def main():
data = Z0Data.fromROOTFile('../data/daten/daten_1.root', 'h33')
energiedatas = data.splitEnergies()
xmin, xmax = -0.9, 0.9
binsizes = {88.48021:80, 89.47158:80, 90.22720:80, 91.23223:50, 91.97109:25, 92.97091:59, 93.71841:80}
integrals = []
eds = list(energiedatas.items()) # energy datas sorted after energy
eds.sort(key=lambda x: x[0])
table = []
for energie, data in eds:
(s, ss), (t, st) = stFit(data, energie, xmin, xmax, binsizes[energie])
# s intergral:
Is = s * (xmax - xmin + (xmax ** 3 - xmin ** 3) / 3)
sIs = Is * ss / s
# t integral
It = t * (1 / (1 - xmax) - 1 / (1 - xmin))
sIt = It * st / t
r = Is / (Is + It) # s-ratio
sr = r * sqrt((sIs / Is) ** 2 + (sIs ** 2 + sIt ** 2) / ((Is + It) ** 2))
integrals.append((energie, Is, sIs, It, sIt, r, sr))
table.append([energie, r, sr])
with TxtFile('../calc/s-t-integrals.txt', 'w') as f:
f.write2DArrayToFile(integrals, ['%.5f'] + ['%.3f'] * 6)
with TxtFile('../src/tab_st_ratios.tex', 'w') as f:
f.write2DArrayToLatexTable(table, [r"$\sqrt{s}$ / GeV", r"$c_{\text{st}}$", r"$s_{c_{\text{st}}}$"],
["%.2f", "%.2f", "%.2f"],
r"Korrekturfaktoren $c_{\text{st}}$ der s-t-Kanal Trennung für verschiedene Schwerpunktsenergien.",
"tab:st:corrs")
def evalEnergyCalibration(peaks, percents):
maxenergy = 1.95 * 0.87 * 84
smaxenergy = maxenergy * sqrt((0.05 / 1.95)**2 + (0.01 / 0.87)**2 +
(5 / 84)**2)
channels = list(list(zip(*peaks))[0])
schannels = list(list(zip(*peaks))[1])
energies = list(map(lambda x: x / 100 * maxenergy, percents))
senergies = list(map(lambda x: x / 100 * smaxenergy, percents))
print(energies)
print(senergies)
with TxtFile('../src/tab_energycalibration.tex', 'w') as f:
f.write2DArrayToLatexTable(
list(zip(*[percents, channels, schannels, energies, senergies])),
['\% energy', '$c$', '$s_c$', '$E$ / MeV', '$s_E$ / MeV'],
['%d', '%.3f', '%.3f', '%.1f', '%.1f'],
"Channels of fitted peaks and their theoretical energy for the energy calibration.",
"tab:ecal")
data = DataErrors.fromLists(channels, energies, schannels, senergies)
c = TCanvas('c_energycalibration', '', 1280, 720)
g = data.makeGraph('g_energycalibration', 'channel c', 'energy E / MeV')
g.Draw('AP')
fit = Fitter('fit_energycalibration', 'pol1(0)')
fit.function.SetNpx(1000)
fit.setParam(0, 'a', 0)
fit.setParam(1, 'b', 1 / 3)
fit.fit(g, 0, max(channels) + 5)
fit.saveData('../fit/energyCalibration.txt')
l = TLegend(0.15, 0.6, 0.575, 0.85)
l.SetTextSize(0.03)
l.AddEntry(g, 'Peaks of flight through spectra / pedestal', 'p')
l.AddEntry(fit.function, 'fit with E(c) = a + b * c', 'l')
fit.addParamsToLegend(l, (('%.2f', '%.2f'), ('%.3f', '%.3f')),
chisquareformat='%.2f',
units=('MeV', 'MeV / channel'),
lang='en')
l.Draw()
c.Update()
c.Print('../img/energyCalibration.pdf', 'pdf')
with TxtFile('../calc/energyCalibration.txt', 'w') as f:
f.writeline('\t', str(fit.params[0]['value']),
str(fit.params[0]['error']))
f.writeline('\t', str(fit.params[1]['value']),
str(fit.params[1]['error']))
f.writeline('\t', str(fit.getCovMatrixElem(0, 1)))
def main():
effmatrix = loadCSVToList('../calc/efficencies.txt')
seffmatrix = loadCSVToList('../calc/efficencies_error.txt')
t1 = time.time()
#generate matrices
ms = []
for i in range(100000):
m = generateErrorMatrix(effmatrix, seffmatrix)
ms.append(inv(m))
#group values
sigmas = [[[] for i in range(4)] for j in range(4)] # empty 4x4 matrix
for i in range(4):
for j in range(4):
entries = []
for m in ms:
entries.append(m[i][j])
sigmas[i][j] = std(entries, ddof=1)
t2 = time.time()
print('%.3f' % (t2 - t1))
print(matrix(sigmas))
with TxtFile('../calc/invEfficencies_error.txt', 'w') as f:
f.write2DArrayToFile(sigmas, ['%.7f'] * 4)
def evalIntervalConst(avgspectrum):
def avg2vals(val1, val2):
return avgerrors([val1[0], val2[0]], [val1[1], val2[1]])
def sub2vals(val1, val2):
return val1[0] - val2[0], sqrt(val1[1] ** 2 + val2[1] ** 2)
s = avgspectrum
sfreq85 = sub2vals(s[3], s[2]) # 85 S delta freq
s = avgspectrum[:2] + avgspectrum[-2:]
sfreq87 = avg2vals(sub2vals(s[2], s[0]), sub2vals(s[3], s[1])) # 87 S delta freq
pfreq87 = avg2vals(sub2vals(s[3], s[2]), sub2vals(s[1], s[0])) # 87 P delta freq
freqs = [sfreq85, sfreq87, pfreq87]
Fs = [2, 1, 1] # F of HFS
names = [r"\rb{85}: ${}^2\text{S}_{1/2}$", r"\rb{87}: ${}^2\text{S}_{1/2}$", r"\rb{87}: ${}^2\text{P}_{1/2}$"]
litvals = ["4.185", "14.13", "1.692"]
As = []
for name, litval, (freq, sfreq87), F in zip(*[names, litvals, freqs, Fs]):
A = freq * h_eVs / (F + 1) * 1e15 # in µeV and GHz in Hz
sA = sfreq87 * h_eVs / (F + 1) * 1e15
As.append([name, litval, A, sA])
with TxtFile('../src/tab_part2_A.tex', 'w') as f:
f.write2DArrayToLatexTable(As,
["Isotop / Feinstruktur", r"$A^\text{Lit.}$ / \textmu eV",
r"$A^\text{exp}$ / \textmu eV", r"$s_{A^\text{exp}}$ / \textmu eV"],
['%s', '%s', '%.2f', '%.2f'],
r"Errechnete HFS-Intervallkonstanten $A$ für das ${}^2\text{S}_{1/2}$ Niveau von \rb{85} " +
r"und für das ${}^2\text{S}_{1/2}$- und ${}^2\text{P}_{1/2}$ Niveau von \rb{87}.",
"tab:hfs:intervalconsts")
def saveDataToLaTeX(self,
thead,
format,
caption,
label,
path,
mode,
encoding='utf-8'):
"""prints all points formatted into an latex file and saves it.
