def plotElement(anodenstrom, spannung, V_N, R):
spannung /= (V_N**2 * 1000**2 * 10) # verstärkung rausrechnen
x = anodenstrom*10**(-3)
y = spannung/(R**2) # I^2 bestimmt
plt.errorbar(noms(x), noms(y),
xerr=stds(x), yerr=stds(y), fmt='kx', label='Messwerte')
# fitten:
params, covariance = curve_fit(fitfunktion, unp.nominal_values(x),
unp.nominal_values(y),
p0=[1])
errors = np.sqrt(np.diag(covariance))
print('m= ', params[0], '±', errors[0])
m = ufloat(params[0], errors[0])
x_fit = np.linspace(-0.0001, max(noms(x))+0.001)
plt.plot(x_fit, fitfunktion(x_fit, *params), label='Fit')
plt.xlim(0, 0.0045)
plt.ylim(0, 1.75e-17)
plt.xlabel(r'$I_0 \:/\: \si{\ampere}$')
plt.ylabel(r'$I^2 \:/\: \si{\ampere\squared}$')
delta_nu = ufloat(24.4, 0.4)
delta_nu *= 10**3
e0 = m/(2*delta_nu)
print("e0 = ", e0)
e0theorie = ufloat(constants.physical_constants["elementary charge"][0],
constants.physical_constants["elementary charge"][2])
print("Abweichung von Theorie= ", abweichungen(e0theorie, e0))
plt.legend(loc='best')
# in matplotlibrc leider (noch) nicht möglich
plt.tight_layout(pad=0.2, h_pad=1.08, w_pad=1.08)
plt.savefig('build/plotElement.pdf')
plt.close()
def plotalpha(alpha_mz, mass_Z):
mu = np.logspace(-1, 30, 10000)
alf = alpha(alpha_mz, mass_Z, mu)
plt.fill_between(mu,
noms(alf) + stds(alf),
noms(alf) - stds(alf),
color='red',
label='1$\sigma$-Intervall')
plt.plot(mu, noms(alf), label='Kurve')
d = np.zeros(len(alf))
d = noms(alf) - 1 / 128
print(d)
for i in range(len(d) - 1):
if d[i] == 0. or d[i] * d[i + 1] < 0.: # crossover at i
print('Grafische Lösung:', alf[i])
plt.xlim(0.1, 1000)
plt.xlabel(r'$\mu \:/\: \si{\giga\electronvolt}$')
plt.ylabel(r'$\alpha_S$')
plt.legend(loc='best')
plt.xscale('log')
# in matplotlibrc leider (noch) nicht möglich
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig('build/plotalpha.pdf')
plt.close()
def Plot(x=[], y=[], limx=None, limy=None, xname='', yname='', name='', markername='Wertepaare', marker='rx', linear=True, linecolor='b-', linename='Ausgleichsgerade', xscale=1, yscale=1, save=True, Plot=True):
uParams = None
if(Plot):
dx = abs(x[-1]-x[0])
if(limx==None):
xplot = np.linspace((x[0]-0.05*dx)*xscale,(x[-1]+0.05*dx)*xscale,1000)
else:
xplot = np.linspace(limx[0]*xscale,limx[1]*xscale,1000)
if(save):
plt.cla()
plt.clf()
plt.errorbar(noms(x)*xscale, noms(y)*yscale, xerr=stds(x)*xscale, yerr=stds(y)*yscale, fmt=marker, markersize=6, elinewidth=0.5, capsize=2, capthick=0.5, ecolor='g',barsabove=True ,label=markername)
if(linear == True):
params, covar = curve_fit(Line, noms(x), noms(y))
uParams=uncertainties.correlated_values(params, covar)
if(Plot):
plt.plot(xplot*xscale, Line(xplot, *params)*yscale, linecolor, label=linename)
if(Plot):
if(limx==None):
plt.xlim((x[0]-0.05*dx)*xscale,(x[-1]+0.05*dx)*xscale)
else:
plt.xlim(limx[0]*xscale,limx[1]*xscale)
if(limy != None):
plt.ylim(limy[0]*yscale,limy[1]*yscale)
plt.xlabel(xname)
plt.ylabel(yname)
plt.legend(loc='best')
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
if(save):
plt.savefig('build/'+name+'.pdf')
if(linear):
return(uParams)
def make_table(columns, figures=None):
assert hasattr(columns[0],'__iter__'), "Wenn nur eine Zeile von Daten vorliegt, funktioniert zip nicht mehr; die Elemente von columns müssen Listen sein, auch wenn sie ihrerseits nur ein Element enthalten."
if figures is None:
figures = [None] * len(columns)
cols = []
for column, figure in zip(columns, figures):
assert (type(column) != str), "Hier ist ein einzelner String übergeben worden. Baue daraus eine Liste und alles ist gut ( column = [string] )."
if (type(column) == list):
col = zip(*zip(column)) # hard to find this kind of code... this will unzip the list column, ref: https://docs.python.org/3/library/functions.html#zip
cols.extend(col)
elif np.any(stds(column)):
if figure is None:
figure = ''
col = list(zip(*['{0:.{1:}uf}'.format(x, figure).split('+/-') for x in column]))
else:
col = list(zip(*[['{0:.{1:}f}'.format(x, figure)] for x in noms(column)]))
cols.extend(col)
max_lens = [max(len(s) for s in col) for col in cols]
cols = [['{0:<{1:}}'.format(s, ml) for s in col] for col, ml in zip(cols, max_lens)]
rows = list(itertools.zip_longest(*cols))
return (r' \\' + '\n').join([' & '.join(s for s in row if s is not None) for row in rows]) + r' \\'
def write_table(columns, filename, figures=None, row_names=None, column_names=None, dont_align=False):
"""Generates just the table contents and writes it to the given file."""
assert hasattr(columns[0], '__iter__'), "Wenn nur eine Zeile von Daten vorliegt, funktioniert zip nicht mehr; die Elemente von columns müssen Listen sein, auch wenn sie ihrerseits nur ein Element enthalten."
if figures is None:
figures = [None] * len(columns)
if dont_align:
number_format = '\\num{{{0:.{1:}g}}}'
else:
number_format = '{0:.{1:}g}'
cols = []
for column, figure in zip(columns, figures):
if np.any(stds(column)):
if figure is None:
figure = ''
col = list(zip(*['{0:.{1:}uf}'.format(x, figure).split('+/-') for x in column]))
else:
col = list(zip(*[[number_format.format(x, figure)] for x in noms(column)]))
cols.extend(col)
max_lens = [max(len(s) for s in col) for col in cols]
cols = [['{0:<{1:}}'.format(s, ml) for s in col] for col, ml in zip(cols, max_lens)]
rows = list(itertools.zip_longest(*cols))
if row_names is not None:
for i in range(len(rows)):
rows[i] = [row_names[i]] + list(rows[i])
if column_names is not None:
rows = [column_names] + list(rows) # ["$\text{{{0}}}".format(i) for i in column_names]
filecontent = (r' \\' + '\n').join([' & '.join(s for s in row if s is not None) for row in rows]) + r' \\'
write(filename, filecontent)
def make_table(columns, figures=None):
assert hasattr(
columns[0], '__iter__'
), "Wenn nur eine Zeile von Daten vorliegt, funktioniert zip nicht mehr; die Elemente von columns müssen Listen sein, auch wenn sie ihrerseits nur ein Element enthalten."
