def k_ruechhardt(m, V, r, n, t): global p_0 T = t / n print papstats.pformat(T, 'T') p = p_0 + m * const.g / const.pi / r**2 k = 4 * m * V / r**4 / T**2 / p return k
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 print_w(T1, T2): print papstats.pformat(T1, unit='s', label='T_1') print papstats.pformat(T2, unit='s', label='T_2') w1 = 2*const.pi/T1 w2 = 2*const.pi/T2 w = np.mean([w1, w2]) print papstats.pformat(w1, unit='Hz', label='w_1') print papstats.pformat(w2, unit='Hz', label='w_2') print papstats.pformat(w, unit='Hz', label='w') return (w1, w2, w)
def print_w(T1, T2):
print papstats.pformat(T1, unit='s', label='T_1')
print papstats.pformat(T2, unit='s', label='T_2')
w1 = 2 * const.pi / T1
w2 = 2 * const.pi / T2
w = np.mean([w1, w2])
print papstats.pformat(w1, unit='Hz', label='w_1')
print papstats.pformat(w2, unit='Hz', label='w_2')
print papstats.pformat(w, unit='Hz', label='w')
return (w1, w2, w)
def vergleich_table(l, w, w_erw):
diff = w - w_erw
return papstats.table(
labels=['Kopplung', 'w', 'w_erw', 'w-w_erw', 'Sigmabereich'],
units=[None, 'Hz', 'Hz', 'Hz', None],
columns=[
papstats.pformat(l / const.centi, label='l', unit='cm',
format='c'), w, w_erw, diff,
unp.nominal_values(np.abs(diff)) / unp.std_devs(diff)
])
def macheSchoenenSchwingungsGraphen(filename, xmin, xmax):
data = np.loadtxt(filename + '.txt', skiprows=2)
with open(filename + '.txt') as file:
title = file.readline()
try:
l = unc.ufloat(float(file.readline()), 0.1)*const.centi
title = title + 'mit Kopplung bei $' + papstats.pformat(l / const.centi, label='l', unit='cm', format='l') + '$'
except ValueError, e:
pass
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 schwingung_table(l, t1, t2, n):
T1, T2 = t1 / n, t2 / n
T = np.mean([T1, T2], axis=0)
w = 2 * const.pi / T
return (papstats.table(labels=['Kopplung', 'T_1', 'T_2', 'T', 'w'],
units=[None, 's', 's', 's', 'Hz'],
columns=[
papstats.pformat(l / const.centi,
label='l',
unit='cm',
format='c'), T1, T2, T, w
]), w)
print k_L_erw, k_Ar_erw
#####
print u"# Methode nach Clement und Desormes"
#####
data = np.loadtxt('2.1.txt', skiprows=1)
d_h = 0.2
h1 = unp.uarray(data[:,0], d_h) - unp.uarray(data[:,1], d_h)
h3 = unp.uarray(data[:,2], d_h) - unp.uarray(data[:,3], d_h)
k = h1 / (h1 - h3)
print papstats.table(labels=['k'], columns=[k])
k = np.mean(k)
print papstats.pformat(k, label='k')
papstats.print_rdiff(k, k_L_erw)
#####
print u"# Methode nach Rüchhardt"
#####
p_0 = unc.ufloat(1004.6, 0.2) * const.hecto
def k_ruechhardt(m, V, r, n, t):
global p_0
T = t / n
print papstats.pformat(T, 'T')
p = p_0 + m * const.g / const.pi / r**2
k = 4 * m * V / r**4 / T**2 / p
def vergleich_table(l, w, w_erw):
diff = w - w_erw
return papstats.table(labels=['Kopplung', 'w', 'w_erw', 'w-w_erw', 'Sigmabereich'], units=[None, 'Hz', 'Hz', 'Hz', None], columns=[papstats.pformat(l / const.centi, label='l', unit='cm', format='c'), w, w_erw, diff, unp.nominal_values(np.abs(diff))/unp.std_devs(diff)])
# Konstanten
dt = 0.05
print '\n# 2.1 Offsets'
data = np.loadtxt('offset.txt', skiprows=1)
offset1 = np.mean(data[:,1])
offset2 = np.mean(data[:,2])
print papstats.pformat(offset1, label='Offset phi_1', unit='grad')
print papstats.pformat(offset2, label='Offset phi_2', unit='grad')
print "\n# 2.2 Eigenfrequenzen der ungekoppelten Pendel"
t1 = unc.ufloat(25.51, dt) - unc.ufloat(1.27, dt)
t2 = unc.ufloat(25.17, dt) - unc.ufloat(0.88, dt)
n = 15
T1, T2 = t1 / n, t2 / n
print_w(T1, T2)
print "\n# 2.3 Gekoppelte Pendel"
data_symm = []
import matplotlib.pyplot as plt
import uncertainties as unc
import uncertainties.unumpy as unp
import os
parentdir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
os.sys.path.insert(0,parentdir)
import papstats
# Eichung
d = unp.uarray([2. * 71.3, 2. * 52.8, 2. * 31.0], 2 * 0.2) * const.milli / 100.
