mpv, eta=eta, sigma=0., A=A)
self.assertTrue(np.all(y_1 == y_2))
def test_landau_fallback(self, pars):
''' Check if langau is landau for sigma = 0 '''
(mpv, eta, A) = pars
x = np.linspace(mpv - 5 * eta, mpv + 5 * eta, 1000)
y_1 = pylandau.landau(x, mpv=mpv, eta=eta, A=A)
y_2 = pylandau.langau(x, mpv=mpv, eta=eta, sigma=0., A=A)
self.assertTrue(np.all(y_1 == y_2))
def _calc_landau(x):
if self.simulate_data.dut_noise[dut_index]:
# PyLandau Langau MPV parameter is the MPV of the Langau not the Landau only!
y = pylandau.langau(
x,
mpv=mpv_charge,
eta=mpv_charge / 10.,
sigma=self.simulate_data.dut_noise[dut_index],
scale_langau=False)
else:
y = pylandau.landau(x,
mpv=mpv_charge,
eta=mpv_charge / 10)
return y
def fitfunction_testbeam_array(x, mu, eta, sigma, A, p4, p5):
global c
c+=1
return pylandau.langau(x, mu, eta, sigma, A) + p4 * np.exp(-x / p5)
def run(self):
"""Runs the routines to generate all langau specific data"""
# Here events with only one cluster are choosen or two, you decide
indNumClus = self.get_num_clusters(self.data, self.numClusters)
indizes = np.concatenate(indNumClus)
# Slice the data from the bas analysis for further calculations
valid_events_clustersize = np.take(self.data["base"]["Clustersize"], indizes)
valid_events_clusters = np.take(self.data["base"]["Clusters"], indizes)
valid_events_Signal = np.take(self.data["base"]["Signal"],indizes)
self.results_dict["Clustersize"] = []
# TODO: here a non numba optimized version is used. We should use numba here!
# Calculate the energy deposition PER Clustersize and add it to self.results_dict["Clustersize"]
self.cluster_analysis(valid_events_Signal,
valid_events_clusters,
valid_events_clustersize)
# With all the data from every clustersize add all together and fit the main langau to it
finalE = np.zeros(0)
finalNoise = np.zeros(0)
for cluster in self.results_dict["Clustersize"]:
# Clean up and extra energy cut
indi = np.nonzero(cluster["signal"] > 0)[0]
nogarbage = cluster["signal"][indi]
# ultra_high_energy_cut
indi = np.nonzero(nogarbage < self.Ecut)[0]
cluster["signal"] = cluster["signal"][indi]
finalE = np.append(finalE, cluster["signal"])
finalNoise = np.append(finalNoise, cluster["noise"])
# Fit the langau to the summ of all individual clusters
coeff, _, _, error_bins, edges= self.fit_langau(finalE,
finalNoise,
bins=self.results_dict["bins"],
cut = self.ClusterCut)
self.results_dict["signal"] = finalE
self.results_dict["noise"] = finalNoise
self.results_dict["langau_coeff"] = coeff
plotxrange = np.arange(0., edges[-1], edges[-1] / 1000.)
self.results_dict["langau_data"] = [
plotxrange,pylandau.langau(plotxrange,*coeff)
] # aka x and y data
self.results_dict["data_error"] = error_bins
# Seed cut langau, taking only the bare hit channels which are above seed cut levels
if self.seed_cut_langau:
seed_cut_channels = self.data["base"]["Channel_hit"]
signals = self.data["base"]["Signal"]
seedcutADC = []
seedcutChannels = []
for i, signal in enumerate(tqdm(signals, desc="(langau SC) Processing events")):
if signal[seed_cut_channels[i]].any():
seedcutADC.append(signal[seed_cut_channels[i]])
seedcutChannels.append(seed_cut_channels[i])
if self.Charge_scale:
self.log.info("Converting ADC to electrons for SC Langau...")
converted = self.main.calibration.convert_ADC_to_e(np.concatenate(seedcutADC), np.concatenate(seedcutChannels))
else:
converted = np.absolute(np.concatenate(seedcutADC))
finalE = np.array(converted, dtype=np.float32)
# get rid of 0 events
indizes = np.nonzero(finalE > 0)[0]
nogarbage = finalE[indizes]
indizes = np.nonzero(nogarbage < self.Ecut)[0] # ultra_high_energy_cut
coeff, _, _, error_bins, edges = self.fit_langau(
nogarbage[indizes], bins=self.results_dict["bins"], cut = self.SCCut)
self.results_dict["signal_SC"] = nogarbage[indizes]
self.results_dict["langau_coeff_SC"] = coeff
plotxrange = np.arange(0., edges[-1], edges[-1]/1000.)