if figures is None:
figures = [None] * len(columns)
cols = []
for column, figure in zip(columns, figures):
if np.any(stds(column)):
if figure is None:
figure = ''
col = list(
zip(*[
'{0:.{1:}uf}'.format(x, figure).split('+/-')
for x in column
]))
else:
col = list(
zip(*[['{0:.{1:}f}'.format(x, figure)] for x in noms(column)]))
cols.extend(col)
max_lens = [max(len(s) for s in col) for col in cols]
cols = [['{0:<{1:}}'.format(s, ml) for s in col]
for col, ml in zip(cols, max_lens)]
rows = list(itertools.zip_longest(*cols))
return (r' \\' + '\n').join(
[' & '.join(s for s in row if s is not None) for row in rows]) + r' \\'
def transform2latex_tab_2(data, dir, dataname):
if not os.path.exists(dir):
os.makedirs(dir)
size = len(data)
save_data = open((dir + 'latex_' + dataname), 'w')
print('\nSaving data to "%s"' % (dir + dataname))
for i in range(0, size):
array_len = len(data[i])
for j in range(0, array_len):
if (j == array_len - 1):
save_data.write("\\num{" + str(noms(data[i][j])) + " \\pm " +
str(stds(data[i][j])) + "}\t \\\\ \n")
else:
save_data.write("\\num{" + str(noms(data[i][j])) + " \\pm " +
str(stds(data[i][j])) + "}\t & \t")
save_data.close()
def make_SI(num, unit, exp='', figures=None):
if np.any(stds([num])):
if figures is None:
figures = ''
x = '{0:.{1:}uf}'.format(num, figures).replace('/', '')
else:
x = '{0:.{1:}f}'.format(num, figures)
return r'\SI{{{}{}}}{{{}}}'.format(x, exp, unit)
def getOutValues(pFighterStrings, pEnemieStrings, pAttStats, pDefStats):
vOutputString = 'Kampfstats fuer ' + pFighterStrings[
0] + ' gegen ' + pEnemieStrings[0] + ':'
for u in range(0, len(pAttStats[0])):
vOutLine = '\n' + pEnemieStrings[0] + ' ' + pEnemieStrings[u +
1] + ':\t\t'
for i in range(0, len(pAttStats)):
vAT = ufloat(np.round(noms(pAttStats[i][u]), 1),
np.round(stds(pAttStats[i][u]), 1))
vPA = ufloat(np.round(noms(pDefStats[i][u]), 1),
np.round(stds(pDefStats[i][u]), 1))
vOutLine += 'AT {}, PA {};\t'.format(vAT, vPA)
vOutputString += vOutLine
return vOutputString
def tabelle_fertig(r, winkel, hkl, a_m_hkl, name):
hkl_sum = hkl[:, 0]**2 + hkl[:, 1]**2 + hkl[:, 2]**2
rundung = np.array([1, 2, 0, 0, 0, 0, 2, 2, 3])
hkl_table = np.array([
r * 100, winkel, hkl[:, 0], hkl[:, 1], hkl[:, 2], hkl_sum,
noms(a_m_hkl) * 10**(10),
stds(a_m_hkl) * 10**(10),
np.cos(inrad(winkel))**2
])
tabelle(hkl_table, name + "_table", rundung)
def make_SI(num, unit, exp='', figures=None):
''' Format an uncertainties ufloat as a \SI quantity '''
if np.any(stds([num])):
if figures is None:
figures = ''
x = '{0:.{1:}uf}'.format(num, figures).replace('/', '')
else:
x = '{0:.{1:}f}'.format(num, figures)
return r'\SI{{{}{}}}{{{}}}'.format(x, exp, unit)
def make_SI(num, unit, exp='', figures=None):
''' Format an uncertainties ufloat as a \SI quantity '''
if np.any(stds([num])):
if figures is None:
figures = ''
x = '{0:.{1:}uf}'.format(num, figures).replace('/', '')
else:
x = '{0:.{1:}f}'.format(num, figures)
return r'\SI{{{}{}}}{{{}}}'.format(x, exp, unit)
def make_SI(num, unit, exp='', figures=None):
y = ufloat(0.0, 0) #siunitx mag kein 0 +- 0, deshalb hier der workaround
if num == y:
return "(0 \pm 0) ~ \si{" + unit + "}"
if np.any(stds([num])):
if figures is None:
figures = ''
x = '{0:.{1:}uf}'.format(num, figures).replace('/', '')
else:
x = '{0:.{1:}f}'.format(num, figures)
return r'\SI{{{}{}}}{{{}}}'.format(x, exp, unit)
def make_SI(num, unit, exp='', figures=None):
y = ufloat(0.0, 0) #siunitx mag kein 0 +- 0, deshalb hier der workaround
if num == y:
return "(0 \pm 0) ~ \si{" + unit + "}"
if np.any(stds([num])):
if figures is None:
figures = ''
x = '{0:.{1:}uf}'.format(num, figures).replace('/', '')
else:
x = '{0:.{1:}f}'.format(num, figures)
return r'\SI{{{}{}}}{{{}}}'.format(x, exp, unit)
def Plot(x,
y,
limx,
xname,
yname,
params,
name,
linear=True,
xscale=1,
yscale=1,
limy=None):
xplot = np.linspace(limx[0] * xscale, limx[1] * xscale, 1000)
plt.cla()
plt.clf()
plt.errorbar(noms(x) * xscale,
noms(y) * yscale,
xerr=stds(x) * xscale,
yerr=stds(y) * yscale,
fmt='rx',
markersize=6,
elinewidth=0.5,
capsize=2,
capthick=0.5,
ecolor='g',
barsabove=True,
label='Wertepaare')
if (linear == True):
plt.plot(xplot * xscale,
Line(xplot, *params) * yscale,
'b-',
label='Ausgleichsgerade')
plt.xlim(limx[0] * xscale, limx[1] * xscale)
if (limy != None):
plt.ylim(limy[0] * yscale, limy[1] * yscale)
plt.xlabel(xname)
plt.ylabel(yname)
plt.legend(loc='best')
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig('build/' + name + '.pdf')
def make_SI(num, unit, exp='', figures=None):
''' Format an uncertainties ufloat as a \SI quantity '''
if np.any(stds([num])):
if figures is None:
figures = ''
x = '{0:.{1:}uf}'.format(num, figures).replace('/', '')
else:
x = '{0:.{1:}f}'.format(num, figures)
return r'\SI{{{}{}}}{{{}}}'.format(x, exp, unit)
#with open('build/M_BH.tex', 'w') as f:
# f.write(make_SI(M*1e-08,r'M_{\odot}',exp='e08' ,figures=2))
def printScores(pScores, pID):
vX = np.linspace(0, 100, len(pScores[0]))
if pID == 0:
vTitle = 'NaiveBayes'
elif pID == 1:
vTitle = 'RandomForest'
elif pID == 2:
vTitle = 'KNN'
else:
vTitle = 'Default'
plt.errorbar(vX,
noms(pScores[0]),
yerr=stds(pScores[0]),
color='g',
fmt=',',
label='Reinheit')
plt.errorbar(vX,
noms(pScores[1]),
yerr=stds(pScores[1]),
color='b',
fmt=',',
label='Effizienz')
plt.plot(vX, noms(pScores[0]), 'g-')
plt.plot(vX, noms(pScores[1]), 'b-')
plt.ylim(-0.05, 1.05)
plt.xlabel('Konfidenzniveau in %', {'size': '16'})
plt.ylabel('Wert', {'size': '16'})
plt.title(vTitle)
plt.legend(loc='best', prop={'size': 16})
plt.tight_layout()
plt.savefig('Bilder/' + vTitle + '.pdf')
plt.show()
plt.clf()
def make_SI(num, unit, exp='', figures=None):
''' Format an uncertainties ufloat as a \SI quantity '''
if np.any(stds([num])):
if figures is None:
figures = ''
x = '{0:.{1:}uf}'.format(num, figures).replace('/', '')
else:
x = '{0:.{1:}f}'.format(num , figures)
return r'\SI{{{}{}}}{{{}}}'.format(x, exp, unit)
## tex file for P_1
#
#with open('build/P_1.tex', 'w') as f:
# f.write(make_SI(P_1*1e+57,r'\percent', exp='1e-55', figures=1))
def plot(axes, x, y, V_strich_theorie, label, filename, x_label, y_label, grenze, ylim=None, logy=None, uebergang=None, letzter_wert_kacke=False):
#label = 'test'
flanke_grenze = grenze
flanke_grenze_oben = None
if letzter_wert_kacke:
flanke_grenze_oben = -1
axes.errorbar(noms(x[-1:]), noms(y[-1:]),
xerr=stds(x[-1:]), yerr=stds(y[-1:]),
fmt='kx', label='Unberücksichtigt bei {}'.format(label))
if uebergang is not None:
flanke_grenze = grenze + 1
axes.errorbar(noms(x[uebergang:uebergang+1]), noms(y[uebergang:uebergang+1]),
xerr=stds(x[uebergang:uebergang+1]), yerr=stds(y[uebergang:uebergang+1]),
fmt='gx', label='Messwerte Übergang bei {}'.format(label))
axes.errorbar(noms(x[flanke_grenze:flanke_grenze_oben]), noms(y[flanke_grenze:flanke_grenze_oben]),
xerr=stds(x[flanke_grenze:flanke_grenze_oben]), yerr=stds(y[flanke_grenze:flanke_grenze_oben]),
fmt='rx', label='Messwerte Flanke bei {}'.format(label))
axes.errorbar(noms(x[:grenze]), noms(y[:grenze]),
xerr=stds(x[:grenze]), yerr=stds(y[:grenze]),
fmt='bx', label='Messwerte Plateau bei {}'.format(label))
