def test_x2_in_x1_2():
"""
x2 has a couple of bins, each of which span more than one original bin
"""
# old size
m = 10
# bin edges
x_old = np.linspace(0., 1., m+1)
x_new = np.array([0.25, 0.55, 0.75])
# some arbitrary distribution
y_old = 1. + np.sin(x_old[:-1]*np.pi) / np.ediff1d(x_old)
y_old = unp.uarray(y_old, 0.1*y_old*uniform((m,)))
# rebin
y_new = rebin.rebin(x_old, y_old, x_new, interp_kind='piecewise_constant')
# compute answer here to check rebin
y_new_here = unp.uarray(np.zeros(2), np.zeros(2))
y_new_here[0] = 0.5 * y_old[2] + y_old[3] + y_old[4] + 0.5 * y_old[5]
y_new_here[1] = 0.5 * y_old[5] + y_old[6] + 0.5 * y_old[7]
assert_allclose(unp.nominal_values(y_new),
unp.nominal_values(y_new_here))
# mean or nominal value comparison
assert_allclose(unp.std_devs(y_new),
unp.std_devs(y_new_here))
def day3_vacuum():
plt.clf()
ux = unp.uarray([800, 1000, 500], ux_error) # V
ug_crit = unp.uarray([110, 140, 30], ug_error) # V
omega = 2 * math.pi * ufloat(48, 1) # Hz
ug_crit = _apply_additional_proportional_error(ug_crit, stability_uncertainty_vacuum)
ux *= ux_correction
ug_crit *= ug_correction
stability(ux, ug_crit, omega, label="Particle V1")
plt.title("p = 300 mbar")
plt.legend(loc=2)
plt.savefig("images/stability_vacuum_1.pdf")
plt.clf()
ux = unp.uarray([700, 800], ux_error) # V
ug_crit = unp.uarray([100, 140], ug_error) # V
omega = 2 * math.pi * ufloat(45, 1) # Hz
ug_crit = _apply_additional_proportional_error(ug_crit, stability_uncertainty_vacuum)
ux *= ux_correction
ug_crit *= ug_correction
stability(ux, ug_crit, omega, label="Particle V2")
plt.title("p = 180 mbar")
plt.legend(loc=2)
plt.savefig("images/stability_vacuum_2.pdf")
def other(g=True):
freq = unumpy.uarray([100, 500, 1000, 5000, 10000, 50000], np.array([100, 500, 1000, 5000, 10000, 50000]) * 0.01)
vin = ufloat(1.01, 0.01)
vout = unumpy.uarray([0.640, 3.02, 5.27, 9.2, 9.6, 6.4], [0.01, 0.01, 0.01, 0.1, 0.1, 0.1])
fase = unumpy.uarray([92, 108, 123, 166, 178, -125], [1, 2, 1, 1, 1, 1])
Gs = vout / vin
dB = 10 * unumpy.log10(Gs)
if not g:
return None
f = plt.figure(figsize=(8, 8))
f.suptitle("Differenziatore", fontsize=15, y=0.98)
ax = f.add_subplot(211)
ax.errorbar(x=unumpy.nominal_values(freq),
y=unumpy.nominal_values(Gs),
c='black', fmt='o-')
ax.set_xlabel('Frequenza', fontsize=14)
ax.set_ylabel('Guadagno G', fontsize=14)
ax.set_xscale('log')
#ax.set_ylim((-13, 1))
#ax.set_yticklabels(('', 2, 4, 6, 8, 10, 12))
ax.set_xticklabels(('', '100 Hz', u"1 kHz", u"10 kHz", u"100 kHz", u"1 MHz"))
ax.minorticks_on()
ax.grid(b=True, which='major', color='0.7', linestyle='-', zorder=-5)
ax.grid(b=True, which='minor', color='0.9', linestyle='-', zorder=-9)
ax.set_axisbelow(True)
ax2 = f.add_subplot(212)
ax2.errorbar(x=unumpy.nominal_values(freq),
y=unumpy.nominal_values(fase),
c='black', fmt='o-')
ax2.set_ylabel('Sfasamento [Gradi]', fontsize=14)
ax2.set_xscale('log')
#ax2.set_yticklabels(('', 25, 50, 75, 100))
ax2.set_xticklabels(('', '100 Hz', u"1 kHz", u"10 kHz", u"100 kHz"))
ax2.minorticks_on()
ax2.grid(b=True, which='major', color='0.7', linestyle='-', zorder=-5)
ax2.grid(b=True, which='minor', color='0.9', linestyle='-', zorder=-9)
ax2.set_axisbelow(True)
ax3 = ax2.twiny()
ax3.set_xticks((0, 0.333, 0.666, 1))
ax3.set_xticklabels(('', "1 kHz", u"10 kHz", u"100 kHz"))
f.subplots_adjust(top=0.93, hspace=0.25, bottom=0.07, right=0.95)
plt.savefig("../latex/diff.pdf")
plt.show()
def g_1000hz():
g_1000hz = np.genfromtxt("../dati/g_1000hz.csv", skip_header=1, delimiter=",")
vin = unumpy.uarray(g_1000hz[:,0] * 0.001, g_1000hz[:,1] * 0.001)
vout = unumpy.uarray(g_1000hz[:,2], g_1000hz[:,3])
Gs = vout / vin
G = sum(Gs) / float(len(Gs))
print Gs, "\n", G
def usum(self, width=False):
"""
Return the sum of the bin contents and uncertainty.
See sum().
"""
if width:
return np.dot(np.diff(self.bins), uarray((self.hist, self.errs)))
else:
return np.sum(uarray((self.hist, self.errs)))
def I_with_err(f_val=1, f_err=0, g_val=g_DEFAULT, g_err=0,
e=1, e1=1, e2=E_INF):
"""Wrapper for f so the user doesn't have to know about
the uncertainties module"""
from uncertainties import unumpy
f = unumpy.uarray(f_val, f_err)
g = unumpy.uarray(g_val, g_err)
_I = power_law_integral_flux(f, g, e, e1, e2)
I_val = unumpy.nominal_values(_I)
I_err = unumpy.std_devs(_I)
return I_val, I_err
def plot_u(cal_file, fm_file, offset_file, description, accidental_offset,
results_file):
M = np.genfromtxt(cal_file)
N = np.genfromtxt(fm_file)
O = np.genfromtxt(offset_file)
i_helm = M[:,1] #current applied to helmholtz for calibration measurement
b_helm = M[:,2] #field applied to helmholtz coil for calibration measurement
p, cov = np.polyfit(i_helm, b_helm, 1, cov=True) #fit a line to calibration measurement so that we get a calibration
i_fm = N[:,1] #current applied to helmmholtz for shielding measurement
b_fm = unumpy.uarray(N[:,2],0.0005) - accidental_offset #field measured inside of ferromagnet shield
B_earth = np.polyval(p,0) #We get the Earths magnetic field from i=0 of the Helmholtz calibration
B_fm_no_i = unumpy.uarray(np.mean(O[:,2]), np.std(O[:,2])) #Get average and error for initial magnetization
mag = B_fm_no_i - B_earth #initial magnetization is the field inside of the ferromagnet before any field is applied minus the earths magnetic field
Bin = b_fm - mag #internal magnetization is the measured internal field minus the initial magnetization. This correction might not be necessary for a soft ferromagnet
Bext = unumpy.uarray(np.polyval(p,i_fm), 0.0005) #external field
Bext_nom = unumpy.nominal_values(Bext)
Bext_err = unumpy.std_devs(Bext)
B = Bext/Bin
c = a/b
u=(-2*B + c**2 - 2*unumpy.sqrt(B**2 - B*c**2 - B + c**2) + 1)/(c**2 - 1)
u_nom = unumpy.nominal_values(u)
u_err = unumpy.std_devs(u)
#cakculate uerr with just point to point uncertainties. I define this as just
#uncertainty from the field measurements
u_pp=(-2*B + c.nominal_value**2 - 2*unumpy.sqrt(B**2 - B*c.nominal_value**2 - B + c.nominal_value**2) + 1)/(c.nominal_value**2 - 1)
#calculate uerr from just geometry uncertainties
u_geom=(-2*unumpy.nominal_values(B) + c**2 - 2*unumpy.sqrt(unumpy.nominal_values(B)**2 - unumpy.nominal_values(B)*c**2 - unumpy.nominal_values(B) + c**2) + 1)/(c**2 - 1)
##obtain uncertainties from field
u_err_pp = unumpy.std_devs(u_pp)
##obtain uncertainties from geometry
u_err_geom = unumpy.std_devs(u_geom)
with open(results_file, "w") as myfile:
myfile.write('#Bext, sig_Bext, ur, sig_ur, sig_ur_pp, sig_ur_corr\n')
for j in range(0, len(u_nom)):
myfile.write('%s\t%s\t%s\t%s\t%s\t%s\n' %(
Bext_nom[j], Bext_err[j],
u_nom[j], u_err[j], u_err_pp[j], u_err_geom[j]))
plt.errorbar(Bext_nom, u_nom, u_err, marker = '.', label = description)
def f_with_err(I_val=1, I_err=0, g_val=g_DEFAULT, g_err=0,
e=1, e1=1, e2=E_INF):
"""Wrapper for f so the user doesn't have to know about
the uncertainties module"""
from uncertainties import unumpy
I = unumpy.uarray(I_val, I_err)
g = unumpy.uarray(g_val, g_err)
_f = power_law_flux(I, g, e, e1, e2)
f_val = unumpy.nominal_values(_f)
f_err = unumpy.std_devs(_f)
return f_val, f_err
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 evaluate_permeability( fname_data="samplemeasurement.csv", Bin="B1", Bout="B2", fname_do="fm618_do_cryo.txt", fname_th="fm618_th_cryo.txt" ):
print ("Evaluating permeability for: ", fname_data, Bin, Bout, fname_do, fname_th )
# prepare result dataframe
result = pd.DataFrame(columns = ["Bout","Bout_sdev","mu","mu_err_pp","mu_err_geom"])
# get data
data = pd.read_csv(fname_data)
print(data.head(10))
# set uncertainty for field reading manually to 0 if it does not exist
if Bin + '_sdev' not in data:
print ("Use uncertainty of 0.005 for " , Bin+'_sdev')
data[Bin + '_sdev'] = 0.005 #Gaussmeter precision 0.01 mT above 30 mT)
# set uncertainty for field reading manually to 0 if it does not exist
if Bout + '_sdev' not in data:
print ("Use uncertainty of 0.005 for " , Bout+'_sdev')
data[Bout + '_sdev'] = 0.005
# copy Bin and Bout to results
result['Bout_c'] = unumpy.uarray( abs( data[Bout].values ), data[Bout + '_sdev'].values)
result['Bin_c'] = unumpy.uarray( abs( data[Bin].values ), data[Bin + '_sdev'].values)
# get inner and outer diameter
diam_out = mean_from_file('diameter_files/'+fname_do)
thickness = mean_from_file('diameter_files/'+fname_th)
diam_in = diam_out - 2*thickness
# check ideal permeability
calc_mu_cloak(diam_in, diam_out)
# calculate permeability and store values and uncertainties in arrays
(mu_c, mu_err, mu_err_pp, mu_err_geom) = calc_mu(Bin=result['Bin_c'], Bout=result['Bout_c'], radius_inner=diam_in, radius_outer=diam_out)
result["mu"] = mu_c
result["mu_err"] = mu_err
result["mu_err_pp"] = mu_err_pp
result["mu_err_geom"] = mu_err_geom
# same for Bout
result["Bout"] = unumpy.nominal_values(result["Bout_c"])
result["Bout_sdev"] = unumpy.std_devs(result["Bout_c"])
#print(result.head(10))
# drop 'mu_c' and 'Bout_c'
result.drop('Bin_c', axis=1, inplace=True)
result.drop('Bout_c', axis=1, inplace=True)
return (result)
def plot_u(cal_file, fm_file, description, accidental_offset,
results_file):
M = np.genfromtxt(cal_file) #turn calibration file into a matrix
N = np.genfromtxt(fm_file) #turn fm_scan file into a matrix