self.results_dict["langau_data_SC"] = [
plotxrange,pylandau.langau(plotxrange,*coeff)
] # aka x and y data
# Old attempts for multiprocessing, no speed up seen here
# # Try joblib
# #start = time()
# #arg_instances = [(size, valid_events_clustersize,
# # valid_events_Signal, valid_events_clusters,
# # noise, charge_cal) for size in clustersize_list]
# #results = Parallel(n_jobs=4, backend="threading")(map(delayed(self.process_cluster_size),
# # arg_instances))
# #for res in results:
# # self.results_dict[data]["Clustersize"].append(res)
#
# !!!!!!!!!!!!!!! NO SPEED BOOST HERE!!!!!!!!!!!!!!!!!!!!
# General langau, where all clustersizes are considered
# if self.poolsize > 1:
# paramslist = []
# for size in self.cluster_size_list:
# cls_ind = np.nonzero(valid_events_clustersize == size)[0]
# paramslist.append((cls_ind, valid_events_Signal,
# valid_events_clusters,
# self.main.calibration.convert_ADC_to_e,
# self.main.noise))
# COMMENT: lagau_cluster not defined!!!!
# Here multiple cpu calculate the energy of the events per clustersize
# results = self.pool.starmap(self.langau_cluster, paramslist,
# chunksize=1)
# self.results_dict["Clustersize"] = results
return self.results_dict.copy()
def minimizeMe(mpv, eta, sigma, A):
chi2 = np.sum(
np.square(y - langau(x, mpv, eta, sigma, A).astype(float)) /
np.square(yerr.astype(float)))
return chi2 / (x.shape[0] - 5) # devide by NDF
def fit_landau_migrad(x, y, p0, limit_mpv, limit_eta, limit_sigma, limit_A):
def minimizeMe(mpv, eta, sigma, A):
chi2 = np.sum(
np.square(y - langau(x, mpv, eta, sigma, A).astype(float)) /
np.square(yerr.astype(float)))
return chi2 / (x.shape[0] - 5) # devide by NDF
# Prefit to get correct errors
yerr = np.sqrt(y) # Assume error from measured data
yerr[y < 1] = 1
m = iminuit.Minuit(minimizeMe,
mpv=p0[0],
limit_mpv=limit_mpv,
error_mpv=1,
eta=p0[1],
error_eta=0.1,
limit_eta=limit_eta,
sigma=p0[2],
error_sigma=0.1,
limit_sigma=limit_sigma,
A=p0[3],
error_A=1,
limit_A=limit_A,
errordef=1,
print_level=2)
m.migrad()
if not m.get_fmin().is_valid:
raise RuntimeError('Fit did not converge')
# Main fit with model errors
yerr = np.sqrt(
langau(x,
mpv=m.values['mpv'],
eta=m.values['eta'],
sigma=m.values['sigma'],
A=m.values['A'])) # Assume error from measured data
yerr[y < 1] = 1
m = iminuit.Minuit(minimizeMe,
mpv=m.values['mpv'],
limit_mpv=limit_mpv,
error_mpv=1,
eta=m.values['eta'],
error_eta=0.1,
limit_eta=limit_eta,
sigma=m.values['sigma'],
error_sigma=0.1,
limit_sigma=limit_sigma,
A=m.values['A'],
error_A=1,
limit_A=limit_A,
errordef=1,
print_level=2)
m.migrad()
fit_values = m.values
values = np.array([
fit_values['mpv'], fit_values['eta'], fit_values['sigma'],
fit_values['A']
])
m.hesse()
m.minos()
minos_errors = m.get_merrors()
if not minos_errors['mpv'].is_valid:
print(
'Warning: MPV error determination with Minos failed! You can still use Hesse errors.'
)
errors = np.array([(minos_errors['mpv'].lower, minos_errors['mpv'].upper),
(minos_errors['eta'].lower, minos_errors['eta'].upper),
(minos_errors['sigma'].lower,
minos_errors['sigma'].upper),
(minos_errors['A'].lower, minos_errors['A'].upper)])
return values, errors, m
def test_langau_mpv(self, mpv):
''' Check Langau MPV position '''
x = np.linspace(mpv - 10, mpv + 10, 1000)
y = pylandau.langau(x, mpv=mpv, eta=1., sigma=1., A=1.)
delta = x[1] - x[0]
self.assertAlmostEqual(x[np.argmax(y)], mpv, delta=delta)
def _fitfunction_testbeam(self, x, *p):
'''
Custom fit function for testbeam histograms.
