def perform_fit(m, y_m, series):
global j
m = m[y_m!=0]
y_m = y_m[y_m!=0]
popt, pstats = papstats.curve_fit(fit_y_m, m, y_m, p0=[E_Ry, E_3p.nominal_value, 0])
popt_fixedERy, pstats_fixedERy = papstats.curve_fit(fit_y_m_fixedERy, m, y_m, p0=[E_3p.nominal_value, 0])
D_index = ['d', 's'][series-1]
D = [0, d_s][series-1]
plt.clf()
plt.title(u'Diagramm 3.6.' + str(j) + u': Spektrallinien der ' + str(series) + u'. Nebenserie: $m' + D_index + ur' \rightarrow 3p$')
papstats.plot_data(m, y_m)
papstats.plot_fit(fit_y_m, popt, pstats, xspace=np.linspace(m[0], m[-1], 100), eq=r'\lambda_m = h*c/(E_{Ry}/(m - \Delta_' + D_index + ')^2 - E_{3p})', plabels=['E_{Ry}', 'E_{3p}', '\Delta_' + D_index], punits=['eV', 'eV', None])
papstats.plot_fit(fit_y_m_fixedERy, popt_fixedERy, pstats_fixedERy, xspace=np.linspace(m[0], m[-1], 100), eq=r'E_{Ry}=13.605eV', plabels=['E_{3p}', '\Delta_' + D_index], punits=['eV', None])
plt.ylabel(u'Wellenlänge der Spektrallinie $\lambda \, [nm]$')
plt.xlabel(u'Anfangsniveau $m$')
plt.legend(loc='upper right')
papstats.savefig_a4('5.' + str(j) + '.png')
j = j + 1
erw = np.array([E_Ry, E_3p, D])
res_fit = np.array(popt)
diff = np.abs(erw - res_fit)
res_fit_fixedERy = [E_Ry, popt_fixedERy[0], popt_fixedERy[1]]
diff_fixedERy = np.abs(erw - res_fit_fixedERy)
print papstats.table(labels=['', 'Erwartung', 'Fit', 'Abweichung', u'σ-Bereich', 'Fit mit E_Ry fixiert', 'Abweichung', u'σ-Bereich'], columns=[['E_Ry [eV]', 'E_3p [eV]', 'D_' + D_index], erw, res_fit, diff, unp.nominal_values(diff)/unp.std_devs(diff), res_fit_fixedERy, diff_fixedERy, unp.nominal_values(diff_fixedERy)/unp.std_devs(diff_fixedERy)])
def perform_fit(m, y_m, series):
global j
m = m[y_m != 0]
y_m = y_m[y_m != 0]
popt, pstats = papstats.curve_fit(fit_y_m,
m,
y_m,
p0=[E_Ry, E_3p.nominal_value, 0])
popt_fixedERy, pstats_fixedERy = papstats.curve_fit(
fit_y_m_fixedERy, m, y_m, p0=[E_3p.nominal_value, 0])
D_index = ['d', 's'][series - 1]
D = [0, d_s][series - 1]
plt.clf()
plt.title(u'Diagramm 3.6.' + str(j) + u': Spektrallinien der ' +
str(series) + u'. Nebenserie: $m' + D_index +
ur' \rightarrow 3p$')
papstats.plot_data(m, y_m)
papstats.plot_fit(fit_y_m,
popt,
pstats,
xspace=np.linspace(m[0], m[-1], 100),
eq=r'\lambda_m = h*c/(E_{Ry}/(m - \Delta_' + D_index +
')^2 - E_{3p})',
plabels=['E_{Ry}', 'E_{3p}', '\Delta_' + D_index],
punits=['eV', 'eV', None])
papstats.plot_fit(fit_y_m_fixedERy,
popt_fixedERy,
pstats_fixedERy,
xspace=np.linspace(m[0], m[-1], 100),
eq=r'E_{Ry}=13.605eV',
plabels=['E_{3p}', '\Delta_' + D_index],
punits=['eV', None])
plt.ylabel(u'Wellenlänge der Spektrallinie $\lambda \, [nm]$')
plt.xlabel(u'Anfangsniveau $m$')
plt.legend(loc='upper right')
papstats.savefig_a4('5.' + str(j) + '.png')
j = j + 1
erw = np.array([E_Ry, E_3p, D])
res_fit = np.array(popt)
diff = np.abs(erw - res_fit)
res_fit_fixedERy = [E_Ry, popt_fixedERy[0], popt_fixedERy[1]]
diff_fixedERy = np.abs(erw - res_fit_fixedERy)
print papstats.table(
labels=[
'', 'Erwartung', 'Fit', 'Abweichung', u'σ-Bereich',
'Fit mit E_Ry fixiert', 'Abweichung', u'σ-Bereich'
],
columns=[['E_Ry [eV]', 'E_3p [eV]',
'D_' + D_index], erw, res_fit, diff,
unp.nominal_values(diff) / unp.std_devs(diff),
res_fit_fixedERy, diff_fixedERy,
unp.nominal_values(diff_fixedERy) /
unp.std_devs(diff_fixedERy)])
def analyze_spektrallinien(fileprefix, figindex, crstl, sl, d=None, y=None):
data = np.append(np.loadtxt(fileprefix+'.b.1.txt', skiprows=1), np.loadtxt(fileprefix+'.b.2.txt', skiprows=1), axis=0)
b, n = data[:,0], data[:,1]
n = unp.uarray(n, np.sqrt(n*20)/20)
sl = [ [(b >= bounds[0]) & (b <= bounds[1]) for bounds in sl_row] for sl_row in sl]
def fit_gauss(x, m, s, A, n_0):
return A/np.sqrt(2*const.pi)/s*np.exp(-((x-m)**2)/2/(s**2))+n_0
r = []
plt.clf()
papstats.plot_data(b,n)
papstats.savefig_a4('3.'+str(figindex)+'.a.png')
plt.clf()
plt.suptitle('Diagramm 3.'+str(figindex)+u': Spektrallinien von Molybdän bei Vermessung mit einem '+crstl+'-Kristall')
for i in range(2):
r.append([])
# Linie
for k in range(2):
# Ordnung
b_k = b[sl[i][k]]
n_k = n[sl[i][k]]
xspace = np.linspace(b_k[0], b_k[-1], num=1000)
plt.subplot(2,2,i*2+k+1)
plt.xlim(xspace[0], xspace[-1])
if i==1:
plt.xlabel(u'Bestrahlungswinkel '+r'$\beta \, [^\circ]$')
if k==0:
plt.ylabel(u'Zählrate '+r'$n \, [\frac{Ereignisse}{s}]$')
plt.title('$K_{'+(r'\alpha' if i==0 else r'\beta')+'}$ ('+str(k+1)+'. Ordnung)')
papstats.plot_data(b_k, n_k)
# Gauss-Fit
popt, pstats = papstats.curve_fit(fit_gauss, b_k, n_k, p0=[b_k[0]+(b_k[-1]-b_k[0])/2, (b_k[-1]-b_k[0])/4, np.sum(n_k).n, n_k[0].n])
plt.fill_between(b_k, 0, unp.nominal_values(n_k), color='g', alpha=0.2)
FWHM = popt[1]*2*unp.sqrt(2*unp.log(2))
plt.hlines(popt[3].n+(fit_gauss(xspace, *unp.nominal_values(popt)).max()-popt[3].n)/2, popt[0].n-FWHM.n/2, popt[0].n+FWHM.n/2, color='black', lw=2, label='$'+papstats.pformat(FWHM, label='FWHM', unit=r'^\circ')+'$')
papstats.plot_fit(fit_gauss, popt, xspace=xspace, plabels=[r'\mu', r'\sigma', 'A', 'n_0'], punits=['^\circ', '^\circ', 's^{-1}', 's^{-1}'])
plt.ylim(unp.nominal_values(n_k).min()-n_k[unp.nominal_values(n_k).argmin()].s, unp.nominal_values(n_k).max()+(unp.nominal_values(n_k).max()-unp.nominal_values(n_k).min()))
plt.legend(loc='upper center', prop={'size':10})
b_S = unc.ufloat(popt[0].n, np.abs(popt[1].n))
print "Winkel:", papstats.pformat(b_S, unit='°', format='.2u')
if y is None:
r[i].append(y_bragg(b_S, n=k+1))
print "Wellenlänge der Linie:", papstats.pformat(r[i][k]/const.pico, label='y', unit='pm', format='.2u')
if d is None:
r[i].append((k+1)*y[i][k]/unc.umath.sin(b_S*const.degree))
print "Gitterkonstante:", papstats.pformat(r[i][k]/const.pico, label='a', unit='pm', format='.2u')
papstats.savefig_a4('3.'+str(figindex)+'.png')
return r
def compute_hwz(N_list, ttor, fit, plotname, title, sl=slice(None,None), Uscale=1, p0=None, eq=None, plabels=None, punits=None, Th_erw=None):
N = np.sum(unp.uarray(N_list,np.sqrt(N_list)), axis=0)
t = np.arange(len(N))*ttor+ttor/2.