Arguments:
thead -- list of descriptions for columns, is used as first row
format -- list of formatting rules, how to convert numbers into strings
caption -- caption of table in latex
label -- label of table in latex
path -- relative path to file in which the data is saved to
mode -- write mode (usually 'w' for overwriting or 'a' for appending)
encoding -- file encoding (default = 'utf-8')
"""
i = ' ' # intendation
with TxtFile(path, mode, encoding) as f:
f.writeline('\\begin{table}[H]')
f.writeline('\\caption{' + caption + '}')
f.writeline('\\begin{center}')
f.writeline('\\begin{tabular}{' + '|c' * len(self.points[0]) +
'|}')
f.writeline(i + '\hline')
f.writeline(i + ' & '.join(thead) + ' \\\\ \hline ')
for point in self.points:
f.writeline(i + ' & '.join(format) % (point[0], point[1]) +
' \\\\ \hline')
f.writeline('\\end{tabular}')
f.writeline('\\end{center}')
f.writeline('\\label{' + label + '}')
f.writeline('\\end{table}')
def evalTotalGamma(gammas):
gammas.append(avgerrors(list(zip(*gammas))[0], list(zip(*gammas))[1]))
with TxtFile('../calc/gamma_total.txt', 'w') as f:
f.write2DArrayToFile(gammas, ['%f'] * 2)
table = []
desc = [LATEXE, LATEXM, LATEXT, LATEXQ, "gew. Mittel"]
for i, (gamma, sgamma) in enumerate(gammas):
table.append([desc[i], gamma, sgamma])
with TxtFile('../src/tab_gamma_total.tex', 'w') as f:
f.write2DArrayToLatexTable(
table, [
"Zerfallskanal", r"$\Gamma_\text{Z}$ / GeV",
r"$s_{\Gamma_\text{Z}}$ / GeV"
], ['%s', '%.3f', '%.3f'],
r"Durch Fits bestimmte totale Zerfallsbreite des \Z-Bosons und gewichtetes Mittel.",
"tab:gamma:total")
def makeProgTables():
name = 'prog%dnl.txt'
for i in range(1, 3 + 1):
prog = I2Data.fromPath('../data/' + name % i)
x = prog.getX()
y = prog.getY()
prog.correctValues(False)
yc = prog.getY()
yce = prog.getEY()
f = TxtFile('../src/prog%d.tex' % i, 'w')
f.write2DArrayToLatexTable(zip(x, y, yc, yce),
['$\\nu\'$', r'$\lambda_{\text{exp}}$ / nm', r'$\lambda_{\text{cor}}$ / nm', r'$s_{\lambda_{\text{cor}}}$ / nm'],
['%0.f', '%3.2f', '%3.2f', '%.8f'],
'Measured position of transmission minima in $I_2$-spectrum and corrected values of progession %d.' % i,
'tab:prog%d' % i)
f.close()
def evalMasses(masses):
masses.append(avgerrors(list(zip(*masses))[0], list(zip(*masses))[1]))
with TxtFile('../calc/mass.txt', 'w') as f:
f.write2DArrayToFile(masses, ['%f'] * 2)
table = []
desc = [LATEXE, LATEXM, LATEXT, LATEXQ, "gew. Mittel"]
for i, (mass, smass) in enumerate(masses):
table.append([desc[i], mass, smass])
with TxtFile('../src/tab_mass.tex', 'w') as f:
f.write2DArrayToLatexTable(
table, [
"Zerfallskanal", r"$M_\text{Z}$ / GeV",
r"$s_{M_\text{Z}}$ / GeV"
], ['%s', '%.3f', '%.3f'],
r"Durch Fits bestimmte Masse des \Z-Bosons und gewichtetes Mittel.",
"tab:mass")
def calibrateNDFilters():
errorp = 0.01 # percentage error
offset = 70
data = loadCSVToList('../data/part5/04.10/filters.txt')
ref = data[0][2] + offset
sref = sqrt((data[0][2] * errorp)**2 + (offset * errorp)**2)
newdata = []
filters = dict()
for d in data:
int = (d[2] + offset) / ref
if int == 1:
sint = 0
else:
sint = int * sqrt((sqrt((d[2] * errorp)**2 +
(offset * errorp)**2) /
(d[2] + offset))**2 + (sref / ref)**2)
newdata.append(d + [int * 100, sint * 100])
filters[d[0]] = (int, sint)
with TxtFile('../src/tab_part5_NDFilters.tex', 'w') as f:
f.write2DArrayToLatexTable(
newdata, [
"Stärke des Filters", r"$I_\text{nominell}$ / \%",
r"$U_\text{ph}$ / mV", r"$I_\text{mess}$ / \%",
r"$s_{I_\text{mess}}$ / \%"
], ['%.1f', '%.3f', '%d', '%.2f', '%.2f'],
r'Kalibrierung der Neutraldichtefilter: Nominelle Transmission $I_{\text{nominell}}$, gemessene Spannung an der Photodiode $U_{\text{ph}}$ und daraus berechnete Transmission $I_{\text{mess}}$. ',
'tab:deh:dnfilter')
return filters
def saveData(self, path, mode='w', enc='utf-8'):
"""saves fitting info (chi^2, DoF, chi^2/DoF, paramters with values and errors, covariance and correlation matrix)
Arguments:
path -- relative path to file
mode -- write mode (usually 'w' for overwriting or 'a' for appending)
enc -- encoding (default = 'utf-8')
"""
with TxtFile.fromRelPath(path, mode) as f:
f.writeline('fitting info')
f.writeline('============')
f.writeline(TxtFile.CHISQUARE + ':\t\t' + str(self.getChisquare()))
f.writeline('DoF:\t' + str(self.getDoF()))
f.writeline(TxtFile.CHISQUARE + '/DoF:\t' + str(self.getChisquareOverDoF()))
f.writeline('\t', 'p-value:', *map(str, self.getPValue()))
f.writeline('')
f.writeline('parameters')
f.writeline('==========')
for i, param in self.params.iteritems():
f.writeline('\t', str(i), param['name'], str(param['value']), TxtFile.PM, str(param['error']))
f.writeline('')