'''
mu, eta, sigma, A, p4, p5 = p
return landau.langau(x, mu, eta, sigma, A) + p4*np.exp(-x/p5)
if not minos_errors['mpv'].is_valid:
print('Warning: MPV error determination with Minos failed! You can still use Hesse errors.')
errors = np.array([(minos_errors['mpv'].lower, minos_errors['mpv'].upper),
(minos_errors['eta'].lower, minos_errors['eta'].upper),
(minos_errors['sigma'].lower, minos_errors['sigma'].upper),
(minos_errors['A'].lower, minos_errors['A'].upper)])
return values, errors, m
if __name__ == '__main__':
# Fake counting experiment with Landgaus distribution
x = np.arange(100).astype(np.float)
y = langau(x,
mpv=30.,
eta=5.,
sigma=4.,
A=1000.)
# Add poisson error
y += np.random.normal(np.zeros_like(y), np.sqrt(y))
# Fit the data with numerical exact error estimation
# Taking into account correlations
values, errors, m = fit_landau_migrad(x,
y,
p0=[x.shape[0] / 2., 10., 10., np.max(y)],
limit_mpv=(10., 100.),
limit_eta=(2., 20.),
limit_sigma=(2., 20.),
limit_A=(500., 1500.))
def fitfunction(x, *p):
'''
Fitfunction used for testbeam data
'''
mu, eta, sigma, A, p4, p5 = p
return landau.langau(x, mu, eta, sigma, A) + p4*np.exp(-x/p5)
def fit_testbeam_spectrum(self, x, y, p0, fit_range=None, ymax=None, debug=False, detail=False):
'''
Fit custom fitfunction to spectrum from testbeam and plot both data and fitted function.
Parameters:
x:np.ndarray - x-values of histogrammed data.
y:np.ndarray - y-values of histogrammed data.
p0:tuple - Set of startparameters for fit. Format: (mu, eta, sigma, A).
fit_range:tuple - [Optional] Region where the fit should be performed. Obtained automatically if None.
ymax:int - [Optional] Maximum of y-axis of plot. Obtained automatically if None.
debug:boolean - [Optional] If set, the fitfunction is plotted with startparameters for debugging.
'''
self.error = False
threshold = self.find_threshold(y)
if not fit_range or fit_range == 'auto':
fit_range = (threshold, np.round(np.amax(x)))
if ymax is None:
ymax = 1.1*np.amax(y)
plot_range = (threshold, np.round(np.amax(x)))
try:
p, _ = curve_fit(self._fitfunction_testbeam, x[(x > fit_range[0]) & (x < fit_range[1])], y[(x > fit_range[0]) & (x < fit_range[1])], p0=p0)
mpv = float(x[np.argmax(landau.langau(x, p[0], p[1], p[2], p[3]))])
if debug:
p = p0
if p[0] <= threshold:
logging.error('Encountered an error during analysis of file %s: Peak is below threshold!' % (self.f))
self.errorfiles.append([os.path.join(self.dirpath, self.f), 'Fit: Peak below threshold!'])
self.error = True
elif p[3] <= 0:
logging.error('Encountered an error during analysis of file %s: Amplitude is negative!' % (self.f))
self.errorfiles.append([os.path.join(self.dirpath, self.f), 'Fit: Amplitude is negative!'])
self.error = True
elif (10. * float(p[1]) < float(p[2])):
logging.error('Encountered an error during analysis of file %s: Oscillation occurred!' % (self.f))
self.errorfiles.append([os.path.join(self.dirpath, self.f), 'Fit: Oscillation occurred!'])
#self.error = True
except RuntimeError as e:
logging.error('Encountered an error during analysis of file %s: %s' % (self.f, e))
self.errorfiles.append([os.path.join(self.dirpath, self.f), e])
self.error = True
if self.error:
p = p0
mpv = p0[0]
else:
p = tuple([abs(e) for e in p])
logging.debug('Fitparameters:\nMPV = %1.2f\nmu = %1.3f\neta = %1.3f\nsigma = %1.3f\nA = %1.3f\np4 = %1.3f\np5 = %1.3f' % ((mpv,) + p))
plt.cla()
plt.plot(x[(x > plot_range[0]) & (x < plot_range[1])], y[(x > plot_range[0]) & (x < plot_range[1])], label='Data', color='blue', zorder=0, linewidth=1)
plt.fill_between(x[(x > plot_range[0]) & (x < plot_range[1])], y[(x > plot_range[0]) & (x < plot_range[1])], facecolor='blue', alpha=0.3, zorder=0)
plt.plot(x[(x > fit_range[0]) & (x < fit_range[1])], self._fitfunction_testbeam(x, *p)[(x > fit_range[0]) & (x < fit_range[1])], label='Fit', color='red', zorder=2, linewidth=1)
if detail:
plt.plot(x[(x > fit_range[0]) & (x < fit_range[1])], landau.langau(x, *p[:4])[(x > fit_range[0]) & (x < fit_range[1])], label='Langau', color='purple', linestyle='--', zorder=2, linewidth=1)
plt.plot(x[(x > fit_range[0]) & (x < fit_range[1])], p[4]*np.exp(-x/p[5])[(x > fit_range[0]) & (x < fit_range[1])], label='Exponential', color='yellow', linestyle='--', zorder=2, linewidth=1)
plt.plot([mpv, mpv], [0., ymax], label='MPV', color='green', linestyle='--')
if self._energy_calibrated:
plt.xlim(self._energy_intercept, np.round(np.amax(x)))
else:
plt.xlim(0, np.round(np.amax(x)))
plt.ylim(0, ymax)
plt.legend(loc=1, fontsize=12)
plt.grid()
plt.title(self.title)
plt.xlabel('Energy [%s]' % self._energy_unit)
plt.ylabel('Count')
ax = plt.axes()
textstr = '$N = %i$' % self.event_count
if self._darkframe_corrected:
textstr += '\nDarkframe-cor.'