table = pt.PrettyTable()
table.add_column('t [s]', t.astype(int), align='r')
if len(N_list) > 1:
for i in range(len(N_list)):
table.add_column('N'+str(i+1), N_list[i].astype(int), align='r')
table.add_column('Summe', N, align='r')
else:
table.add_column('N', N, align='r')
with open("Resources/table_"+plotname+".txt", "w") as text_file:
text_file.write(table.get_string())
global N_U
N_U = N_U0*Uscale*ttor
popt, pstats = papstats.curve_fit(fit, t[sl], N[sl], p0=p0)
# Untergrundfehler
N_U = (N_U0-N_U0.s)*Uscale*ttor
popt_min, pstats_min = papstats.curve_fit(fit, t[sl], N[sl], p0=p0)
N_U = (N_U0+N_U0.s)*Uscale*ttor
popt_max, pstats_max = papstats.curve_fit(fit, t[sl], N[sl], p0=p0)
N_U = N_U0*Uscale*ttor
s_U = unp.nominal_values(((np.abs(popt-popt_min)+np.abs(popt-popt_max))/2.))
s_corrected = np.sqrt(unp.std_devs(popt)**2 + s_U**2)
popt_corrected = unp.uarray(unp.nominal_values(popt),s_corrected)
# Halbwertszeit
Th = popt_corrected[::2]*unc.umath.log(2)
for i in range(len(Th)):
papstats.print_rdiff(Th[i]/60, Th_erw[i]/60)
# Plot
plt.clf()
plt.title('Diagramm '+plotname+': '+title)
plt.xlabel('Messzeit $t \, [s]$')
plt.ylabel('Ereigniszahl $N$')
xspace = np.linspace(0, t[-1])
papstats.plot_data(t, N, label='Messpunkte')
papstats.plot_fit(fit, popt, pstats, xspace, eq=eq, plabels=plabels, punits=punits)
plt.fill_between(xspace, fit(xspace, *unp.nominal_values(popt_min)), fit(xspace, *unp.nominal_values(popt_max)), color='g', alpha=0.2)
Nmin = np.amin(unp.nominal_values(N))
for i in range(len(Th)):
plt.hlines(popt[1::2][i].n/2.+N_U.n, 0, Th[i].n, lw=2, label='Halbwertszeit $'+papstats.pformat(Th[i], label=r'T_{\frac{1}{2}}'+('^'+str(i+1) if len(Th)>1 else ''), unit='s')+'$')
handles, labels = plt.gca().get_legend_handles_labels()
p = plt.Rectangle((0, 0), 1, 1, color='g', alpha=0.2)
handles.append(p)
labels.append('Fit im '+r'$1 \sigma$'+'-Bereich von $N_U$:'+''.join(['\n$'+papstats.pformat(s_U[i], label='\Delta '+plabels[i]+'^{U}', unit=punits[i])+'$' for i in range(len(plabels))]))
plt.legend(handles, labels)
papstats.savefig_a4(plotname+'.png')
def compare_gauss_poisson(t, data, p0, title, filename, xlim, ylim):
N = data[:,0]
n = data[:,1]
n = unp.uarray(n,np.sqrt(n))
sl = (n >= 10) # TODO: Häufigkeit n mindestens 10
# Fit
popt_gauss, pstats_gauss = papstats.curve_fit(fit_gauss, N[sl], n[sl], p0=p0, sigma=unp.std_devs(n[sl]))
popt_poisson, pstats_poisson = papstats.curve_fit(fit_poisson, N[sl], n[sl], p0=[p0[0],p0[2]], sigma=unp.std_devs(n[sl]))
# Plot
for log in [False, True]:
plt.clf()
plt.title('Diagramm '+filename+('.b' if log else '.a')+': '+title + (' (logarithmisch)' if log else ''))
if log:
plt.yscale('log')
papstats.plot_data(N/t, n)
xrange = 4*popt_gauss[1].n
xspace = np.linspace(xlim[2 if log else 0]*t,xlim[3 if log else 1]*t,num=200)
papstats.plot_fit(fit_gauss, popt_gauss, pstats_gauss, xspace, xscale=1./t, eq=r'G(N;\mu,\sigma)', plabels=[r'\mu',r'\sigma','A'])
papstats.plot_fit(fit_poisson, popt_poisson, pstats_poisson, xspace, xscale=1./t, eq=r'P(N;\mu)', plabels=[r'\mu','A'], ls='dashed')
plt.xlim(xspace[0]/t,xspace[-1]/t)
plt.ylim(ylim[2 if log else 0],ylim[3 if log else 1])
plt.xlabel(u'Zählrate '+r'$Z=\frac{N}{t} \, [\frac{Ereignisse}{s}]$')
plt.ylabel(u'Häufigkeit '+r'$n$')
plt.legend(loc=('lower center' if log else 'upper right'))
papstats.savefig_a4(filename+('.b' if log else '.a')+'.png')
# Residuum
plt.clf()
plt.title('Diagramm '+filename+'.c: Residuum')
plt.hist(fit_gauss(unp.nominal_values(N), *unp.nominal_values(popt_gauss))-unp.nominal_values(n), bins=30)
plt.hist(pstats_gauss.residual, bins=30)
plt.hist(pstats_poisson.residual, bins=30)
papstats.savefig_a4(filename+'.c.png')
label='b',
unit='°',
format='.2u')
# Plot
plt.clf()
plt.title(
u'Diagramm 3.1: Bremsspektrum von LiF mit Untergrund und Extrapolation am kurzwelligen Ende'
)
axmain = plt.subplot(111)
plt.xlabel(ur'Bestrahlungswinkel $\beta \, [^\circ]$')
plt.ylabel(ur'Zählrate $n \, [\frac{Ereignisse}{s}]$')
xlim = [b[0], b[-1]]
xspace = np.linspace(*xlim, num=1000)
axmain.set_xlim(*xlim)
papstats.plot_data(b, n, label='Messpunkte')
plt.fill_between(unp.nominal_values(b),
0,
unp.nominal_values(n),
color='g',
alpha=0.2)
from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes
from mpl_toolkits.axes_grid1.inset_locator import mark_inset
zoomxlim = [3, 7]
zoomylim = [0, 200]
zoomxspace = np.linspace(*zoomxlim, num=100)
axzoom = zoomed_inset_axes(axmain, 2.5, loc=1)
axzoom.set_xlim(*zoomxlim)
axzoom.set_ylim(*zoomylim)
print "Grenzwellenlänge:", papstats.pformat(y_G/const.pico, label='y_G', unit='pm', format='.2u')
print "Plancksches Wirkungsquantum:"
papstats.print_rdiff(h_planck(y=y_G, U_B=30*const.kilo), h_erw)
# 2. Ordnung
print "2. Ordung ab:", papstats.pformat(unp.arcsin(y_G/d)/2/const.pi*360, label='b', unit='°', format='.2u')