f.writeline('covariance matrix')
f.writeline('=================')
f.writelines('\t'.join(str(j) for j in i) + '\n' for i in self._covMatrix)
f.writeline('')
f.writeline('correlation matrix')
f.writeline('==================')
f.writelines('\t'.join(str(j) for j in i) + '\n' for i in self._corrMatrix)
f.writeline()
f.close()
def main():
# load data
data = Z0Data.fromROOTFile('../data/daten/daten_1.root', 'h33')
energiedatas = data.splitEnergies()
inveffmatrix, sinveffmatrix = loadInvEffMatrix()
stRatios = loadSTRatios()
lums = loadLums()
corrs = loadCorrections()
plotDataDistributions(data)
trueVectors = dict()
sTrueVectors = dict()
for energie, data in energiedatas.items():
# print("E_lep: ", energie)
# energies = []
# for event in data.getEvents():
# energies.append(event["E_lep"])
# print("E_lep_data: ", average(energies) * 2)
MeasVector = makeDataCut(data)
# print("MeasVector: ")
# print(MeasVector)
# print("TrueVector:")
trueVector = list(dot(inveffmatrix, MeasVector))
sTrueVector = [
sqrt(
sum((inveffmatrix[i][j] * MeasVector[j])**2 *
((sinveffmatrix[i][j] / inveffmatrix[i][j])**2 +
(sqrt(MeasVector[j]) / MeasVector[j])**2)
for j in range(4))) for i in range(4)
]
old = trueVector[0]
trueVector[0] = old * stRatios[energie][0]
sTrueVector[0] = trueVector[0] * sqrt(
(sTrueVector[0] / old)**2 +
(stRatios[energie][1] / stRatios[energie][0])**2)
# print(trueVector)
# print("")
trueVectors[energie] = trueVector
sTrueVectors[energie] = sTrueVector
NDatas = [[] for i in range(4)]
names = ['ee', 'mm', 'tt', 'qq']
for energie in trueVectors.keys():
for i in range(4):
NDatas[i].append(
(energie, trueVectors[energie][i], sTrueVectors[energie][i]))
crosssections = dict()
for ctype, NData in zip(*[names, NDatas]):
sigmas = calcCrossSection(ctype, NData, lums, corrs)
crosssections[ctype] = sigmas
with TxtFile('../calc/crosssections_%s.txt' % ctype, 'w') as f:
for sigma in sigmas:
f.writeline('\t', *list(map(str, sigma)))
def main():
evalUnderground()
makeEnergyPlot()
e, se = makeFermiKuriePlot()
E = e * 2
sE = se * 2
print(E, sE)
with TxtFile('../calc/energy.txt', 'w') as f:
f.writeline('\t', *map(lambda x: '%.2f' % x, (e, se)))
f.writeline('\t', *map(lambda x: '%.2f' % x, (E, sE)))
def makeTable():
sigmas = loadCSVToList('../calc/invEfficencies_error.txt')
thead = [r"Schnitt$\backslash$MC-Daten", LATEXE, LATEXM, LATEXT, LATEXQ]
firstrow = [LATEXE, LATEXM, LATEXT, LATEXQ]
with TxtFile('../src/tab_effmat_inv_err.tex', 'w') as f:
f.write2DArrayToLatexTable(
list(zip(*([firstrow] + list(zip(*sigmas))))), thead,
['%s'] + ['%.7f'] * 4,
'Fehler der inversen Effizienzmatrix, berechnet mit einem toy-experiment.',
'tab:inveffmat:err')
def evalPartGamma(gammas):
with TxtFile('../calc/gamma_part.txt', 'w') as f:
f.write2DArrayToFile(gammas, ['%f'] * 2)
table = []
desc = [LATEXE, LATEXM, LATEXT, LATEXQ]
litvals = [
r"$83.91 \pm 0.12$", r"$83.99\pm0.18$", r"$84.04\pm0.22$",
r"$1744.4\pm2.0$"
]
for i, (gamma, sgamma) in enumerate(gammas):
table.append([desc[i], gamma * 1e3, sgamma * 1e3, litvals[i]])
with TxtFile('../src/tab_gamma_part.tex', 'w') as f:
f.write2DArrayToLatexTable(
table, [
"Zerfallskanal $i$", r"$\Gamma_i$ / MeV",
r"$s_{\Gamma_i}$ / MeV", r"$\Gamma_i^{\text{Lit.}}$ / MeV"
], ['%s', '%.1f', '%.1f', '%s'],
r"Durch Fits bestimmte partielle Zerfallsbreiten des \Z-Bosons und Literaturwerte \cite{pdg}.",
"tab:gamma:part")
def main():
E, sE = 107.7, 1.42
t, st = 2.237, 0.052
tToeV = 1 / hbar_eVs * 1e-6
nt, snt = tToeV * t, tToeV * st
A = 192 * pi**3
G = sqrt(A / (nt * E**5)) * 1e3
sG = 1 / 2 * sqrt(A * (E**2 * snt**2 + 25 * sE**2 * nt**2) /
(E**7 * nt**3)) * 1e3
print(G, sG)
with TxtFile('../calc/G.txt', 'w') as f:
f.writeline('\t', '%.4e' % G, '%.2e' % sG)
def main():
# luminosity
lums = loadCSVToList('../data/daten/lum.txt')
with TxtFile('../src/tab_lums.tex', 'w') as f:
f.write2DArrayToLatexTable(
lums, [
r"$\sqrt{s}$ / GeV", r"$L$ / (1/nb)",
r"$s_L^\text{stat}$ / (1/nb)", r"$s_L^\text{sys}$ / (1/nb)",
r"$s_L^\text{tot}$ / (1/nb)"
], ["%.2f"] + ["%.0f"] * 4,
"Zeitlich integrierte Luminosität mit statistischem, systematischem und totalem "
+ "Fehler für verschiedene Schwerpunktsenergien.", "tab:lums")
# beam correction
corr = loadCSVToList('../data/daten/corr.txt')
with TxtFile('../src/tab_beamcorr.tex', 'w') as f:
f.write2DArrayToLatexTable(
corr, [
r"$\sqrt{s}$ / GeV", r"$c_\text{beam, \qq}$ / nb",
r"$c_\text{beam, \leplep}$ / nb"
], ["%.2f", "%.1f", "%.2f"],
r"Strahlungskorrekturen für hadronische und leptonische Zerfälle bei verschiedenen Schwerpunktsenergien.",
"tab:beamcorrs")
def main():
peak100, sigma100 = evalFlythroughSpectrum('energiekalibration_100', 275,