i_helm = M[:,1] #current applied to helmholtz for calibration measurement
b_helm = M[:,2] #field applied to helmholtz coil for calibration measurement
p, cov = np.polyfit(i_helm, b_helm, 1, cov=True) #fit a line to calibration measurement so that we get a calibration
i_fm = N[:,1] #current applied to helmmholtz for shielding measurement
Bin = unumpy.uarray(N[:,2],0.0005) - accidental_offset #field measured inside of ferromagnet shield
Bin_nom = unumpy.nominal_values(Bin)
Bin_err = unumpy.std_devs(Bin)
Bext = unumpy.uarray(np.polyval(p,i_fm), 0.0005) #external field
Bext_nom = unumpy.nominal_values(Bext)
Bext_err = unumpy.std_devs(Bext)
B = Bin/Bext #ratio of internal to external field
#calculate permeability
u = (B*c**2 + B -2 -2*unumpy.sqrt(B**2*c**2 - B*c**2 - B + 1))/(B*c**2-B)
print(u)
u_nom = unumpy.nominal_values(u)
u_err = unumpy.std_devs(u)
#cakculate uerr with just point to point uncertainties. I define this as just
#uncertainty from the field measurements
u_pp = (B*c.n**2 + B -2 -2*unumpy.sqrt(B**2*c.n**2 - B*c.n**2 - B +
1))/(B*c.n**2-B)
u_err_pp = unumpy.std_devs(u_pp)
#calculate uerr from just geometry uncertainties
u_geom = (unumpy.nominal_values(B)*c**2 + unumpy.nominal_values(B) -2 -2*unumpy.sqrt(unumpy.nominal_values(B)**2*c**2 - unumpy.nominal_values(B)*c**2 - unumpy.nominal_values(B) +
1))/(unumpy.nominal_values(B)*c**2-unumpy.nominal_values(B))
u_err_geom = unumpy.std_devs(u_geom)
#write results onto a text file
with open(results_file, "w") as myfile:
myfile.write('#Bext, sig_Bext, Bi, sig_Bi, ur, sig_ur, sig_ur_pp, sig_ur_corr\n')
for j in range(0, len(u_nom)):
myfile.write('%s\t%s\t%s\t%s\t%s\t%s\t%s\t%s\n' %(
Bext_nom[j], Bext_err[j], Bin_nom[j], Bin_err[j],
u_nom[j], u_err[j], u_err_pp[j], u_err_geom[j]))
plt.errorbar(Bext_nom, u_nom, u_err, marker = '.', label = description)
def power_law_I_with_err(
f_val=1, f_err=0, g_val=g_DEFAULT, g_err=0, e=1, e1=1, e2=E_INF
):
"""Evaluate power-law flux and propagate errors."""
from uncertainties import unumpy
f = unumpy.uarray(f_val, f_err)
g = unumpy.uarray(g_val, g_err)
_I = power_law_integral_flux(f, g, e, e1, e2)
I_val = unumpy.nominal_values(_I)
I_err = unumpy.std_devs(_I)
return I_val, I_err
def power_law_f_with_err(
I_val=1, I_err=0, g_val=g_DEFAULT, g_err=0, e=1, e1=1, e2=E_INF
):
"""Evaluate power-law ``dnde`` and propagate errors."""
from uncertainties import unumpy
I = unumpy.uarray(I_val, I_err)
g = unumpy.uarray(g_val, g_err)
_f = power_law_flux(I, g, e, e1, e2)
f_val = unumpy.nominal_values(_f)
f_err = unumpy.std_devs(_f)
return f_val, f_err
def calcGasMass(DMpc, FHI, FCO, FCOerr): # Calculate HI gas mass FHI = unumpy.uarray(FHI,(FHI*0.2)) MHI = (2.356E5)*((DMpc)**2.)*(FHI) # Calculate H2 gas mass FCO = unumpy.uarray(FCO,FCOerr) MH2 = 7845*FCO*((DMpc)**2.) where_are_nans = unumpy.isnan(MH2) MH2[where_are_nans] = 0 # Total gas mass Mgas = MHI + MH2 return MHI, MH2, Mgas
def __init__( self, x, y, text, saveAffix, execludeLast = False):
from ROOT import TPaveText
self.x = x
self.y = y
self.text = text
self.saveAffix = saveAffix
error_ug = 15
error_ux = 10 * sqrt(2)
x = uarray(( array( x ), [ error_ug ]*len( x )))
y = uarray(( array( y ), [ error_ux]*len( y )))
x = x**2
self.reg = linearRegression(x, y, execludeLast )
self.reg.func.SetParNames('a','b')
self.reg.draw(";U^{2}_{i} [V^{2}];U_{g} [V]" )
self.reg.canvas.cd()
label = TPaveText(0.1, 0.95, .86, 1, "NDC")
label.AddText( text )
label.SetFillStyle(0)
label.SetBorderSize(0)
label.Draw()
ROOT.kPrint = 0
'''
ROOT.kInfo = 1000
ROOT.kWarning = 2000;
ROOT.kError = 3000;
ROOT.Break = 4000;
ROOT.kSysError = 5000;
ROOT.kFatal = 6000;
'''
self.reg.canvas.SaveAs('linReg%s.pdf'%saveAffix)
# calculate q_m
# variable definitions:
from math import pi
K = 8
w = 2. * pi * 30
e_w = 2. * pi
r = 0.0305 / 2
e_r = 0.0002 / 2
#print( '"{} +/- {}",'.format(self.reg.func.GetParameter(0), self.reg.func.GetParError(0) ) )
b = self.reg.func.GetParameter(1)
if b == 0:
return
e_b = self.reg.func.GetParError(1)
q_m = -2. * w**2 * r**2 * b / ( 3 * K ) * 1e6
stat = abs( 1.* q_m * e_b / b )
sys = abs (2. * q_m * sqrt( (e_w/w)**2 + (e_r/r)**2 ) )
#print('{}: q/m = {:.4e} ± {:.2e} (stat) ± {:.2e} (sys) ± {:.2e} (gesamt) μC/kg\n'.format(saveAffix, q_m, stat, sys, sqrt(stat**2 + sys**2)))
druck = { 'Luft1': 1000, 'Luft2': 1000, '375bar': 375, '400bar': 400, '425bar': 425, '425bar2': 425 }
print('{} & {:.3g} ± {:.2g} (stat) ± {:.2g} (sys) {:2g}\\\\'.format(druck[saveAffix], -q_m, stat, sys, sqrt( stat**2 + sys**2) ))
def uintegrate(self, x1, x2, width=False):
"""
Return the integral of the bin contents from `x1` to `x2` and
uncertainty.
See integrate().
"""
i1, i2 = self.findbin([x1,x2])
if width:
return np.dot(np.diff(self.bins[i1:i2+2]),
uarray((self.hist[i1:i2+1], self.errs[i1:i2+1])))
else:
return np.sum(uarray((self.hist[i1:i2+1], self.errs[i1:i2+1])))
def efficiencies(input, ht_val, alphat_binning, mhtmet_binning):
vals = np.zeros((len(mhtmet_binning), len(alphat_binning)))
errs = np.zeros_like(vals)
diff = unumpy.uarray(vals, errs)
cumu = unumpy.uarray(vals, errs)
for imht in range(len(mhtmet_binning)):
mhtmet_val = mhtmet_binning[imht]
for ialphat in range(len(alphat_binning)):
alphat_val = alphat_binning[ialphat]
diff[imht][ialphat] = efficiency(input, ht_val, alphat_val, mhtmet_val, True)
cumu[imht][ialphat] = efficiency(input, ht_val, alphat_val, mhtmet_val, False)
# if ialphat == len(alphat_binning)-1 :
# diff[imht][ialphat] = cumu[imht][ialphat]
return diff, cumu
def auswerten(name, d, n, t, z, V_mol, eps, raw):
d *= 1e-3
N = unp.uarray(n/t, np.sqrt(n)/t) - N_u
if name=="Cu":
tools.table((raw[0], raw[1], N), ("D/mm", "n", "(N-N_U)/\per\second"), "build/{}.tex".format(name), "Messdaten von {}.".format(name), "tab:daten{}".format(name), split=2, footer=r"$\Delta t = \SI{60}{s}$")#"(N-N_U)/\per\second"
else:
tools.table((raw[0], raw[1], raw[2], N), ("D/mm", "n", "\Delta t/s", "(N-N_U)/\per\second"), "build/{}.tex".format(name), "Messdaten von {}.".format(name), "tab:daten{}".format(name), split=2)
mu = z * const.N_A / V_mol * 2 * np.pi * (const.e**2 / (4 * np.pi * const.epsilon_0 * const.m_e * const.c**2))**2 * ((1+eps)/eps**2 * ((2 * (1+eps))/(1+2*eps) - 1/eps * np.log(1+2*eps)) + 1/(2*eps) * np.log(1+ 2*eps) - (1+ 3*eps)/(1+2*eps)**2)
params, pcov = curve_fit(fit, d, unp.nominal_values(N), sigma=unp.std_devs(N))
params_ = unc.correlated_values(params, pcov)
print("{}: N(0) = {}, µ = {}, µ_com = {}".format(name, params_[0], -params_[1], mu))
sd = np.linspace(0, .07, 1000)
valuesp = (fit(sd, *(unp.nominal_values(params_) + 10*unp.std_devs(params_)))).astype(float)
valuesm = (fit(sd, *(unp.nominal_values(params_) - 10*unp.std_devs(params_)))).astype(float)
#plt.xlim(0,7)
plt.xlabel(r"$D/\si{mm}$")
plt.ylabel(r"$(N-N_U)/\si{\per\second}$")
plt.plot(1e3*sd, fit(sd, *params), 'b-', label="Fit")
plt.fill_between(1e3*sd, valuesm, valuesp, facecolor='blue', alpha=0.125, edgecolor='none', label=r'$1\sigma$-Umgebung ($\times 10$)')
plt.errorbar(1e3*d, unp.nominal_values(N), yerr=unp.std_devs(N), fmt='rx', label="Messdaten")
plt.legend(loc='best')
plt.yscale('linear')
plt.tight_layout(pad=0)
plt.savefig("build/{}.pdf".format(name))
plt.yscale('log')
plt.savefig("build/{}_log.pdf".format(name))
plt.clf()
def test_Estrainfit(self):
#create some fake strains
d0=2.34
E0 = 6.19920965/(d0*np.sin(np.radians(4.5/2)))
e1=0.002
e2=-0.0012
e12=0.0008
#the azimuthal angle
phi = np.linspace(-np.pi/2,np.pi/2,23)
#distort the lattice as function of phi
edata = E0 + E0*(e1*np.cos(phi)**2 + e2*np.sin(phi)**2 + e12*np.sin(2*phi))
edata += np.random.uniform(-0.00002,0.00002,edata.size)
edata = unumpy.uarray((edata,np.sqrt(edata)))
#fit
result = strain.strain_from_E(edata,phi,E0)
#check the results
self.assertAlmostEqual(e1,result['strain_x'].nominal_value,4)
self.assertAlmostEqual(e2,result['strain_y'].nominal_value,4)
self.assertAlmostEqual(e12,result['strain_xy'].nominal_value,4)
#fit with d0
result = strain.strain_from_E(edata,phi,d0=d0,tth=4.5)
#check the results
self.assertAlmostEqual(e1,result['strain_x'].nominal_value,4)
self.assertAlmostEqual(e2,result['strain_y'].nominal_value,4)
self.assertAlmostEqual(e12,result['strain_xy'].nominal_value,4)
def fit_stretched_exp(x, y, yerr, xlong):
start = time.time()
p0 = (-1.5, 100, 0.15, 2)
p, cov = curve_fit(func_stretched_exp, x, y, p0=p0, sigma = yerr, maxfev = 100000)
print(p)
perr = np.sqrt(np.diag(cov))
yfit = func_stretched_exp(x, p[0], p[1], p[2], p[3])
resid = y-yfit
dof = y.size - len(p)
chi2 = np.sum((resid/yerr)**2)
chi2red = chi2/dof
p_val = 1 - stats.chi2.cdf(chi2,dof)
yfit = func_stretched_exp(xlong, p[0], p[1], p[2], p[3])
p = unumpy.uarray(p,perr)
extrapolate_val = p[0]*unumpy.exp(-(extrapolate_times/p[1])**p[2])+p[3]
if p[2]>0:
extrap_inf = p[3]
elif p[2]<0:
extrap_inf = p[0]+p[3]
end = time.time()
elapsed = end-start
return (chi2red, resid, extrapolate_val, extrap_inf, 1, unumpy.nominal_values(p),
unumpy.std_devs(p), yfit, elapsed, p_val)
def mean(values, axis=0):
"""Returns mean values and their mean errors of a given array. Return value will be a unp.uarray
Args:
values: (list) Array containing numbers whose mean is desired.