if self.error:
textstr += '\nFit failed!'
else:
textstr += '\nFit parameters:\n$MPV = %1.2f$\n$\mu=%.2f$\n$\eta=%.2f$\n$\sigma=%.2f$\n$A=%.2f$\n$p_4=%.2f$\n$p_5=%.2f$' % ((mpv,) + p)
box = AnchoredText(textstr, loc=5)
ax.add_artist(box)
ax.annotate('Threshold', xy=(threshold,0), xytext=(threshold,-0.1*ymax), horizontalalignment='center', arrowprops=dict(facecolor='black', shrink=0.05, width=0, headwidth=0))
plt.savefig(self.outfile + '.' + self.outformat)
def minimizeMe(mpv, eta, sigma, A):
chi2 = np.sum(np.square(y - langau(x, mpv, eta, sigma, A).astype(float)) / np.square(yerr.astype(float)))
return chi2 / (x.shape[0] - 5) # devide by NDF
def lnlike(theta):
#parameters.set_params(pd.pyListToVec(theta))
#params = pd.vector()
#params[:] = theta
#parameters.set_params(params)
#f = pd.fit(parameters)
#chisq = f.generateChiSquare()
#print "chisq = " + str(chisq)
#below is OK for traditional chisquared calculation
#should find a way to do this dynamically at some point, based on input parameters.
#y = pylandau.langau(E, float(theta[0]), 64, 45, float(theta[1])) #units in keV, mpv, width, sigma, scale
#y2 = pylandau.langau(E,float(theta[2]), 64, 45, float(theta[3]))
#y3 = pylandau.langau(E,float(theta[4]), 64, 45, float(theta[5]))
#y4 = y+y2#+y3
chisq = 0.0
#for value1,value2 in zip(C,y4):
# chisq += math.pow((value1-value2),2)/np.sqrt(value1)
#I have to figure out ssh for this computer, or put all of this on the server at UML!(DUH OF COURSE)
#At least for the doublet,I have to reduce scale parameter to relative ratio
#For triplet, I could proceed with same scale parameter and normalize using 3 parameter
#could reduce parameters by turning scale between 2 low energy peaks into a ratio
#ratioLowE = theta[1]/theta[5]
#changing to correlation between scale factors (ratio dependence)
#could also introduce scale factor
#below is for "unbinned" log(likelihood) calculation
#for doublet
#fractionTot = float(theta[2]+theta[3])
#ratio is better constrained
y = pylandau.langau(x1, float(theta[0]), 64, 45, float(theta[2])) #units in keV, mpv, width, sigma, scale
y2 = pylandau.langau(x1,float(theta[1]), 64, 45, 1.-float(theta[2])) #if prior between 0 and 1 this should converge to fractional distribution
# #remember to redo params and priors dan!
y4 = y+y2
#for triplet
# fractionTot = float(theta[3]+theta[4]+theta[5])
# #fractionTot = float(theta[5])
#going to make theta[3] the log of the intensity ratio between low energy peak1 to peak2
#theta[4] is then fraction that goes to high energy peak (I hope the math below works out for the individual fractions)
# fraction12 = theta[3]
# # fraction12 = np.exp(theta[3])
# y = pylandau.langau(x1, float(theta[0]), 64, 45, float(1.-theta[4])/float(1+fraction12)) #units in keV, mpv, width, sigma, scale
# y2 = pylandau.langau(x1,float(theta[1]), 64, 45, float(theta[4])) #if prior between 0 and 1 this should converge to fractional distribution
# y3 = pylandau.langau(x1,float(theta[2]), 64, 45, float(fraction12)*float(1.-theta[4])/float(1+fraction12))
# #remember to redo params and priors dan!
# y4 = y+y2+y3
#original
#y = pylandau.langau(x1, float(theta[0]), 64, 45, float(theta[1])) #units in keV, mpv, width, sigma, scale
#y2 = pylandau.langau(x1,float(theta[2]), 64, 45, float(theta[3]))
#y3 = pylandau.langau(x1,float(theta[4]), 64, 45, float(theta[5]))
#if I get rid of normalize perhaps I will recover absolute heigh information
#of course it collapses to largest values since this "maximizes" probability
normalize = np.trapz(y4)
#normalize = 1.