d_px = unp.uarray([1380.44, 1297.31, 1188.49], 5) - unp.uarray([710.88, 803.07, 908.87], 5)
px = np.mean(d / d_px)
print "Eichung: " + papstats.pformat(px / const.milli, unit='mm/px') + " <=> " + papstats.pformat(1. / px * const.milli, unit='px/mm')
px_erw = 14 * const.micro
#####
print "# 3.1: Quantitative Beobachtungen am Einzelspalt"
#####
# Messung bei hoher Intensität
n, x, dx, I, dI = np.loadtxt('2.1.2.txt', skiprows=1, unpack=True)
x = unp.uarray(x, dx)
I = unp.uarray(I, dI)
# Messung bei niedriger Intensität
n_low, x_low, dx_low, I_low, dI_low = np.loadtxt('2.1.1.txt', skiprows=1, unpack=True)
x_low = unp.uarray(x_low, dx_low)
I_low = unp.uarray(I_low, dI_low)
def fit_y_m(m, E_Ry, E_to, D):
global hc
return hc / (E_Ry / (m - D)**2 - E_to)
def fit_y_m_fixedERy(m, E_to, D):
global hc, E_Ry
return hc / (E_Ry / (m - D)**2 - E_to)
# 1. Nebenserie
y_m1 = unp.uarray([820.5, 569.5, 499.2, 467.9, 451.3, 440.1, 434.4, 0, 0, 0],
[2, 1.5, 1.3, 1.1, 1.6, 1.5, 1.3, 0, 0, 0])
y_3p = y_m1[0]
E_3p = E_Ry / 3**2 - hc / y_3p
print papstats.pformat(E_3p, label='E_3p', unit='eV')
m_1 = np.arange(10) + 3
y_m1_erw = fit_y_m(m_1, E_Ry, E_3p, 0)
# 2. Nebenserie
y_m2 = unp.uarray([0, 617.1, 516.1, 476.3, 456.3], [0, 1.5, 1.3, 1.1, 1])
y_d = unc.ufloat(590, 4)
E_3s = E_3p - hc / y_d
print papstats.pformat(E_3s, label='E_3s', unit='eV')
d_s = 3 - unp.sqrt(E_Ry / E_3s)
print papstats.pformat(d_s, label='D_s')
m_2 = np.arange(5) + 4
y_m2_erw = fit_y_m(m_2, E_Ry, E_3p, d_s)
# 3. Nebenserie
y_m3 = unp.uarray([331.6, 0], [1.5, 0])
plt.title('Frequenzgang des Messaufbaus')
plt.xlabel(r'Frequenz $f$ in $Hz$')
plt.ylabel(r'$g(f)=\frac{1}{D} \frac{U_{aus}}{U_{ein}}$')
plt.legend()
text = r"$g(f)=\frac{V}{\sqrt{1+(\frac{\Omega_1}{f})^{2*n_1}}\sqrt{1+(\frac{f}{\Omega_2})^{2*n_2}}}$" + "\n"
parameters = np.array([
['V', None],
[r"\Omega_1", 'Hz'],
[r"\Omega_2", 'Hz'],
[r"n_1", None],
[r"n_2", None]
])
for i in range(parameters.shape[0]):
text += papstats.pformat(v=popt[i], dv=pcov[i,i], label=parameters[i,0], unit=parameters[i,1]) + "\n"
text += pstat.legendstring().replace(', ', "\n") + "\n"
text += r"$B = \int_0^\infty g(f)^2 df$" + "\n"
text += papstats.pformat(v=B, dv=None, label='B', prec=3)
plt.text(2e3, 6e2, text, verticalalignment='top', backgroundcolor='#eeeeee')
plt.savefig('frequenzgang.png')