axis: (int) Axis along which the means are computed. The default is to compute the mean of the flattened array.
"""
return unp.uarray((np.mean(noms(values), axis=axis), scipy.stats.sem(noms(values), axis=axis)))
def fit_func(func, x, y, yerr, xlong,ylong):
start = time.time()
p, cov = curve_fit(func, x, y, p0 = initial_guess(func,x,y), sigma = yerr,
maxfev = 1000000)
# print(p)
if func == func_power:
pi = p
p, cov = curve_fit(func, x, y, p0 = initial_guess(func, x+p[2], y),
sigma = yerr, maxfev = 1000000)
while (np.any((pi/p-1)>0.001)):
pi=p
p, cov = curve_fit(func, x, y, p0 = initial_guess(func, x+p[2], y),
sigma = yerr, maxfev = 1000000)
perr = np.sqrt(np.diag(cov))
chi2red, pval = calculate_stats(x, y, yerr, p, perr, func)
yfit = func(xlong,*p)
resid = ylong-yfit
p = unumpy.uarray(p,perr)
extrapolate_val = func_err_prop(func,extrapolate_times,p)
print(extrapolate_val)
end = time.time()
elapsed = end-start
return (p, yfit, resid, extrapolate_val, chi2red, pval, elapsed)
def test_integrate_spectrum_ecpl():
"""
Test ecpl integration. Regression test for
https://github.com/gammapy/gammapy/issues/687
"""
from uncertainties import unumpy
amplitude = unumpy.uarray(1E-12, 1E-13)
index = unumpy.uarray(2.3, 0.2)
reference = 1
lambda_ = 0.1
ecpl = ExponentialCutoffPowerLaw(index, amplitude, reference, lambda_)
emin, emax = 1, 1E10
val = ecpl.integral(emin, emax)
assert_allclose(unumpy.nominal_values(val), 5.956578235358054e-13)
assert_allclose(unumpy.std_devs(val), 9.278302514378108e-14)
def estimate_sigmas(values, ableseunsicherheit):
"""Generates std deviations for analoge instruments. Returns a ufloatarray."""
nominal = values
magnitude = np.floor(np.log10(nominal))
error = [ableseunsicherheit * 10**mag for mag in magnitude]
return uarray(nominal, error)
def uarray(x,errx):
"""
With the new releases of the uncertainties and astropy.io.ascii (0.2.3, the
replacement of asciitable), if I try to create an uncertainties array with
the column of a table imported with ascii I run into trouble. For instance,
if I use the sequence of commands below:
>>> import astropy.io.ascii as asciitable
>>> raff= asciitable.read('data/rafferty06.dat')
>>> m,errm=raff['mass'],raff['errm']
>>> mass=unumpy.uarray(m,errm)
>>> x=0.2*mass
I get the error message:
>>> TypeError: unsupported operand type(s) for *: 'float' and 'Column'
which I can only assume is due to the new way ascii handles tables.
I created this method to use as a replacement for unumpy.uarray that handles
the tables created with astropy.io.ascii.
Usage is the same as uncertainties.unumpy.uarray.
:type x,errx: arrays created with astropy.io.ascii.
:returns: uncertainties array.
"""
import uncertainties.unumpy as unumpy
x=numpy.array(x)
errx=numpy.array(errx)
return unumpy.uarray(x,errx)
def propReg2(xdata,ydata):
m = np.sum(xdata*ydata)/np.sum(xdata*xdata)
stddev = np.sqrt( np.sum((ydata - m*xdata)**2)/(len(xdata)-1) )
uydata = unumpy.uarray(ydata,stddev)
#uxdata = unumpy.uarray(xdata,stddev)
um = np.sum(xdata*uydata)/np.sum(xdata*xdata)
return np.array([uc.nominal_value(um), 0]), np.array([uc.std_dev(um), 0])
def regression(f, x_u, y_u, beta0 ):
for i, y in enumerate(y_u):
if ustd(y) == 0:
y_u[i] = ufloat(y_u[i].nominal_value, y_u[i].nominal_value/1e15)
if len(x_u.shape) == 2:
x_nom = range(len(x_u))
x_error = range(len(x_u))
for i, col in enumerate(x_u):
for j, elem in enumerate(col):
if ustd(elem) == 0:
x_u[i,j] = ufloat(elem.nominal_value, elem.nominal_value/1e15)
x_nom[i] = unom(x_u[i])
x_error[i] = ustd(x_u[i])
x_nom = np.array(x_nom)
x_error = np.array(x_error)
elif np.sum(ustd(x_u)) == 0:
x_error = None
else:
x_error = ustd(x_u)
x_nom = unom(x_u)
linear = odrpack.Model(f)
mydata = odrpack.RealData(x_nom, unom(y_u),sy=ustd(y_u), sx=x_error)
myodr = odrpack.ODR(mydata, linear, beta0=beta0)
myoutput = myodr.run()
#myoutput.pprint()
#print "Chi-squared =", np.sum((myoutput.delta**2 + myoutput.eps**2)/(ustd(x_u)**2+ ustd(y_u)**2))
print "Chi-squared =", myoutput.sum_square
beta_u = unumpy.uarray(myoutput.beta, myoutput.sd_beta)
print "beta = ", beta_u
print "reduced chi-square =", myoutput.res_var
degrees_of_freedom = myoutput.sum_square/myoutput.res_var
p_value = 1-scipy.stats.chi2.cdf(myoutput.sum_square, degrees_of_freedom)
print "p-value =", p_value
return beta_u
def get_contents( h ) :
if h is None : return None
values = np.zeros((h.GetNbinsX(),h.GetNbinsY()))
errors = np.zeros((h.GetNbinsX(),h.GetNbinsY()))
tuple = weight(h) # val,err,wei
for i in range(h.GetNbinsX()) :
for j in range(h.GetNbinsY()) :
val = h.GetBinContent(i+1,j+1)
err = h.GetBinError(i+1,j+1)
values[i][j] = val
errors[i][j] = err
wei = err*err/val if val > 0. else tuple[2]
entries = int(abs(val/wei if wei > 0. else val))
if entries < 10 :
max_err = pois_h[entries]
if pois_l[entries] > pois_h[entries] :
max_err = pois_l[entries]
errors[i][j] = max_err*wei
mhtmet = []
alphat = []
for i in range(h.GetNbinsX()) :
mhtmet.append(h.GetXaxis().GetBinLowEdge(i+1))
#mhtmet.append(h.GetXaxis().GetBinUpEdge(h.GetNbinsX()))
for j in range(h.GetNbinsY()) :
alphat.append(h.GetYaxis().GetBinLowEdge(j+1))
#alphat.append(h.GetYaxis().GetBinUpEdge(h.GetNbinsY()))
temp = unumpy.uarray(values,errors)
return temp#(mhtmet,alphat,temp)
def import_data_from_objLog(FilesList, Objects_Include, pv):
List_Abundances = ['OI_HI', 'NI_HI', 'SI_HI', 'SI_HI_ArCorr', 'Y_Mass_O', 'Y_Mass_S', 'Y_Inference_O', 'Y_Inference_S']
#List_Abundances = ['OI_HI', 'NI_HI', 'SI_HI', 'SI_HI_ArCorr', 'Y_Mass_O', 'Y_Mass_S', 'Y_inf_O', 'Y_inf_S']
#Dictionary of dictionaries to store object abundances
Abund_dict = OrderedDict()
for abund in List_Abundances:
Abund_dict[abund] = OrderedDict()
#Loop through files
for i in range(len(FilesList)):
#Analyze file address
CodeName, FileName, FileFolder = pv.Analyze_Address(FilesList[i])
if CodeName in Objects_Include:
#Loop through abundances in the log
for abund in List_Abundances:
Abund_Mag = pv.GetParameter_ObjLog(CodeName, FileFolder, Parameter = abund, Assumption = 'float')
#If the abundance was measure store it
if Abund_Mag != None:
Abund_dict[abund][CodeName] = Abund_Mag
#Dictionary to store objects with abundances pairs for regressions.