plateau_mittel = ufloat(np.mean(np.exp(noms(y[:grenze]))), np.std(np.exp(noms(y[:grenze]))))
plateau_mittel_halb = unp.log(plateau_mittel / unp.sqrt(2)) if plateau_mittel.n >= 1 else unp.log(plateau_mittel * unp.sqrt(2))
label_v_halb = r"$V_\text{Plateau}' / \sqrt{2}$" if plateau_mittel.n >= 1 else r"$V_\text{Plateau}' \cdot \sqrt{2}$"
#label_v_halb = 'test'
axes.plot((min(noms(x)), max(noms(x))), (noms(plateau_mittel_halb), noms(plateau_mittel_halb)), '-', label=label_v_halb)
grenzfrequenz = fitten(axes, x[flanke_grenze:flanke_grenze_oben], y[flanke_grenze:flanke_grenze_oben], linear, [-1, 5], ['m', 'b'], 'r', 'Flanke', schnittwert=plateau_mittel_halb)
print('grenzfrequenz = ', grenzfrequenz)
# fitten(x[:grenze], y[:grenze], linear, [0, 0], ['m', 'b'], 'g', 'Plateau')
print('Mittelwert Plateau = ', plateau_mittel, 'Abweichung von ', abweichungen(V_strich_theorie, plateau_mittel))
# plotting
axes.legend(loc='best')
axes.set_xlim(min(noms(x)) - max(noms(x)) * 0.06, (max(noms(x))) * 1.06)
if ylim is not None:
axes.set_ylim(ylim[0], ylim[1])
#x_label, y_label = 'test', 'test'
axes.set_xlabel(x_label)
axes.set_ylabel(y_label)
plt.close()
return grenzfrequenz, plateau_mittel
def plotPhis(pPhis):
vX = range(1, len(pPhis) + 1)
plt.plot(vX, noms(np.array(pPhis)), 'r-')
plt.errorbar(vX,
noms(np.array(pPhis)),
yerr=stds(np.array(pPhis)),
color='k',
fmt='x')
#plt.ylim(-0.05, 1.05)
plt.xlabel('Anzahl an Bestfeatures', {'size': '16'})
plt.ylabel('$\Phi$', {'size': '16'})
plt.title('$\Phi$-Scores')
plt.legend(loc='best', prop={'size': 16})
plt.tight_layout()
plt.savefig('Bilder/PhiScores.pdf')
plt.show()
plt.clf()
def gk_plot(name, winkel, gk, funktion, korr, fitgrenzen):
params, errors = cf(funktion,
np.cos(inrad(winkel[fitgrenzen[0]:fitgrenzen[1]]))**2,
noms(gk[fitgrenzen[0]:fitgrenzen[1]]))
g_plot = np.linspace(0, 1)
plt.errorbar(np.cos(inrad(winkel))**2,
noms(gk) * 1e10,
xerr=korr(winkel),
yerr=stds(gk) * 1e10,
fmt='x',
label=r'Messwert')
plt.plot(g_plot, funktion(g_plot, *params) * 1e10, label=r'Fit')
plt.xlabel(r'$\cos^2\left(\theta\right)$')
plt.ylabel(r'$a \:/\: \si{\angstrom}$')
plt.legend(loc='best')
plt.tight_layout()
plt.savefig("build/plot_" + name + ".pdf")
plt.close()
return (unp.uarray(params[1], np.sqrt(np.diag(errors)[1])))
def make_table(columns, figures=None):
if figures is None:
figures = [None] * len(columns)
cols = []
for column, figure in zip(columns, figures):
if np.any(stds(column)):
if figure is None:
figure = ''
col = list(zip(*['{0:.{1:}uf}'.format(x, figure).split('+/-') for x in column]))
else:
col = list(zip(*[['{0:.{1:}f}'.format(x, figure)] for x in noms(column)]))
cols.extend(col)
max_lens = [max(len(s) for s in col) for col in cols]
cols = [['{0:<{1:}}'.format(s, ml) for s in col] for col, ml in zip(cols, max_lens)]
rows = list(itertools.zip_longest(*cols))
return (r' \\' + '\n').join([' & '.join(s for s in row if s is not None) for row in rows]) + r' \\'
def plotphase(nu_1, phi_1, nu_2, phi_2, nu_3, phi_3, nu_4, phi_4):
# nu_1, nu_2, nu_3, nu_4 = unp.log(nu_1), unp.log(nu_2), unp.log(nu_3), unp.log(nu_4)
# phi_1, phi_2, phi_3, phi_4 = unp.abs(phi_1), unp.abs(phi_2), unp.abs(phi_3), unp.abs(phi_4)
plt.errorbar(noms(nu_1), np.abs(noms(phi_1)),
xerr=stds(nu_1), yerr=stds(phi_1), label='Messwerte bei 1. Widerstandskombination')
plt.errorbar(noms(nu_2), np.abs(noms(phi_2)),
xerr=stds(nu_2), yerr=stds(phi_2), label='Messwerte bei 2. Widerstandskombination')
plt.errorbar(noms(nu_3), np.abs(noms(phi_3)),
xerr=stds(nu_3), yerr=stds(phi_3), label='Messwerte bei 3. Widerstandskombination')
plt.errorbar(noms(nu_4), np.abs(noms(phi_4)),
xerr=stds(nu_4), yerr=stds(phi_4), label='Messwerte bei 4. Widerstandskombination')
xlabel = r'$\nu\:/\:\si{\kilo\hertz}$'
ylabel = r'$\phi\:/\:\si{\degree}$'
#xlabel = 'test'
#ylabel = 'test'
plt.xlabel(xlabel)
plt.ylabel(ylabel)
plt.xscale('log')
plt.legend(loc='best')
plt.savefig('build/phasen.pdf')
def make_table(columns, figures=None):
if figures is None:
figures = [None] * len(columns)
cols = []
for column, figure in zip(columns, figures):
if (type(column) == str):
column = [column]
if (type(column) == list):
col = zip(
*zip(column)
) # hard to find this kind of code... this will unzip the list column, ref: https://docs.python.org/3/library/functions.html#zip
cols.extend(col)
elif np.any(stds(column)):
if figure is None:
figure = ''
col = list(
zip(*[
'{0:.{1:}uf}'.format(x, figure).split('+/-')
for x in column
]))
else:
try:
test_iterator = iter(
column
) # if only one entry is given, then this will throw a type error exception - handled below
col = list(
zip(*[['{0:.{1:}f}'.format(x, figure)]
for x in noms(column)]))
except TypeError:
col = list(zip(*[['{0:.{1:}f}'.format(column, figure)]]))
cols.extend(col)
max_lens = [max(len(s) for s in col) for col in cols]
cols = [['{0:<{1:}}'.format(s, ml) for s in col]
for col, ml in zip(cols, max_lens)]
rows = list(itertools.zip_longest(*cols))
return (r' \\' + '\n').join(
[' & '.join(s for s in row if s is not None) for row in rows]) + r' \\'
def make_table(columns, figures=None):
assert hasattr(columns[0],'__iter__'), "Wenn nur eine Zeile von Daten vorliegt, funktioniert zip nicht mehr; die Elemente von columns müssen Listen sein, auch wenn sie ihrerseits nur ein Element enthalten."
if figures is None:
figures = [None] * len(columns)
cols = []
for column, figure in zip(columns, figures):
if np.any(stds(column)):
if figure is None:
figure = ''
col = list(zip(*['{0:.{1:}uf}'.format(x, figure).split('+/-') for x in column]))
else:
col = list(zip(*[['{0:.{1:}f}'.format(x, figure)] for x in noms(column)]))
cols.extend(col)
max_lens = [max(len(s) for s in col) for col in cols]
cols = [['{0:<{1:}}'.format(s, ml) for s in col] for col, ml in zip(cols, max_lens)]
rows = list(itertools.zip_longest(*cols))
return (r' \\' + '\n').join([' & '.join(s for s in row if s is not None) for row in rows]) + r' \\'
gr = unp.uarray #Geschw. rückwärts
for v in V:
v *= 1.25e-4 #Zählwerkverzögerung
gv = np.append(gv, np.mean(v))
gv = gv[1:]
gv = s / gv
for r in R:
r *= 1.25e-4 #Zählwerkverzögerung
gr = np.append(gr, np.mean(r))
gr = gr[1:]
gr = s / gr
x = np.linspace(1, 10, num=10)
np.savetxt('GangGeschwVorRueck4Tab.txt',
np.column_stack([x, noms(gv),
stds(gv), -noms(gr),
stds(gr)]),
delimiter=' & ',
newline=r' \\'
'\n ')
np.savetxt('GeschwVorRueck.txt',
np.column_stack([noms(gv), stds(gv), -noms(gr),
stds(gr)]))
#
# x= np.linspace(1,10,num=10)
# np.savetxt('GeschwMittelproGang.txt',y,header='#inMeterproSekund')
#
# Plot der Geschw. im arith. Mittel
# plt.plot(x , y,'rx', label='arith. Mittel der gemessenen Geschwindigkeiten')
# plt.xlabel(r'$ Gäng\;der\; Versuchsapparatur$')
# plt.ylabel(r'$ v\:/\:ms^{-1}$')
v_9_auf, v_9_ab = np.genfromtxt('messdaten/9_Tropfen.txt', unpack=True)
v_9_auf_mittel = ufloat(np.mean(v_9_auf), np.std(v_9_auf)) # s/mm
v_9_ab_mittel = ufloat(np.mean(v_9_ab), np.std(v_9_ab)) # s/mm
v_9_0 = 112 # s/mm
U_9 = 184
v_10_auf, v_10_ab = np.genfromtxt('messdaten/10_Tropfen.txt', unpack=True)
v_10_auf_mittel = ufloat(np.mean(v_10_auf), np.std(v_10_auf)) # s/mm