for energy in E: #because of binning of x1, energy is mapped -0.5 from the entry
chisq += np.log(y4[int(energy-0.5)]/normalize) #for likelihood analysis the the probability that a model is correct for n points is by comparing the model distribution, P, at points, p_n, and multiplying them all P(p_1)*P(p_2)*...*P(p_n). Thus when taking the log these can all be added together. This is the natural way to do these kind of fits, though time consuming.
#I'm appending the temperature parameter beta to the end of the
return chisq
def test_langau_A(self, A):
''' Check Langau amplitude '''
mpv = 1.
x = np.linspace(mpv - 10, mpv + 10, 1000)
y = pylandau.langau(x, mpv=mpv, eta=1., sigma=1., A=A)
self.assertAlmostEqual(y.max(), A, delta=1e-4 * A)
# Plot the functions using matplotlib
import numpy as np
import pylandau
import matplotlib.pyplot as plt
x = np.arange(0, 100, 0.01)
for A, eta, mpv in ((1, 1, 10), (1, 2, 30), (0.5, 5, 50)):
# Use the function that calculates y values when given array
plt.plot(x,
pylandau.landau(x, mpv, eta, A),
'-',
label='mu=%1.1f, eta=%1.1f, A=%1.1f' % (mpv, eta, A))
# Use the function that calculates the y value given a x value, (e.g. needed for minimizers)
y = np.array([pylandau.get_landau(x_value, mpv, eta, A) for x_value in x])
plt.plot(x, y, 'r--', label='mu=%1.1f, eta=%1.1f, A=%1.1f' % (mpv, eta, A))
# Use the function that calculates the y value given a x value, (e.g. needed for minimizers)
sigma = 10
plt.plot(x,
pylandau.langau(x, mpv, eta, sigma, A),
'--',
label='mu=%1.1f, eta=%1.1f, sigma=%1.1f, A=%1.1f' %
(A, eta, sigma, mpv))
plt.legend(loc=0)
plt.show()
def fit_landau_migrad(x, y, p0, limit_mpv, limit_eta, limit_sigma, limit_A):
def minimizeMe(mpv, eta, sigma, A):
chi2 = np.sum(np.square(y - langau(x, mpv, eta, sigma, A).astype(float)) / np.square(yerr.astype(float)))
return chi2 / (x.shape[0] - 5) # devide by NDF
# Prefit to get correct errors
yerr = np.sqrt(y) # Assume error from measured data
yerr[y < 1] = 1
m = iminuit.Minuit(minimizeMe,
mpv=p0[0],
limit_mpv=limit_mpv,
error_mpv=1,
eta=p0[1],
error_eta=0.1,
limit_eta=limit_eta,
sigma=p0[2],
error_sigma=0.1,
limit_sigma=limit_sigma,
A=p0[3],
error_A=1,
limit_A=limit_A,
errordef=1,
print_level=2)
m.migrad()
if not m.get_fmin().is_valid:
raise RuntimeError('Fit did not converge')
# Main fit with model errors
yerr = np.sqrt(langau(x,
mpv=m.values['mpv'],
eta=m.values['eta'],
sigma=m.values['sigma'],
A=m.values['A'])) # Assume error from measured data
yerr[y < 1] = 1
m = iminuit.Minuit(minimizeMe,
mpv=m.values['mpv'],
limit_mpv=limit_mpv,
error_mpv=1,
eta=m.values['eta'],
error_eta=0.1,
limit_eta=limit_eta,
sigma=m.values['sigma'],
error_sigma=0.1,
limit_sigma=limit_sigma,
A=m.values['A'],
error_A=1,
limit_A=limit_A,
errordef=1,
print_level=2)
m.migrad()
fit_values = m.values
values = np.array([fit_values['mpv'],
fit_values['eta'],
fit_values['sigma'],
fit_values['A']])
m.hesse()
m.minos()
minos_errors = m.get_merrors()
if not minos_errors['mpv'].is_valid:
print('Warning: MPV error determination with Minos failed! You can still use Hesse errors.')