600)
peak050, sigma050 = evalFlythroughSpectrum('energiekalibration_50', 120,
400)
peak035, sigma035 = evalFlythroughSpectrum('energiekalibration_35', 75,
240)
peak000 = evalPedestal()
evalEnergyCalibration([peak000, peak035, peak050, peak100],
[0, 35, 50, 100])
with TxtFile('../calc/ecal_sigmas.txt', 'w') as f:
for d in [[peak035, sigma035], [peak050, sigma050],
[peak100, sigma100]]:
f.writeline('\t',
*map(str, [item for sublist in d for item in sublist]))
def makePeakFreqGraph(peaks, name):
xlist = list(list(zip(*peaks))[0])
sxlist = list(list(zip(*peaks))[1])
ylist = list(map(lambda i: i * 9.924, range(len(peaks))))
sylist = list(map(lambda i: i * 0.03, range(len(peaks))))
direction = name.split('-')[0]
tabledata = list(zip(*[list(range(1, len(xlist) + 1)), list(map(lambda x:x * 1000, xlist)), list(map(lambda x:x * 1000, sxlist)),
ylist, sylist]))
with TxtFile('../src/tab_part2_etalonfreqs_%s.tex' % direction, 'w') as f:
f.write2DArrayToLatexTable(tabledata,
["i", r"$x_i$ / ms", r"$0.2 \cdot s_i$ / ms", r"$\nu_i$ / GHz", r"$s_{\nu_i}$ / GHz"],
["%d", "%.3f", "%.3f", "%.2f", "%.2f"],
"Zentren $x_i$ der gefitteten Cauchy-Funktionen mit Fehler aus den " +
"Breiteparametern $s_i$ und Frequenzdifferenzen zum ersten Peak. ",
"tab:etalon:calib:%s" % direction)
etalonData = DataErrors.fromLists(xlist, ylist, sxlist, sylist)
etalonData.multiplyX(1000)
c = TCanvas('c_pf_' + name, '', 1280, 720)
g = etalonData.makeGraph('g_pf_' + name, 'Zeit t / ms', 'Frequenzabstand #Delta#nu / GHz')
g.SetMinimum(etalonData.getMinY() - 5)
g.SetMaximum(etalonData.getMaxY() + 5)
g.Draw('AP')
fit = Fitter('fit_pf_' + name, 'pol1(0)')
fit.setParam(0, 'a')
fit.setParam(1, 'r')
xmin, xmax = etalonData.getMinX(), etalonData.getMaxX()
deltax = (xmax - xmin) / 10
fit.fit(g, xmin - deltax, xmax + deltax)
fit.saveData('../fit/part2/%s-etalon_calibration.txt' % name)
if fit.params[1]['value'] < 0:
l = TLegend(0.575, 0.6, 0.85, 0.85)
else:
l = TLegend(0.15, 0.6, 0.425, 0.85)
l.SetTextSize(0.03)
l.AddEntry(g, 'Etalonpeaks', 'p')
l.AddEntry(fit.function, 'Fit mit #Delta#nu = a + r * t', 'l')
fit.addParamsToLegend(l, [('%.1f', '%.1f'), ('%.2f', '%.2f')], chisquareformat='%.2f', units=('GHz', 'GHz/ms'))
l.Draw()
c.Update()
if not DEBUG:
c.Print('../img/part2/%s-etalon_calibration.pdf' % name, 'pdf')
return (fit.params[1]['value'], fit.params[1]['error'])
def evalTaus(taus, filters):
data = DataErrors()
table = []
for key, (tau, stau) in taus.items():
invtau = 1 / tau
sinvtau = stau / (tau**2)
int, sint = filters[key]
data.addPoint(int, invtau, sint, sinvtau)
table.append([int * 100, sint * 100, tau * 1000, stau * 1000])
table.sort(key=lambda x: x[0], reverse=True)
# make table
with TxtFile('../src/tab_part5_taus.tex', 'w') as f:
f.write2DArrayToLatexTable(
table, [
r'$I_\text{mess}$ / \%', r'$s_{I_\text{mess}}$ / \%',
r'$\tau$ / ms', r'$s_\tau$ / ms'
], ['%.2f', '%.2f', '%.3f', '%.3f'],
r'Orientierungszeiten $\tau$ des Rubidiumensembles bei verschiedenen Pumpintensitäten $I_{\text{mess}}$.',
'tab:deh:fitres')
# make fit
c = TCanvas('c_taus', '', 1280, 720)
g = data.makeGraph('g_taus', r'relative Intensitaet I_{mess}',
'inverse Orientierungszeit #tau^{ -1} / s^{-1}')
g.Draw('APX')
fit = Fitter('fit_taus', '[0]*x + 1/[1]')
fit.setParam(0, '#alpha', 1)
fit.setParam(1, 'T_{R}', 1)
fit.fit(g, 0, 1.1)
fit.saveData('../fit/part5/taufit.txt')
l = TLegend(0.55, 0.15, 0.85, 0.5)
l.SetTextSize(0.03)
l.AddEntry(g, 'Inverse Orientierungszeit #tau^{ -1}', 'p')
l.AddEntry(fit.function,
'Fit mit #tau^{ -1} (I) = #alpha I + #frac{1}{T_{R}}', 'l')
fit.addParamsToLegend(l, [('%.0f', '%.0f'), ('%.5f', '%.5f')],
chisquareformat='%.2f',
units=['s^{-1}', 's'])
l.Draw()
g.Draw('P')
c.Print('../img/part5/taufit.pdf', 'pdf')
def evalHgPeaks():
data = I2Data.fromPath('../data/02_Hg_full_ngg11.txt')
mins = data.findExtrema(10, 425, 630, False)
mins.filterY(1300)
with TxtFile.fromRelPath('../calc/hg_lines.txt', 'w') as f:
for min in mins.points:
f.writeline(str(min[0]))
c = TCanvas('c1', '', 1280, 720)
c.SetLogy()
g = data.makeGraph('g', 'wavelength #lambda / nm', 'intensity / a.u.')
g.GetXaxis().SetRangeUser(415, 620)
g.SetMarkerStyle(1)
g.Draw('AP')
m = mins.makeGraph()
if m:
m.SetMarkerColor(2)
m.Draw('P')
c.Update()
c.Print('../img/HgPeaks.pdf', 'pdf')
def evalNaPeaks():
data = I2Data.fromPath('../data/01_Na_ngg13.txt')
mins = data.findExtrema(200, 508, 630, False)
mins.filterY(40000)
with TxtFile.fromRelPath('../calc/na_lines.txt', 'w') as f:
for min in mins.points:
f.writeline(str(min[0]))
c = TCanvas('c1', '', 1280, 720)
g = data.makeGraph('g', 'wavelength #lambda / nm', 'intensity / a.u.')