# Plot
plt.clf()
plt.title(u'Diagramm 3.1: Bremsspektrum von LiF mit Untergrund und Extrapolation am kurzwelligen Ende')
axmain = plt.subplot(111)
plt.xlabel(ur'Bestrahlungswinkel $\beta \, [^\circ]$')
plt.ylabel(ur'Zählrate $n \, [\frac{Ereignisse}{s}]$')
xlim = [b[0], b[-1]]
xspace = np.linspace(*xlim, num=1000)
axmain.set_xlim(*xlim)
papstats.plot_data(b, n, label='Messpunkte')
plt.fill_between(unp.nominal_values(b), 0, unp.nominal_values(n), color='g', alpha=0.2)
from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes
from mpl_toolkits.axes_grid1.inset_locator import mark_inset
zoomxlim = [3, 7]
zoomylim = [0, 200]
zoomxspace = np.linspace(*zoomxlim, num=100)
axzoom = zoomed_inset_axes(axmain, 2.5, loc=1)
axzoom.set_xlim(*zoomxlim)
axzoom.set_ylim(*zoomylim)
mark_inset(axmain, axzoom, loc1=4, loc2=2, fc="none", ec="0.5")
papstats.plot_data(b, n)
plt.fill_between(unp.nominal_values(b), 0, unp.nominal_values(n), color='g', alpha=0.2)
papstats.plot_fit(fit_U, popt_U, xspace=zoomxspace, eq=ur'n=n_U, \, \beta \in ['+str(b[sl_U][0])+','+str(b[sl_U][-1])+ur']^\circ', punits=['s^{-1}'], lw=2)
def compare_gauss_poisson(t, data, p0, title, filename, xlim, ylim):
N = data[:, 0]
n = data[:, 1]
n = unp.uarray(n, np.sqrt(n))
sl = (n >= 10) # TODO: Häufigkeit n mindestens 10
# Fit
popt_gauss, pstats_gauss = papstats.curve_fit(fit_gauss,
N[sl],
n[sl],
p0=p0,
sigma=unp.std_devs(n[sl]))
popt_poisson, pstats_poisson = papstats.curve_fit(fit_poisson,
N[sl],
n[sl],
p0=[p0[0], p0[2]],
sigma=unp.std_devs(
n[sl]))
# Plot
for log in [False, True]:
plt.clf()
plt.title('Diagramm ' + filename + ('.b' if log else '.a') + ': ' +
title + (' (logarithmisch)' if log else ''))
if log:
plt.yscale('log')
papstats.plot_data(N / t, n)
xrange = 4 * popt_gauss[1].n
xspace = np.linspace(xlim[2 if log else 0] * t,
xlim[3 if log else 1] * t,
num=200)
papstats.plot_fit(fit_gauss,
popt_gauss,
pstats_gauss,
xspace,
xscale=1. / t,
eq=r'G(N;\mu,\sigma)',
plabels=[r'\mu', r'\sigma', 'A'])
papstats.plot_fit(fit_poisson,
popt_poisson,
pstats_poisson,
xspace,
xscale=1. / t,
eq=r'P(N;\mu)',
plabels=[r'\mu', 'A'],
ls='dashed')
plt.xlim(xspace[0] / t, xspace[-1] / t)
plt.ylim(ylim[2 if log else 0], ylim[3 if log else 1])
plt.xlabel(u'Zählrate ' + r'$Z=\frac{N}{t} \, [\frac{Ereignisse}{s}]$')
plt.ylabel(u'Häufigkeit ' + r'$n$')
plt.legend(loc=('lower center' if log else 'upper right'))
papstats.savefig_a4(filename + ('.b' if log else '.a') + '.png')
# Residuum
plt.clf()
plt.title('Diagramm ' + filename + '.c: Residuum')
plt.hist(
fit_gauss(unp.nominal_values(N), *unp.nominal_values(popt_gauss)) -
unp.nominal_values(n),
bins=30)
plt.hist(pstats_gauss.residual, bins=30)
plt.hist(pstats_poisson.residual, bins=30)
papstats.savefig_a4(filename + '.c.png')
# Kombiniertes Spektrum
#####
data = np.array(
[np.loadtxt('data/' + e[0] + '.txt', skiprows=1) for e in elements],
dtype=object)
data[:, :, 1] = unp.uarray(data[:, :, 1], data[:, :, 1] / np.sqrt(180))
plt.clf()
plt.title(u'Diagramm 3.1: Röntgenfluoreszenzspektrum verschiedener Elemente')
plt.xlabel('Strahlungsenergie $E \, [keV]$')
plt.ylabel(u'Zählrate ' + r'$n \, [\frac{Ereignisse}{s}]$')
for i in range(data.shape[0]):
p = papstats.plot_data(data[i, :, 0],
data[i, :, 1],
label=elements[i][0] + ' (' + str(elements[i][1]) +
')',
elinewidth=0.5,
capsize=4)
plt.fill_between(data[i, :, 0],
0,
unp.nominal_values(data[i, :, 1]),
color=p[0].get_color(),
alpha=0.1)
#plt.xlim(np.min(data[:,:,0]), np.max(data[:,:,0]))
#plt.ylim(np.min(unp.nominal_values(data[:,:,1])), np.max(unp.nominal_values(data[:,:,1])))
plt.xlim(0, 26)
plt.legend()
papstats.savefig_a4('3.1.png')
#####
# Spektrallinien
def fit_linear_origin(x, m):
return m * x
popt, pstats = papstats.curve_fit(fit_linear_origin, r_sq, v_k)
popt_l, pstats_l = papstats.curve_fit(fit_linear_origin, r_sq, v_kl)
eta = 2. / 9. * const.g / popt_l[0]
print papstats.pformat(eta, label='eta')
v_lam = 2. / 9. * const.g * drho / eta * r_sq
plt.clf()
plt.title(u'Diagramm 3.1: Bestimmung der Viskosität nach Stokes')
papstats.plot_data(r_sq / const.centi**2, v_k, label='Messwerte')
papstats.plot_data(r_sq / const.centi**2,
v_kl,
label='Ladenburgkorrigierte Messwerte',
color='red')
papstats.plot_data(r_sq / const.centi**2,
v_lam / drho,
label='Erwartungswerte',
color='orange')
papstats.plot_fit(fit_linear_origin,
popt,
pstats,
xspace=unp.nominal_values(r_sq),
xscale=1. / const.centi**2,
eq=r'\frac{v}{\rho_K-\rho_F}=m*r^2',
punits=[r'\frac{m^2}{kg*s}'])
converters=dict.fromkeys([1], unc.ufloat_fromstr),
dtype=object,
unpack=True)
f, dt = np.array(f, dtype=float) * const.kilo, dt * const.micro
phi = 360 * dt * f
plt.clf()
plt.title(u'Diagramm 3.1: Phasengang eines RC-Glieds')