plt.cla()
data = np.loadtxt('2.1.txt', skiprows=1)
N = data[1:, 0]
papstats.pformat(l / const.centi, label='l', unit='cm',
format='c'), w, w_erw, diff,
unp.nominal_values(np.abs(diff)) / unp.std_devs(diff)
])
# Konstanten
dt = 0.05
print '\n# 2.1 Offsets'
data = np.loadtxt('offset.txt', skiprows=1)
offset1 = np.mean(data[:, 1])
offset2 = np.mean(data[:, 2])
print papstats.pformat(offset1, label='Offset phi_1', unit='grad')
print papstats.pformat(offset2, label='Offset phi_2', unit='grad')
print "\n# 2.2 Eigenfrequenzen der ungekoppelten Pendel"
t1 = unc.ufloat(25.51, dt) - unc.ufloat(1.27, dt)
t2 = unc.ufloat(25.17, dt) - unc.ufloat(0.88, dt)
n = 15
T1, T2 = t1 / n, t2 / n
print_w(T1, T2)
print "\n# 2.3 Gekoppelte Pendel"
data_symm = []
data_anti = []
#####
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
sl_grenz=slice(13, 18)
import papstats # Konstanten y_erw = 546.07 * const.nano ##### print u"3.1: Wellenlänge" ##### dx = ( unp.uarray([11.2201, 11.426, 10.844], 2e-3 ) - unp.uarray([10.958, 11.169, 10.550], 2e-3 ) ) * const.milli / 5. dm = unp.uarray([200, 201, 220], 5.) y_list = 2 * dx / dm y = np.mean(y_list) print papstats.pformat(y / const.nano, label='y', unit='nm', format='c') papstats.print_rdiff(y / const.nano, y_erw / const.nano) ##### print u"3.2: Brechungsindex von Luft" ##### a = unc.ufloat(50, 0.05) * const.milli T = unc.ufloat(24.6 + const.zero_Celsius, 2) T_0 = const.zero_Celsius p_0 = const.atm / const.torr p = unp.uarray([[-746, -592, -438, -284, -130], [-745, -595, -443, -287, -133], [-745, -597, -444, -290, -136]], 5) dm = np.array([0, 10, 20, 30, 40]) m_0 = np.array([48, 49, 49])
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"
#####
data = np.loadtxt('2.3.txt', skiprows=1)
w_1 = unp.uarray(data[:,0], 10) * 2 * const.pi / const.minute
T_P = unp.uarray(np.transpose(data[:,1::2]), 2)
w_2 = unp.uarray(np.transpose(data[:,2::2]), 10) * 2 * const.pi / const.minute
w_2_erw = w_1 * unp.exp(-T_P / tau)
diff = w_2 - w_2_erw
w_2 = np.mean([w_2, w_2_erw], axis=0)
w_F = unp.uarray(unp.nominal_values(w_1 + w_2) / 2., np.sqrt((unp.nominal_values(w_1 - w_2) / 2)**2 + unp.std_devs(w_1 + w_2)**2))
# plot
plt.clf()
#plt.title(u'Diagramm 3.1: Frequenzgang der Messelektronik mit Verstärker und Bandfilter')
plt.title(