g.GetXaxis().SetRangeUser(415, 620)
g.GetYaxis().SetTitleOffset(1.2)
g.SetMarkerStyle(1)
g.Draw('AP')
m = mins.makeGraph()
if m:
m.SetMarkerColor(2)
m.Draw('P')
c.Update()
c.Print('../img/NaPeaks.pdf', 'pdf')
def main():
datas = Z0Data.fromROOTFile('../data/daten/daten_1.root', 'h33')
energiedatas = datas.splitEnergies()
binsizes = {
88.48021: 30,
89.47158: 30,
90.22720: 28,
91.23223: 75,
91.97109: 31,
92.97091: 30,
93.71841: 30
}
results = dict()
for energy, data in energiedatas.items():
res = makeFBAFit(energy, data, binsizes[energy])
if res:
results[energy] = res
ressort = list(results.items())
ressort.sort(key=lambda x: x[0])
with TxtFile('../calc/FBA.txt', 'w') as f:
for energy, res in ressort:
f.writeline('\t', *map(lambda x: '%.5f' % x, [energy] + list(res)))
def saveData(self, path, mode='w', enc='utf-8'):
"""saves fitting info (chi^2, DoF, chi^2/DoF, paramters with values and errors, covariance and correlation matrix)
Arguments:
path -- relative path to file
mode -- write mode (usually 'w' for overwriting or 'a' for appending)
enc -- encoding (default = 'utf-8')
"""
with TxtFile.fromRelPath(path, mode) as f:
f.writeline('fitting info')
f.writeline('============')
f.writeline(TxtFile.CHISQUARE + ':\t\t' + str(self.getChisquare()))
f.writeline('DoF:\t' + str(self.getDoF()))
f.writeline(TxtFile.CHISQUARE + '/DoF:\t' +
str(self.getChisquareOverDoF()))
#f.writeline('\t', 'p-value:', *map(str, self.getPValue()))
f.writeline('')
f.writeline('parameters')
f.writeline('==========')
for i, param in self.params.items():
f.writeline('\t', str(i), param['name'], str(param['value']),
TxtFile.PM, str(param['error']))
f.writeline('')
f.writeline('covariance matrix')
f.writeline('=================')
if self._covMatrix:
f.writelines('\t'.join(str(j) for j in i) + '\n'
for i in self._covMatrix)
f.writeline('')
f.writeline('correlation matrix')
f.writeline('==================')
if self._corrMatrix:
f.writelines('\t'.join(str(j) for j in i) + '\n'
for i in self._corrMatrix)
f.writeline()
f.close()
def makeCuts(datas):
efficencies = []
sefficencies = []
purities = []
for cutnum, cutinfo in enumerate(CUTS):
name, cut = cutinfo
(effs, seffs), purity = makeCut(datas, cut, cutnum, name)
efficencies.append(effs)
sefficencies.append(seffs)
purities.append(purity)
# output for further calculations
with TxtFile('../calc/efficencies.txt', 'w') as f:
f.write2DArrayToFile(efficencies, ['%.8f'] * 4)
with TxtFile('../calc/efficencies_error.txt', 'w') as f:
f.write2DArrayToFile(sefficencies, ['%.8f'] * 4)
with TxtFile('../calc/invEfficencies.txt', 'w') as f:
f.write2DArrayToFile(inv(efficencies), ['%.8f'] * 4)
with TxtFile('../calc/purities.txt', 'w') as f:
f.write2DArrayToFile(list(zip(*[purities])), ['%.6f'])
# output for protocol
thead = [r"Schnitt$\backslash$MC-Daten", LATEXE, LATEXM, LATEXT, LATEXQ]
firstrow = [LATEXE, LATEXM, LATEXT, LATEXQ]
with TxtFile('../src/tab_effmat_val.tex', 'w') as f:
f.write2DArrayToLatexTable(
list(zip(*([firstrow] + list(zip(*efficencies))))), thead,
['%s'] + ['%.6f'] * 4, 'Effizienzmatrix.', 'tab:effmat:val')
with TxtFile('../src/tab_effmat_err.tex', 'w') as f:
f.write2DArrayToLatexTable(
list(zip(*([firstrow] + list(zip(*sefficencies))))), thead,
['%s'] + ['%.6f'] * 4, 'Fehler der Effizienzmatrix.',
'tab:effmat:err')
with TxtFile('../src/tab_effmat_inv_val.tex', 'w') as f:
f.write2DArrayToLatexTable(
list(zip(*([firstrow] + list(zip(*inv(efficencies)))))), thead,
['%s'] + ['%.6f'] * 4, 'Inverse Effizienzmatrix.',
'tab:inveffmat:val')
def getExcitedStateOscillationConstants():
# plot spectrum
data = I2Data.fromPath('../data/04_I2_ngg10_10ms.txt')
progression = dict()
for i in range(1, 3 + 1):
progression[i] = I2Data.fromPath('../data/prog%d.txt' % i)
c = TCanvas('c', '', 1280, 720)
g = data.makeGraph('spectrum', 'wavelength #lambda / nm', 'intensity / a.u.')