v_10_ab_mittel = ufloat(np.mean(v_10_ab), np.std(v_10_ab)) # s/mm
v_10_0 = 59.4 # s/mm
U_10 = 286
v_auf_mittel_nom=[ noms(v_2_auf_mittel), noms(v_3_auf_mittel), noms(v_4_auf_mittel), noms(v_5_auf_mittel), noms(v_6_auf_mittel), noms(v_7_auf_mittel), noms(v_8_auf_mittel), noms(v_9_auf_mittel), noms(v_10_auf_mittel)]
v_auf_mittel_stds=[ stds(v_2_auf_mittel), stds(v_3_auf_mittel), stds(v_4_auf_mittel), stds(v_5_auf_mittel), stds(v_6_auf_mittel), stds(v_7_auf_mittel), stds(v_8_auf_mittel), stds(v_9_auf_mittel), stds(v_10_auf_mittel)]
v_ab_mittel_nom=[ noms(v_2_ab_mittel), noms(v_3_ab_mittel), noms(v_4_ab_mittel), noms(v_5_ab_mittel), noms(v_6_ab_mittel), noms(v_7_ab_mittel), noms(v_8_ab_mittel), noms(v_9_ab_mittel), noms(v_10_ab_mittel)]
v_ab_mittel_stds=[ stds(v_2_ab_mittel), stds(v_3_ab_mittel), stds(v_4_ab_mittel), stds(v_5_ab_mittel), stds(v_6_ab_mittel), stds(v_7_ab_mittel), stds(v_8_ab_mittel), stds(v_9_ab_mittel), stds(v_10_ab_mittel)]
# v_0 = array(1/v_2_0, 1/v_3_0, 1/v_4_0, 1/v_5_0, 1/v_6_0, 1/v_7_0, 1/v_8_0, 1/v_9_0, 1/v_10_0)
v_0 = np.genfromtxt('messdaten/V_0.txt', unpack=True)
v_0 = 1/v_0
U = np.genfromtxt('messdaten/Spannung.txt', unpack=True)
v_auf = unp.uarray(v_auf_mittel_nom, v_auf_mittel_stds)
v_auf = 1/v_auf
v_ab = unp.uarray(v_ab_mittel_nom, v_ab_mittel_stds)
v_ab = 1/v_ab
write('build/Tabelle_Geschwindigkeiten.tex', make_table([v_auf, v_auf ,v_0, U],[1, 1, 3, 0])) # Jeder fehlerbehaftete Wert bekommt zwei Spalten
write('build/Tabelle_Geschwindigkeiten_texformat.tex', make_full_table(
bbox_inches='tight',
pad_inches=0)
#Bestimmung der Debye-Temperatur
C_p = C_p(U[:-1], I[:-1], Q_(np.diff(t), 'second'),
Q_(np.diff(T_prob), 'kelvin'))
alpha = Q_(model_alpha(noms(T_mean[:-1])), '1 / kelvin')
C_v = C_v(C_p[:-1], alpha, T_mean[:-1]).to('joule / kelvin / mol')
rcParams['figure.figsize'] = 5.906, 6.2
fig, ax = plt.subplots(1, 1)
ax.errorbar(x=noms(T_mean[:-1]),
y=noms(C_v),
xerr=stds(T_mean[:-1]),
yerr=stds(C_v),
fmt='.',
label='Daten',
linestyle=None)
ax.errorbar(x=noms(T_mean[1]),
y=noms(C_v)[1],
xerr=stds(T_mean[1]),
yerr=stds(C_v)[1],
fmt='.',
label='Ausreißer',
linestyle=None,
color='r')
def c_v_debye(T, T_D):
def wellenlaenge(d_array, mitte, L):
d_links = unp.uarray(np.zeros(mitte), np.zeros(mitte))
d_rechts = unp.uarray(np.zeros(12-mitte), np.zeros(12-mitte))
for i in range(0, mitte, 1):
d_links[i] = np.sum(d_array[mitte-(i+1):mitte])
for i in range(0, 12-mitte, 1):
d_rechts[i] = np.sum(d_array[mitte:mitte+(i+1)])
g = (10**-3)/80
print('g = ', g*10**6, 'micro meter')
d_links = d_links*10**-2
d_rechts = d_rechts*10**-2
d_all = np.concatenate((noms(d_links), noms(d_rechts)))
n_links = np.linspace(1, 6, 6)
lamda_links = g * unp.sin(unp.arctan(d_links/L))/n_links
n_rechts = range(1, len(d_rechts)+1, 1)
n_all = np.concatenate((n_links, n_rechts))
lamda_rechts = g * unp.sin(unp.arctan(d_rechts/L))/n_rechts
lamda_all = np.concatenate((lamda_links, lamda_rechts))
werteZuTabelle(d_all*100, n_all.astype(int), (noms(lamda_all)*10**9).astype(int), (stds(lamda_all)*10**9).astype(int), rundungen=[3, 0, 0, 0])
print('lambda = ', (np.sum(lamda_all))/12)
print('Abweichung = ', abweichungen(632.8*10**-9, (np.sum(lamda_all))/12))
print('Mittelwert = ', np.mean(noms(lamda_all)), '±', np.std(noms(lamda_all)))
# fitten
params_1 = ucurve_fit(reg.reg_quadratic, t, T1) # quadratischer Fit
a_1, b_1, c_1 = params_1
write('build/Fit1-a.tex', make_SI(a_1 * 1e6, r'\kelvin\per\square\second', 'e-6', figures=1))
write('build/Fit1-b.tex', make_SI(b_1 * 1e3, r'\kelvin\per\second', 'e-3', figures=1))
write('build/Fit1-c.tex', make_SI(c_1, r'\kelvin', figures=1))
params_2 = ucurve_fit(reg.reg_quadratic, t, T2) # quadratischer Fit
a_2, b_2, c_2 = params_2
write('build/Fit2-a.tex', make_SI(a_2 * 1e6, r'\kelvin\per\square\second', 'e-6', figures=1))
write('build/Fit2-b.tex', make_SI(b_2 * 1e3, r'\kelvin\per\second', 'e-3', figures=1))
write('build/Fit2-c.tex', make_SI(c_2, r'\kelvin', figures=1))
# Plot Temperaturverlauf mit der Zeit
plt.clf()
plt.errorbar(t, noms(T1_unc),yerr=stds(T1_unc), fmt='r.', label=r'$Messdaten T_1$')
plt.errorbar(t, noms(T2_unc),yerr=stds(T2_unc), fmt='b.', label=r'$Messdaten T_2$')
x_plot = np.linspace(0, 31*60, 1000)
plt.plot(x_plot, reg.reg_quadratic(x_plot, *noms(params_1)), 'r-', label=r'Fit $T_1$', linewidth=1)
plt.plot(x_plot, reg.reg_quadratic(x_plot, *noms(params_2)), 'b-', label=r'Fit $T_2$', linewidth=1)
plt.xlabel(r'$t \:/\: \si{\second}$')
plt.ylabel(r'$T \:/\: \si{\kelvin}$')
plt.legend(loc='best')
plt.xlim(0, 31*60)
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig('build/Temperaturverlauf.pdf')
## Differentialquotienten
# wähle 8, 16, 24, 32 Minuten
parameter1 = params_1
plt.legend(loc='best')
plt.savefig('build/Energiespektrum.pdf')
#Würfel 1, Bestimmung von I_0
I0_gerade = unp.uarray(50636, 254) / 300
print('I0_gerade', I0_gerade)
I0_schraeg1 = unp.uarray(16660, 146) / 100
I0_schraeg2 = unp.uarray(16417, 145) / 100
#I0_schraeg = np.mean([I0_schraeg1,I0_schraeg2])
I0_schraeg = avg_and_sem([noms(I0_schraeg1), noms(I0_schraeg2)])
I0_schraeg = unp.uarray(I0_schraeg[0], I0_schraeg[1])
print('I0_schraeg', I0_schraeg)
makeTable([
noms([I0_gerade * 300, I0_schraeg1 * 100, I0_schraeg2 * 100]),
stds([I0_gerade * 300, I0_schraeg1 * 100, I0_schraeg2 * 100]),
[300, 100, 100],
noms([I0_gerade, I0_schraeg1, I0_schraeg2]),
stds([I0_gerade, I0_schraeg1, I0_schraeg2])
], r'\multicolumn{2}{c}{' + r'$N_0$' + r'} & {' +
r'$\Delta t_0/\si{\second}$' + r'} & \multicolumn{2}{c}{' +
r'$I_0/\si{\becquerel}$' + r'}', 'tabReferenzmessung', [
'S[table-format=5.0]', '@{${}\pm{}$}S[table-format=3.0]',
'S[table-format=3.0]', 'S[table-format=3.1]',
'@{${}\pm{}$}S[table-format=1.1]'
], ["%5.0f", "%3.0f", "%3.0f", "%3.1f", "%1.1f"])
#Würfel 2
I2_gerade = unp.uarray(8054, 103) / 300
I2_schraeg1 = unp.uarray(4864, 81) / 300
I2_schraeg2 = unp.uarray(8707, 106) / 300
T_VI.addColumn(g_VI_err, title="Gegenstandsweite",
symbol="g'", unit="\centi\meter")
T_VI.addColumn(b_VI_err, title="Bildweite",
symbol="b'", unit="\centi\meter")
T_VI.addColumn(V_err, title="Abbildungsmaßstab",
symbol="V")
#T_VI.show()
#T_VI.save("Tabellen/Messwerte_VI.tex")
#Regression der Messwerte
popt_VI_g, pcov_VI_g = curve_fit(gerade, abbeX_g(noms(V_err)), noms(g_VI_err),
sigma=stds(g_VI_err))
error_VI_g = np.sqrt(np.diag(pcov_VI_g))
param_VI_g_M = ufloat(popt_VI_g[0], error_VI_g[0])
param_VI_g_B = ufloat(popt_VI_g[1], error_VI_g[1])
print("Regressionsparameter g(V):\n", param_VI_g_M, param_VI_g_B)
def geradeF(x, b):
return noms(param_VI_g_M) * x + b
popt_VI_b, pcov_VI_b = curve_fit(gerade, abbeX_b(noms(V_err)), noms(b_VI_err),
sigma=stds(b_VI_err))
error_VI_b = np.sqrt(np.diag(pcov_VI_b))
param_VI_b_M = ufloat(popt_VI_b[0], error_VI_b[0])
param_VI_b_B = ufloat(popt_VI_b[1], error_VI_b[1])
print("Regressionsparameter b(V):\n", param_VI_b_M, param_VI_b_B)
distance_avr_I = intercept_x
#energy_I = distanceToEnergy(distance_avr_I)
energy_I = distanceToEnergy(ufloat(distance_avr_I, 0.5))
print("Energie der Alphateilchen:", energy_I)
# Erstellen des Plots
plt.clf()
plt.xlim(-5, 20)