plt.xlabel('Wechselstromfrequenz der Eingangsspannung $f \, [kHz]$')
plt.ylabel(ur'Phasenverschiebung der Ausgangsspannung $\Phi \, [^\circ]$')
plt.xscale('log')
xspace = np.logspace(0.2, 1) * const.kilo
yspace = np.linspace(0, 90)
plt.ylim(yspace[0], yspace[-1])
plt.xlim(xspace[0] / const.kilo, xspace[-1] / const.kilo)
papstats.plot_data(f / const.kilo, phi, label='Messpunkte')
extrapolater = ip.UnivariateSpline(unp.nominal_values(f),
unp.nominal_values(phi),
k=3)
plt.plot(xspace / const.kilo,
extrapolater(xspace),
label='Extrapolation',
color='b')
plt.axhline(45, color='black', label='$\Phi = 45^\circ$')
plt.axvline(f_G_theo.n / const.kilo,
label='Theoretische Grenzfrequenz $f_G^{theo}$\nmit Fehlerbereich',
color='g')
plt.fill_betweenx(yspace, (f_G_theo.n - f_G_theo.s) / const.kilo,
(f_G_theo.n + f_G_theo.s) / const.kilo,
color='g',
alpha=0.2)
print u"# 3.2: Dämpfung des Kreisels"
#####
def fit_exp(x, a, A):
return A * np.exp(a * x)
t, w = np.loadtxt('2.2.txt', skiprows=1, unpack=True)
t = t
w = unp.uarray(w, 10)
popt, pstats = papstats.curve_fit(fit_exp, t, w)
plt.clf()
plt.title(u'Diagramm 3.1: Dämpfung des Kreisels')
papstats.plot_data(t, w)
papstats.plot_fit(fit_exp,
popt,
pstats,
xspace=np.linspace(t[0], t[-1], 100),
eq=r'w_0*e^{\lambda * t}',
plabels=[r'\lambda', '\omega_0'],
punits=[ur'\frac{1}{min}', ur'\frac{2π}{min}'])
plt.xlabel('Zeit $t \, [min]$')
plt.ylabel(ur'Drehfrequenz $\omega_F \, [\frac{2π}{min}]$')
plt.yscale('log')
plt.legend()
papstats.savefig_a4('3.1.png')
tau = -1. / popt[0] * const.minute
t_H = np.log(2) * tau
def fit_dm(x, d):
global m_0_i
return d * x + m_0_i
plt.clf()
plt.suptitle(u'Diagramm 3.1: Vorbeigezogene Interferenzmaxima über Druck in der Küvette')
xspace = np.linspace(- const.atm / const.torr, 0)
ax = None
d_list = []
for i in range(len(p)):
m_0_i = m_0[i]
popt, pstats = papstats.curve_fit(fit_dm, p[i], dm)
ax = plt.subplot(len(p), 1, i + 1, sharex=ax, sharey=ax)
plt.title('Messung '+str(i+1))
papstats.plot_data(p[i], dm, label='Messwerte')
papstats.plot_fit(fit_dm, popt, xspace=xspace, eq='\Delta m=p*d+\Delta m_0', punits=['Torr^{-1}'])
if i != len(p) - 1:
plt.setp(ax.get_xticklabels(), visible=False)
else:
plt.xlabel(u'Druck $p \, [Torr]$')
plt.ylabel(u'$\Delta m$')
plt.xlim(xspace[0], xspace[-1])
plt.ylim(0, 50)
plt.legend(loc='upper left')
d_list.append(popt[0])
papstats.savefig_a4('3.1.png')
print d_list
d = np.mean(d_list)
print papstats.pformat(d, label='d', unit='Torr^(-1)', format='c')
w = unp.uarray(data[:,0], data[:,1])*2*const.pi
Uind = unp.uarray(data[:,2], data[:,3])/2
popt, pstats = papstats.curve_fit(fit_Uind, w, Uind)
# Berechnung der Magnetfeldstärke
B = popt[0]/nF/AF
papstats.print_rdiff(B, B_helmh(I))
Uind_true = nF*B_helmh(I)*AF*w
plt.clf()
plt.title(u'Diagramm 3.1: Induktionsspannung in Abhängigkeit von der Rotationsfrequenz der Flachspule')
plt.xlabel('Kreisfrequenz $\omega \, [Hz]$')
plt.ylabel('Max. Induktionsspannung $U_{ind} \, [V]$')
papstats.plot_data(w, Uind, label='Messpunkte')
papstats.plot_fit(fit_Uind, popt, pstats, np.linspace(w[0].n, w[-1].n), eq='U_{ind}=c*\omega', punits=[r'T \times m^2'])
papstats.plot_data(w, Uind_true, label='Erwartungswerte '+r'$U_{ind}=\frac{8*\mu_0*n_H*I}{\sqrt{125}*R}*n_F*A_F*\omega$')
plt.legend(loc='lower right')
papstats.savefig_a4('3.1.png')
# Vergleich mit Erwartungswerten
V = Uind/Uind_true
sigma_upper = unp.nominal_values(V+unp.std_devs(V)*3)
sigma_lower = unp.nominal_values(V-unp.std_devs(V)*3)
plt.clf()
plt.title(u'Diagramm 3.1.b: Verhältnis aus gemessener und erwarteter Induktionsspannung mit $3 \sigma$-Bereich')
plt.xlabel('Kreisfrequenz $\omega \, [Hz]$')
np.savetxt('data/'+filenames[i]+'.txt', data[:,2*i:2*i+2], delimiter='\t', header='E [eV]\tn [1/s]')
#####
# Kombiniertes Spektrum
#####
data = np.array([np.loadtxt('data/'+e[0]+'.txt', skiprows=1) for e in elements], dtype=object)
data[:,:,1] = unp.uarray(data[:,:,1], data[:,:,1]/np.sqrt(180))
plt.clf()
plt.title(u'Diagramm 3.1: Röntgenfluoreszenzspektrum verschiedener Elemente')
plt.xlabel('Strahlungsenergie $E \, [keV]$')
plt.ylabel(u'Zählrate '+r'$n \, [\frac{Ereignisse}{s}]$')
for i in range(data.shape[0]):
p = papstats.plot_data(data[i,:,0], data[i,:,1], label=elements[i][0]+' ('+str(elements[i][1])+')', elinewidth=0.5, capsize=4)
plt.fill_between(data[i,:,0], 0, unp.nominal_values(data[i,:,1]), color=p[0].get_color(), alpha=0.1)
#plt.xlim(np.min(data[:,:,0]), np.max(data[:,:,0]))
#plt.ylim(np.min(unp.nominal_values(data[:,:,1])), np.max(unp.nominal_values(data[:,:,1])))
plt.xlim(0, 26)
plt.legend()
papstats.savefig_a4('3.1.png')
#####
# Spektrallinien
#####
Z = np.array([e[1] for e in elements])
converters = dict.fromkeys(range(1, 4), unc.ufloat_fromstr)