g.SetMarkerStyle(1)
g.GetXaxis().SetRangeUser(505, 620)
g.SetMinimum(18000)
g.SetMaximum(49000)
myY = TGaxis()
myY.ImportAxisAttributes(g.GetYaxis())
myY.SetMaxDigits(3)
g.Draw('AL')
pg1 = progression[1].makeGraph('prog1')
pg1.SetMarkerColor(2)
pg1.Draw('P')
pg2 = progression[2].makeGraph('prog2')
pg2.SetMarkerColor(3)
pg2.Draw('P')
pg3 = progression[3].makeGraph('prog3')
pg3.SetMarkerColor(4)
pg3.Draw('P')
l = TLegend(0.6, 0.15, 0.85, 0.4)
l.AddEntry('spectrum', 'measurement', 'l')
l.AddEntry('prog1', 'first progression (#nu\'\' = 1)', 'p')
l.AddEntry('prog2', 'second progression (#nu\'\' = 2)', 'p')
l.AddEntry('prog3', 'third progression (#nu\'\' = 3)', 'p')
l.Draw()
c.Update()
c.Print('../img/I2_absorption.pdf', 'pdf')
# calculations
start = [18, 7, 9]
prog1ord = {'a': [], 'ae': [], 'b': [], 'be': []}
for i, prog in progression.iteritems():
# Calculate vacuum wavelength and create Birge-Sponer plot
prog.correctValues()
c = TCanvas('c%d' % i, '', 1280, 720)
g = makeBirgeSponer(prog, start[i - 1]).makeGraph('prog%d_bs' % i, '#nu\' + 1/2', '#Delta G (#nu\' + 1/2) / (cm^{-1})')
g.Draw('AP')
# fit 2nd-order
fit2ord = Fitter('prog%d_2ord' % i, '[0]-[1]*(2*x+2)+[2]*(3*x^2+6*x+13/4)')
fit2ord.setParam(0, 'a', 120)
fit2ord.setParam(1, 'b', 1)
fit2ord.setParam(2, 'c', 0)
fit2ord.fit(g, 4, 50)
fit2ord.saveData('../calc/prog%d_fit2ord.txt' % i, 'w')
l2 = TLegend(0.6, 0.7, 0.95, 0.95)
l2.AddEntry(0, 'Fit 2nd. order', '')
l2.AddEntry(fit2ord.function, 'y = a - b*(2*x+2) + c*(3*x^2+6*x+13/4)', 'l')
fit2ord.addParamsToLegend(l2)
l2.SetTextSize(0.03)
l2.Draw()
# fit 1st-order
fit1ord = Fitter('prog%d_1ord' % i, '[0]-[1]*(2*x+2)')
fit1ord.setParam(0, 'a', 120)
fit1ord.setParam(1, 'b', 1)
fit1ord.fit(g, 4, 50, '+')
g.GetFunction('prog%d_1ord' % i).SetLineColor(4)
fit1ord.saveData('../calc/prog%d_fit1ord.txt' % i, 'w')
prog1ord['a'].append(fit1ord.params[0]['value'])
prog1ord['ae'].append(fit1ord.params[0]['error'])
prog1ord['b'].append(fit1ord.params[1]['value'])
prog1ord['be'].append(fit1ord.params[1]['error'])
l1 = TLegend(0.125, 0.15, 0.5, 0.4)
l1.AddEntry(0, 'Fit 1st. order', '')
l1.AddEntry(g.GetFunction('prog%d_1ord' % i), 'y = a - b*(2*x+2)', 'l')
fit1ord.addParamsToLegend(l1)
l1.SetTextSize(0.03)
l1.Draw()
c.Update()
c.Print('../img/prog%d_birgesponer.pdf' % i, 'pdf')
# save vibrational constants to latex file
nus = [0, 1, 2]
f = TxtFile('../src/ExcitedStateOscillationConstants.tex', 'w')
f.write2DArrayToLatexTable(zip(nus, prog1ord['a'], prog1ord['ae'], prog1ord['b'], prog1ord['be']),
['$\\nu\'\'$', '$\omega_e\' / \\text{cm}^{-1}$', '$s_{\omega_e\'} / \\text{cm}^{-1}$',
'$\omega_e\' x_e\' / \\text{cm}^{-1}$', '$s_{\omega_e\' x_e\'} / \\text{cm}^{-1}$'],
['%0.f', '%3.1f', '%.1f', '%.3f', '%.3f'],
'Oscillation constants for first order fit of Birge-Sponer plots', 'tab:prog1ord')
f.close()
# calculate weighted average for fit 1st- order
with TxtFile.fromRelPath('../calc/ExcitedStateOscillationConstants.txt', 'w') as f:
f.writeline('\t', *map(lambda x: str(x), avgerrors(prog1ord['a'], prog1ord['ae'])))
f.writeline('\t', *map(lambda x: str(x), avgerrors(prog1ord['b'], prog1ord['be'])))
def evalNuclearSpin():
results = []
data = loadCSVToList('../data/part3/part3.txt')
tabledata = []
for d in data[-4:]:
tabledata.append([d[0], d[2]] + d[4:-2])
with TxtFile('../src/tab_part3_data.tex', 'w') as f:
f.write2DArrayToLatexTable(tabledata, [
r"$I_\text{L}$ / mA", r"$\nu$ / kHz", "$I_1$ / mA",
"$s_{I_1}$ / mA", "$I_1'$ / mA", "$s_{I_1'}$ / mA"
], ['%.1f', '%.2f', '%d', '%d', '%d', '%d'],
'Messdaten des Doppelresonanzexperiments.',
'tab:part3:data')
for iL, siL, f, sf, i1, si1, i1_, si1_, i4, si4 in data: # I-Laser, frequency, I1, I1', I4 with respective errors
# from mA to A
i1 *= 1e-3
si1 *= 1e-3
i1_ *= 1e-3
si1_ *= 1e-3
i4 *= 1e-3
si4 *= 1e-3
# from kHz to Hz
f *= 1e3
sf *= 1e3
# calc B1, B1'
B1, sB1 = inductorIToB(1, i1, si1)
B1_, sB1_ = inductorIToB(1, i1_, si1_)
# calc B for nuclear spin
B, sB = (B1 + B1_) / 2, sqrt(sB1**2 + sB1_**2) / 2
# calc horizontal B-Field
Bhor, sBhor = abs(B1 - B1_) / 2, sqrt(sB1**2 + sB1_**2) / 2
# calc vertical B-Field
Bvert, sBvert = inductorIToB(4, i4, si4)
# calc nuclear spin
I = mub_JT * B / (h_Js * f) - 0.5
sI = mub_JT * B / (h_Js * f) * sqrt((sB / B)**2 + (sf / f)**2)
results.append([["I_L/mA", (iL, siL)],
["f/kHz", (f * 1e-3, sf * 1e-3)],
["Bhor/µT", (Bhor * 1e6, sBhor * 1e6)],
["Bver/µT", (Bvert * 1e6, sBvert * 1e6)],
["I\t", (I, sI)]])
# print out results
with TxtFile('../calc/part3.txt', 'w') as f:
for result in results:
for description, values in result:
f.writeline(
'\t',
*([description] + list(map(lambda x: '%.2f' % x, values))))
f.writeline('')
tableresults = []
for result in results:
flattend = [item for sublist in result for item in sublist[1]]