u'Diagramm 3.2: Frequenzgang der Messelektronik mit Verstärker und Bandfilter (Korrektur)'
)
plt.scatter(f, gf, label='Messpunkte', s=10, c='black', marker='s')
fspace = np.logspace(np.log10(sl_bounds[0]), np.log10(sl_bounds[1]), num=200)
plt.plot(
fspace,
fit_gf(fspace, *unp.nominal_values(popt)),
label=
r'Fit $g(f)=\frac{V}{\sqrt{1+(\frac{\Omega_1}{f})^{2*n_1}}\sqrt{1+(\frac{f}{\Omega_2})^{2*n_2}}}$ mit:'
+ '\n%s\n%s\n$B=\int_0^\infty \! g(f)^2 \mathrm{d}f=$%s\n\n%s' % (''.join([
'\n' + papstats.pformat(popt[i], label=plabel[i], unit=punit[i])
for i in range(len(popt))
]), pstats.legendstring(), papstats.pformat(
B, unit='Hz'), r'(mit $2\%$ system. Fehler)'))
ybounds = (5, 1.5e3)
for i in range(len(sl_bounds)):
plt.annotate('Fit-Bereich Grenze\nbei %s' %
papstats.pformat(sl_bounds[i], unit='Hz'),
(sl_bounds[i], ybounds[1]),
ha=['right', 'left'][i],
va='top',
textcoords='offset points',
xytext=([-1, 1][i] * 10, 0))
plt.vlines(sl_bounds[i], *ybounds)
plt.xscale('log')
plt.yscale('log')
#####
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],
import matplotlib.pyplot as plt
import uncertainties as unc
import uncertainties.unumpy as unp
import os
parentdir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
os.sys.path.insert(0, parentdir)
import papstats
# Eichung
d = unp.uarray([2. * 71.3, 2. * 52.8, 2. * 31.0], 2 * 0.2) * const.milli / 100.
d_px = unp.uarray([1380.44, 1297.31, 1188.49], 5) - unp.uarray(
[710.88, 803.07, 908.87], 5)
px = np.mean(d / d_px)
print "Eichung: " + papstats.pformat(
px / const.milli, unit='mm/px') + " <=> " + papstats.pformat(
1. / px * const.milli, unit='px/mm')
px_erw = 14 * const.micro
#####
print "# 3.1: Quantitative Beobachtungen am Einzelspalt"
#####
# Messung bei hoher Intensität
n, x, dx, I, dI = np.loadtxt('2.1.2.txt', skiprows=1, unpack=True)
x = unp.uarray(x, dx)
I = unp.uarray(I, dI)
# Messung bei niedriger Intensität
n_low, x_low, dx_low, I_low, dI_low = np.loadtxt('2.1.1.txt',
skiprows=1,
unpack=True)
table = pt.PrettyTable()
table.add_column('x [mm]', x/const.milli, align='r')
table.add_column('(n-n_U^b) [1/s]', n, align='r')
with open('Resources/3.1.txt', 'w') as file:
file.write(table.get_string())
# Abschätzung der Maximalreichweite aus dem Diagramm
x1 = 3.3*const.milli
x2 = 3.8*const.milli
xM = unc.ufloat(x1+np.abs(x1-x2)/2., np.abs(x1-x2)/2.)