plt.ylim(0, 300)
plt.grid()
plt.xlabel("Effektive Länge $x\ [\mathrm{mm}]$", fontsize=14, family='serif')
plt.ylabel("Zerfallsrate $A\ [\mathrm{s^{-1}}]$", fontsize=14, family='serif')
#Messwerte für Regression
#plt.plot(x_eff[0:-7], rate_I[0:-7], "rx", label="Messwerte")
plt.errorbar(x_eff[0:-7], rate_I[0:-7], xerr=stds(x_eff_err[0:-7]) ,fmt="rx", label="Messwerte")
#Messwerte ohne Regression
plt.plot(x_eff[-7:], rate_I[-7:], "kx")
#Fit
plt.plot(X, func(X, popt[0], popt[1]), label="Regressionsgerade", color="gray")
#Halbesmaximum
plt.plot(X, len(X)*[rate_max_half_I],"r--", alpha=0.7, label="Halbe maximal Zerfallsrate")
#Schnittpunkt
plt.plot(intercept_x, rate_max_half_I, "ko", alpha=0.7,
label="Schnittpunkt ({}|{})".format(round(intercept_x, 2),
round(rate_max_half_I, 2)))
plt.tight_layout()
plt.legend(loc="best")
plt.show() if SHOW else plt.savefig("Grafiken/MittlereReichweiteI.pdf")
N[no_of_first_ignored_values:-no_of_last_ignored_values]) # skip first 3 and last 5 values as they dont belong to the plateau
write('build/plateaulaenge.tex', make_SI(U[-no_of_last_ignored_values] - U[no_of_first_ignored_values], r'\volt', figures = 0))
a, b = params
write('build/parameter_a.tex', make_SI(a, r'\per\second\per\volt', figures=1))
write('build/plateaumitte.tex', make_SI(reg_linear(500, *noms(params)), r'\per\second', figures=1) ) # Der Wert in der Hälfte des Plateaus als Referenz für die plateausteigung
write('build/plateausteigung.tex', make_SI(a*100*100/reg_linear(500, *noms(params)), r'\percent', figures=1)) # %/100V lässt sich nicht mit siunitx machen -> wird in latex hart reingeschrieben
write('build/parameter_b.tex', make_SI(b, r'\per\second', figures=1))
#### Plot ####
t_plot = np.linspace(350, 650, 2)
plt.xlim(290,710)
plt.plot(t_plot, reg_linear(t_plot, *noms(params)), 'b-', label='Fit')
U[no_of_first_ignored_values:-no_of_last_ignored_values]
plt.errorbar(U[no_of_first_ignored_values:-no_of_last_ignored_values],
noms(N[no_of_first_ignored_values:-no_of_last_ignored_values]),
fmt='bx', yerr=stds(N[no_of_first_ignored_values:-no_of_last_ignored_values]),
label='Messdaten auf dem Plateau')
plt.errorbar(U[0:no_of_first_ignored_values],
noms(N[0:no_of_first_ignored_values]),
fmt='rx', yerr=stds(N[0:no_of_first_ignored_values]),
label='Messdaten außerhalb des Plateaus')
plt.errorbar(U[-no_of_last_ignored_values:],
noms(N[-no_of_last_ignored_values:]),
fmt='rx', yerr=stds(N[-no_of_last_ignored_values:]))
plt.ylabel(r'$N \:/\: \si{\per\second}$')
plt.xlabel(r'$U \:/\: \si{\volt}$')
plt.grid()
plt.legend(loc='best')
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig('build/aufgabenteil_a_plot.pdf')
std_devs as stds)
import uncertainties.unumpy as unp
from linregress import linregress
print('################################################################################a')
####################orange########################
Udata,Idata=np.genfromtxt('orange.txt',unpack=True)
U=unp.uarray(Udata,0.005)
I=unp.uarray(Idata*10**-9,0.1*10**-9)
sqI=unp.uarray(np.sqrt(noms(I*10**9)),np.sqrt(0.001))
print('farbe',sqI)
i=range(2,9)
a,aerr,b,berr=linregress(noms(U[i]),noms(sqI[i]*10**-9))
x=np.linspace(noms(U[0]),noms(U[len(U)-1]),100)
plt.errorbar(noms(U),noms(sqI),xerr=stds(U),yerr=stds(sqI),fmt='k+',label="Daten")
plt.plot(x,a*x*10**9+b*10**9,'k-',label="Fit")
plt.xlabel(r'Gegenspannung $ U\ / \ \mathrm{V}$')
plt.ylabel(r'reduzierter Photostrom $ \sqrt{I}\ / \ \mathrm{\sqrt{nA}}$')
plt.xlim(noms(U[0]),noms(U[len(U)-1]))
plt.legend(loc='best')
plt.tight_layout()
plt.grid()
plt.savefig('plotorange.pdf')
plt.close()
b=ufloat(b,berr)
a=ufloat(a,aerr)
print(a,b,'m,b')
Ugo=-b/a
print(Ugo,'Ug orange')
print("Eta, bestimmt mit der kleinen Kugel, ist in Pa*sec:")
print(etaK)
print("Mit diesem Eta ist die Apparaturkonstante in willkuerlichen Einheiten:")
print(apparatG)
print("")
print("Viskositaet in Pa*sec:")
print(etaG_2)
print("")
print("Viskositaet in mPa*sec, vgl. Literatur:")
print(etaG_2*1000)
print("")
print("Geschwindigkeiten in m/s:")
print((0.1/fallzeit))
print("")
print("Reynoldzahlen:")
print(Re)
np.savetxt("Auswertung/Viskositaeten.txt", np.array([noms(etaG_2),stds(etaG_2)]).T)
np.savetxt("Auswertung/Reynoldzahlen.txt", np.array([noms(Re),stds(Re)]).T)
np.savetxt("Auswertung/Geschwindigkeiten.txt", np.array([noms((0.1/fallzeit)),stds((0.1/fallzeit))]).T)
np.savetxt("Auswertung/Zeiten.txt", np.array([noms((fallzeit)),stds((fallzeit))]).T)
params = ucurve_fit(reg.reg_linear, B, y) # linearer Fit
m, D = params
write('build/m.tex', make_SI(m*1e3, r'\ampere\square\meter', 'e-3', figures=1))
write('build/D.tex', make_SI(D*1e5, r'\kilogram\square\meter\per\square\second', 'e-5', figures=1))
# D = 4*(np.pi**2)*(Theta_Kugel+Theta_Aufhaengung)/(T**2)
m_th = 1/B * (4*(np.pi**2) * (Theta_Kugel+Theta_Aufhaengung) / T**2 - D_ohneB)
m_th_unc = ufloat(np.mean(noms(m_th)), MeanError(noms(m_th)))
write('build/m_th.tex', make_SI(m_th_unc*1e3, r'\ampere\square\meter', 'e-3', figures=1))
# print(m_th)
t_plot = np.linspace(np.amin(B), np.amax(B), 100)
#
plt.plot(t_plot*1e3, reg.reg_linear(t_plot, *noms(params))*1e5, 'b-', label='Methode 1')
plt.plot(t_plot*1e3, reg.reg_linear(t_plot, np.mean(noms(m_th)), np.mean(noms(D)))*1e5, 'g-', label='Methode 2')
# plt.plot(B * 1e3, noms(y)*1e5, 'rx', label='Messdaten')
plt.errorbar(B * 1e3, noms(y) * 1e5, fmt='r.', yerr=stds(y) * 1e5, label='Messdaten')
## plt.xscale('log') # logarithmische x-Achse
plt.xlim((t_plot[0]-1/np.size(B)*(t_plot[-1]-t_plot[0]))*1e3, (t_plot[-1]+1/np.size(B)*(t_plot[-1]-t_plot[0]))*1e3)
plt.xlabel(r'$B \:/\: \SI{e-3}{\tesla}$')
plt.ylabel(r'$\frac{4\pi^2 \Theta_\text{Gesamt}}{T^2} \:/\: \SI{e-5}{\kilogram\square\meter\per\square\second}$')
plt.legend(loc='best')
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig('build/zeta.pdf')
# Berechnung des Erdmagnetfeldes
B_Erde = (D_mitB-D_ohneB)/m
write('build/B_Erde.tex', make_SI(B_Erde*1e6, r'\micro\tesla', figures=1))
T_FehlerDesMittelwerts = unp.uarray(noms(T),[MeanError(noms(T_10)), MeanError(noms(T_08)), MeanError(noms(T_06)), MeanError(noms(T_04)), MeanError(noms(T_02))])
write('build/Tabelle_Magnet.tex', make_table([I,T_FehlerDesMittelwerts,B*1e3],[1,1,3]))
# FULLTABLE
content = []
error = []
x_value.append(i)
y_value.append(0)
for j in range(ymin,ymax): # going thru all rows
content.append( qMap_Ag_C0_V0.GetBinContent(i,j))
error.append( qMap_Ag_C0_V0.GetBinError(i,j)) # Is this the real error
content_bin = unp.uarray( content, error)
mean_content_col = content_bin.mean() # mean value of each bin in the col
# Saving values in lists
mean_value_col_list.append( noms(mean_content_col))
mean_error_col_list.append( stds(mean_content_col))
########################### Create errorbar plot #####################################
errorbar_plot_col = root.TGraphErrors( len(x_value), array( 'f', x_value), array( 'f', mean_value_col_list), array( 'f', y_value), array( 'f', mean_error_col_list) )
############################## Set axis label of errobar plot ##################################
errorbar_plot_col.GetXaxis().SetTitle("Col")
errorbar_plot_col.GetYaxis().SetTitle("Mean Hit / Vcal")