# Berechnung der Maximalenergie
RbES = 0.13*const.gram/const.centi**2
rAl = 2.7*const.gram/const.centi**3
Rb = RbES + xM * rAl
print "Flächendichte:", papstats.pformat(Rb/(const.gram/const.centi**2), label='R^b', unit='g/cm^2', format='.2u')
print "Maximalenergie:"
EM = unc.ufloat(2.25,0.1) # Aus Diagramm in Versuchsanleitung abgelesen
papstats.print_rdiff(EM,unc.ufloat(2.274,0))
# Plot
plt.clf()
plt.title(u'Diagramm 3.1: '+r'$\beta$'+u'-Strahlung in Abhängigkeit der Absorberdicke mit Extrapolation')
plt.yscale('log', nonposy='clip')
plt.xlabel('Absorberdicke $x \, [mm]$')
plt.ylabel(u'korrigierte Zählrate '+r'$(n-n_U^{\beta}) \, [\frac{Ereignisse}{s}]$')
papstats.plot_data(x/const.milli, n, label='Messpunkte')
sl_upper = 10
sl = (n > 0) & (n <= sl_upper)
k = 5
xspace = np.linspace(x[sl][0].n, 0.004, num=1000)
extrapolater = ip.UnivariateSpline(unp.nominal_values(x[sl]), np.log(unp.nominal_values(n[sl])), k=k)
plt.plot(xspace/const.milli, np.exp(extrapolater(xspace)), color='r', label='Extrapolation mit Polynom der Ordnung $k='+str(k)+'$ mit $n \in (0,'+str(sl_upper)+']$')
plt.fill_betweenx(np.linspace(1e-3,1e2), x1/const.milli, x2/const.milli, color='g', alpha=0.2)
plt.xlim(0, xspace[-1]/const.milli)
plt.ylim(1e-3,1e2)
handles, labels = plt.gca().get_legend_handles_labels()
p = plt.Rectangle((0, 0), 1, 1, color='g', alpha=0.2)
handles.append(p)
labels.append(u'Abschätzung der Maximalreichweite:\n$'+papstats.pformat(xM/const.milli, label='x_M', unit='mm')+'$')
plt.legend(handles, labels, loc='lower left')
papstats.savefig_a4('3.1.png')
def approximate_I(n):
x = n * const.pi + 1e-6
return np.sin(x)**2 / x**2
# Fit Minima
popt, pstats = papstats.curve_fit(fit_linear, n[1::2], x[1::2])
# Plot Abstand
plt.clf()
plt.title(
u'Diagramm 3.1: Abstand der Interferenzmaxima und -minima vom Hauptmaximum'
)
papstats.plot_data(n[1::2], x[1::2], c='b', label='Minima')
papstats.plot_data(n[0::2], x[0::2], c='r', label='Maxima')
papstats.plot_fit(fit_linear, popt, xspace=n, eq='x_{Min}=m*n', punits=['px'])
plt.legend(loc='upper left')
plt.xlabel('Ordnung $n$')
plt.ylabel('Abstand vom Hauptmaximum $x \, [px]$')
papstats.savefig_a4('3.1.png')
# Spaltweite
d = 80 * const.milli * 635 * const.nano / (popt[0] * px) # TODO: use px_erw?
print papstats.pformat(d / const.micro, label='Spaltweite d', unit='um')
# Maxima nach Fit
n_maxima_fit = x[0::2] / popt[0]
diff = np.abs(n[0::2] - n_maxima_fit)
print papstats.table(labels=['n_erw', 'n', u'|n-n_erw|', u'σ-Bereich'],
popt, pstats = papstats.curve_fit(fit_Uind, w, Uind)
# Berechnung der Magnetfeldstärke
B = popt[0] / nF / AF
papstats.print_rdiff(B, B_helmh(I))
Uind_true = nF * B_helmh(I) * AF * w
plt.clf()
plt.title(
u'Diagramm 3.1: Induktionsspannung in Abhängigkeit von der Rotationsfrequenz der Flachspule'
)
plt.xlabel('Kreisfrequenz $\omega \, [Hz]$')
plt.ylabel('Max. Induktionsspannung $U_{ind} \, [V]$')
papstats.plot_data(w, Uind, label='Messpunkte')
papstats.plot_fit(fit_Uind,
popt,
pstats,
np.linspace(w[0].n, w[-1].n),
eq='U_{ind}=c*\omega',
punits=[r'T \times m^2'])
papstats.plot_data(
w,
Uind_true,
label='Erwartungswerte ' +
r'$U_{ind}=\frac{8*\mu_0*n_H*I}{\sqrt{125}*R}*n_F*A_F*\omega$')
plt.legend(loc='lower right')
papstats.savefig_a4('3.1.png')
# Vergleich mit Erwartungswerten
#####
print u"# 3.2: Dämpfung des Kreisels"
#####
def fit_exp(x, a, A):
return A * np.exp(a * x)
t, w = np.loadtxt('2.2.txt', skiprows=1, unpack=True)
t = t
w = unp.uarray(w, 10)
popt, pstats = papstats.curve_fit(fit_exp, t, w)
plt.clf()
plt.title(u'Diagramm 3.1: Dämpfung des Kreisels')
papstats.plot_data(t, w)
papstats.plot_fit(fit_exp, popt, pstats, xspace=np.linspace(t[0], t[-1], 100), eq=r'w_0*e^{\lambda * t}', plabels=[r'\lambda', '\omega_0'], punits=[ur'\frac{1}{min}', ur'\frac{2π}{min}'])
plt.xlabel('Zeit $t \, [min]$')
plt.ylabel(ur'Drehfrequenz $\omega_F \, [\frac{2π}{min}]$')
plt.yscale('log')
plt.legend()
papstats.savefig_a4('3.1.png')
tau = -1. / popt[0] * const.minute
t_H = np.log(2) * tau
print papstats.pformat(tau / const.minute, label=u'Dämpfungskonstante tau', unit='min')
print papstats.pformat(t_H / const.minute, label=u'Halbwertszeit t_H', unit='min')
#####
print u"# 3.3: Präzession"
def analyze_spektrallinien(fileprefix, figindex, crstl, sl, d=None, y=None):
data = np.append(np.loadtxt(fileprefix + '.b.1.txt', skiprows=1),
np.loadtxt(fileprefix + '.b.2.txt', skiprows=1),
axis=0)
b, n = data[:, 0], data[:, 1]
n = unp.uarray(n, np.sqrt(n * 20) / 20)
sl = [[(b >= bounds[0]) & (b <= bounds[1]) for bounds in sl_row]
for sl_row in sl]
def fit_gauss(x, m, s, A, n_0):
return A / np.sqrt(2 * const.pi) / s * np.exp(-((x - m)**2) / 2 /
(s**2)) + n_0
r = []
plt.clf()
papstats.plot_data(b, n)
papstats.savefig_a4('3.' + str(figindex) + '.a.png')
plt.clf()
plt.suptitle('Diagramm 3.' + str(figindex) +
