I = unc.ufloat(4, 0.05)
# U_ind(t) = -B*A*N*omega*sin(omega*t)
# U_ind_max = -B*A*N*omega
def U_ind_max(omega, B):
return B * A_F * n_F * omega
U_ind_exp = U_ind_max(omega, B_H(I))
popt, pcov = opt.curve_fit(f=U_ind_max, xdata=unp.nominal_values(omega), ydata=unp.nominal_values(U_ind),
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.setp(ax1.get_xticklabels(), visible=False)
ax2.set_xlabel('Ordnungszahl $Z$')
ax2.set_ylabel(u'Abschirmungskonstante $\sigma$')
ax3 = ax1.twiny()
ax3.set_xlim(20, 50)
ax3.set_xticks(np.sort(Z))
ax3.set_xticklabels(np.array(elements)[:, 0][np.argsort(Z)])
for k in range(np.shape(E)[1]):
l = 'K_' + [r'\alpha', r'\beta'][k]
p = papstats.plot_data(Z,
ERy[:, k],
label='$' + l + '$ Messpunkte',
ax=ax1)
pstats = papstats.PAPStats(
ydata=unp.nominal_values(ERy[:, k][unp.std_devs(ERy[:, k]) > 0]),
ymodel=moseley(Z[unp.std_devs(ERy[:, k]) > 0], s=k + 1, n1=1,
n2=k + 2),
sigma=unp.std_devs(ERy[:, k])[unp.std_devs(ERy[:, k]) > 0],
ddof=2)
ax1.plot(xspace,
moseley(xspace, s=k + 1, n1=1, n2=k + 2),
ls='dotted',
label='$' + l + '$ nach Moseley\'schem Gesetz\n' +
pstats.legendstring(),
color=p[0].get_color())
papstats.plot_data(Z, s[:, k], ax=ax2, color=p[0].get_color())
ax2.axhline(k + 1, color=p[0].get_color())
ax2.fill_between(np.sort(Z),
k + 1,
unp.nominal_values(s[:, k])[np.argsort(Z)],
alpha=0.15,
color=p[0].get_color())
opt_chisq = None
sl_bounds = opt_bounds
'''
sl_bounds = [4.5e2, 1e5] # passender Fit-Bereich
sl = (f > sl_bounds[0]) & (f < sl_bounds[1])
# Fit mit Startwerten
popt, pcov = opt.curve_fit(fit_gf,
f[sl],
unp.nominal_values(gf[sl]),
p0=[1000, 1000, 50000, 5, 5])
pstats = papstats.PAPStats(unp.nominal_values(gf[sl]),
fit_gf(f[sl], *popt),
ddof=5)
popt = [unc.ufloat(popt[i], pcov[i, i]) for i in range(len(popt))]
plabel = ['V', '\Omega_1', '\Omega_2', 'n_1', 'n_2']
punit = [None, 'Hz', 'Hz', None, None]
# 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]
popt, pcov = opt.curve_fit(fit_g,
f[selectedRange],
g_f[selectedRange],
p0=[1000, 1000, 50000, 5, 5])
def integrate_g_f(f, popt):
return fit_g(f, *popt)**2
integrated = scipy.integrate.quad(integrate_g_f, 0, np.infty, args=popt)
B = integrated[0]
dB = integrated[1]
pstat = papstats.PAPStats(g_f[selectedRange],
fit_g(f[selectedRange], *popt),
ddof=5)
plt.xscale('log')
plt.yscale('log')
plt.plot(f, g_f, '.', ls='none', label='Messdaten')
plt.vlines(lower_f, 5, 1e3)
plt.vlines(upper_f, 5, 1e3)
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()
popt, pcov = opt.curve_fit(lin, Ue[sl[0]], Ua[sl[0], 0], sigma=dUa[sl[0], 0])
V0[0] = popt[0]
dV0[0] = pcov[0, 0]
popt, pcov = opt.curve_fit(lin, Ue[sl[1]], Ua[sl[1], 1], sigma=dUa[sl[1], 1])
V0[1] = popt[0]
dV0[1] = pcov[0, 0]
V0 *= -1
print "Linearer Fit Ua = -V0 * Ue:"
print "V0 = " + str(V0) + "+/-" + str(dV0)
pstats = [
papstats.PAPStats(Ua[sl[i], i],
lin(Ue[sl[i]], -V0[i]),
std=dUa[sl[i], i],
ddof=1) for i in range(2)
]
# plot
plt.clf()
plt.title(
u'Diagramm 3.1: Ausgangsspannung als Funktion der Eingangsspannung für Gleichstrom'
)
for i in range(2):
plt.errorbar(Ue,
Ua[:, i],
xerr=dUe,
yerr=dUa[:, i],
ls='none',
label='Messpunkte zu $R_G=R_{G,%d}=%.1fk\Omega$' %
print "Fit-Werte:"
print "V_0:"
for i in range(V_0.size):
print float("%.4g" % V_0[i]), "+/-", dV_0[i]
# Berechnete Verstärkung
V_b = R_G[0:2] / R_E
dV_b_rel = np.sqrt(2) * dR_rel
dV_b = dV_b_rel * V_b
print "Berechnete Betriebsverstärkung:"
print "V_b:", V_b, "+/-", dV_b
pstats = [papstats.PAPStats(U_A[pktSelect[i],i], fU_A(U_E[pktSelect[i]], V_0[i]), dU_A[pktSelect[i], i], 1) for i in range(2)]
# Plot 1 48.7kOhm
plt.errorbar(x=U_E, y=U_A[:,0], xerr=dU_E, yerr=dU_A[:,0],ls='none')
plt.plot(U_E, fU_A(U_E, V_0[0]))
plt.title(ur'Ausgangsspannung als Funktion der Eingangsspannung für $R_G = 48.7k\Omega$')
setAxesLabel()
i = 0
text = ur"$V_{fit} = %.4f \pm %.4f$" % (V_0[i], dV_0[i]) + "\n"
text += ur"$V_{berechnet} = %.2f \pm %.2f$" % (V_b[i], dV_b[i]) + "\n"
text += pstats[i].legendstring()
plt.text(-0.25, 0, text, verticalalignment="top")
plt.savefig('1.a.1.png')
plt.cla()