####################### create Canvas ##########################################
c1 = root.TCanvas("c1", "c1", 1980, 1080)
errorbar_plot_col.Fit('gaus')
[1, 1, 1, 2, 2],
caption=
'Aus Abbildung \\ref{fig: messkurve_energie_hot} abgelesene Steigungen.',
label='steigungen_hot')
#########Tabellen
##Sapnnugnsfit
liste_steigungen = [
float(noms(parmeter_zim['Steigung'])),
float(noms(parmeter_hot['Steigung'])),
float(noms(parmeter_frank_hertz['Steigung'])),
float(noms(parmeter_ioni['Steigung']))
]
liste_steigungen_fehler = [
float(stds(parmeter_zim['Steigung'])),
float(stds(parmeter_hot['Steigung'])),
float(stds(parmeter_frank_hertz['Steigung'])),
float(stds(parmeter_ioni['Steigung']))
]
liste_abschnitt = [
float(noms(parmeter_zim['Achsenabschnitt'])),
float(noms(parmeter_zim['Achsenabschnitt'])),
float(noms(parmeter_frank_hertz['Achsenabschnitt'])),
float(noms(parmeter_ioni['Achsenabschnitt']))
]
liste_abschnitt_fehler = [
float(stds(parmeter_zim['Achsenabschnitt'])),
float(stds(parmeter_hot['Achsenabschnitt'])),
float(stds(parmeter_frank_hertz['Achsenabschnitt'])),
float(stds(parmeter_ioni['Achsenabschnitt']))
ba_events.append([x, s, I])
ax.set_xlabel('Energie / keV')
ax.set_ylabel('Ereignisse')
fig.savefig('../build/plots/ba_gauss-'+str(maximum[0])+'.pdf')
fig.clf()
ba_events = np.array(ba_events)
# efficiency-parameters
ba_energies, ba_props = np.genfromtxt('../data/ba_spectrum_lit.txt',
unpack=True)
eff_coeff, eff_errs = np.genfromtxt('../build/data/efficiency-params.txt',
unpack=True)
xs = ba_props * eff(noms(ba_events[:, 0]), *eff_coeff)
ys = np.abs(noms(ba_events[:, 2]))
y_errs = stds(ba_events[:, 2])
act_coeff, act_covar = curve_fit(activity_func, xs, ys, sigma=y_errs)
act_errs = np.sqrt(np.diag(act_covar))
x = np.linspace(0, 0.25)
plt.plot(x, activity_func(x, *act_coeff), label='Fit')
plt.errorbar(xs, ys, yerr=y_errs, fmt='+', label='Datenpunkte')
plt.legend(loc='best')
plt.xlabel(r'$W \cdot Q$')
plt.ylabel('Ereignisse')
plt.savefig('../build/plots/ba_activity.pdf')
plt.clf()
np.savetxt('../build/data/ba_activity-params.txt',
np.array([act_coeff, act_errs]).T)
Begin der Auswertung zum Dopplereffekt
"""
# Laden der Daten zur Bestimmung der Geschwindigkeit
## Laden der Strecke
l = np.loadtxt("Messdaten/Strecke.txt", unpack=True)
l_err = np.loadtxt("Messdaten/Fehler_Strecke.txt")
### Fehler behaftete Messwerte
ul = unp.uarray(l, [l_err]*len(l))
### Mittelwert
ul_avr = Umean(ul)
ul_avr = ufloat(noms(ul_avr), stds(ul_avr))
ul_avr *= 1e-02 # [cm] --> [m]
## Laden der Zeiten in den verschiedenen Gängen
G, t_h1, t_h2, t_r1, t_r2 = np.loadtxt("Messdaten/Zeiten.txt", unpack=True)
t_err = np.loadtxt("Messdaten/Fehler_Zeiten.txt")
### Fehlerbehaftete Messwerte
ut_h1 = unp.uarray(t_h1, [t_err]*len(t_h1))
ut_h2 = unp.uarray(t_h2, [t_err]*len(t_h2))
ut_r1 = unp.uarray(t_r1, [t_err]*len(t_r1))
ut_r2 = unp.uarray(t_r2, [t_err]*len(t_r2))
### Mittelwerte der Zeiten
uT_h_avr = unp.uarray(np.zeros(len(G)), np.zeros(len(G)))
N_Rh -= A_null*dt_Rh
# Berechnung der Fehler
n_Rh_err = np.sqrt(N_Rh)
# Fehlerbehafteter Messwert
N_Rh_err = unp.uarray(N_Rh, n_Rh_err)
# Plot aller Messwerte
T_Rh = np.arange(20, 740, dt_Rh)
plt.errorbar(T_Rh, np.log(N_Rh), yerr=stds(N_Rh_err)/N_Rh, fmt="rx", label="Messwerte")
plt.xlim(0,730)
plt.ylim(1.5, 5.5)
plt.xlabel(r"Zeit $t\ [s]$", fontsize=14, family="serif")
plt.ylabel(r"Logarithmierte Zerfälle $\ln(N)$", fontsize=14, family="serif")
plt.grid()
plt.legend(loc="best")
plt.tight_layout()
plt.savefig("Grafiken/Messwerte_Rh.pdf")
#plt.show()
plt.clf()
# Wählen des Zeitpunkts t*
t_x = 480
def f(x, m, b):
return m*x+b
def linregress(x, y):
N = len(y)
Delta = N*np.sum(x**2)-(np.sum(x))**2
m = (N*np.sum(x*y)-np.sum(x)*np.sum(y))/Delta
b = (np.sum(x**2) * np.sum(y) - np.sum(x) * np.sum(x * y)) / Delta
sigma_y = np.sqrt(np.sum((y - m * x - b)**2) / (N - 2))
m_error = sigma_y * np.sqrt(N / Delta)
b_error = sigma_y * np.sqrt(np.sum(x**2) / Delta)
print ("Die Regressionssteigung/B ist:", m,"+/-", m_error)
print ("Der Regressions-Y-Achsenabschnitt ist:", b,"+/-", b_error)
print("Die Konstante A im Andradeschen Gesetz ist:",np.exp(b),"+/-",np.sqrt(np.exp(2*b)*b_error**2))
return(m,m_error,b,b_error)
#### Plots
etaG =unp.log(apparatG*(rhoG-rhoW)*fallzeit)
linregress(1/T,noms(etaG))
reg, cov = curve_fit(f, 1/T, noms(etaG))
plt.plot(T_func, f(T_func, *reg), 'r-', label='Fit')
plt.text(0.0031,-7.8, r"$x_{lin}= \; T^{-1} \; \lbrack a.u.\rbrack$", horizontalalignment='center',fontsize=12)
plt.text(0.00285,-7.1, r"$y = 29.61x+7.43$", horizontalalignment='center',color="r",fontsize=12)
plt.ylabel(r'$ln(\eta)\;\lbrack a.u.\rbrack$')
plt.errorbar(1/T, noms(etaG) ,yerr=stds(etaG),fmt="bx", label="Werte")
plt.legend(loc="best")
plt.tight_layout
plt.show()
MB=unp.uarray(mB,stdB)
BB=unp.uarray(bB,fehler_b(stdB,U_B))
MG=unp.uarray(mG,stdG)
BG=unp.uarray(bG,fehler_b(stdG,U_G))
MO=unp.uarray(mO,stdO)
BO=unp.uarray(bO,fehler_b(stdO,U_O))
MT=unp.uarray(mT,stdT)
BT=unp.uarray(bT,fehler_b(stdT,U_T)) # könnte wegen der länge scjeiteren
MV=unp.uarray(mV,stdV)
BV=unp.uarray(bV,fehler_b(stdV,U_V))
M_ges=unp.uarray([noms(MO),noms(MG),noms(MT),noms(MB),noms(MV)],
[stds(MO),stds(MG),stds(MT),stds(MB),stds(MV)])
B_ges=unp.uarray([noms(BO),noms(BG),noms(BT),noms(BB),noms(BV)],
[stds(BO),stds(BG),stds(BT),stds(BB),stds(BV)])
def Ug(M,B):
return(-B/M)
U_gO=Ug(MO,BO)
U_gG=Ug(MG,BG)
U_gT=Ug(MT,BT)
U_gB=Ug(MB,BB)
U_gV=Ug(MV,BV)
amplitude_of_peaks.append(amplitude)
sigma_of_peaks.append(sigma)
offset_of_peak.append(offset)
area_under_peak.append(area)
# Save data in table
print(index)
l.Latexdocument(
filename=abs_path('tabs/europium/peak_charakteristiken_eu.tex')).tabular(
data=[
index,
unp.uarray(noms(amplitude_of_peaks), stds(amplitude_of_peaks)),
unp.uarray(noms(sigma_of_peaks), stds(sigma_of_peaks)),
unp.uarray(noms(offset_of_peak), stds(offset_of_peak))
],
header=['Kanal / ', r'A / ', r'\sigma / ', r'\mu / '],
places=[0, (2.2, 2.2), (1.2, 1.2), (4.2, 1.2)],
caption='Bestimmte Eigenschaften der Peaks von $^{152}\ce{Eu}$.',
label='results_peaks_eu')
# ########################################################################### #
# ## --- Linear Regression to get transformations parameters--- ## #
# ########################################################################### #
def g(x, m, b):
'''Define linear function for Transformation purpose'''
return m * x + b
uP_2 = unp.uarray(P_2, P_dim * [P_2_err])
#%%
## Plots der Temperaturverläufe
# 16 t- Werte in Sekunden (0, 90, 180, ..., 1350)
t = np.linspace(0, (T_dim - 1) * DELTA_T, num=T_dim)
# "Kontinuierliche" Werte von -10 bis 2000
x = np.linspace(-10, 2000, num=1000)
# Bearbeitung von T_1
#Berechnung der Fit-Parameter
poptI_T1, pcovI_T1 = curve_fit(T_FitI, t, noms(uT_1), sigma=stds(uT_1))
poptII_T1, pcovII_T1 = curve_fit(T_FitII, t, noms(uT_1), sigma=stds(uT_1))
poptIII_T1, pcovIII_T1 = curve_fit(T_FitIII, t, noms(uT_1), sigma=stds(uT_1))
# Berechnung der Fit-Fehler
errorI_T1 = np.sqrt(np.diag(pcovI_T1))
#errorII_T1 = np.sqrt(np.diag(pcovII_T1))
#errorIII_T1 = np.sqrt(np.diag(pcovIII_T1))