#As an initial value for the keys we define the abundances we want to use for the regression
Abundances_Pairs_dict = OrderedDict()
Abundances_Pairs_dict['O_Regression'] = ('OI_HI','Y_Mass_O')
Abundances_Pairs_dict['N_Regression'] = ('NI_HI','Y_Mass_O')
Abundances_Pairs_dict['S_Regression'] = ('SI_HI','Y_Mass_S')
Abundances_Pairs_dict['S_ArCorr_Regression'] = ('SI_HI_ArCorr','Y_Mass_S')
Abundances_Pairs_dict['O_Regression_Inference'] = ('OI_HI','Y_Inference_O')
Abundances_Pairs_dict['N_Regression_Inference'] = ('NI_HI','Y_Inference_O')
Abundances_Pairs_dict['S_Regression_Inference'] = ('SI_HI','Y_Inference_S')
Abundances_Pairs_dict['S_ArCorr_Regression_Inference'] = ('SI_HI_ArCorr','Y_Inference_S')
#Loop through the regression lists and get objects with both abundances observed
for j in range(len(Abundances_Pairs_dict)):
#Get the elements keys for the regression
Vector, Elem_X, Elem_Y = Abundances_Pairs_dict.keys()[j], Abundances_Pairs_dict.values()[j][0], Abundances_Pairs_dict.values()[j][1]
#Determine objects with both abundances observed
Obj_vector = intersect1d(Abund_dict[Elem_X].keys(), Abund_dict[Elem_Y].keys(), assume_unique = True)
X_vector = zeros(len(Obj_vector))
Y_vector = zeros(len(Obj_vector))
X_vector_E = zeros(len(Obj_vector))
Y_vector_E = zeros(len(Obj_vector))
#Generate abundances vectors
for z in range(len(Obj_vector)):
X_vector[z] = nominal_values(Abund_dict[Elem_X][Obj_vector[z]])
X_vector_E[z] = std_devs(Abund_dict[Elem_X][Obj_vector[z]])
Y_vector[z] = nominal_values(Abund_dict[Elem_Y][Obj_vector[z]])
Y_vector_E[z] = std_devs(Abund_dict[Elem_Y][Obj_vector[z]])
Abundances_Pairs_dict[Vector] = (list(Obj_vector), uarray(X_vector, X_vector_E), uarray(Y_vector, Y_vector_E))
return Abundances_Pairs_dict
def test_nom_ueig():
sA = array([[1, 2], [3, 4]])
A = array([[0.1, 0.2], [0.1, 0.3]])
w, v = eig(A)
uA = uarray((A, sA))
uw, uv = ueig(A)
assert nominal_values(uw) == w
assert nominal_values(uv) == v
def setUp(self):
self.x = numpy.array([[-1.0], [0.0], [1.0]])
self.y = unumpy.uarray([2.0, 1.0, 6.0], [0.1, 0.1, 0.1])
self.a = 1.0
self.b = numpy.array([2.0])
self.c = numpy.array([[3.0]])
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
from uncertainties import ufloat
import uncertainties.unumpy as unp
import scipy.constants as const
from pylab import *
#C Wert 3
C20 = np.array([399 * 10**(-9), 450 * 10**(-9), 750 * 10**(-9)])
R3 = np.array([203, 222, 323])
R4 = np.array([797, 778, 677])
C2 = unp.uarray(C20, 0.002 * C20)
X = unp.uarray(R4 / R3, (R4 / R3) * 0.005) #R4/R3
Cx = C2 * X
M = np.mean(Cx) #Mittelwert
V = np.var(Cx) #Fehler des Mittelwerts
F = V**(0.5) / 3**(0.5)
print('Mittelwert Cx: ', "{:.12f}".format(M))
print('Fehler des Mittelwerts Cx: ', "{:.12f}".format(F))
differenz[i] = f_array[i]
else:
differenz[i] = f_array[i] - f_array[i-1]
print(differenz)
differenz *= 10**6
L = c/((np.sum(differenz)/4)*2)
print('L = ', L)
print('Abweichung = ', abweichungen(L_vergleich, L))
if __name__ == '__main__':
# polarisation
I = np.genfromtxt('daten/polarisation.txt',
unpack='True')
phi = np.linspace(0, 180, 19)
phi = unp.uarray(phi, 1)
phi_rad = (phi/360)*2*np.pi
I = unp.uarray(I, 0.005)
werteZuTabelle(noms(phi).astype(int), noms(I), rundungen=[0, 2])
plot(phi_rad, I, "Polarisation", "polarisation", r'$\phi/\si{\radian}$', r'$I/\si{\micro\ampere}$', fitfunktion_pol,
[0.8, 2, 0], ["I_0", "phi_verschieb", "m"])
# moden
x, I = np.genfromtxt('daten/tem00.txt',
unpack='True')
x = unp.uarray(x, 0.5)
I = unp.uarray(I, 0.01)
werteZuTabelle(noms(x).astype(int), noms(I), rundungen=[0, 3])
plot(x, I, r'TEM$_{00}$', 'grundmode', r'$x/\si{\milli\meter}$',
axis=1)
filenames = list(np.array(elements, dtype=object)[:, 0]) + legierungen
for i in range(len(filenames)):
np.savetxt('data/' + filenames[i] + '.txt',
data[:, 2 * i:2 * i + 2],
delimiter='\t',
header='E [eV]\tn [1/s]')
#####
# Kombiniertes Spektrum
#####
data = np.array(
[np.loadtxt('data/' + e[0] + '.txt', skiprows=1) for e in elements],
dtype=object)
data[:, :, 1] = unp.uarray(data[:, :, 1], data[:, :, 1] / np.sqrt(180))
plt.clf()
plt.title(u'Diagramm 3.1: Röntgenfluoreszenzspektrum verschiedener Elemente')
plt.xlabel('Strahlungsenergie $E \, [keV]$')
plt.ylabel(u'Zählrate ' + r'$n \, [\frac{Ereignisse}{s}]$')
for i in range(data.shape[0]):
p = papstats.plot_data(data[i, :, 0],
data[i, :, 1],
label=elements[i][0] + ' (' + str(elements[i][1]) +
')',
elinewidth=0.5,
capsize=4)
plt.fill_between(data[i, :, 0],
0,
unp.nominal_values(data[i, :, 1]),
F = 130 * 10**(-3) # meter
def uncertainty_theta(theta):
print('Delta theta in deg: ',
np.degrees(theta * (lam_2 - lam_1) / lam_m * np.tan(theta)))
return np.radians(1) * np.ones(
len(theta)) + theta * (lam_2 - lam_1) / lam_m * np.tan(theta)
theta_1_deg = 0.5 * np.array(
[44.5, 51.5, 75.0, 90.6, 96.6, 117.5, 135.0, 144.6]) #mm
theta_2_deg = 0.5 * np.array([
29.0, 47.5, 57.0, 69.6, 76.5, 88.0, 94.7, 106.5, 113.4, 126.5, 135.5,
156.0
]) #mm
theta_1 = np.radians(theta_1_deg)
theta_1 = unumpy.uarray(theta_1, uncertainty_theta(theta_1))
theta_2 = np.radians(theta_2_deg)
theta_2 = unumpy.uarray(theta_2, uncertainty_theta(theta_2))
def gittertest(m, theta):
return m / (unumpy.sin(theta)**2)
def gitterabstand(lam, m, theta):
return np.sqrt(m) * (lam / 2) / unumpy.sin(theta)
def linear_func(x, a, b):
return a * x + b
def output(n_refl,
gitter,
theta,
print(peak_two_3mm)
print(peak_two_9mm)
print(peak_two_12mm)
print()
Aufspaltung = [
peak_two_3mm - peak_one_3mm, peak_two_9mm - peak_one_9mm,
peak_two_12mm - peak_one_12mm
]
for i in Aufspaltung:
print(i)
Dicke = [3, 9, 12]
x_plot = np.linspace(3, 12, 2)
params, covar_matrix = curve_fit(linear, Dicke, Aufspaltung)
error = np.sqrt(np.diag(covar_matrix))
uparams = unp.uarray(params, error)
for i in range(2):
print(uparams[i])
plt.figure()
plt.plot(Dicke, Aufspaltung, "rx")
plt.plot(x_plot, linear(x_plot, *params))
plt.xlabel("d / mm")
plt.ylabel(r"$\Delta$ f / Hz")
#plt.savefig("../latex-template/figure/Peak_Aufspaltung.pdf")
plt.close()
import matplotlib.pyplot as plt
import numpy as np
import uncertainties.unumpy as unp
from scipy.optimize import curve_fit
from uncertainties import correlated_values, correlation_matrix
from uncertainties import ufloat
Uio, tio = np.genfromtxt('5awerteoben.txt', unpack=True)
Uiu, tiu = np.genfromtxt('5awerteunten.txt', unpack=True)
Uio /= 1000
Uiu /= 1000
tiu /= 1000000
tio /= 1000000
U = np.append(Uio, Uiu)
t = np.append(tio, tiu)
Uer = unp.uarray(U, 5e-5)
ter = unp.uarray(t, 1e-7)
#UUo = np.log((np.absolute(U[0 : -3])))
def f1(x, a, b):
return a * np.exp(-2 * np.pi * x * b)
oparam, ocvar = curve_fit(f1, tio, Uio) #oben
uparam, ucvar = curve_fit(f1, tiu[3:-1], Uiu[3:-1]) #unten
oparams = correlated_values(oparam, ocvar)
uparams = correlated_values(uparam, ucvar)
d_LiF *= 10**(-12)
alpha = 7.297 * 10**(-3)
h_eV = 4.1357 * 10**(-15)
# read vals
theta_zn, N_zn = np.genfromtxt('Zink.dat', unpack=True)
theta_ga, N_ga = np.genfromtxt('Gallium.dat', unpack=True)
theta_br, N_br = np.genfromtxt('Brom.dat', unpack=True)
theta_rb, N_rb = np.genfromtxt('Rubidium.dat', unpack=True)
theta_st, N_st = np.genfromtxt('Strontium.dat', unpack=True)
theta_zk, N_zk = np.genfromtxt('Zirkonium.dat', unpack=True)
names = ['Zink', 'Gallium', 'Brom', 'Rubidium', 'Strontium', 'Zirkonium']
thetas = [theta_zn, theta_ga, theta_br, theta_rb, theta_st, theta_zk]
Ns = [N_zn, N_ga, N_br, N_rb, N_st, N_zk]
theos = unp.uarray([9668.55, 10377.76, 13483.86, 15207.74, 16115.26, 18008.15],
[15, 16, 19, 22, 23, 26])
Zs = [30, 31, 35, 37, 38, 40]
E_K_array = np.empty(len(Zs))
i = 0
# make loop for all other stuffs
for name, theta, N, Z, theo in zip(names, thetas, Ns, Zs, theos):
print(f'-> {name}')