u': Spektrallinien von Molybdän bei Vermessung mit einem ' +
crstl + '-Kristall')
for i in range(2):
r.append([])
# Linie
for k in range(2):
# Ordnung
b_k = b[sl[i][k]]
n_k = n[sl[i][k]]
xspace = np.linspace(b_k[0], b_k[-1], num=1000)
plt.subplot(2, 2, i * 2 + k + 1)
plt.xlim(xspace[0], xspace[-1])
if i == 1:
plt.xlabel(u'Bestrahlungswinkel ' + r'$\beta \, [^\circ]$')
if k == 0:
plt.ylabel(u'Zählrate ' + r'$n \, [\frac{Ereignisse}{s}]$')
plt.title('$K_{' + (r'\alpha' if i == 0 else r'\beta') + '}$ (' +
str(k + 1) + '. Ordnung)')
papstats.plot_data(b_k, n_k)
# Gauss-Fit
popt, pstats = papstats.curve_fit(fit_gauss,
b_k,
n_k,
p0=[
b_k[0] +
(b_k[-1] - b_k[0]) / 2,
(b_k[-1] - b_k[0]) / 4,
np.sum(n_k).n, n_k[0].n
])
plt.fill_between(b_k,
0,
unp.nominal_values(n_k),
color='g',
alpha=0.2)
FWHM = popt[1] * 2 * unp.sqrt(2 * unp.log(2))
plt.hlines(popt[3].n +
(fit_gauss(xspace, *unp.nominal_values(popt)).max() -
popt[3].n) / 2,
popt[0].n - FWHM.n / 2,
popt[0].n + FWHM.n / 2,
color='black',
lw=2,
label='$' +
papstats.pformat(FWHM, label='FWHM', unit=r'^\circ') +
'$')
papstats.plot_fit(fit_gauss,
popt,
xspace=xspace,
plabels=[r'\mu', r'\sigma', 'A', 'n_0'],
punits=['^\circ', '^\circ', 's^{-1}', 's^{-1}'])
plt.ylim(
unp.nominal_values(n_k).min() -
n_k[unp.nominal_values(n_k).argmin()].s,
unp.nominal_values(n_k).max() +
(unp.nominal_values(n_k).max() -
unp.nominal_values(n_k).min()))
plt.legend(loc='upper center', prop={'size': 10})
b_S = unc.ufloat(popt[0].n, np.abs(popt[1].n))
print "Winkel:", papstats.pformat(b_S, unit='°', format='.2u')
if y is None:
r[i].append(y_bragg(b_S, n=k + 1))
print "Wellenlänge der Linie:", papstats.pformat(r[i][k] /
const.pico,
label='y',
unit='pm',
format='.2u')
if d is None:
r[i].append(
(k + 1) * y[i][k] / unc.umath.sin(b_S * const.degree))
print "Gitterkonstante:", papstats.pformat(r[i][k] /
const.pico,
label='a',
unit='pm',
format='.2u')
papstats.savefig_a4('3.' + str(figindex) + '.png')
return r
v_kl = v_k * y
r_sq = r**2
def fit_linear_origin(x, m):
return m * x
popt, pstats = papstats.curve_fit(fit_linear_origin, r_sq, v_k)
popt_l, pstats_l = papstats.curve_fit(fit_linear_origin, r_sq, v_kl)
eta = 2. / 9. * const.g / popt_l[0]
print papstats.pformat(eta, label='eta')
v_lam = 2. / 9. * const.g * drho / eta * r_sq
plt.clf()
plt.title(u'Diagramm 3.1: Bestimmung der Viskosität nach Stokes')
papstats.plot_data(r_sq / const.centi**2, v_k, label='Messwerte')
papstats.plot_data(r_sq / const.centi**2, v_kl, label='Ladenburgkorrigierte Messwerte', color='red')
papstats.plot_data(r_sq / const.centi**2, v_lam / drho, label='Erwartungswerte', color='orange')
papstats.plot_fit(fit_linear_origin, popt, pstats, xspace=unp.nominal_values(r_sq), xscale=1./const.centi**2, eq=r'\frac{v}{\rho_K-\rho_F}=m*r^2', punits=[r'\frac{m^2}{kg*s}'])
papstats.plot_fit(fit_linear_origin, popt_l, pstats_l, xspace=unp.nominal_values(r_sq), xscale=1./const.centi**2, eq=r'\frac{v}{\rho_K-\rho_F}=m*r^2', punits=[r'\frac{m^2}{kg*s}'])
plt.xlabel('$r^2 \, [cm^2]$ mit $r$: Kugelradius')
plt.ylabel(r'$\frac{v}{\rho_K-\rho_F}$ mit $v$: mittlere Sinkgeschwindigkeit')
plt.legend(loc='upper left')
papstats.savefig_a4('1.png')
V = v / v_lam
Re = rho_F * v * 2. * r / eta
plt.clf()
plt.title(u'Diagramm 3.2: Abschätzung der kritischen Reynoldszahl')
plt.xscale('log')
label='R^b',
unit='g/cm^2',
format='.2u')
print "Maximalenergie:"
EM = unc.ufloat(2.25, 0.1) # Aus Diagramm in Versuchsanleitung abgelesen
papstats.print_rdiff(EM, unc.ufloat(2.274, 0))
# Plot
plt.clf()
plt.title(u'Diagramm 3.1: ' + r'$\beta$' +
u'-Strahlung in Abhängigkeit der Absorberdicke mit Extrapolation')
plt.yscale('log', nonposy='clip')
plt.xlabel('Absorberdicke $x \, [mm]$')
plt.ylabel(u'korrigierte Zählrate ' +
r'$(n-n_U^{\beta}) \, [\frac{Ereignisse}{s}]$')
papstats.plot_data(x / const.milli, n, label='Messpunkte')
sl_upper = 10
sl = (n > 0) & (n <= sl_upper)
k = 5
xspace = np.linspace(x[sl][0].n, 0.004, num=1000)
extrapolater = ip.UnivariateSpline(unp.nominal_values(x[sl]),
np.log(unp.nominal_values(n[sl])),
k=k)
plt.plot(xspace / const.milli,
np.exp(extrapolater(xspace)),
color='r',
label='Extrapolation mit Polynom der Ordnung $k=' + str(k) +
'$ mit $n \in (0,' + str(sl_upper) + ']$')
plt.fill_betweenx(np.linspace(1e-3, 1e2),
x1 / const.milli,
x2 / const.milli,
# Phasengang
f, dt = np.loadtxt('3.txt', skiprows=1, converters=dict.fromkeys([1], unc.ufloat_fromstr), dtype=object, unpack=True)
f, dt = np.array(f, dtype=float)*const.kilo, dt*const.micro
phi = 360*dt*f
plt.clf()
plt.title(u'Diagramm 3.1: Phasengang eines RC-Glieds')
plt.xlabel('Wechselstromfrequenz der Eingangsspannung $f \, [kHz]$')
plt.ylabel(ur'Phasenverschiebung der Ausgangsspannung $\Phi \, [^\circ]$')
plt.xscale('log')
