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 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 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 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')
d = d_LiF
#####
print u"\n# a: Grenzwellenlänge und Plancksche Konstante aus LiF Spektrum"
#####
b, n = np.loadtxt('1.a.txt', skiprows=1, unpack=True)
n = unp.uarray(n, np.sqrt(n*5)/5)
# Untergrund
def fit_U(b, n_U):
return b-b+n_U
sl_U = slice(0, 13)
popt_U, pstats_U = papstats.curve_fit(fit_U, b[sl_U], n[sl_U])
n_U = popt_U[0]
print "Untergrund:", papstats.pformat(n_U, format='.2u')
# Bremsspektrum-Fit mit Kramerscher Regel
def kramer(y, ymin, K):
y = unp.nominal_values(y)
return K*(y/ymin-1)/y**2
def fit_brems(b, ymin, K):
return kramer(y=y_bragg(b), ymin=ymin, K=K)
sl_brems = ( (n <= 200) & ( (b <= 17) | (n <= 45) ) ) & (n > 20)
popt_brems, pstats_brems = papstats.curve_fit(fit_brems, b[sl_brems], n[sl_brems], p0=[4.133e-11, 1e-18])
# Extrapolation
def fit_lin(b, a, n_0):
return a*b + n_0
n[i] = n[i] + 0.5
return n
n = nspace_centered_offset(I)
print papstats.table(labels=['n', 'x', 'I'], units=[None, 'px', None], columns=[n, x, I])
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')
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)
t = np.reshape(t, (len(r), 5))
t = unp.uarray(np.mean(t, axis=1), np.std(t, axis=1) / np.sqrt(len(t)))
v = s / t
v_k = v / drho
y = (1 + 2.1 * r / 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,
dm = np.array([0, 10, 20, 30, 40])
m_0 = np.array([48, 49, 49])
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')
parentdir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
os.sys.path.insert(0,parentdir)
import papstats
#####
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')
# Fit Uind = n*B*A*w
def fit_Uind(x, c):
return c*x
# a) Abhängigkeit von der Frequenz
I = unc.ufloat(4, 0.05)
data = np.loadtxt('2.a.txt', skiprows=1)
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')
#####
print "\n# 3 Absorption von y-Strahlung in Blei"
#####
data = np.loadtxt('2.txt', skiprows=1)
x = data[:,0]*const.milli
N = data[:,1]
n = unp.uarray(N, np.sqrt(N))/60
n = n-nU
def fit_damp(x, mu, n_0):
return n_0*np.exp(-mu*x)
popt, pstats = papstats.curve_fit(fit_damp, x, n)
rhoPb = 11.34*const.gram/const.centi**3
k = popt[0]/rhoPb
print "Materialunabhängiger Schwächungskoeffizient:", papstats.pformat(k/(const.centi**2/const.gram), label='k', unit='cm^2/g', format='.2u')
Ey = unc.ufloat(1.45, 0.15)
print "Energie der y-Quanten"
papstats.print_rdiff(Ey,unc.ufloat((1.173+1.333)/2,0))
plt.clf()
plt.title('Diagramm 3.2: '+r'$\gamma$'+u'-Strahlung in Abhängigkeit der Absorberdicke')
plt.yscale('log')
plt.xlabel('Absorberdicke $x \, [mm]$')
plt.ylabel(u'korrigierte Zählrate '+r'$(n-n_U) \, [\frac{Ereignisse}{s}]$')
ylim = [1.5,1e2]
xlim = np.array([0,55])*const.milli
print papstats.table(labels=['n', 'x', 'I'],
units=[None, 'px', None],
columns=[n, x, I])
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
def fit_Uind(x, c):
return c * x
# a) Abhängigkeit von der Frequenz
I = unc.ufloat(4, 0.05)
data = np.loadtxt('2.a.txt', skiprows=1)
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,
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')
os.sys.path.insert(0, parentdir)
import papstats
#####
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()
#####
print u"\n# a: Grenzwellenlänge und Plancksche Konstante aus LiF Spektrum"
#####
b, n = np.loadtxt('1.a.txt', skiprows=1, unpack=True)
n = unp.uarray(n, np.sqrt(n * 5) / 5)
# Untergrund
def fit_U(b, n_U):
return b - b + n_U
sl_U = slice(0, 13)
popt_U, pstats_U = papstats.curve_fit(fit_U, b[sl_U], n[sl_U])
n_U = popt_U[0]
print "Untergrund:", papstats.pformat(n_U, format='.2u')
# Bremsspektrum-Fit mit Kramerscher Regel
def kramer(y, ymin, K):
y = unp.nominal_values(y)
return K * (y / ymin - 1) / y**2
def fit_brems(b, ymin, K):
return kramer(y=y_bragg(b), ymin=ymin, K=K)
sl_brems = ((n <= 200) & ((b <= 17) | (n <= 45))) & (n > 20)
# kombiniertes Histogramm der x- und y-Daten
dr = np.append(dx, dy) / const.micro
n, bins, patches = plt.hist(dr, bins=13, label="Messungen")
bin_centers = bins[:-1] + np.diff(bins) / 2.
