Example #1
0
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)])
Example #2
0
File: n.py Project: knly/PAP2
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
Example #3
0
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)])
Example #4
0
File: n.py Project: knly/PAP2
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')
Example #5
0
File: n.py Project: knly/PAP2
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')
Example #6
0
File: n.py Project: knly/PAP2
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)

t = data[:,0]
N1 = data[:,1]
N1 = unp.uarray(N1,np.sqrt(N1))
N2 = data[:,2]
N2 = unp.uarray(N2,np.sqrt(N2))

Ndiff = N1-N2
papstats.print_rdiff(N1[0],N2[0])
Example #7
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)
E = np.loadtxt('elements.txt',
               skiprows=1,
               usecols=range(1, 3),
               converters=converters,
               dtype=object) * const.kilo * const.eV

# Abschirmungskonstante
Example #8
0
                  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')
papstats.plot_data(Re, V, color='black')
plt.xlabel('$Re$')
plt.ylabel(r'$\frac{v}{v_{lam}}$')
papstats.savefig_a4('2.png')

print papstats.table(labels=[
    'd=2r', 'r^2', 'v', 'v/(rho_K-rho_F)', u'λ', 'v_k', 'v_k/(rho_K-rho_F)',
    'v_lam', 'v/v_lam', 'Re'
Example #9
0
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')
papstats.plot_data(Re, V, color='black')
plt.xlabel('$Re$')
plt.ylabel(r'$\frac{v}{v_{lam}}$')
papstats.savefig_a4('2.png')

print papstats.table(labels=['d=2r', 'r^2', 'v', 'v/(rho_K-rho_F)', u'λ', 'v_k', 'v_k/(rho_K-rho_F)', 'v_lam', 'v/v_lam', 'Re'], units=['mm', 'mm^2', 'mm/s', 'mm^4/(g*s)', None, 'mm/s', 'mm^4/(g*s)', 'mm/s', None, None], columns=[2 * r / const.milli, r_sq / const.milli**2, v / const.milli, v_k / const.milli**4 * const.gram, y, v * y / const.milli, v_kl / const.milli**4 * const.gram, v_lam / const.milli, V, Re])

#####
Example #10
0
	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"
#####

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
Example #11
0
    ax1.plot(x[xrange], y1[xrange])
    ax2.plot(x[xrange], y2[xrange])

    ax1.yaxis.set_label_position("right")
    ax2.yaxis.set_label_position("right")
    ax1.set_ylabel(u'Pendel 1')
    ax2.set_ylabel(u'Pendel 2')

    ax.set_title('Diagramm 2.' + filename + ': ' + title)
    ax.set_xlabel(ur'Zeit $t \, [s]$')
    ax.set_ylabel(ur'Auslenkung $\phi \, [^\circ]$')

    ax1.set_xlim([xmin, xmax])

    papstats.savefig_a4(filename + '.png')


macheSchoenenSchwingungsGraphen('1', 0, 10)

macheSchoenenSchwingungsGraphen('2.1', 0, 10)
macheSchoenenSchwingungsGraphen('2.2', 0, 10)
macheSchoenenSchwingungsGraphen('2.3', 0, 10)
macheSchoenenSchwingungsGraphen('2.4', 0, 10)
macheSchoenenSchwingungsGraphen('2.5', 0, 10)
macheSchoenenSchwingungsGraphen('2.6', 0, 10)

macheSchoenenSchwingungsGraphen('3.1', 0, 50)
macheSchoenenSchwingungsGraphen('3.2', 0, 30)
macheSchoenenSchwingungsGraphen('3.3', 0, 15)
Example #12
0
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
Example #13
0
#####
print u"# 1: Sonnenspektrum"
#####

y, I_0 = np.loadtxt('1.1.txt', skiprows=2, unpack=True)
I_G = np.loadtxt('1.2.txt', skiprows=2)[:,1]

plt.clf()
plt.title(u'Diagramm 3.1: Sonnenspektrum bei geöffnetem und geschlossenem Fenster')
plt.plot(y, I_0, label=u'geöffnetes Fenster', color='black')
plt.plot(y, I_G, label=u'geschlossenes Fenster', color='grey')
plt.xlim(y[0], y[-1])
plt.xlabel(ur'Wellenlänge $\lambda \, [nm]$')
plt.ylabel(ur'Intensität $I \, [cnt]$')
plt.legend(loc='upper left')
papstats.savefig_a4('1.png')

# Absorption

A_G = 1 - I_G / I_0
y_min = 320
y_range = y > y_min

plt.clf()
plt.title(u'Diagramm 3.2: Absorption von Glas')
plt.plot(y[y_range], A_G[y_range], color='black')
plt.xlabel(ur'Wellenlänge $\lambda \, [nm]$')
plt.ylabel(ur'Absorption $A_G = 1 - \frac{I_G}{I_0}$')
plt.xlim(y_min, y[-1])
papstats.savefig_a4('2.png')
Example #14
0
# 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)
                     ])

# Plot Intensität
Example #15
0
print u"# 1: Sonnenspektrum"
#####

y, I_0 = np.loadtxt('1.1.txt', skiprows=2, unpack=True)
I_G = np.loadtxt('1.2.txt', skiprows=2)[:, 1]

plt.clf()
plt.title(
    u'Diagramm 3.1: Sonnenspektrum bei geöffnetem und geschlossenem Fenster')
plt.plot(y, I_0, label=u'geöffnetes Fenster', color='black')
plt.plot(y, I_G, label=u'geschlossenes Fenster', color='grey')
plt.xlim(y[0], y[-1])
plt.xlabel(ur'Wellenlänge $\lambda \, [nm]$')
plt.ylabel(ur'Intensität $I \, [cnt]$')
plt.legend(loc='upper left')
papstats.savefig_a4('1.png')

# Absorption

A_G = 1 - I_G / I_0
y_min = 320
y_range = y > y_min

plt.clf()
plt.title(u'Diagramm 3.2: Absorption von Glas')
plt.plot(y[y_range], A_G[y_range], color='black')
plt.xlabel(ur'Wellenlänge $\lambda \, [nm]$')
plt.ylabel(ur'Absorption $A_G = 1 - \frac{I_G}{I_0}$')
plt.xlim(y_min, y[-1])
papstats.savefig_a4('2.png')
Example #16
0
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')
Example #17
0

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_cos(a, c, d):
    return c * np.abs(np.cos(a + d))

Example #18
0
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')