uA_1 = ufloat(poptI_T1[0], errorI_T1[0])
uB_1 = ufloat(poptI_T1[1], errorI_T1[1])
uC_1 = ufloat(poptI_T1[2], errorI_T1[2])
# Plot Einstellungen
# Erstellen von 3x3 Matrizen für die Werte von Cu und Al
# Spalte entspricht einer Versuchsreihe, Zeile: Entspricht einer Größe
uU_CU = unp.matrix([uU_CU_C, uU_CU_H, uU_CU_M])
uU_AL = unp.matrix([uU_AL_C, uU_AL_H, uU_AL_M])
# Umrechnung der Spannungen in Temperaturen
uT_CU = TensToTemp(uU_CU)
uT_AL = TensToTemp(uU_AL)
TEST = True
if TEST:
for i in range(3):
for j in range(3):
uT_CU[i, j] = ufloat(noms(uT_CU[i, j]), stds(uT_CU[i, j]))
if TEST:
for i in range(3):
for j in range(3):
uT_AL[i, j] = ufloat(noms(uT_AL[i, j]), stds(uT_AL[i, j]))
## Versuchsergebnisse der Kalorimetermessung:M_c, M_h, M_m, U_c, U_h, U_m
M_W_C, M_W_H, M_W_M, U_W_C, U_W_H, U_W_M = np.loadtxt(
"Messdaten/Messung_Kalorimeter.txt", unpack=True)
# Umrechnung in SI-Einheiten
if SI:
M_W_C *= 1e-03 # kg
M_W_H *= 1e-03 # kg
M_W_M *= 1e-03 # kg
plt.figure(2)
plt.plot(Ud2,D_U2,'cx',label=r'$\mathrm{Messwerte \ für \ U_b=250\mathrm{V}}$')
plt.errorbar(Ud2,D_U2,xerr=0,yerr=0.002, fmt='cx')
plt.plot(Ud4,D_U4,'gx',label=r'$\mathrm{Messwerte \ für \ U_b=400\mathrm{V}}$')
plt.errorbar(Ud4,D_U4,xerr=0,yerr=0.002, fmt='gx')
plt.plot(x_U,m2*x_U+b2,'c-',label=r'$\mathrm{Ausgleichsfunkion \ für\ U_b=250V }$')
plt.plot(x_U,m4*x_U+b4,'g-',label=r'$\mathrm{Ausgleichsfunkion \ für\ U_b=400V }$')
plt.legend(loc='best')
plt.xlabel(r'$\mathrm{Ablenkspannung \ U_d/V}$')
plt.ylabel(r'$\mathrm{Verschiebung \ D/m}$')
plt.savefig('plotV5012.pdf')
np.savetxt('1tabelle.txt',np.column_stack((D_U1,Ud1,Ud2,Ud3)),fmt='%r',delimiter=' & ')
Mges=unp.uarray([m1,m2,m3,m4,m5],[stds(M1),stds(M2),stds(M3),stds(M4),stds(M5)])
Ubges=np.array([Ub1,Ub2,Ub3,Ub4,Ub5])
print(noms(Mges))
ma , ba , ra ,pa ,stda =stats.linregress(1/Ubges,noms(Mges))
x_ub=np.linspace(0,0.006)
plt.figure(3)
plt.plot(1/Ubges,noms(Mges),'rx',label=r'$\mathrm{Messwerte}$')
plt.errorbar(1/Ubges,noms(Mges),xerr=0,yerr=stds(Mges), fmt='rx')
plt.plot(x_ub,ma*x_ub+ba,'c-',label=r'$\mathrm{Ausgleichsfunkion}$')
plt.legend(loc='best')
plt.xlabel(r'$\mathrm{U_b^{-1}/V^{-1}}$')
plt.ylabel(r'$D\,U_d^{-1}\mathrm{/m V^{-1} }$')
plt.savefig('plotV501a.pdf')
def weight_mean(X):
n = noms(X)
s = stds(X)
mean = sum(n * 1 / s**2) / sum(1 / s**2)
std = np.sqrt(1 / sum(1 / s**2))
return ufloat(mean, std)
# Spalte entspricht einer Versuchsreihe, Zeile: Entspricht einer Größe
uU_CU = unp.matrix([uU_CU_C, uU_CU_H, uU_CU_M])
uU_AL = unp.matrix([uU_AL_C, uU_AL_H, uU_AL_M])
# Umrechnung der Spannungen in Temperaturen
uT_CU = TensToTemp(uU_CU)
uT_AL = TensToTemp(uU_AL)
TEST = True
if TEST:
for i in range(3):
for j in range(3):
uT_CU[i,j] = ufloat(noms(uT_CU[i,j]), stds(uT_CU[i,j]))
if TEST:
for i in range(3):
for j in range(3):
uT_AL[i,j] = ufloat(noms(uT_AL[i,j]), stds(uT_AL[i,j]))
## Versuchsergebnisse der Kalorimetermessung:M_c, M_h, M_m, U_c, U_h, U_m
M_W_C, M_W_H, M_W_M, U_W_C, U_W_H, U_W_M = np.loadtxt("Messdaten/Messung_Kalorimeter.txt",
unpack=True)
# Umrechnung in SI-Einheiten
if SI:
M_W_C *= 1e-03 # kg
M_W_H *= 1e-03 # kg
M_W_M *= 1e-03 # kg
plt.savefig('build/zoom.pdf')
plt.clf()
print(noms(U_c_ges[Indem_max]/U_er_ges[Indem_max]))
# Abgelesene Werte
V_abgelesen = np.array([ufloat(33.925, 0.005)])
w_0_abgelesen = V_abgelesen *2*np.pi
print('Vergleiche')
print(w_0_abgelesen)
v_minus_abgelesen = V_abgelesen - X
w_minus_abgelesen = v_minus_abgelesen *(-2)*np.pi + w_0_abgelesen
v_plus_abgelesen = Y-V_abgelesen
w_plus_abgelesen = v_plus_abgelesen *2*np.pi + w_0_abgelesen
q_abgelesen = (w_0_abgelesen)/(w_plus_abgelesen - w_minus_abgelesen)
print('HEY')
print(stds(w_minus_abgelesen))
write('build/Tabelle_aufgabenteil_c_exp.tex', make_table([[q_abgelesen[0]], [w_0_abgelesen[0]], [w_minus_abgelesen[0]],
[w_plus_abgelesen[0]]] ,[1,1,1,1]))
# L = np.array([ufloat(10.11, 0.03)]) # in mH
print('Hier')
print(q_abgelesen)
# Aufgabenteil d)
fre_ges *=1e3 # umrechnung in Hz
w_ges = fre_ges * 2* np.pi *(1/1000)
Takt = 1/fre_ges
def phi(a,T):
U_0=unp.uarray(19.4,0.05)
y=1-(U_c/U_0)
#phi=(a/b)*2*np.pi
#plt.figure(1)
#plt.plot(1/(b*10**-3),phi,'rx')
#plt.savefig('plot.pdf')
print(T)
index= [12,13]
Tt=np.delete(T, index)
print(Tt)
yy=np.delete(y, index)
m , b , r ,p ,std =stats.linregress(noms(Tt),np.log(noms(yy)))
print('m', m)
plt.figure(1)
plt.errorbar(t ,noms(y),xerr=stds(T),yerr=stds(y), fmt='rx')
plt.plot(noms(T),noms(y),'kx',label=r'$Messwerte$')
x=np.linspace(0,5)
plt.plot(t, np.exp(m*t+b),label=r'$Ausgleichsfunktion$')
plt.yscale('log')
plt.legend(loc='best')
plt.xlabel(r'$t/s$')
plt.ylabel(r'$ln(1-(U_c/U_0)) $')
plt.savefig('a.pdf')
M=unp.uarray(m,std)
print('RC ist = ', 1/M, M)
print('Delta Rc',std/m**2)
w , a_w =np.genfromtxt('b.txt',unpack=True)
# RC=0.001388
A_w=unp.uarray(a_w,0.0005)
m4 * x_U + b4,
'g-',
label=r'$\mathrm{Ausgleichsfunkion \ für\ U_b=400V }$')
plt.legend(loc='best')
plt.xlabel(r'$\mathrm{Ablenkspannung \ U_d/V}$')
plt.ylabel(r'$\mathrm{Verschiebung \ D/m}$')
plt.savefig('plotV5012.pdf')
np.savetxt('1tabelle.txt',
np.column_stack((D_U1, Ud1, Ud2, Ud3)),
fmt='%r',
delimiter=' & ')
Mges = unp.uarray(
[m1, m2, m3, m4, m5],
[stds(M1), stds(M2), stds(M3),
stds(M4), stds(M5)])
Ubges = np.array([Ub1, Ub2, Ub3, Ub4, Ub5])
print(noms(Mges))
ma, ba, ra, pa, stda = stats.linregress(1 / Ubges, noms(Mges))
x_ub = np.linspace(0, 0.006)
plt.figure(3)
plt.plot(1 / Ubges, noms(Mges), 'rx', label=r'$\mathrm{Messwerte}$')
plt.errorbar(1 / Ubges, noms(Mges), xerr=0, yerr=stds(Mges), fmt='rx')
plt.plot(x_ub, ma * x_ub + ba, 'c-', label=r'$\mathrm{Ausgleichsfunkion}$')
plt.legend(loc='best')
plt.xlabel(r'$\mathrm{U_b^{-1}/V^{-1}}$')
plt.ylabel(r'$D\,U_d^{-1}\mathrm{/m V^{-1} }$')
plt.savefig('plotV501a.pdf')
def do_job_a(filename, error, j, filename_out=None):
# Einlesen der Messdaten
P, Delta_f_30, Delta_f_15, Delta_f_60 = np.genfromtxt(filename, unpack=True)
#
di = [7, 10, 16]
colors = ["rx", "bx", "gx"]
Delta_f_30_error = Delta_f_30 * error
Delta_f_30 = unp.uarray(Delta_f_30, Delta_f_30_error)
Delta_f_15_error = Delta_f_15 * error
Delta_f_15 = unp.uarray(Delta_f_15, Delta_f_15_error)
Delta_f_60_error = Delta_f_60 * error
Delta_f_60 = unp.uarray(Delta_f_60, Delta_f_60_error)
v = unp.uarray(np.zeros(3), np.zeros(3))
v[0] = c_L / 2 / nu_0 * Delta_f_30 / np.cos(alpha[0])
v[1] = c_L / 2 / nu_0 * Delta_f_15 / np.cos(alpha[1])
v[2] = c_L / 2 / nu_0 * Delta_f_60 / np.cos(alpha[2])
v_mean = mean([v[0], v[1], v[2]], 0)
# TABLES
write(
"build/Tabelle_a_" + str(di[j]) + ".tex",
make_table([P, Delta_f_30, Delta_f_15, Delta_f_60, v[0], v[1], v[2], v_mean], [0, 1, 1, 1, 1, 1, 1, 1]),
)
write(
"build/Tabelle_a_" + str(di[j]) + "_texformat.tex",
make_full_table(
r"Messdaten und daraus errechnete Geschwindikgiet für $\d_i = $" + str(di[j]) + r"$\si{\milli\meter}$.",
"table:A" + str(j),
"build/Tabelle_a_" + str(di[j]) + ".tex",
[1, 2, 3, 4, 5, 6, 7],
[
r"$\frac{P}{P_\text{max}} \:/\: \si{\percent}$",
r"$\Delta f_{30°} \:/\: \si{\hertz}$",
r"$\Delta f_{15°} \:/\: \si{\hertz}$",
r"$\Delta f_{60°} \:/\: \si{\hertz}$",
r"$v_{30°} \:/\: \si{\meter\per\second}$",