flattend.pop(7)
flattend.pop(6)
flattend.pop(3)
flattend.pop(1)
tableresults.append(flattend)
with TxtFile('../src/tab_part3_results.tex', 'w') as f:
f.write2DArrayToLatexTable(
tableresults[-4:], [
r"$I_\text{L}$ / mA", r"$\nu$ / kHz",
r"$B_\text{hor}$ / \textmu T",
r"$s_{B_\text{hor}}$ / \textmu T", "$I$", "$s_I$"
], ['%.1f', '%.2f', '%.1f', '%.1f', '%.2f', '%.2f'],
r"Berechnete horizontale Komponenten des Erdmagnetfeldes und Kernspin von Rubidium für das "
+
r"Doppelresonanzexperiment bei verschiedenen Lasterströmen $I_\text{L}$ und RF-Sender-Frequenzen $\nu$.",
"tab:part3:results")
from z0 import Z0Data
from txtfile import TxtFile
if __name__ == '__main__':
files = [('mc/ee', 'h3'), ('mc/mm', 'h3'), ('mc/tt', 'h3'),
('mc/qq', 'h3'), ('daten/daten_1', 'h33')]
for file, treename in files:
data = Z0Data.fromROOTFile("../data/%s.root" % file, treename)
with TxtFile('../data/%s.txt' % file, 'w') as f:
for event in data.getEvents():
f.writeline(
'\t',
*list(
map(str, [
event["run"], event["event"], event["Ncharged"],
event["Pcharged"], event["E_ecal"],
event["E_hcal"], event["E_lep"], event["cos_thru"],
event["cos_thet"]
])))
def makeHFSGraph(name, xmin, xmax):
ch2 = OPData.fromPath('../data/part2/04.16/%s.tab' % name, 2)
ch2.filterX(xmin, xmax)
deltaY = 0.05
c = TCanvas('c-%s' % name, '', 1280, 720)
g2 = ch2.makeGraph('g2-%s' % name, "Zeit t / s", "Spannung U_{ph} / V")
prepareGraph(g2, 2)
g2.GetXaxis().SetRangeUser(xmin, xmax)
g2.SetMinimum(ch2.getMinY() - deltaY)
g2.SetMaximum(ch2.getMaxY() + deltaY)
g2.Draw('APX')
fitStartParams = getHFSFitStartParams(name)
fitres = []
tablefitres = []
tablepeakcount = 0
legendInfo = []
isUp = name[:2] == 'up'
if fitStartParams:
print('got start params, starting to building fit functions')
peakNum = 0
offset = ch2.getY()[0] # approx offset of underground
slope = (ch2.getY()[-1] - ch2.getY()[0]) / (xmax - xmin) # approx slope of underground
for peakparams, xstartend in fitStartParams:
xstart, xend = xstartend
peakcount = len(peakparams)
print('peakNum: ', peakNum)
fitfunc = 'pol1(0)+gaus(2)'
dpc = 2 # delta param count
for i in range(1, peakcount):
fitfunc += '+gaus(%d)' % (i * 3 + dpc)
fit = Fitter('fitHFS%s_%d' % (name, peakNum), fitfunc)
fit.function.SetLineColor(getRootColor(peakNum))
fit.setParam(0, 'a', offset)
fit.setParamLimits(0, 0, offset * 2)
fit.setParam(1, 'b', slope)
if isUp:
fit.setParamLimits(1, 0, 2 * slope)
else:
fit.setParamLimits(1, 2 * slope, 0)
for i, params in enumerate(peakparams):
fit.setParam(i * 3 + dpc, 'A%d' % i, params[0])
fit.setParam(i * 3 + dpc + 1, 'c%d' % i, params[1])
fit.setParam(i * 3 + dpc + 2, 's%d' % i, params[2])
if params[0] < 0:
fit.setParamLimits(i * 3 + dpc, 3 * params[0], 0)
else:
fit.setParamLimits(i * 3 + dpc, 0, 2 * params[0])
fit.setParamLimits(i * 3 + dpc + 1, params[1] - 2 * params[2], params[1] + 2 * params[2])
fit.setParamLimits(i * 3 + dpc + 2, 0, 20 * params[2])
fit.fit(g2, xstart, xend, 'M+')
fit.saveData('../fit/part2/%s-%d.txt' % (name, peakNum))
legendpeaks = []
for i in range(len(peakparams)):
fitres.append((fit.params[i * 3 + dpc + 1]['value'], 0.2 * fit.params[i * 3 + dpc + 2]['value']))
tablepeakcount += 1
legendpeaks.append(tablepeakcount)
tablefitres.append((tablepeakcount, fit.params[i * 3 + dpc + 1]['value'] * 1e3, fit.params[i * 3 + dpc + 1]['error'] * 1e3,
fit.params[i * 3 + dpc + 2]['value'] * 1e6, fit.params[i * 3 + dpc + 2]['error'] * 1e6))
legendInfo.append((fit.function, tuple(legendpeaks)))
peakNum += 1
tablename = 'up' if isUp else 'down'
with TxtFile('../src/tab_part2_hfspeaks_%s.tex' % tablename, 'w') as f:
f.write2DArrayToLatexTable(tablefitres,
['Peak $i$', r'$\mu_i$ / ms', r'$s_{\mu_i}$ / ms', r'$\sigma_i$ / \textmu s', r'$s_{\sigma_i}$ / \textmu s'],
['%d', '%.5f', '%.5f', '%.1f', '%.1f'],
r"Erwartungswerte $\mu_i$ und Standardabweichungen $\sigma_i$ der gefitteten Peaks des HFS-Spektrums.",
"tab:hfs:peaks:%s" % tablename)
g2.Draw('P')
if isUp:
l = TLegend(0.725, 0.15, 0.99, 0.45)
else:
l = TLegend(0.725, 0.55, 0.99, 0.85)
l.SetTextSize(0.03)
l.AddEntry(g2, 'Photodiodenspannung U_{ph}', 'l')
for fitfunc, legendpeaks in legendInfo:
n = len(legendpeaks)
if n == 1:
lstring = '%d' % legendpeaks
elif n == 2:
lstring = '%d und %d' % legendpeaks
elif n == 3:
lstring = '%d, %d und %d' % legendpeaks
l.AddEntry(fitfunc, "Fit von Peak %s" % lstring, 'l')
l.Draw()
c.Update()
if not DEBUG:
c.Print('../img/part2/%s_fit.pdf' % name, 'pdf')
return fitres
def main():
print('make graphs')
print('===========')
makeGraphs()
print('eval etalon data')
print('================')
freqCalibrations = evalEtalonData()
print('eval hfs peak data')
print('==================')
hfspeaks = evalHFSPeakData()
litvals = (-3.07, -2.25, mean([-1.48, -1.12]), mean([1.56, 1.92]), 3.76, 4.58)
reflit = litvals[3]