# 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)
def schwingung_table(l, t1, t2, n): T1, T2 = t1 / n, t2 / n T = np.mean([T1, T2], axis=0) w = 2 * const.pi / T return (papstats.table(labels=['Kopplung', 'T_1', 'T_2', 'T', 'w'], units=[None, 's', 's', 's', 'Hz'], columns=[papstats.pformat(l / const.centi, label='l', unit='cm', format='c'), T1, T2, T, w]), w)
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,
def vergleich_table(l, w, w_erw): diff = w - w_erw return papstats.table(labels=['Kopplung', 'w', 'w_erw', 'w-w_erw', 'Sigmabereich'], units=[None, 'Hz', 'Hz', 'Hz', None], columns=[papstats.pformat(l / const.centi, label='l', unit='cm', format='c'), w, w_erw, diff, unp.nominal_values(np.abs(diff))/unp.std_devs(diff)])
tau_exp = T_H / np.log(2)
tau_theo = R * C
print papstats.table(
labels=[
'C', 'R', 'f', u'τ_exp', u'τ_theo', 'Abweichung', 'rel. Abw.',
u'σ-Bereich'
],
units=['nF', u'kΩ', 'Hz', u'µs', u'µs', u'µs', None, None],
columns=[
C / const.nano, R / const.kilo, f, tau_exp / const.micro,
tau_theo / const.micro
] + list(papstats.rdiff(tau_exp / const.micro, tau_theo / const.micro)))
print "Messung aus Stromverlauf:", papstats.pformat(unc.ufloat(37.2, 2) /
np.log(2),
unit='us')
#####
print "# 3: Frequenz- und Phasengang eines RC-Glied"
#####
# Theoretische Grenzfrequenz
R = 1 * const.kilo * unc.ufloat(1, 0.05)
C = 47 * const.nano * unc.ufloat(1, 0.1)
f_G_theo = 1. / 2. / const.pi / R / C
print "Theoretische Grenzfrequenz:", papstats.pformat(f_G_theo / const.kilo,
unit='kHz',
format='c')
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
E_Ry = -const.Rydberg * const.h * const.c / const.eV
hc = const.h * const.c / const.nano / const.eV
def fit_y_m(m, E_Ry, E_to, D):
global hc
return hc / (E_Ry / (m - D)**2 - E_to)
def fit_y_m_fixedERy(m, E_to, D):
global hc, E_Ry
return hc / (E_Ry / (m - D)**2 - E_to)
# 1. Nebenserie
y_m1 = unp.uarray([820.5, 569.5, 499.2, 467.9, 451.3, 440.1, 434.4, 0, 0, 0], [2, 1.5, 1.3, 1.1, 1.6, 1.5, 1.3, 0, 0, 0])
y_3p = y_m1[0]
E_3p = E_Ry / 3**2 - hc / y_3p
print papstats.pformat(E_3p, label='E_3p', unit='eV')
m_1 = np.arange(10) + 3
y_m1_erw = fit_y_m(m_1, E_Ry, E_3p, 0)
# 2. Nebenserie
y_m2 = unp.uarray([0, 617.1, 516.1, 476.3, 456.3], [0, 1.5, 1.3, 1.1, 1])
y_d = unc.ufloat(590, 4)
E_3s = E_3p - hc / y_d
print papstats.pformat(E_3s, label='E_3s', unit='eV')
d_s = 3 - unp.sqrt(E_Ry / E_3s)
print papstats.pformat(d_s, label='D_s')
m_2 = np.arange(5) + 4
y_m2_erw = fit_y_m(m_2, E_Ry, E_3p, d_s)
# 3. Nebenserie
y_m3 = unp.uarray([331.6, 0], [1.5, 0])
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"
#####
data = np.loadtxt('2.3.txt', skiprows=1)
w_1 = unp.uarray(data[:, 0], 10) * 2 * const.pi / const.minute
T_P = unp.uarray(np.transpose(data[:, 1::2]), 2)
w_2 = unp.uarray(np.transpose(data[:, 2::2]), 10) * 2 * const.pi / const.minute
w_2_erw = w_1 * unp.exp(-T_P / tau)