r"$v_{15°} \:/\: \si{\meter\per\second}$",
r"$v_{60°} \:/\: \si{\meter\per\second}$",
r"$\overline{v} \:/\: \si{\meter\per\second}$",
],
),
)
# Plotting
plt.figure(1)
y = Delta_f_30 / np.cos(alpha[0])
plt.errorbar(
noms(v[0]),
noms(y),
fmt=colors[j],
xerr=stds(v[0]),
yerr=stds(y),
label=r"$d_i = " + str(di[j]) + r"\si{\milli\meter}$",
)
plt.figure(2)
y = Delta_f_15 / np.cos(alpha[1])
plt.errorbar(
noms(v[1]),
noms(y),
fmt=colors[j],
xerr=stds(v[1]),
yerr=stds(y),
label=r"$d_i = " + str(di[j]) + r"\si{\milli\meter}$",
)
plt.figure(3)
y = Delta_f_60 / np.cos(alpha[2])
plt.errorbar(
noms(v[2]),
noms(y),
fmt=colors[j],
xerr=stds(v[2]),
yerr=stds(y),
label=r"$d_i = " + str(di[j]) + r"\si{\milli\meter}$",
)
i = 1
if filename_out:
for name in filename_out:
plt.figure(i)
plt.xlabel(r"$v \:/\: \si{\meter\per\second}$")
plt.ylabel(r"$\Delta\nu / \cos{\alpha} \:/\: \si{\kilo\volt}$")
plt.legend(loc="best")
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig(name)
i += 1
#Messung 2
def Brech(z,lamb,T,p0,b,T0,deltaP):
n=1+z*lamb*T*p0/(2*b*T0*deltaP)
return n
p1,p2,ticks =np.genfromtxt('Messung2.txt', unpack = True)
deltaP=p2-p1
p0=1.0132
T0=273.15
b=50e-3
T=293.15
n=unp.uarray(noms(Brech(ticks,L,T,p0,b,T0,deltaP)),stds(Brech(ticks,L,T,p0,b,T0,deltaP)))
# n=Brech(ticks,L,T,p0,b,T0,deltaP)
print(n,'n Luft')
print(np.mean(noms(n)),stats.sem(noms(n)),'Luft np.mean(noms(n)),stats.sem(noms(n))')
nL=ufloat(np.mean(noms(n)),stats.sem(noms(n)))
#Messung3
p1,p2,ticks =np.genfromtxt('Messung3.txt', unpack = True)
deltaP=p2-p1
n=unp.uarray(noms(Brech(ticks,L,T,p0,b,T0,deltaP)),stds(Brech(ticks,L,T,p0,b,T0,deltaP)))
print(n,'n 1-Butylen')
delta_E_natrium = h*c*delta_lambda_natrium/(lambda_natrium_mean**2) # # in eV (wegen h in eVs)
delta_E_rubidium = h*c*delta_lambda_rubidium/(lambda_rubidium_mean**2) # # in eV (wegen h in eVs)
# final step : calculate sigma_2
def sigma_2 (n, l, Delta_E, z):
return z-unp.sqrt(unp.sqrt(Delta_E * l * (l+1) * n**3 / (R*a**2)))
sigma_2_kalium = sigma_2(4, 1, delta_E_kalium, 19) # Kalium : z=19, 4P1/2 Übergang (P bedeutet l=1)
sigma_2_natrium = sigma_2(3, 1, delta_E_natrium, 11) # Kalium : z=11, 3P1/2 Übergang (P bedeutet l=1)
sigma_2_rubidium = sigma_2(5, 1, delta_E_rubidium, 37) # Kalium : z=37, 5P1/2 Übergang (P bedeutet l=1)
# da der Fehler systematische Fehler der Eingangsgrößen klein ist, geben wir nur den Fehler des Mittelwerts an.
sigma_2_kalium_mean = ufloat(np.mean(noms(sigma_2_kalium)), np.std(noms(sigma_2_kalium)))
sigma_2_natrium_mean = ufloat(np.mean(noms(sigma_2_natrium)), np.std(noms(sigma_2_natrium)))
# Für Rubidium haben wir nur einen Messwert, daher gibts auch nichts zu mitteln
sigma_2_rubidium_unc = ufloat(noms(sigma_2_rubidium), stds(sigma_2_rubidium))
write('build/sigma_kalium.tex', make_SI(sigma_2_kalium_mean, r'', figures=1))
write('build/sigma_natrium.tex', make_SI(sigma_2_natrium_mean, r'', figures=1))
write('build/sigma_rubidium.tex', make_SI(sigma_2_rubidium_unc, r'', figures=1))
#### TABELLEn ####
write('build/Tabelle_c_kalium.tex', make_table([
-phi_kalium_mean,
lambda_kalium_mean*1e9,
delta_s_kalium,
delta_lambda_kalium*1e9,
delta_E_kalium*1e3,
sigma_2_kalium
],
[1, 1, 2, 1, 1, 1]))
from linregress import ulinregress
Delta_t_0 = np.loadtxt('Delta_t_0.txt')
N_0 = np.loadtxt('N_0.txt')
N_0 = unc.ufloat(N_0, np.sqrt(N_0))
Delta_t = np.loadtxt('Delta_t.txt')
N_g = np.loadtxt('N_g.txt', unpack=True)
N_g = unp.uarray(N_g, np.sqrt(N_g))
t = Delta_t * np.arange(1, len(N_g) + 1)
N = N_g - N_0 / Delta_t_0 * Delta_t
A, B = ulinregress(t, unp.log(N))
print(A, B, sep='\n')
lambda_ = -A
print("λ =", lambda_)
x = np.linspace(0, 4000)
plt.plot(x, np.exp(noms(A * x + B)), 'b-', label='Regressionsgerade')
plt.errorbar(t, noms(N), yerr=stds(N), fmt='rx', label='Messwerte')
plt.yscale('log', nonposy='clip')
plt.xlabel(r'$t \,/\, \mathrm{s}$')
plt.ylabel(r'$N$')
plt.ylim(8e2, 3e3)
plt.yticks([8e2, 1e3, 3e3], [r"$8 \cdot 10^2$", r"$10^3$", r"$3 \cdot 10^3$"])
plt.legend(loc='upper right')
plt.tight_layout()
plt.savefig('loesung.pdf')
##print(P_C_j_err)
#
## Regression der Messwerte
#popt_C, pcov_C = curve_fit(func_gerade, noms(U_C_j_err),
# noms(P_C_j_err), sigma=stds(P_C_j_err))
#error = np.sqrt(np.diag(pcov_C))
#param_m_C = ufloat(popt_C[0], error[0])
#param_b_C = ufloat(popt_C[1], error[1])
#
#print("Steigung:", param_m_C)
#print("Steigung in % pro 100V:", param_m_C*100,"%")
#print("y-Abschnitt:", param_b_C)
# Regression der Messwerte
popt_C, pcov_C = curve_fit(func_gerade, noms(U_C_err),
noms(P_C_err), sigma=stds(P_C_err))
error = np.sqrt(np.diag(pcov_C))
param_m_C = ufloat(popt_C[0], error[0])
param_b_C = ufloat(popt_C[1], error[1])
print("Steigung:", param_m_C)
print(func_gerade(100, param_m_C,param_b_C))
print(func_gerade(0, param_m_C,param_b_C))
print((func_gerade(100, param_m_C,param_b_C)- func_gerade(0, param_m_C,param_b_C))/func_gerade(0, param_m_C,param_b_C))
print("Steigung in % pro 100V:", 100 * (func_gerade(100, param_m_C,param_b_C)- func_gerade(0, param_m_C,param_b_C))/func_gerade(0, param_m_C,param_b_C),"%")
print("y-Abschnitt:", param_b_C)
# Plot der Messwerte
plt.errorbar(noms(U_C_err), noms(P_C_err), yerr=stds(P_C_err), fmt="rx", label="Messwerte")
omega_x.SetParameter(0, 1e-10)
omega_x.SetParameter(1, 0.00898)
omega_x.SetParameter(2, (1060e-9)**2 / np.pi**2)
omega_y.SetParameter(0, 1e-10)
omega_y.SetParameter(1, 0.00898)
omega_y.SetParameter(2, (1060e-9)**2 / np.pi**2)
c1 = root.TCanvas("c1", "c1", 1980, 1080)
c1.SetGrid()
mg = root.TMultiGraph() #Create multigraph
plot_xsigma = root.TGraphErrors(len(xsigma), array('f', noms(uheight)),
array('f', noms(usigma_x)),
array('f', stds(uheight)),
array('f', stds(usigma_x)))
plot_ysigma = root.TGraphErrors(len(xsigma), array('f', noms(uheight)),
array('f', noms(usigma_y)),
array('f', stds(uheight)),
array('f', stds(usigma_y)))
mg.GetXaxis().SetRangeUser(2., 10.)
plot_xsigma.GetXaxis().SetMaxDigits(2)
plot_xsigma.GetXaxis().SetLimits(0, 1) #Set xLimits
plot_ysigma.GetXaxis().SetLimits(0, 1) #Set xLimits
plot_xsigma.SetMarkerColor(1756)
plot_xsigma.SetLineColor(1756)
omega_x.SetLineColor(1758) #Set Linecolor xsigma
### Noch ein paar Plots
plt.clf()
CAP = np.linspace(1e-20, 14e-09, num=1e02)
plt.grid()
plt.tick_params("both", labelsize=14)
plt.ylim(20e03, 1e05)
plt.xlabel(r"Koppelkondensatoren $C_{K}\ [\mathrm{nF}]$", fontsize=14)
plt.gca().xaxis.set_major_formatter(mpl.ticker.FuncFormatter(lambda x, _: float(x * 1e09)))
plt.ylabel(r"Frequenz $f\ [\mathrm{kHz}]$", fontsize=14)
plt.gca().yaxis.set_major_formatter(mpl.ticker.FuncFormatter(lambda x, _: float(x * 1e-03)))
plt.plot(CAP, len(CAP)*[resFreq_plus(noms(uC), C_sp, noms(uL))], color="blue",
label="Theoretischer Kurve $v^{+}(C_{K})$")
plt.errorbar(noms(uC1), noms(uf_p), yerr=stds(uf_p), fmt="bo",
label="Messwerte $v^{+}(C_{K})$")
plt.plot(CAP, resFreq_minus(noms(uC), CAP, C_sp, noms(uL)), color="green",
label="Theoretischer Kurve $v^{-}(C_{K})$")
plt.errorbar(noms(uC1), noms(uf_m), yerr=stds(uf_m), fmt="go",
label="Messwerte $v^{-}(C_{K})$")
plt.legend(loc="best")
plt.tight_layout()
plt.savefig("Grafiken/Frequenz_CK.pdf")
## Print Funktionen