# make plot
plt.figure()
plt.plot(theta, N, 'b.', label=f'{name}')
plt.xlabel('Theta [°]')
plt.ylabel('Anzahl Impulse')
plt.legend()
def get_results(self):
# planet search files
fs = np.array(glob.glob('%s/EPIC_*/K2LC_-00099' % self.folder))
self.fs, self.epicnums = [], np.zeros(0)
# detected planet params
self.Ndetected, self.params_guess = np.zeros(0), np.zeros((0, 4))
self.params_optimized = np.zeros((0, 5))
self.Ps, self.e_Ps = np.zeros(0), np.zeros(0)
self.rps, self.e_rps = np.zeros(0), np.zeros(0)
# POI params
self.cond_vals, self.cond_free_params = np.zeros((0, 7)), np.zeros(
(0, 7))
# stellar params
self.Kepmags, self.efs = np.zeros(0), np.zeros(0)
self.Mss, self.e_Mss = np.zeros(0), np.zeros(0)
self.Rss, self.e_Rss = np.zeros(0), np.zeros(0)
self.Teffs, self.e_Teffs = np.zeros(0), np.zeros(0)
self.loggs, self.e_loggs = np.zeros(0), np.zeros(0)
for i in range(fs.size):
print float(i) / fs.size, fs[i]
d = loadpickle(fs[i])
if d.DONE:
for j in range(d.Ndet + 1):
self.fs.append(fs[i])
self.epicnums = np.append(self.epicnums, d.epicnum)
self.Ndetected = np.append(self.Ndetected, d.Ndet)
self.Kepmags = np.append(self.Kepmags, d.Kepmag)
self.efs = np.append(self.efs, d.ef.mean())
self.Mss = np.append(self.Mss, d.Ms)
self.e_Mss = np.append(self.e_Mss, d.e_Ms)
self.Rss = np.append(self.Rss, d.Rs)
self.e_Rss = np.append(self.e_Rss, d.e_Rs)
self.Teffs = np.append(self.Teffs, d.Teff)
self.e_Teffs = np.append(self.e_Teffs, d.e_Teff)
self.loggs = np.append(self.loggs, d.logg)
self.e_loggs = np.append(self.e_loggs, d.e_logg)
# save parameter guesses of detected planets
params = d.params_guess[j-1] if j > 0 \
else np.repeat(np.nan,4)
self.params_guess = np.append(self.params_guess,
params.reshape(1, 4),
axis=0)
# save optimized parameters
params_opt = d.params_optimized[j-1] if j > 0 \
else np.repeat(np.nan,5)
params_res = d.params_results[j-1] if j > 0 \
else np.repeat(np.nan,15).reshape(3,5)
assert params_res.shape == (3, 5)
self.params_optimized = np.append(self.params_optimized,
params_opt.reshape(1, 5),
axis=0)
# save transit vetting results
P = params[0]
Pss = d.params_guess_priorto_confirm[:, 0]
if Pss.size > 0:
g = abs(Pss - P) == np.min(abs(Pss - P))
assert g.sum() in range(2)
cond_vals = d.transit_condition_values[g] if j > 0 \
else np.repeat(np.nan,7)
else:
cond_vals = np.repeat(np.nan, 7)
self.cond_vals = np.append(self.cond_vals,
cond_vals.reshape(1, 7),
axis=0)
self.cond_free_params = np.append(
self.cond_free_params,
d.transit_condition_free_params.reshape(1, 7),
axis=0)
# save periods and planets radii
self.Ps = np.append(self.Ps, params_opt[0])
self.e_Ps = np.append(self.e_Ps,
get_1sigma(params_res[:, 0]))
rpRs = unp.uarray(params_opt[3],
get_1sigma(params_res[:, 3]))
Rs = unp.uarray(d.Rs, d.e_Rs)
rp, e_rp = rpRs2rp(rpRs, Rs)
self.rps = np.append(self.rps, rp)
self.e_rps = np.append(self.e_rps, e_rp)
_, self.unique_inds = np.unique(self.epicnums, return_index=True)
self.Nstar = self.unique_inds.size
assert self.unique_inds.size == self.Nstar
self.Nplanets = self.Ndetected[self.unique_inds].sum()
self.fs = np.array(self.fs)
abstand = abstand + hoehe_zylinder
abstand *= 1e-2
schwingungsdauer *= (1 / 5)
schwingungsdauer_hilf = []
schwingungsdauer_abweichung = []
#print(abstand[::3])
for i in range(len(schwingungsdauer))[::3]:
schwingungsdauer_hilf.append(np.mean(schwingungsdauer[i:i + 3]))
schwingungsdauer_abweichung.append(
1 / (np.sqrt(len(schwingungsdauer[i:i + 3]))) *
np.std(schwingungsdauer[i:i + 3]))
schwingungsdauer_mittel = np.array(schwingungsdauer_hilf)
schwingungsdauer_u = unp.uarray(schwingungsdauer_hilf,
schwingungsdauer_abweichung)
print(schwingungsdauer_u)
#print('Zeitlichesmittel_abweichung ', schwingungsdaer_abweichung_mitt)
def f(m, u, b):
return m * u + b
params_p, covarian = curve_fit(f, abstand[::3]**2, schwingungsdauer_mittel**2)
def linregress(x, y):
assert len(x) == len(y)
x, y = np.array(x), np.array(y)
N_E = np.genfromtxt('scripts/RolfBlank/0.Spe', unpack=True)
x = np.linspace(0, len(N_E), len(N_E))
E = 662 / 113.48 * x
plt.cla()
plt.clf()
plt.plot(E, N_E, 'r-', label=r'Energiespektrum')
plt.xlabel(r'$E/\si{\kilo\electronvolt}$')
plt.ylabel(r'N')
plt.xlim(0, 800)
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.legend(loc='best')
plt.savefig('build/Energiespektrum.pdf')
#Würfel 1, Bestimmung von I_0
I0_gerade = unp.uarray(50636, 254) / 300
print('I0_gerade', I0_gerade)
I0_schraeg1 = unp.uarray(16660, 146) / 100
I0_schraeg2 = unp.uarray(16417, 145) / 100
#I0_schraeg = np.mean([I0_schraeg1,I0_schraeg2])
I0_schraeg = avg_and_sem([noms(I0_schraeg1), noms(I0_schraeg2)])
I0_schraeg = unp.uarray(I0_schraeg[0], I0_schraeg[1])
print('I0_schraeg', I0_schraeg)
makeTable([
noms([I0_gerade * 300, I0_schraeg1 * 100, I0_schraeg2 * 100]),
stds([I0_gerade * 300, I0_schraeg1 * 100, I0_schraeg2 * 100]),
[300, 100, 100],
noms([I0_gerade, I0_schraeg1, I0_schraeg2]),
stds([I0_gerade, I0_schraeg1, I0_schraeg2])
], r'\multicolumn{2}{c}{' + r'$N_0$' + r'} & {' +
f1 = '/media/naikymen/SD64/Unsam/FQ/TP4 2016/Errores/vol08.csv' f2 = '/media/naikymen/SD64/Unsam/FQ/TP4 2016/Errores/vol008.csv' f3 = '/media/naikymen/SD64/Unsam/FQ/TP4 2016/Errores/abs.csv' f4 = '/media/naikymen/SD64/Unsam/FQ/TP4 2016/Errores/volAgua.csv' f5 = '/media/naikymen/SD64/Unsam/FQ/TP4 2016/Errores/volVBC.csv' f6 = '/media/naikymen/SD64/Unsam/FQ/TP4 2016/Errores/vol8.csv' d1 = genfromtxt(f1, delimiter=',') d2 = genfromtxt(f2, delimiter=',') d3 = genfromtxt(f3, delimiter=',') d4 = genfromtxt(f4, delimiter=',') d5 = genfromtxt(f5, delimiter=',') d6 = genfromtxt(f6, delimiter=',') ar8 = unumpy.uarray(d6[:, 0], d6[:, 1]) ar08 = unumpy.uarray(d1[:, 0], d1[:, 1]) ar008 = unumpy.uarray(d2[:, 0], d2[:, 1]) arabs = unumpy.uarray(d3[:, 0], d3[:, 1]) aragua = unumpy.uarray(d4[:, 0], d4[:, 1]) arVBC = unumpy.uarray(d5[:, 0], d4[:, 1]) vol = (ar8 + ar08 + ar008 + aragua + arVBC) mol = (ar8 * 0.8 + ar08 * 0.08 + ar008 * 0.008) conc = mol / vol mT = unumpy.matrix(conc) filename = "resconc.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n')
def plot_u(cal_file, fm_file, offset_file, description, accidental_offset,
results_file):
M = np.genfromtxt(cal_file)
N = np.genfromtxt(fm_file)
O = np.genfromtxt(offset_file)
i_helm = M[:, 1] #current applied to helmholtz for calibration measurement
b_helm = M[:,
2] #field applied to helmholtz coil for calibration measurement
p, cov = np.polyfit(
i_helm, b_helm, 1, cov=True
) #fit a line to calibration measurement so that we get a calibration
i_fm = N[:, 1] #current applied to helmmholtz for shielding measurement
b_fm = unumpy.uarray(
N[:, 2], 0.0005
) - accidental_offset #field measured inside of ferromagnet shield
B_earth = np.polyval(
p, 0
) #We get the Earths magnetic field from i=0 of the Helmholtz calibration
B_fm_no_i = unumpy.uarray(np.mean(O[:, 2]), np.std(
O[:, 2])) #Get average and error for initial magnetization
mag = B_fm_no_i - B_earth #initial magnetization is the field inside of the ferromagnet before any field is applied minus the earths magnetic field
Bin = b_fm - mag #internal magnetization is the measured internal field minus the initial magnetization. This correction might not be necessary for a soft ferromagnet
Bext = unumpy.uarray(np.polyval(p, i_fm), 0.0005) #external field
Bext_nom = unumpy.nominal_values(Bext)
Bext_err = unumpy.std_devs(Bext)
B = Bext / Bin
c = a / b
u = (-2 * B + c**2 - 2 * unumpy.sqrt(B**2 - B * c**2 - B + c**2) +
1) / (c**2 - 1)
u_nom = unumpy.nominal_values(u)
u_err = unumpy.std_devs(u)
#cakculate uerr with just point to point uncertainties. I define this as just
#uncertainty from the field measurements
u_pp = (-2 * B + c.nominal_value**2 - 2 *