errors = np.array([(minos_errors['mpv'].lower, minos_errors['mpv'].upper),
(minos_errors['eta'].lower, minos_errors['eta'].upper),
(minos_errors['sigma'].lower, minos_errors['sigma'].upper),
(minos_errors['A'].lower, minos_errors['A'].upper)])
return values, errors, m
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import numpy as np
import pylandau
import math
import csv
# Create fake data with possion error
mpv, eta, sigma, A = 30, 5, 4, 1000
x = np.arange(0, 100, 0.5)
y = pylandau.langau(x, mpv, eta, sigma, A)
yerr = np.random.normal(np.zeros_like(x), np.sqrt(y))
yerr[y < 1] = 1
y += yerr
#read in tab delimited data file
energies = []
counts = []
countsErr = np.array([])
with open('decayEnergy_100kevBins_filter2.txt', 'r') as f:
next(f) # skip headings
reader = csv.reader(f, delimiter='\t')
for energy, count in reader:
energies.append(energy)
counts.append(count)
E = np.array(energies, dtype=float)
C = np.array(counts, dtype=float)
#np.sqrt(E)
'Warning: MPV error determination with Minos failed! You can still use Hesse errors.'
)
errors = np.array([(minos_errors['mpv'].lower, minos_errors['mpv'].upper),
(minos_errors['eta'].lower, minos_errors['eta'].upper),
(minos_errors['sigma'].lower,
minos_errors['sigma'].upper),
(minos_errors['A'].lower, minos_errors['A'].upper)])
return values, errors, m
if __name__ == '__main__':
# Fake counting experiment with Landgaus distribution
x = np.arange(100).astype(np.float)
y = langau(x, mpv=30., eta=5., sigma=4., A=1000.)
# Add poisson error
y += np.random.normal(np.zeros_like(y), np.sqrt(y))
# Fit the data with numerical exact error estimation
# Taking into account correlations
values, errors, m = fit_landau_migrad(
x,
y,
p0=[x.shape[0] / 2., 10., 10., np.max(y)],
limit_mpv=(10., 100.),
limit_eta=(2., 20.),
limit_sigma=(2., 20.),
limit_A=(500., 1500.))
# Plot fit result
def fit_langau(self, x, y, p0, fit_range, ymax=None, debug=False):
'''
Fit a simple langau function only to peak of arbitrary spectrum and plot both data and fitted function.
Parameters:
x:np.ndarray - x-values of histogrammed data.
y:np.ndarray - y-values of histogrammed data.
p0:tuple - Set of startparameters for fit. Format: (mu, eta, sigma, A).
fit_range:tuple - Approximate region of peak where the fit should be performed.
ymax:int - [Optional] Maximum of y-axis of plot. Obtained automatically if None.
debug:boolean - [Optional] If set, the fitfunction is plotted with startparameters for debugging.
'''
self.error = False
threshold = self.find_threshold(y)
plot_range = (threshold, np.round(np.amax(x)))
if fit_range is None:
fit_range = (threshold, np.round(np.amax(x)))
if ymax is None:
ymax = 1.1*np.amax(y)
try:
p, _ = curve_fit(landau.langau, x[(x > fit_range[0]) & (x < fit_range[1])], y[(x > fit_range[0]) & (x < fit_range[1])], p0=p0)
if debug:
p = p0
except RuntimeError as e:
logging.error('Encountered an error during analysis of file %s: %s' % (os.path.join(self.dirpath, self.f), e))
self.errorfiles.append([os.path.join(self.dirpath, self.f), e])
self.error = True
p = p0
if p[3] <= 0:
logging.error('Encountered an error during analysis of file %s: Amplitude is negative!' % (os.path.join(self.dirpath, self.f)))
self.errorfiles.append([os.path.join(self.dirpath, self.f), 'Fit: Amplitude is negative!'])
self.error = True
p = p0
p = tuple([abs(e) for e in p])
logging.debug('Fitparameters:\nmu = %1.3f\neta = %1.3f\nsigma = %1.3f\nA = %1.3f' % tuple(p))
plt.cla()
plt.plot(x[(x > plot_range[0]) & (x < plot_range[1])], y[(x > plot_range[0]) & (x < plot_range[1])], label='Data', color='blue', zorder=0, linewidth=1)
plt.fill_between(x[(x > plot_range[0]) & (x < plot_range[1])], y[(x > plot_range[0]) & (x < plot_range[1])], facecolor='blue', alpha=0.3, zorder=0)
plt.plot(x[(x > fit_range[0]) & (x < fit_range[1])], landau.langau(x, *p)[(x > fit_range[0]) & (x < fit_range[1])], label='Fit', color='red', zorder=2, linewidth=1)
if self._energy_calibrated:
plt.xlim(self._energy_intercept,np.round(np.amax(x)))
else:
plt.xlim(0,np.round(np.amax(x)))
plt.ylim(0,ymax)
plt.legend(loc=1, fontsize=12)
plt.grid()
plt.title(self.title)
plt.xlabel('Energy [%s]' % self._energy_unit)
plt.ylabel('Count')
ax = plt.axes()
textstr = '$N = %i$' % self.event_count
if self._darkframe_corrected:
textstr += '\nDarkframe-cor.'