xspace = np.logspace(0.2,1)*const.kilo
yspace = np.linspace(0,90)
plt.ylim(yspace[0], yspace[-1])
plt.xlim(xspace[0]/const.kilo, xspace[-1]/const.kilo)
papstats.plot_data(f/const.kilo, phi, label='Messpunkte')
extrapolater = ip.UnivariateSpline(unp.nominal_values(f), unp.nominal_values(phi), k=3)
plt.plot(xspace/const.kilo, extrapolater(xspace), label='Extrapolation', color='b')
plt.axhline(45, color='black', label='$\Phi = 45^\circ$')
plt.axvline(f_G_theo.n/const.kilo, label='Theoretische Grenzfrequenz $f_G^{theo}$\nmit Fehlerbereich', color='g')
plt.fill_betweenx(yspace, (f_G_theo.n-f_G_theo.s)/const.kilo, (f_G_theo.n+f_G_theo.s)/const.kilo, color='g', alpha=0.2)
f_G_phas = unc.ufloat(3.09, 0.2)*const.kilo
plt.axvline(f_G_phas.n/const.kilo, color='r', label='Grenzfrequenz $'+papstats.pformat(f_G_phas/const.kilo, unit='kHz', label='f_G^{phas}')+'$\nnach Extrapolation mit Fehlerbereich')
plt.fill_betweenx(yspace, (f_G_phas.n-f_G_phas.s)/const.kilo, (f_G_phas.n+f_G_phas.s)/const.kilo, color='r', alpha=0.2)
plt.legend()
papstats.savefig_a4('3.1.png')
#####
print "# 4: Frequenzgang eines Serienschwingkreises"
#####
[31140, 30857, 30474], [29626, 29808, 30999]]) * 1e-4
W_pV = unp.uarray(np.mean(W_pV, axis=1), np.std(W_pV, axis=1))
f = np.array([[304.5, 303.1, 303.4], [271.4, 270.3, 269.9],
[233.3, 238.4, 230.5], [170.2, 185.5, 183.3]]) / const.minute
f = unp.uarray(np.mean(f, axis=1),
np.sqrt(np.std(f, axis=1)**2 + (2 / const.minute)**2))
Q_el = unc.ufloat(13.21, 0.01) * unc.ufloat(2.9, 0.01) * 5 / f
eta_th = W_pV / Q_el
W_D = 2 * const.pi * 0.25 * F
eta_eff = W_D / Q_el
print papstats.table(
labels=['F', 'W_pV', 'f_M', 'Q_el', 'eta_th', 'W_D', 'eta_eff'],
units=['N', 'J', 'Hz', 'J', '%', 'J', '%'],
columns=[F, W_pV, f, Q_el, eta_th * 100, W_D, eta_eff * 100])
# plot
plt.clf()
plt.suptitle(
u'Diagramm 3.1: Der Heißluftmoter als Kältemaschine - Thermischer und effektiver Wirkungsgrad über der Motordrehzahl'
)
ax1 = plt.subplot(211)
papstats.plot_data(f, eta_th * 100)
plt.setp(ax1.get_xticklabels(), visible=False)
plt.ylabel(u'Thermischer Wirkungsgrad $\eta_{th} \, [\%]$')
ax2 = plt.subplot(212, sharex=ax1)
papstats.plot_data(f, eta_eff * 100)
plt.ylabel(u'Effektiver Wirkungsgrad $\eta_{eff} \, [\%]$')
plt.xlabel(u'Motordrehzahl $f \, [Hz]$')
papstats.savefig_a4('3.1.png')
print papstats.pformat(Q_V, format='c', unit='J', label=u'Motorverluste Q_V')
# Drehmomentmessung
F = unp.uarray([0.2, 0.4, 0.6, 0.8], 0.02)
W_pV = np.array([[28832, 28393, 28432], [29848, 29640, 29525], [31140, 30857, 30474], [29626, 29808, 30999]]) * 1e-4
W_pV = unp.uarray(np.mean(W_pV, axis=1), np.std(W_pV, axis=1))
f = np.array([[304.5, 303.1, 303.4], [271.4, 270.3, 269.9], [233.3, 238.4, 230.5], [170.2, 185.5, 183.3]]) / const.minute
f = unp.uarray(np.mean(f, axis=1), np.sqrt(np.std(f, axis=1)**2 + (2 / const.minute)**2))
Q_el = unc.ufloat(13.21, 0.01) * unc.ufloat(2.9, 0.01) * 5 / f
eta_th = W_pV / Q_el
W_D = 2 * const.pi * 0.25 * F
eta_eff = W_D / Q_el
print papstats.table(labels=['F', 'W_pV', 'f_M', 'Q_el', 'eta_th', 'W_D', 'eta_eff'], units=['N', 'J', 'Hz', 'J', '%', 'J', '%'], columns=[F, W_pV, f, Q_el, eta_th*100, W_D, eta_eff*100])
# plot
plt.clf()
plt.suptitle(u'Diagramm 3.1: Der Heißluftmoter als Kältemaschine - Thermischer und effektiver Wirkungsgrad über der Motordrehzahl')
ax1 = plt.subplot(211)
papstats.plot_data(f, eta_th * 100)
plt.setp(ax1.get_xticklabels(), visible=False)
plt.ylabel(u'Thermischer Wirkungsgrad $\eta_{th} \, [\%]$')
ax2 = plt.subplot(212, sharex=ax1)
papstats.plot_data(f, eta_eff * 100)
plt.ylabel(u'Effektiver Wirkungsgrad $\eta_{eff} \, [\%]$')
plt.xlabel(u'Motordrehzahl $f \, [Hz]$')
papstats.savefig_a4('3.1.png')
def compute_hwz(N_list,
ttor,
fit,
plotname,
title,
sl=slice(None, None),
Uscale=1,
p0=None,
eq=None,
plabels=None,
punits=None,
Th_erw=None):
N = np.sum(unp.uarray(N_list, np.sqrt(N_list)), axis=0)
t = np.arange(len(N)) * ttor + ttor / 2.
table = pt.PrettyTable()
table.add_column('t [s]', t.astype(int), align='r')
if len(N_list) > 1:
for i in range(len(N_list)):
table.add_column('N' + str(i + 1),
N_list[i].astype(int),
align='r')
table.add_column('Summe', N, align='r')
else:
table.add_column('N', N, align='r')
with open("Resources/table_" + plotname + ".txt", "w") as text_file:
text_file.write(table.get_string())
global N_U
N_U = N_U0 * Uscale * ttor
popt, pstats = papstats.curve_fit(fit, t[sl], N[sl], p0=p0)
# Untergrundfehler
N_U = (N_U0 - N_U0.s) * Uscale * ttor
popt_min, pstats_min = papstats.curve_fit(fit, t[sl], N[sl], p0=p0)
N_U = (N_U0 + N_U0.s) * Uscale * ttor
popt_max, pstats_max = papstats.curve_fit(fit, t[sl], N[sl], p0=p0)
N_U = N_U0 * Uscale * ttor
s_U = unp.nominal_values(
((np.abs(popt - popt_min) + np.abs(popt - popt_max)) / 2.))