unumpy.sqrt(B**2 - B * c.nominal_value**2 - B + c.nominal_value**2)
+ 1) / (c.nominal_value**2 - 1)
#calculate uerr from just geometry uncertainties
u_geom = (-2 * unumpy.nominal_values(B) + c**2 - 2 * unumpy.sqrt(
unumpy.nominal_values(B)**2 - unumpy.nominal_values(B) * c**2 -
unumpy.nominal_values(B) + c**2) + 1) / (c**2 - 1)
##obtain uncertainties from field
u_err_pp = unumpy.std_devs(u_pp)
##obtain uncertainties from geometry
u_err_geom = unumpy.std_devs(u_geom)
with open(results_file, "w") as myfile:
myfile.write('#Bext, sig_Bext, ur, sig_ur, sig_ur_pp, sig_ur_corr\n')
for j in range(0, len(u_nom)):
myfile.write('%s\t%s\t%s\t%s\t%s\t%s\n' %
(Bext_nom[j], Bext_err[j], u_nom[j], u_err[j],
u_err_pp[j], u_err_geom[j]))
plt.errorbar(Bext_nom, u_nom, u_err, marker='.', label=description)
plt.close()
return (unp.uarray(params[1], np.sqrt(np.diag(errors)[1])))
# RECHNEN
# berechne zugehoerige winkel theta
meta_winkel = winkel(camera_rad, r_meta)
# gitterkonstanten bcc metall
gk_m_bcc = gitter(bcc, wavelen, meta_winkel)
gk_m_fcc = gitter(fcc, wavelen, meta_winkel)
gk_m_dia = gitter(dia, wavelen, meta_winkel)
a_m_bcc = unp.uarray(
gk_m_bcc,
gk_korrektur_a(gk_m_bcc, meta_winkel, proben_rad, camera_rad) +
gk_korrektur_v(gk_m_bcc, meta_winkel, camera_rad, v))
a_m_fcc = unp.uarray(
gk_m_fcc,
gk_korrektur_a(gk_m_fcc, meta_winkel, proben_rad, camera_rad) +
gk_korrektur_v(gk_m_fcc, meta_winkel, camera_rad, v))
a_m_dia = unp.uarray(
gk_m_dia,
gk_korrektur_a(gk_m_dia, meta_winkel, proben_rad, camera_rad) +
gk_korrektur_v(gk_m_dia, meta_winkel, camera_rad, v))
# auf konsole ausgeben
#
# print("\n\n\nwinkel metall:\n")
# for element in meta_winkel:
# print(element)
def mag2flux(mag, err_mag):
umag = unumpy.uarray(mag, err_mag)
uflux = 10**(-0.4 * umag)
flux = unumpy.nominal_values(uflux)
err_flux = unumpy.std_devs(uflux)
return flux, err_flux
def salz_auswerten(atomfakt, fobj_out):
lit_cae_clo = 4.119e-10 #wiki
ss = generate_miller(
10, s_s, 1,
atomfakt) # atomfakt = 1 -> gleiche vorfakoren, 2 -> fuer ungleiche
ss = ss[:len(salz_winkel), :]
# print("len winkel",len(salz_winkel))
# print("len ss",len(ss[:,1]))
# print("ss=",ss)
cc = generate_miller(10, cs_cl, 1, atomfakt)
cc = cc[:len(salz_winkel), :]
# ss = np.array([[1, 1, 1],#3 ggu und guu verboten #stein_salz
# [0, 0, 2], # 4
# [0, 2, 2], # 8
# [1, 1, 3], # 11
# [2, 2, 2], # 12
# [0, 0, 4], # 16
# [1, 3, 3], # 19
# [0, 2, 4], # 20
# [2, 2, 4], # 24
# [3, 3, 3], # 27
# [0, 4, 4], # 32
# [1, 3, 5], # 35
# [2, 4, 4], # 36
# [0, 2, 6], # 40
# [3, 3, 5], # 43
# [4, 4, 4], # 48
# [1, 5, 5], # 51
# [0, 4, 6], # 52
# [2, 4, 6], # 56
# [3, 5, 5], # 59
# [4, 4, 6], # 68
# [0, 6, 6], # 72
# [5, 5, 5], # 75
# ])
#
# cc = np.array([[0, 0, 1],#1
# [0, 1, 1],#2
# [1, 1, 1],#3
# [0, 0, 2],#4 abgeschwächt
# [0, 1, 2],#5
# [1, 1, 2],#6
# [0, 2, 2],#8 abgeschwächt
# [0, 0, 3],#9
# [0, 1, 3],#10
# [1, 1, 3],#11
# [2, 2, 2],#12
# [0, 2, 3],#13
# [1, 2, 3],#14
# [0, 0, 4],#16
# [0, 1, 4],#17
# [1, 1, 4],#18
# [1, 3, 3],#19
# [0, 2, 4],#20
# [1, 2, 4],#21
# [2, 3, 3],#22
# [2, 2, 4],#24
# [0, 0, 5],#25
# [0, 1, 5],#26
# ])
zb = generate_miller(10, z_b, 1, atomfakt)
zb = zb[:len(salz_winkel), :]
# zb = np.array([[1, 1, 1],#3
# [0, 0, 2],#4
# [0, 2, 2],#8
# [1, 1, 3],#11
# [2, 2, 2],#12
# [0, 0, 4],#16
# [1, 3, 3],#19
# [0, 2, 4]#20
# ])
fluor = generate_miller(10, fluorit, 1, atomfakt)
fluor = fluor[:len(salz_winkel), :]
gk_s_ss = gitter(ss, wavelen, salz_winkel)
gk_s_cc = gitter(cc, wavelen, salz_winkel)
gk_s_fluor = gitter(fluor, wavelen, salz_winkel)
gk_s_zb = gitter(zb, wavelen, salz_winkel)
# gk_m_dia = gitter(dia, wavelen, salz_winkel)
a_s_ss = unp.uarray(
gk_s_ss,
gk_korrektur_a(gk_s_ss, salz_winkel, proben_rad, camera_rad) +
gk_korrektur_v(gk_s_ss, salz_winkel, camera_rad, v))
a_s_cc = unp.uarray(
gk_s_cc,
gk_korrektur_a(gk_s_cc, salz_winkel, proben_rad, camera_rad) +
gk_korrektur_v(gk_s_cc, salz_winkel, camera_rad, v))
a_s_fluor = unp.uarray(
gk_s_fluor,
gk_korrektur_a(gk_s_fluor, salz_winkel, proben_rad, camera_rad) +
gk_korrektur_v(gk_s_fluor, salz_winkel, camera_rad, v))
a_s_zb = unp.uarray(
gk_s_zb,
gk_korrektur_a(gk_s_zb, salz_winkel, proben_rad, camera_rad) +
gk_korrektur_v(gk_s_zb, salz_winkel, camera_rad, v))
# a_s_dia=unp.uarray(gk_s_dia,gk_korrektur_a(gk_s_dia, salz_winkel, proben_rad, camera_rad) + gk_korrektur_v(gk_s_dia, salz_winkel, camera_rad, v))
a_ss_end = gk_plot("ss" + str(atomfakt), salz_winkel, a_s_ss, gerade,
winkel_korrektur, [0, 23])
a_cc_end = gk_plot("cc" + str(atomfakt), salz_winkel, a_s_cc, gerade,
winkel_korrektur, [0, 23])
a_fluor_end = gk_plot("fluor" + str(atomfakt), salz_winkel, a_s_fluor,
gerade, winkel_korrektur, [0, 23])
a_zb_end = gk_plot("zb" + str(atomfakt), salz_winkel, a_s_zb, gerade,
winkel_korrektur, [0, 23])
fobj_out.write("\nFall:" + str(atomfakt) + "\n")
fobj_out.write("Salz ss a=" + str(a_ss_end) + "\n")
fobj_out.write("Salz Fluorit a=" + str(a_fluor_end) + "\n")
fobj_out.write("Salz zb =" + str(a_zb_end) + "\n")
fobj_out.write("Salz cc =" + str(a_cc_end) + "\n")
lit_LiI = 6e-10
lit_NH4Cl = 3.87e-10
if (atomfakt == 2):
fobj_out.write(
"\n\nSteinsalz LiI ist auserwählt!!!!! Die relative Abweichung beträgt:"
+ str((a_ss_end - lit_LiI) / lit_LiI) + "\n")
fobj_out.write(
"\n\nNH4CL ist auserwählt!!!!! Die relative Abweichung beträgt:" +
str((a_cc_end - lit_NH4Cl) / lit_NH4Cl) + "\n")
tabelle_fertig(r_salz, salz_winkel, ss, a_s_ss, "ss" + str(atomfakt))
tabelle_fertig(r_salz, salz_winkel, cc, a_s_cc, "cc" + str(atomfakt))
tabelle_fertig(r_salz, salz_winkel, fluor, a_s_fluor,
"fluor" + str(atomfakt))
tabelle_fertig(r_salz, salz_winkel, zb, a_s_zb, "zb" + str(atomfakt))
print("Gleich=1, Ungleich=2 =>", atomfakt)
print(" \nSalz ss", a_ss_end)
print(" \nSalz cc", a_cc_end)
print(" \nSalz fluor", a_fluor_end)
print(" \nSalz zb", a_zb_end)
# # 3. Setup data
# Read data file. Data points are stored in `csv` files.
# In[9]:
data = pd.read_csv('./data/Lundin2007.csv')
# Make error propagation possible.
# In[10]:
v = {
'en100':
unp.uarray(data['v(en100)'][~np.isnan(data['v(en100)'])],
data['sv(en100)'][~np.isnan(data['v(en100)'])]),
'en91':
unp.uarray(data['v(en91)'], data['sv(en91)']),
'en85':
unp.uarray(data['v(en85)'], data['sv(en85)'])
}
p_org = {
'en100':
unp.uarray(data['p(en100)'][~np.isnan(data['v(en100)'])],
data['sp(en100)'][~np.isnan(data['v(en100)'])]),
'en91':
unp.uarray(data['p(en91)'], data['sp(en91)']),
'en85':
unp.uarray(data['p(en85)'], data['sp(en85)'])
}
v_std = {}
def plot_on(
self,
ax1: plt.axis,
ax2,
style="stacked",
ylabel="Events",
sum_color=plot_style.KITColors.kit_purple,
draw_legend: bool = True,
legend_inside: bool = True,
):
bin_edges, bin_mids, bin_width = self._get_bin_edges()
self._bin_edges = bin_edges
self._bin_mids = bin_mids
self._bin_width = bin_width
sum_w = np.sum(np.array([
binned_statistic(comp.data,
comp.weights,
statistic="sum",
bins=bin_edges)[0]
for comp in self._mc_components["MC"]
]),
axis=0)
sum_w2 = np.sum(np.array([
binned_statistic(comp.data,
comp.weights**2,
statistic="sum",
bins=bin_edges)[0]
for comp in self._mc_components["MC"]
]),
axis=0)
hdata, _ = np.histogram(self._data_component.data, bins=bin_edges)
if style.lower() == "stacked":
ax1.hist(
x=[comp.data for comp in self._mc_components['MC']],
bins=bin_edges,
weights=[comp.weights for comp in self._mc_components['MC']],
stacked=True,
edgecolor="black",
lw=0.3,
color=[comp.color for comp in self._mc_components['MC']],
label=[comp.label for comp in self._mc_components['MC']],
histtype='stepfilled')
ax1.bar(x=bin_mids,
height=2 * np.sqrt(sum_w2),
width=self.bin_width,
bottom=sum_w - np.sqrt(sum_w2),
color="black",
hatch="///////",
fill=False,
lw=0,
label="MC stat. unc.")