diff = w_2 - w_2_erw
# Berechnung der Bandbreite
def gf_sq(f, *p):
return fit_gf(f, *p)**2
# Integral der Quadratfunktion von g(f) von 0 bis Unendlich
B = int.quad(gf_sq, 0, np.inf, args=tuple(unp.nominal_values(popt)))[0]
B = unc.ufloat(B, B*0.02, 'B') # 2% systematischer Fehler auf B
# plot
plt.clf()
#plt.title(u'Diagramm 3.1: Frequenzgang der Messelektronik mit Verstärker und Bandfilter')
plt.title(u'Diagramm 3.2: Frequenzgang der Messelektronik mit Verstärker und Bandfilter (Korrektur)')
plt.scatter(f, gf, label='Messpunkte', s=10, c='black', marker='s')
fspace = np.logspace(np.log10(sl_bounds[0]),np.log10(sl_bounds[1]), num=200)
plt.plot(fspace, fit_gf(fspace, *unp.nominal_values(popt)), label=r'Fit $g(f)=\frac{V}{\sqrt{1+(\frac{\Omega_1}{f})^{2*n_1}}\sqrt{1+(\frac{f}{\Omega_2})^{2*n_2}}}$ mit:'+'\n%s\n%s\n$B=\int_0^\infty \! g(f)^2 \mathrm{d}f=$%s\n\n%s' % (''.join(['\n'+papstats.pformat(popt[i], label=plabel[i], unit=punit[i]) for i in range(len(popt))]), pstats.legendstring(), papstats.pformat(B, unit='Hz'), r'(mit $2\%$ system. Fehler)'))
ybounds = (5,1.5e3)
for i in range(len(sl_bounds)):
plt.annotate('Fit-Bereich Grenze\nbei %s' % papstats.pformat(sl_bounds[i], unit='Hz'), (sl_bounds[i], ybounds[1]), ha=['right','left'][i], va='top', textcoords='offset points', xytext=([-1,1][i]*10,0))
plt.vlines(sl_bounds[i], *ybounds)
plt.xscale('log')
plt.yscale('log')
plt.xlim(5e1,1e6)
plt.ylim(2.5,2e3)
plt.xlabel('Frequenz $f \, [Hz]$')
plt.ylabel('$g(f)$')
plt.legend(loc='lower center')
fig = plt.gcf()
fig.set_size_inches(11.69,8.27)
plt.savefig('3.png', dpi=144)
minimum = quantities.min(axis=1)
maximum = quantities.max(axis=1)
print papstats.table(
labels=['dt', 'dx', 'dy', 'dx^2', 'dy^2', 'r^2'],
units=['s', 'um', 'um', 'um^2', 'um^2', 'um^2'],
columns=np.transpose([mean, std, std_mean, minimum, maximum]),
rowlabels=[
'Mittelwert', 'Standardabw.', 'SE des MW', 'Minimum', 'Maximum'
],
prec=5)
# Mittelwerte
t_mean = unc.ufloat(mean[0], std_mean[0])
r2_mean = unc.ufloat(mean[-1], std_mean[-1]) * const.micro**2
print papstats.pformat(r2_mean / const.micro**2,
label='r^2',
unit='um^2',
format='c')
print papstats.pformat(t_mean, label='t', unit='s', format='c')
# Boltzmannkonstante
k_B = 3. / 2. * const.pi * eta * a / T / t_mean * r2_mean
print papstats.pformat(k_B, format='c', label='k_B', unit='J/K')
papstats.print_rdiff(k_B, k_B_erw)
# Diffusionskoeffizient
D = k_B * T / (6 * const.pi * eta * a)
print papstats.pformat(D, format='c', label='D', unit='m^2/s')
#####
print "3.2: Kontrollverteilung"
#####
table.add_column('x [mm]', x / const.milli, align='r')
table.add_column('(n-n_U^b) [1/s]', n, align='r')
with open('Resources/3.1.txt', 'w') as file:
file.write(table.get_string())
# Abschätzung der Maximalreichweite aus dem Diagramm
x1 = 3.3 * const.milli
x2 = 3.8 * const.milli
xM = unc.ufloat(x1 + np.abs(x1 - x2) / 2., np.abs(x1 - x2) / 2.)