# Gauss Fit
def fit_gauss(x, mu, sigma, A):
return A / np.sqrt(
(sigma**2) * 2 * const.pi) * np.exp(-((x - mu)**2) / 2 / (sigma**2))
popt, pstats = papstats.curve_fit(fit_gauss,
bin_centers,
n,
p0=[dr.mean(),
dr.std(), 1. / np.sum(n)])
xspace = np.linspace(popt[0].nominal_value - 4 * popt[1].nominal_value,
popt[0].nominal_value + 4 * popt[1].nominal_value, 100)
papstats.plot_fit(fit_gauss,
popt,
xspace=xspace,
plabels=['\mu', '\sigma', 'A'],
punits=['\mu m', '\mu m', None])
plt.xlim(xspace[0], xspace[-1])
plt.xlabel(ur'Verschiebung $\Delta x$ und $\Delta y$ $[\mu m]$')
plt.ylabel(ur'Häufigkeit $N$')
plt.legend()
papstats.savefig_a4('2.png')
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
rho_F = unc.ufloat(1.1442, 0.0002) * const.gram/const.centi**3
drho = rho_K - rho_F
t = np.reshape(t, (len(r), 5))
t = unp.uarray(np.mean(t, axis=1), np.std(t, axis=1)/np.sqrt(len(t)))
v = s / t
v_k = v / drho
y = (1 + 2.1 * r / 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')
#####
data = np.loadtxt('2.txt', skiprows=1)
x = data[:, 0] * const.milli
N = data[:, 1]
n = unp.uarray(N, np.sqrt(N)) / 60
n = n - nU
def fit_damp(x, mu, n_0):
return n_0 * np.exp(-mu * x)
popt, pstats = papstats.curve_fit(fit_damp, x, n)
rhoPb = 11.34 * const.gram / const.centi**3
k = popt[0] / rhoPb
print "Materialunabhängiger Schwächungskoeffizient:", papstats.pformat(
k / (const.centi**2 / const.gram), label='k', unit='cm^2/g', format='.2u')
Ey = unc.ufloat(1.45, 0.15)
print "Energie der y-Quanten"
papstats.print_rdiff(Ey, unc.ufloat((1.173 + 1.333) / 2, 0))
plt.clf()
plt.title('Diagramm 3.2: ' + r'$\gamma$' +
u'-Strahlung in Abhängigkeit der Absorberdicke')
plt.yscale('log')
plt.xlabel('Absorberdicke $x \, [mm]$')
plt.ylabel(u'korrigierte Zählrate ' + r'$(n-n_U) \, [\frac{Ereignisse}{s}]$')
#####
print('# 1 (Plateaubereich des Zählrohrs)')
#####
data = np.loadtxt('2.txt', skiprows=1)
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')
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')
f = unc.ufloat(10.1, 0.1)
omega = f * 2 * c.pi
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)
#####
print "3.2: Kontrollverteilung"
#####
plt.cla()
plt.title(ur'Diagramm 3.2: Histogramm der Verschiebungen mit Gauß-Fit')
# kombiniertes Histogramm der x- und y-Daten
dr = np.append(dx, dy) / const.micro
n, bins, patches = plt.hist(dr, bins=13, label="Messungen")
bin_centers = bins[:-1] + np.diff(bins) / 2.
# Gauss Fit
def fit_gauss(x, mu, sigma, A):
return A/np.sqrt((sigma**2)*2*const.pi)*np.exp(-((x-mu)**2)/2/(sigma**2))
popt, pstats = papstats.curve_fit(fit_gauss, bin_centers, n, p0=[dr.mean(), dr.std(), 1./np.sum(n)])
xspace = np.linspace(popt[0].nominal_value - 4 * popt[1].nominal_value, popt[0].nominal_value + 4 * popt[1].nominal_value, 100)
papstats.plot_fit(fit_gauss, popt, xspace=xspace, plabels=['\mu', '\sigma', 'A'], punits=['\mu m', '\mu m', None])
plt.xlim(xspace[0], xspace[-1])
plt.xlabel(ur'Verschiebung $\Delta x$ und $\Delta y$ $[\mu m]$')
plt.ylabel(ur'Häufigkeit $N$')
plt.legend()
papstats.savefig_a4('2.png')
# Berechnung der Konstanten
mu, sigma = popt[0] * const.micro, popt[1] * const.micro
D_fit = sigma**2 / 2. / t_mean
print papstats.pformat(D_fit, format='c', label='D_fit', unit='m^2/s')
papstats.print_rdiff(D_fit, D)
k_B_fit = 6 * const.pi * eta * D_fit * a / T