litvals = list(map(lambda x: x - reflit, litvals))
spectra = dict()
for key in freqCalibrations.keys():
gps, sgps = freqCalibrations[key]
isUp = key[:2] == "up"
spectrum = []
if isUp:
refpeak, srefpeak = hfspeaks[key][2]
m = 1
else:
refpeak, srefpeak = hfspeaks[key][3]
m = -1
for peak, speak in hfspeaks[key]:
freq = m * (refpeak - peak) * 1000 * gps
if not compare2Floats(refpeak, peak):
sfreq = abs(freq) * sqrt((sgps / gps) ** 2 + (sqrt(srefpeak ** 2 + speak ** 2) / (refpeak - peak)) ** 2)
else:
sfreq = 1000 * gps * speak
if compare2Floats(freq, 0):
freq = abs(freq)
spectrum.append((freq, sfreq))
if isUp:
spectrum.reverse()
spectra['up' if isUp else 'down'] = spectrum
compareSpectrum('up' if isUp else 'down', spectrum, litvals)
tabledata = []
names = [r"\rb{87}, F:2$\to$1", r"\rb{87}, F:2$\to$2", r"\rb{85}, F:3$\to$2, 3$\to$3", r"\rb{85}, F:2$\to$2, 2$\to$3",
r"\rb{87}, F:1$\to$1", r"\rb{87}, F:1$\to$2"] # Übergänge
for i, litval in enumerate(litvals):
tabledata.append([names[i]] + [litval] + list(spectra['up'][i]) + list(spectra['down'][i]))
with TxtFile('../src/tab_part2_spectrum.tex', 'w') as f:
f.write2DArrayToLatexTable(tabledata,
["Übergang",
r'$\Delta \nu^\text{theo}$ / GHz',
r'$\Delta \nu^\text{exp}_\text{up}$ / GHz', r'$s_{\Delta \nu^\text{exp}_\text{up}}$ / GHz',
r'$\Delta \nu^\text{exp}_\text{down}$ / GHz', r'$s_{\Delta \nu^\text{exp}_\text{down}}$ / GHz'],
['%s', '%.2f', '%.2f', '%.2f', '%.2f', '%.2f'],
"Theoretisches und (steigende und fallende Flanke) experimentell bestimmtes Hyperfeinstrukturspektrum von Rubidium.",
"tab:hfs:spectrum")
avgdata = []
avgspectrum = []
for name, lit, f1, sf1, f2, sf2 in tabledata:
f, sf = avgerrors([f1, f2], [sf1, sf2])
avgdata.append([name, lit, f, sf])
avgspectrum.append((f, sf))
compareSpectrum('avg', avgspectrum, litvals)
with TxtFile('../src/tab_part2_spectrum_avg.tex', 'w') as f:
f.write2DArrayToLatexTable(avgdata,
["Übergang",
r'$\Delta \nu^\text{theo}$ / GHz',
r'$\Delta \nu^\text{exp}_\text{avg}$ / GHz', r'$s_{\Delta \nu^\text{exp}_\text{avg}}$ / GHz'],
['%s', '%.2f', '%.2f', '%.2f', ],
r"Theoretisches und aus den experimentellen Daten (\autoref{tab:hfs:spectrum}) gemitteltes Hyperfeinstrukturspektrum von Rubidium.",
"tab:hfs:spectrum:avg")
evalIntervalConst(avgspectrum)
def makeMassFit():
# config files
# file = [mass, path]
files = []
files.append([2.0123, "../data/11_K_m9_3200_t420.txt", 420])
files.append([2.0123, "../data/11b_K_m9_3200_t420.txt", 420])
files.append([1.9047, "../data/13_K_m8_3200_t420.txt", 420])
files.append([1.6812, "../data/15_K_m7_3200_t420.txt", 420])
files.append([1.4827, "../data/17_K_m6_3200_t420.txt", 420])
files.append([1.2952, "../data/19_K_m5_3200_t480.txt", 480])
files.append([1.0993, "../data/21_K_m4_3200_t480.txt", 480])
files.append([0.8086, "../data/23_K_m3_3200_t540.txt", 540])
files.append([0.6954, "../data/25_K_m2_3200_t540.txt", 540])
files.append([0.5007, "../data/27_K_m1_3200_t660.txt", 660])
files.append([0.3030, "../data/29_K_m0_3200_t780.txt", 780])
u = 0.760
tu = 50
d = DataErrors()
for file in files:
n = readSingleEntryFile(file[1])
d.addPoint(file[0], n - u, 0.001, np.sqrt(n / file[2] + u / tu))
d.saveDataToLaTeX(['Masse $m /$g', '$s_m /$g', 'Z\"ahlrate $n / (1/\\text{s})$', '$s_n / (1/\\text{s})$'],
['%.3f', '%.3f', '%.3f', '%.3f'],
'Z\"ahlraten von \\kalium\,f\"ur verschiedene Massen mit Fehlern', 'tab:data:kalium', '../src/data_kalium.tex', 'w')
c = TCanvas('c2', '', 800, 600)
g = d.makeGraph('g', 'Masse m / g', 'Z#ddot{a}hlrate n / (1/s)')
g.SetMaximum(6)
g.SetMinimum(2)
g.Draw('AP')
fit = Fitter('f', '[0]*(1-exp(-[1]*x))')
fit.setParam(0, 'a')
fit.setParam(1, 'b')
fit.fit(g, 0.1, 2.5)
fit.saveData('../fit/kalium.txt')
a = fit.params[0]['value']
sa = fit.params[0]['error']
b = fit.params[1]['value']
sb = fit.params[1]['error']
l = TLegend(0.4, 0.15, 0.85, 0.5)
l.AddEntry('g', '{}^{40} Kalium ohne Untergrund', 'p') # TODO with error bar? (options +'e')
l.AddEntry(fit.function, 'Fit mit n(m)=a(1-exp(-b*m))', 'l')
l.AddEntry(0, '#chi^{2} / DoF : %f' % fit.getChisquareOverDoF(), '')
l.AddEntry(0, 'Paramter:', '')
l.AddEntry(0, 'a: %e #pm %e' % (a, sa), '')
l.AddEntry(0, 'b: %e #pm %e' % (b, sb), '')
l.SetTextSize(0.03)
l.Draw()
NA = 6.02214129e23
hrel = 0.000118
mrel = 39.0983 + 35.45
f = 1.29
rho = fit.getCorrMatrixElem(1, 0)
thalf = (np.log(2) * NA * hrel * f) / (1.12 * mrel * 2 * a * b) / (3600 * 24 * 365.242)
sthalf = thalf * np.sqrt((sa / a) ** 2 + (sb / b) ** 2 + 2 * rho * (sa / a) * (sb / b))
with TxtFile.fromRelPath('../fit/kalium.txt', 'a') as f:
f.writeline()
f.writeline('calculations')
f.writeline('============')
f.writeline('\t', 'half-life of Kalium:', '%e' % thalf, TxtFile.PM, '%e' % sthalf)
c.Update()
c.Print('../img/Kalium40_Massenabhaengigkeit.pdf')