if style.lower() == "summed":
ax1.bar(x=bin_mids,
height=2 * np.sqrt(sum_w2),
width=self.bin_width,
bottom=sum_w - np.sqrt(sum_w2),
color=sum_color,
lw=0,
label="MC")
ax1.errorbar(x=bin_mids,
y=hdata,
yerr=np.sqrt(hdata),
ls="",
marker=".",
color="black",
label=self._data_component.label)
y_label = self._get_y_label(False, bin_width, evts_or_cand=ylabel)
# ax1.legend(loc=0, bbox_to_anchor=(1,1))
ax1.set_ylabel(y_label, plot_style.ylabel_pos)
if draw_legend:
if legend_inside:
ax1.legend(frameon=False)
ylims = ax1.get_ylim()
ax1.set_ylim(ylims[0], 1.4 * ylims[1])
else:
ax1.legend(frameon=False, bbox_to_anchor=(1, 1))
ax2.set_ylabel(r"$\frac{\mathrm{Data - MC}}{\mathrm{Data}}$")
ax2.set_xlabel(self._variable.x_label, plot_style.xlabel_pos)
ax2.set_ylim((-1, 1))
try:
uhdata = unp.uarray(hdata, np.sqrt(hdata))
uhmc = unp.uarray(sum_w, np.sqrt(sum_w2))
ratio = (uhdata - uhmc) / uhdata
ax2.axhline(y=0, color=plot_style.KITColors.dark_grey, alpha=0.8)
ax2.errorbar(bin_mids,
unp.nominal_values(ratio),
yerr=unp.std_devs(ratio),
ls="",
marker=".",
color=plot_style.KITColors.kit_black)
except ZeroDivisionError:
ax2.axhline(y=0, color=plot_style.KITColors.dark_grey, alpha=0.8)
plt.subplots_adjust(hspace=0.08)
plt.savefig('plotabbeb.pdf')
Ag , Bg , rg ,pg ,stdg =stats.linregress(1+(1/V),g_abbe)
Bg_fehler=fehler_b(stdg,1+(1/V))
plt.figure(4)
#plt.errorbar(noms(R),noms(N_b) ,xerr=stds(R),yerr=stds(N_b), fmt='cx')
plt.plot(1+(1/V),g_abbe,'rx',label=r'$\mathrm{Messwerte}$')
plt.plot(x,Ag*x+Bg,'b-',label=r'$\mathrm{Ausgleichsfunktion}$')
plt.legend(loc='best')
plt.xlabel(r'$\mathrm{1+\frac{1}{V}}$')
plt.ylabel(r'$\mathrm{Gegenstandweite \ g/mm}$')
plt.savefig('plotabbeg.pdf')
print('\n f_abbe 1+V',Ab,'+-',stdb)
print('h`',Bg,'+-',Bg_fehler)
print('\n f_abbe 1+1/V',Ag,'+-',stdg)
print('h',Bb,'+-',Bb_fehler)
f_g=unp.uarray(Ag,stdg)
f_b=unp.uarray(Ab,stdb)
print((f_g+f_b)/2)
print(np.mean([f_g,f_b]))
ln = (1 / T - 1 / T0) * B
V_measured = ((np.exp(ln) + 1) / 1023)**(-1)
V_measured_u = unp.uarray([V_measured], [0.5])
lnR_R0_u = unp.log(1023 / V_measured_u - 1)
return lnR_R0_u
"""Calibration -> plots"""
CalibrationFilename = 'Data/MeasurementCalibration2.p'
CalibrationData = pickle.load(open(CalibrationFilename, "rb"))
EstimateB1(CalibrationData)
"""Calibration -> Deming regression"""
CalibrationData = np.array(CalibrationData, dtype=float)
fitparam, b1_std, b0_std = EstimateB_Deming(CalibrationData)
"""Time -> plots"""
#TimeFilename = 'Data/Corrected_MeasurementCalibration2.p'
#TimeData = pickle.load( open(TimeFilename, "rb" ) )
#Time = TimeData[:,0] #in millis
#Temperature = TimeData[:,2] #in celsius
#PlotTemperature(Time, Temperature)
print(
Tgrove_u(293.15 + 0.1,
Bgrove_u=unp.uarray([4680], [12]),
T0_u=unp.uarray([298.15], [0.1])))
from data_analysis_tools import *
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from scipy import optimize
from uncertainties import ufloat, unumpy
df = pd.read_csv('data.csv')
print(df)
# Preparing our data
masses = unumpy.uarray(df.iloc[1:, 0].to_numpy(), 0.004)
counts = unumpy.uarray(df.iloc[1:, 1] - 159,
np.sqrt(df.iloc[1:, 1]) + np.sqrt(159))
counts_per_m = counts / masses
print(counts_per_m)
def p(d, Eff, a):
return Eff * (1 - np.exp(-a * d)) / (a * d)
xdata = unumpy.nominal_values(masses)
ydata = unumpy.nominal_values(counts_per_m)
sigma = unumpy.std_devs(counts_per_m)
print(f"{xdata = }")
print(f"{ydata = }")
print(f"{sigma = }")
amplitude_of_peaks.append(amplitude)
sigma_of_peaks.append(sigma)
offset_of_peak.append(offset)
area_under_peak.append(area)
# Save data in table
print(index)
l.Latexdocument(
filename=abs_path('tabs/europium/peak_charakteristiken_eu.tex')).tabular(
data=[
index,
unp.uarray(noms(amplitude_of_peaks), stds(amplitude_of_peaks)),
unp.uarray(noms(sigma_of_peaks), stds(sigma_of_peaks)),
unp.uarray(noms(offset_of_peak), stds(offset_of_peak))
],
header=['Kanal / ', r'A / ', r'\sigma / ', r'\mu / '],
places=[0, (2.2, 2.2), (1.2, 1.2), (4.2, 1.2)],
caption='Bestimmte Eigenschaften der Peaks von $^{152}\ce{Eu}$.',
label='results_peaks_eu')
# ########################################################################### #
# ## --- Linear Regression to get transformations parameters--- ## #
# ########################################################################### #
def g(x, m, b):
'''Define linear function for Transformation purpose'''
return m * x + b
def main(argv: list) -> int:
# print(list(get_data(data_folder + "F0004CH1.CSV")))
# for xdata, ydata in get_all_data(data_folder, range(4, 42 + 1), [18]):
# plt.plot(xdata, ydata)
# plt.show()
#
# print(xdata)
# print(ydata)
# print()
def loading_dgl(t, loading_rate, alpha, t0):
return (loading_rate / alpha) * (1 - np.exp(-alpha * (t - t0)))
mask_array = [(6.3, 10), (3.9, 9.9), (0.39, 9.8), (0.29, 10.8), (0.244, 10.67), (3.634, 13.5), (0.2705, 10.4),
(-0.195, 10.16), (-0.0872, 10.16), (0.187, 10.7), (0.176, 10.86), (0.2903, 10.48), (0.2384, 10.83),
(0.29, 10.0684), (0.304, 10.5282), (0.452, 10.59), (0.344, 10.5), (0.3077, 9.67), (0.332, 10.31),
(0.332, 10.5), (0.2856, 10.79), (0.265, 10.369), (0.344, 10.32), (0.288, 10.34)]
def fitparameter_getter():
L = []
delta_L = []
A = []
delta_A = []
N_max = []
delta_N_max = []
for i, (xdata, ydata) in enumerate(get_all_data(data_detuning, range(4, 28))): # oder 28 + 1
a, b = mask_array[i]
x, y = zip(*list(get_data("data/detuning_coil_curves/F0028CH1.CSV")))
y = np.array(y)
# y = np.where(y < 0.07993, 0.08505, y)
y = np.mean(y[320:750]) # nominal Background value in volts
# print(y)
# y = np.where(y > 0.0542, 0.05055, y)
y = conv_volts_to_atomnumber(y, 0)
# print([conv_volts_to_atomnumber(0.5,0),conv_volts_to_atomnumber(0.5,4)])
# plt.plot(x[320:750], [y]*len(x[320:750]), marker = ".", linewidth=0)
xdata = np.array(xdata)
ydata = np.array(ydata)
ydata = conv_volts_to_atomnumber(ydata, 0)
ydata = ydata - y
# print(ydata)
# ydata = np.where(ydata < 0, 0, ydata)
omxdata, omydata = xdata, ydata
# n = 5
# omydata = rolling_mean(omydata, n)
@np.vectorize
def mask(x):
nonlocal a, b
return a <= x <= b
# print(a, b)
mxdata, mydata = list(omxdata), list(omydata)
# print(len(mxdata), len(mydata))
mxdata, mydata = tuple(mask_data(mask, mxdata, mydata))
popt, pcov = curve_fit(loading_dgl, mxdata, unp.nominal_values(mydata), maxfev=5000)
# plt.plot(mxdata, loading_dgl(mxdata, *popt), label=r"Loading-Fit-Function $\frac{L}{\alpha}(1-e^{-\alpha x})$")
# plt.plot(mxdata, unp.nominal_values(mydata), marker='.', linewidth=0, label="measured atom number")
# # plt.plot(xdata, unp.nominal_values(ydata), marker=".", linewidth=0)
# plt.xlabel("Time [s]")
# plt.ylabel("Number of Atoms")
# plt.title(r"Coil Current: 10.0A and $f_{AOM}=110.75$ Hz")
# print("L=", popt[0]," alpha=", popt[1], "N_max=", popt[0]/popt[1])
# plt.legend()
# plt.show()
# print(popt[2])
L.append(popt[0])
delta_L.append(np.sqrt(pcov[0][0]))
A.append(popt[1])
delta_A.append(np.sqrt(pcov[1][1]))
N_max.append(popt[0] / popt[1])
delta_N_max.append(
unp.std_devs(ufloat(popt[0], np.sqrt(pcov[0][0])) / ufloat(popt[1], np.sqrt(pcov[1][1]))))
return L, delta_L, A, delta_A, N_max, delta_N_max
L, delta_L, A, delta_A, N_max, delta_N_max = fitparameter_getter()
print(A)
print(delta_A)
print(L)
print(delta_L)
print(N_max)
all_fit_params = []
all_fit_params.append(A)
all_fit_params.append(L)
all_fit_params.append(N_max)
all_fit_params = np.array(all_fit_params)
delta_all_fit_params = []
delta_all_fit_params.append(delta_A)
delta_all_fit_params.append(delta_L)
delta_all_fit_params.append(delta_N_max)
delta_all_fit_params = np.array(delta_all_fit_params)
def detuning_calculator(x):
return (2 * x) - 60 - (2 * 85) # Mhz
titles = np.array([r"$\alpha \ [\frac{1}{s}]$ vs. Detuning Frequency [MHz]",
r"Loss rate L $[\frac{1}{s}]$ vs. Detuning Frequency [MHz]"
, r"$N_{max} \ [-]$ vs. Detuning Frequency [MHz]"])
ylabels = np.array([r"$\alpha \ [\frac{1}{s}]$", r"Loss rate L $[\frac{1}{s}]$", r"$N_{max} \ [-]$"])
for z in range(1, 4):
i = 1
plt.errorbar(detuning_calculator(np.array([109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
all_fit_params[z - 1][6 * (i - 1): (6 * i)],
label="(9.0 +/- 0.1)A", yerr=delta_all_fit_params[z - 1][6 * (i - 1): (6 * i)], fmt=".")
plt.xlabel("Detuning [MHz]")
plt.ylabel(ylabels[z - 1])
i = 2
plt.errorbar(detuning_calculator(np.array([109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
all_fit_params[z - 1][6 * (i - 1): (6 * i)],
label="(9.5 +/- 0.1)A", yerr=delta_all_fit_params[z - 1][6 * (i - 1): (6 * i)], fmt=".")
i = 3
plt.errorbar(detuning_calculator(np.array([109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
all_fit_params[z - 1][6 * (i - 1): (6 * i)],
label="(10.0 +/- 0.1)A", yerr=delta_all_fit_params[z - 1][6 * (i - 1): (6 * i)], fmt=".")
i = 4
plt.errorbar(detuning_calculator(np.array([109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
all_fit_params[z - 1][6 * (i - 1): (6 * i)],
label="(10.35 +/- 0.1)A", yerr=delta_all_fit_params[z - 1][6 * (i - 1): (6 * i)], fmt=".")