# 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
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')
plt.legend(loc='upper left')
papstats.savefig_a4('1.png')
V = v / v_lam
import os
parentdir = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
os.sys.path.insert(0, parentdir)
import papstats
#####
print u"\n# 3.1: Betrieb als Kältemaschine"
#####
# Kompensations-Heizleistung entspricht der Kälteleistung
U_H = unc.ufloat(4.32, 0.01)
I_H = 5 * unc.ufloat(0.91, 0.01)
P_K = U_H * I_H
print papstats.pformat(P_K,
format='c',
unit='W',
label=u'Kälteleistung der Kältemaschine P_K')
print u"Energiebilanz:"
# zugeführte Kompensations-Wärmemenge pro Umdrehung
f_M = unc.ufloat(287.6, 1) / const.minute
Q_2 = P_K / f_M
print papstats.pformat(Q_2, format='c', unit='J', label='Q_2')
# an Kühlwasser abgegebene Wärmemenge
c_W = 4180
rho_W = 998.2
dT = unc.ufloat(2.5, 0.1)
V = unc.ufloat(240, 2) * const.milli * const.liter / const.minute
Q_1 = c_W * rho_W * dT * V / f_M
#####
print "# 1: Bestimmung der Zeitkonstante eines RC-Glieds"
#####
C, R, f, T_H = np.loadtxt('1.txt', skiprows=1, converters=dict.fromkeys([3], unc.ufloat_fromstr), dtype=object, unpack=True)
C, R, f, T_H = np.array(C, dtype=float)*const.nano, np.array(R, dtype=float)*const.kilo, np.array(f, dtype=float), T_H*const.micro
C, R = unp.uarray(C, C*0.1), unp.uarray(R, R*0.05)
tau_exp = T_H/np.log(2)
tau_theo = R*C
print papstats.table(labels=['C', 'R', 'f', u'τ_exp', u'τ_theo', 'Abweichung', 'rel. Abw.', u'σ-Bereich'], units=['nF', u'kΩ', 'Hz', u'µs', u'µs', u'µs', None, None], columns=[C/const.nano, R/const.kilo, f, tau_exp/const.micro, tau_theo/const.micro] + list(papstats.rdiff(tau_exp/const.micro, tau_theo/const.micro)))
print "Messung aus Stromverlauf:", papstats.pformat(unc.ufloat(37.2,2)/np.log(2), unit='us')
#####
print "# 3: Frequenz- und Phasengang eines RC-Glied"
#####
# Theoretische Grenzfrequenz
R = 1*const.kilo * unc.ufloat(1, 0.05)
C = 47*const.nano * unc.ufloat(1, 0.1)
f_G_theo = 1./2./const.pi/R/C
print "Theoretische Grenzfrequenz:", papstats.pformat(f_G_theo/const.kilo, unit='kHz', format='c')
# Phasengang
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')
import os parentdir = os.path.dirname(os.path.dirname(os.path.abspath(__file__))) os.sys.path.insert(0,parentdir) import papstats ##### print u"\n# 3.1: Betrieb als Kältemaschine" ##### # Kompensations-Heizleistung entspricht der Kälteleistung U_H = unc.ufloat(4.32, 0.01) I_H = 5 * unc.ufloat(0.91, 0.01) P_K = U_H * I_H print papstats.pformat(P_K, format='c', unit='W', label=u'Kälteleistung der Kältemaschine P_K') print u"Energiebilanz:" # zugeführte Kompensations-Wärmemenge pro Umdrehung f_M = unc.ufloat(287.6, 1) / const.minute Q_2 = P_K / f_M print papstats.pformat(Q_2, format='c', unit='J', label='Q_2') # an Kühlwasser abgegebene Wärmemenge c_W = 4180 rho_W = 998.2 dT = unc.ufloat(2.5, 0.1) V = unc.ufloat(240, 2) * const.milli * const.liter / const.minute Q_1 = c_W * rho_W * dT * V / f_M print papstats.pformat(Q_1, format='c', unit='J', label='Q_1')
plt.plot(f[selectedRange],
fit_g(f[selectedRange], *popt),
label=r'Fit von $g(f)$')
plt.title('Frequenzgang des Messaufbaus')
plt.xlabel(r'Frequenz $f$ in $Hz$')
plt.ylabel(r'$g(f)=\frac{1}{D} \frac{U_{aus}}{U_{ein}}$')