s_corrected = np.sqrt(unp.std_devs(popt)**2 + s_U**2)
popt_corrected = unp.uarray(unp.nominal_values(popt), s_corrected)
# Halbwertszeit
Th = popt_corrected[::2] * unc.umath.log(2)
for i in range(len(Th)):
papstats.print_rdiff(Th[i] / 60, Th_erw[i] / 60)
# Plot
plt.clf()
plt.title('Diagramm ' + plotname + ': ' + title)
plt.xlabel('Messzeit $t \, [s]$')
plt.ylabel('Ereigniszahl $N$')
xspace = np.linspace(0, t[-1])
papstats.plot_data(t, N, label='Messpunkte')
papstats.plot_fit(fit,
popt,
pstats,
xspace,
eq=eq,
plabels=plabels,
punits=punits)
plt.fill_between(xspace,
fit(xspace, *unp.nominal_values(popt_min)),
fit(xspace, *unp.nominal_values(popt_max)),
color='g',
alpha=0.2)
Nmin = np.amin(unp.nominal_values(N))
for i in range(len(Th)):
plt.hlines(popt[1::2][i].n / 2. + N_U.n,
0,
Th[i].n,
lw=2,
label='Halbwertszeit $' +
papstats.pformat(Th[i],
label=r'T_{\frac{1}{2}}' +
('^' + str(i + 1) if len(Th) > 1 else ''),
unit='s') + '$')
handles, labels = plt.gca().get_legend_handles_labels()
p = plt.Rectangle((0, 0), 1, 1, color='g', alpha=0.2)
handles.append(p)
labels.append('Fit im ' + r'$1 \sigma$' + '-Bereich von $N_U$:' + ''.join([
'\n$' + papstats.pformat(
s_U[i], label='\Delta ' + plabels[i] + '^{U}', unit=punits[i]) +
'$' for i in range(len(plabels))
]))
plt.legend(handles, labels)
papstats.savefig_a4(plotname + '.png')
U = unp.uarray(data[:,0], 10)
N = data[:,1]
N = unp.uarray(N, np.sqrt(N))/30
def fit_platlin(x, c, N_0):
return c*x+N_0
def fit_platconst(x, N_0):
return np.zeros(len(x))+N_0
popt_const, pstats_const = papstats.curve_fit(fit_platconst, U[1:], N[1:], p0=[60])
popt_lin, pstats_lin = papstats.curve_fit(fit_platlin, U[1:], N[1:])
popt_lin2, pstats_lin2 = papstats.curve_fit(fit_platlin, U[8:], N[8:])
plt.clf()
plt.title(u'Diagramm 3.1: Vermessung des Plateaubereichs der Zählrohrkennlinie')
papstats.plot_data(U, N)
papstats.plot_fit(fit_platconst, popt_const, pstats_const, np.linspace(U[1].n, U[-1].n), eq='N=N_0', ls='dashed', lw=2)
papstats.plot_fit(fit_platlin, popt_lin, pstats_lin, np.linspace(U[1].n, U[-1].n), eq='N=c*U_Z+N_0', ls='dotted', lw=2)
papstats.plot_fit(fit_platlin, popt_lin2, pstats_lin2, np.linspace(U[8].n, U[-1].n), eq='N=c*U_Z+N_0, \, U_Z \in [600,700]V', lw=2)
plt.xlabel(u'Zählrohrspannung '+r'$U_Z \, [V]$')
plt.ylabel(u'Zählrate '+r'$\frac{N}{t} \, [\frac{Ereignisse}{s}]$')
plt.xlim(430,720)
plt.ylim(10,65)
plt.legend(loc='lower right')
papstats.savefig_a4('3.1.png')
#####
print('\n# 2 (Untersuchung des Plateauanstiegs)')
#####
data = np.loadtxt('3.txt', skiprows=1)
def fit_linear(x, m):
return m * x
def approximate_I(n):
x = n*const.pi + 1e-6
return np.sin(x)**2/x**2
# Fit Minima
popt, pstats = papstats.curve_fit(fit_linear, n[1::2], x[1::2])
# Plot Abstand
plt.clf()
plt.title(u'Diagramm 3.1: Abstand der Interferenzmaxima und -minima vom Hauptmaximum')
papstats.plot_data(n[1::2], x[1::2], c='b', label='Minima')
papstats.plot_data(n[0::2], x[0::2], c='r', label='Maxima')
papstats.plot_fit(fit_linear, popt, xspace=n, eq='x_{Min}=m*n', punits=['px'])
plt.legend(loc='upper left')
plt.xlabel('Ordnung $n$')
plt.ylabel('Abstand vom Hauptmaximum $x \, [px]$')
papstats.savefig_a4('3.1.png')
# Spaltweite
d = 80 * const.milli * 635 * const.nano / (popt[0] * px) # TODO: use px_erw?
print papstats.pformat(d / const.micro, label='Spaltweite d', unit='um')
# Maxima nach Fit
n_maxima_fit = x[0::2] / popt[0]
diff = np.abs(n[0::2]-n_maxima_fit)
print papstats.table(labels=['n_erw', 'n', u'|n-n_erw|', u'σ-Bereich'], columns=[n[0::2], n_maxima_fit, diff, unp.nominal_values(diff)/unp.std_devs(diff)])
I = unp.uarray(data[:, 0], data[:, 1])
U_ss = unp.uarray(data[:, 2], data[:, 3])
U_ind = U_ss / 2.
U_ind_exp = B_H(I) * A_F * n_F * omega
def U_ind_max(I, c):
return I * c
popt, pstats = papstats.curve_fit(U_ind_max, I, U_ind)
plt.xlabel('Spulenstrom $I$ in $A$')
papstats.plot_data(I, U_ind, label="Messpunkte")
papstats.plot_fit(U_ind_max, popt, pstats, unp.nominal_values(I), eq=u"Û_{ind} = c * I")
papstats.plot_data(I, U_ind_exp, label='Erwartungswerte')
plt.legend(borderpad=1)
papstats.savefig_a4('2.b.png')
print "Induktionspannung bei periodischem Feldstrom"
Omega = unc.ufloat(104, 1) * 2 * c.pi # Kreisfrequenz der Wechselspannung
data = np.loadtxt('3.a.txt', skiprows=1)
a = unp.uarray(data[:, 0], 2) / 360. * 2 * c.pi
U_ind = unp.uarray(data[:, 1], data[:, 2]) / 2
def fit_platconst(x, N_0):
return np.zeros(len(x)) + N_0
popt_const, pstats_const = papstats.curve_fit(fit_platconst,
U[1:],
N[1:],
p0=[60])
popt_lin, pstats_lin = papstats.curve_fit(fit_platlin, U[1:], N[1:])
popt_lin2, pstats_lin2 = papstats.curve_fit(fit_platlin, U[8:], N[8:])
plt.clf()
plt.title(
u'Diagramm 3.1: Vermessung des Plateaubereichs der Zählrohrkennlinie')
papstats.plot_data(U, N)
papstats.plot_fit(fit_platconst,
popt_const,
pstats_const,
np.linspace(U[1].n, U[-1].n),
eq='N=N_0',
ls='dashed',
lw=2)
papstats.plot_fit(fit_platlin,
popt_lin,
pstats_lin,
np.linspace(U[1].n, U[-1].n),
eq='N=c*U_Z+N_0',
ls='dotted',
lw=2)
papstats.plot_fit(fit_platlin,