if self.error:
textstr += '\nFit failed!'
else:
textstr += '\nFit parameters:\n$\mu=%.2f$\n$\eta=%.2f$\n$\sigma=%.2f$\n$A=%.2f$' % (p)
box = AnchoredText(textstr, loc=5)
ax.add_artist(box)
ax.annotate('Threshold', xy=(threshold,0), xytext=(threshold,-0.1*ymax), horizontalalignment='center', arrowprops=dict(facecolor='black', shrink=0.05, width=0, headwidth=0))
plt.savefig(self.outfile + '.' + self.outformat)
# Plot the Landau Gauss convolution (Langau) and cross check with convolution with scipy import numpy as np import pylandau import matplotlib.pyplot as plt from scipy.ndimage.filters import gaussian_filter1d mpv, eta, sigma, A = 10, 1, 3, 1 x = np.arange(0, 50, 0.01) y = pylandau.landau(x, mpv=mpv, eta=eta, A=A) y_gconv = gaussian_filter1d(y, sigma=sigma / 0.01) # Scaled means that the resulting Landau*Gauss function maximum is A at mpv # Otherwise the underlying Landau function before convolution has the # function maximum A at mpv y_gconv_2 = pylandau.langau(x, mpv, eta, sigma, A, scale_langau=False) y_gconv_3 = pylandau.langau(x, mpv, eta, sigma, A, scale_langau=True) plt.plot(x, y, label='Landau') plt.plot(x, y_gconv_2, label='Langau') plt.plot(x, y_gconv, '--', label='Langau Scipy') plt.plot(x, y_gconv_3, label='Langau scaled') plt.legend(loc=0) plt.show()
''' Simple fit without fit error estimation.
For correct fit errors check the advanced example.
Bound should be defined. Eta has to be > 1.
'''
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import numpy as np
import pylandau
# Create fake data with possion error
mpv, eta, sigma, A = 30, 5, 4, 1000
x = np.arange(0, 100, 0.5)
y = pylandau.langau(x, mpv, eta, sigma, A)
yerr = np.random.normal(np.zeros_like(x), np.sqrt(y))
yerr[y < 1] = 1
y += yerr
# Fit with constrains
coeff, pcov = curve_fit(pylandau.langau,
x,
y,
sigma=yerr,
absolute_sigma=True,
p0=(mpv, eta, sigma, A),
bounds=(1, 10000))
# Plot
plt.errorbar(x, y, np.sqrt(pylandau.langau(x, *coeff)), fmt=".")
print coeff
plt.plot(x, pylandau.langau(x, *coeff), "-")
def test_langau_mpv(self, mpv):
''' Check Langau MPV position '''
x = np.linspace(mpv - 10, mpv + 10, 1000)
y = pylandau.langau(x, mpv=mpv, eta=1., sigma=1., A=1.)
delta = x[1] - x[0]
self.assertAlmostEqual(x[np.argmax(y)], mpv, delta=delta)
def test_langau_A(self, A):
''' Check Langau amplitude '''
mpv = 1.