plt.legend()
text = r"$g(f)=\frac{V}{\sqrt{1+(\frac{\Omega_1}{f})^{2*n_1}}\sqrt{1+(\frac{f}{\Omega_2})^{2*n_2}}}$" + "\n"
parameters = np.array([['V', None], [r"\Omega_1", 'Hz'], [r"\Omega_2", 'Hz'],
[r"n_1", None], [r"n_2", None]])
for i in range(parameters.shape[0]):
text += papstats.pformat(v=popt[i],
dv=pcov[i, i],
label=parameters[i, 0],
unit=parameters[i, 1]) + "\n"
text += pstat.legendstring().replace(', ', "\n") + "\n"
text += r"$B = \int_0^\infty g(f)^2 df$" + "\n"
text += papstats.pformat(v=B, dv=None, label='B', prec=3)
plt.text(2e3, 6e2, text, verticalalignment='top', backgroundcolor='#eeeeee')
plt.savefig('frequenzgang.png')
plt.cla()
data = np.loadtxt('2.1.txt', skiprows=1)
N = data[1:, 0]
R = data[1:, 1] * c.kilo
sigma=unp.std_devs(omega + U_ind))
B = unc.ufloat(popt[0], np.sqrt(pcov[0, 0]))
pstats = papstats.PAPStats(ydata=unp.nominal_values(U_ind),
ymodel=U_ind_max(unp.nominal_values(omega), B.nominal_value),
sigma=unp.std_devs(omega + U_ind), ddof=1)
plt.title(u'Induktionspannung in Abhängigkeit von der Rotationsfrequenz der Flachspule')
plt.xlabel(ur'Frequenz $f$ in $Hz$')
plt.ylabel(ur'Max. Induktionsspannung $U_{ind}$ in $V$')
plt.errorbar(x=unp.nominal_values(f), xerr=unp.std_devs(f), y=unp.nominal_values(U_ind), yerr=unp.std_devs(U_ind),
ls='none', label='Messwerte')
label = "Fit-Werte mit \n"
label += ur"$Û_{ind} = B \ast A_F \ast n_F \ast \omega$" + "\n"
label += ur"$n_F=%d$, " % n_F
label += '$' + papstats.pformat(v=A_F, prec=3, label='A_F', unit='m^2') + ur'$, '
label += "$" + papstats.pformat(v=(B * 1000.), label='B', unit='mT') + "$\n"
label += pstats.legendstring()
plt.plot(unp.nominal_values(f), U_ind_max(unp.nominal_values(omega), B.nominal_value), label=label)
plt.errorbar(x=unp.nominal_values(f), xerr=unp.std_devs(f), y=unp.nominal_values(U_ind_exp),
yerr=unp.std_devs(U_ind_exp), ls='none', label='Erwartungswerte')
plt.legend(loc=2, borderpad=1)
plt.savefig('2.a.png')
plt.cla()
print u'b) in Abhängigkeit vom Spulenstrom I'
data = np.loadtxt('2.b.txt', skiprows=1)
dy2 = dy**2 r2 = dx2 + dy2 # Spaltenstatistik quantities = np.array([dt, dx / const.micro, dy / const.micro, dx2 / const.micro**2, dy2 / const.micro**2, r2 / const.micro**2]) mean = quantities.mean(axis=1) std = quantities.std(axis=1) std_mean = std / np.sqrt(n.max()) minimum = quantities.min(axis=1) maximum = quantities.max(axis=1) print papstats.table(labels=['dt', 'dx', 'dy', 'dx^2', 'dy^2', 'r^2'], units=['s', 'um', 'um', 'um^2', 'um^2', 'um^2'], columns=np.transpose([mean, std, std_mean, minimum, maximum]), rowlabels=['Mittelwert', 'Standardabw.', 'SE des MW', 'Minimum', 'Maximum'], prec=5) # Mittelwerte t_mean = unc.ufloat(mean[0], std_mean[0]) r2_mean = unc.ufloat(mean[-1], std_mean[-1]) * const.micro**2 print papstats.pformat(r2_mean / const.micro**2, label='r^2', unit='um^2', format='c') print papstats.pformat(t_mean, label='t', unit='s', format='c') # Boltzmannkonstante k_B = 3./2. * const.pi * eta * a / T / t_mean * r2_mean print papstats.pformat(k_B, format='c', label='k_B', unit='J/K') papstats.print_rdiff(k_B, k_B_erw) # Diffusionskoeffizient D = k_B * T / (6 * const.pi * eta * a) print papstats.pformat(D, format='c', label='D', unit='m^2/s') ##### print "3.2: Kontrollverteilung" #####