x = np.linspace(mpv - 10, mpv + 10, 1000)
y = pylandau.langau(x, mpv=mpv, eta=1., sigma=1., A=A)
self.assertAlmostEqual(y.max(), A, delta=1e-4 * A)
def run(self):
"""Calculates the langau for the specified data"""
# Which clusters need to be considered
clustersize_list = self.main.kwargs["configs"].get("langau", {}).get(
"clustersize", [-1])
if type(clustersize_list) != list:
clustersize_list = list(clustersize_list)
if clustersize_list[0] == -1:
clustersize_list = list(
range(1, self.main.kwargs["configs"]["max_cluster_size"] +
1)) # If nothing is specified
# Go over all datafiles
for data in tqdm(self.data, desc="(langau) Processing file:"):
self.results_dict[data] = {}
indNumClus = self.get_num_clusters(
self.data[data], self.numClusters
) # Here events with only one cluster are choosen
indizes = np.concatenate(indNumClus)
valid_events_clustersize = np.take(
self.data[data]["base"]["Clustersize"], indizes)
valid_events_clusters = np.take(
self.data[data]["base"]["Clusters"], indizes)
valid_events_Signal = np.take(
self.data[data]["base"]["Signal"],
indizes) # Get the clustersizes of valid events
# Get events which show only cluster in its data
charge_cal, noise = self.main.calibration.charge_cal, self.main.noise
self.results_dict[data]["Clustersize"] = []
# General langau, where all clustersizes are considered
if self.main.usejit and self.poolsize > 1:
paramslist = []
for size in clustersize_list:
cls_ind = np.nonzero(valid_events_clustersize == size)[0]
paramslist.append(
(cls_ind, valid_events_Signal, valid_events_clusters,
self.main.calibration.charge_cal, self.main.noise))
# Here multiple cpu calculate the energy of the events per clustersize
results = self.pool.starmap(langau_cluster,
paramslist,
chunksize=1)
self.results_dict[data]["Clustersize"] = results
else:
for size in tqdm(clustersize_list,
desc="(langau) Processing clustersize"):
# get the events with the different clustersizes
ClusInd = [[], []]
for i, event in enumerate(valid_events_clustersize):
# cls_ind = np.nonzero(valid_events_clustersize == size)[0]
for j, clus in enumerate(event):
if clus == size:
ClusInd[0].extend([i])
ClusInd[1].extend([j])
signal_clst_event = []
noise_clst_event = []
for i, ind in tqdm(enumerate(ClusInd[0]),
desc="(langau) Processing event"):
y = ClusInd[1][i]
# Signal calculations
signal_clst_event.append(
np.take(valid_events_Signal[ind],
valid_events_clusters[ind][y]))
# Noise Calculations
noise_clst_event.append(
np.take(noise, valid_events_clusters[ind]
[y])) # Get the Noise of an event
totalE = np.sum(convert_ADC_to_e(signal_clst_event,
charge_cal),
axis=1)
totalNoise = np.sqrt(
np.sum(convert_ADC_to_e(noise_clst_event, charge_cal),
axis=1)
) # eError is a list containing electron signal noise
# incrementor += 1
preresults = {"signal": totalE, "noise": totalNoise}
self.results_dict[data]["Clustersize"].append(preresults)
# With all the data from every clustersize add all together and fit the langau to it
finalE = np.zeros(0)
finalNoise = np.zeros(0)
for cluster in self.results_dict[data]["Clustersize"]:
indi = np.nonzero(
cluster["signal"] > 0)[0] # Clean up and extra energy cut
nogarbage = cluster["signal"][indi]
indi = np.nonzero(
nogarbage < self.Ecut)[0] # ultra_high_energy_cut
cluster["signal"] = cluster["signal"][indi]
finalE = np.append(finalE, cluster["signal"])
finalNoise = np.append(finalNoise, cluster["noise"])
# Fit the langau to it
coeff, pcov, hist, error_bins = self.fit_langau(finalE,
finalNoise,
bins=self.bins)
self.results_dict[data]["signal"] = finalE
self.results_dict[data]["noise"] = finalNoise
self.results_dict[data]["langau_coeff"] = coeff
self.results_dict[data]["langau_data"] = [
np.arange(1., 100000., 1000.),
pylandau.langau(np.arange(1., 100000., 1000.), *coeff)
] # aka x and y data
self.results_dict[data]["data_error"] = error_bins
# Consider now only the seedcut hits for the langau,
if self.main.kwargs["configs"].get("langau",
{}).get("seed_cut_langau",
False):
seed_cut_channels = self.data[data]["base"]["Channel_hit"]
signals = self.data[data]["base"]["Signal"]
finalE = []
seedcutADC = []
for i, signal in enumerate(
tqdm(signals, desc="(langau SC) Processing events")):
if signal[seed_cut_channels[i]].any():
seedcutADC.append(signal[seed_cut_channels[i]])
self.log.info("Converting ADC to electrons...")
converted = convert_ADC_to_e(seedcutADC, charge_cal)
for conv in converted:
finalE.append(sum(conv))
finalE = np.array(finalE, dtype=np.float32)
# get rid of 0 events
indizes = np.nonzero(finalE > 0)[0]
nogarbage = finalE[indizes]
indizes = np.nonzero(
nogarbage < self.Ecut)[0] # ultra_high_energy_cut
coeff, pcov, hist, error_bins = self.fit_langau(
nogarbage[indizes], bins=self.bins)
# coeff, pcov, hist, error_bins = self.fit_langau(nogarbage, bins=500)
self.results_dict[data]["signal_SC"] = nogarbage[indizes]
self.results_dict[data]["langau_coeff_SC"] = coeff
self.results_dict[data]["langau_data_SC"] = [
np.arange(1., 100000., 1000.),
pylandau.langau(np.arange(1., 100000., 1000.), *coeff)
] # aka x and y data
return self.results_dict.copy()