plt.title(titles[z - 1])
plt.legend()
plt.show()
def magnetic_field_gradient(current):
return (1.1E-6 * (90 * current / (8.5 ** 2))) / (10 ** -6) # i: current in Ampere, units: mikroT/cm
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(detuning_calculator(np.array(
[109.75, 110.25, 110.75, 111.25, 111.75, 112.25, 109.75, 110.25, 110.75, 111.25, 111.75, 112.25, 109.75, 110.25,
110.75, 111.25, 111.75, 112.25, 109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
magnetic_field_gradient(np.array(
[9, 9, 9, 9, 9, 9, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 10, 10, 10, 10, 10, 10, 10.35, 10.35, 10.35,
10.35, 10.35, 10.35])), N_max)
ax.plot(detuning_calculator(np.array(
[109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
magnetic_field_gradient(np.array(
[9, 9, 9, 9, 9, 9])), N_max[0:6], label= "9.0 +/- 0.1 A")
ax.plot(detuning_calculator(np.array(
[109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
magnetic_field_gradient(np.array(
[9.5, 9.5, 9.5, 9.5, 9.5, 9.5])), N_max[6:12], label= "9.5 +/- 0.1 A")
ax.plot(detuning_calculator(np.array(
[109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
magnetic_field_gradient(np.array(
[10, 10, 10, 10, 10, 10])), N_max[12:18], label= "10 +/- 0.1 A")
ax.plot(detuning_calculator(np.array(
[109.75, 110.25, 110.75, 111.25, 111.75, 112.25])),
magnetic_field_gradient(np.array(
[10.35, 10.35, 10.35, 10.35, 10.35, 10.35])), N_max[18:24], label= "10.35 +/- 0.1 A")
ax.set_xlabel('Detuning Frequency [MHz]')
ax.set_ylabel(r'Magnetic Field Gradient [$\frac{\mu T}{cm}$]')
ax.set_zlabel(r'$N_{max}$')
plt.legend()
# plt.savefig("3dplot.pdf", format="pdf")
plt.show()
# return 0
titles_load_curve = np.array(
["10ms", "5ms", "3ms", "7ms", "9ms", "12ms", "11ms", "13ms", "14ms", "15ms", "16ms", "17ms", "18ms", "19ms",
"20ms", "21ms", "22ms", "23ms",
"24ms", "25ms", "26ms", "27ms", "28ms", "29ms", "30ms", "40ms", "50ms", "60ms", "70ms", "80ms", "90ms",
"100ms"])
mask_array_N0 = [(-1.14, -0.204), (-1.139, -0.0259), (-1.195, -0.259), (-1.193, -0.244), (-1.138, -0.094),
(-1.194, -0.204), (-1.194, -0.2046), (-1.63, -0.26), (-4.36, -0.63), (-4.47, -0.628),
(-4.259, -0.408), (-4.369, -0.738), (-4.47, -0.29), (-4.259, -0.628), (-4.369, -0.628),
(-4.479, -0.408), (-4.259, -0.408), (-4.479, -0.408), (-4.36, -0.628), (-4.36, -0.298),
(-4.479, -0.298), (-8.73, -1.47), (-8.95, -0.59), (-8.739, -0.59), (-8.739, -0.376),
(-8.739, -0.59), (-22.29, -1.39), (-22.84, -1.39), (-22.84, -3.04), (-23.0, -3.04),
(-22.84, -3.04), (-24.5, -1.39)]
mask_array_Nmax = [(10.0295, 10.5798), (5.077, 5.796), (3.041, 4.08), (7.058, 7.77), (9.04, 9.86), (12.06, 12.83),
(11.075, 11.84), (12.99, 19.98), (14.22, 15.21), (15.108, 16.42), (16.2, 17.74), (17.0, 18.4),
(18.18, 19.5), (19.17, 20.61), (20.17, 22.04),
(21.16, 22.59), (22.04, 23.58), (22.15, 23.9),
(24.13, 25.67), (25.012, 26.99), (26.11, 28.31), (27.35, 29.55), (28.45, 31.09), (29.33, 31.75),
(30.43, 33.73), (40.56, 44.08), (50.88, 59.0), (60.23, 67.0), (70.68, 74.0), (81.69, 85.0),
(89.9, 94.0), (100.4, 105.0)]
averages_N0 = []
std_devs_N0 = []
averages_Nmax = []
std_devs_Nmax = []
for i, (xdata, ydata) in enumerate(get_all_data(data_folder, range(4, 36))):
a, b = mask_array_N0[i]
c, d = mask_array_Nmax[i]
x, y = zip(*list(get_data("data/loading_curves/F0011CH1.CSV")))
y = np.array(y)
y = np.mean(y[1000:1800])
xdata = np.array(xdata)
xdata = xdata / (10 ** -3)
ydata = np.array(ydata) - y
@np.vectorize
def mask1(x):
nonlocal a, b
return a <= x <= b
@np.vectorize
def mask2(x):
nonlocal c, d
return c <= x <= d
xdata, ydata = list(xdata), list(ydata)
m1xdata, m1ydata = tuple(mask_data(mask1, xdata, ydata))
m2xdata, m2ydata = tuple(mask_data(mask2, xdata, ydata))
plt.plot(xdata, ydata , marker=".", linewidth=0)
plt.title(titles_load_curve[i] + " Down time")
plt.xlabel("time [ms]")
plt.ylabel("Intensity [a.u.]")
plt.show()
averages_N0.append(np.mean(m1ydata))
std_devs_N0.append(np.std(m1ydata))
averages_Nmax.append(np.mean(m2ydata))
std_devs_Nmax.append(np.std(m2ydata))
# print(averages_N0)
# print(std_devs_N0)
uarray_Nmax = unp.uarray(averages_Nmax, std_devs_Nmax)
uarray_N0 = unp.uarray(averages_N0, std_devs_N0)
print(uarray_Nmax, uarray_N0)
down_time = np.array(
[10, 5, 3, 7, 9, 12, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 40, 50, 60, 70,
80, 90, 100]) * 10 ** -3
down_time, uarray_N0, uarray_Nmax = tuple(sort_together(down_time, uarray_N0, uarray_Nmax))
uarray_N0 = np.array(uarray_N0)
uarray_Nmax = np.array(uarray_Nmax)
down_time = np.array(down_time)
plt.errorbar(down_time, unp.nominal_values(uarray_Nmax / uarray_N0), marker=".",
yerr=unp.std_devs(uarray_Nmax / uarray_N0), label="data points")
def fitfunc(x, temp):
M = (85.4678 * (1.6605e-27)) # kg
chi = np.sqrt(M / (k * temp)) * ((1.5e-3) / (x))
return scipy.special.erf(chi) - ((2 / np.sqrt(np.pi)) * chi * np.exp(-(chi ** 2)))
popt, pcov = curve_fit(fitfunc, down_time, unp.nominal_values(uarray_Nmax / uarray_N0),
sigma=unp.std_devs(uarray_Nmax / uarray_N0))
plt.plot(down_time, fitfunc(down_time, *popt), label = r"Fit of $\frac{N(t)}{N_0} \ = \ erf(\chi) \ - \ \frac{2}{\sqrt{\pi}}\chi e^{-\chi^2}$")
print("We get a MOT-Temperature of:", "(",popt[0] * 10 ** 6, "+-", np.sqrt(pcov[0][0]) * 10 ** 6,") micro Kelvin")
plt.title("Fraction of Recaptured Atoms vs. Down Time")
plt.xlabel("down time [s]")
plt.ylabel(r"$\frac{N(t)}{N_0}$")
plt.legend()
plt.savefig("releaserecap.pdf", format="pdf")
plt.show()
diffs = (unp.nominal_values(uarray_Nmax / uarray_N0) - fitfunc(down_time, *popt)) / unp.std_devs(uarray_Nmax / uarray_N0)
diffs_squared = diffs ** 2
chi2 = np.sum(diffs_squared)
n_data_points = len(down_time)
n_fit_parameters = 1
n_dof = n_data_points - n_fit_parameters
print("chi2/ndf = " + str(round(chi2, 2)) + "/" + str(n_dof))
print(r"So we get chi2_red$ = ", round(chi2, 2)/n_dof)
return 0
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import uncertainties as u
import uncertainties.unumpy as unp
parser = argparse.ArgumentParser()
parser.add_argument("--path", default="./results/theta-simulation/fresnel-theta-simulation.pkl")
args = parser.parse_args()
df = pd.read_pickle(args.path)
# Bin entries by groove number.
bins = np.arange(0.0, 12.5, 1.0)
groups = df.groupby(np.digitize(df.theta, bins))
x = -groups.mean().centroid_x.values
z_r90 = unp.uarray(-groups.mean().z_r90.values, groups.std().z_r90.values)
# z_r90 = unp.uarray(-groups.mean().centroid_z.values, groups.std().centroid_z.values)
f, ax = plt.subplots()
ax.errorbar(x, unp.nominal_values(z_r90), yerr=unp.std_devs(z_r90), fmt='.', label="Simulated $ r_{90}$")
def fit(x, y):
from ROOT import TF1, TGraphAsymmErrors
g = TGraphAsymmErrors(len(x))
for i in xrange(len(x)):
g.SetPoint(i, x[i], y[i].nominal_value)
g.SetPointError(i, 0, 0, y[i].std_dev, y[i].std_dev)
fit = TF1("fit", "-[1]*x*x+[0]", -40, 120)
fit.SetParNames("z0", "a")
g.Fit(fit)
return fit
print(R_1_4)
# Import Data
nu_1, U_1, dU_1 = np.genfromtxt("data/data_a_1.txt",unpack=True)
nu_2, U_2, dU_2 = np.genfromtxt("data/data_a_2.txt",unpack=True)
nu_3, U_3, dU_3 = np.genfromtxt("data/data_a_3.txt",unpack=True)
nu_4, U_4, dU_4 = np.genfromtxt("data/data_a_4.txt",unpack=True)
print(len(nu_1))
print(len(nu_2))
print(len(nu_3))
print(len(nu_4))
with open('build/a_data_1.tex', 'w') as f:
f.write(table([r'$\nu / \si{\kilo\hertz}$', r'$U / \si{\volt}$',
r'$\nu / \si{\kilo\hertz}$', r'$U / \si{\volt}$'],
[nu_1[0:7]/1e3, unp.uarray(U_1[0:7], dU_1[0:7]),
nu_1[7:14]/1e3, unp.uarray(U_1[7:14], dU_1[7:14])]
))
with open('build/a_data_2.tex', 'w') as f:
f.write(table([r'$\nu / \si{\kilo\hertz}$', r'$U / \si{\volt}$',
r'$\nu / \si{\kilo\hertz}$', r'$U / \si{\volt}$'],
[nu_2[0:9]/1e3, unp.uarray(U_2[0:9], dU_2[0:9]),
nu_2[9:18]/1e3, unp.uarray(U_2[9:18], dU_2[9:18])]
))
with open('build/a_data_3.tex', 'w') as f:
f.write(table([r'$\nu / \si{\kilo\hertz}$', r'$U / \si{\milli\volt}$',
r'$\nu / \si{\kilo\hertz}$', r'$U / \si{\milli\volt}$'],
[nu_3[0:10]/1e3, unp.uarray(U_3[0:10], dU_3[0:10])*1e3,
nu_3[10:20]/1e3, unp.uarray(U_3[10:20], dU_3[10:20])*1e3]
))
with open('build/a_data_4.tex', 'w') as f:
def ab(am,at):
return (am-at)/at
m_g=107.67
m_gw=465.18#
Tgw=293.40
Tgm=296.63
Tg=352.19
ckz=ck(m_zw,m_z,Tzm,Tzw,Tz)
ckg=ck(m_gw,m_g,Tgm,Tgw,Tg)
#ckg=ck(465.18,107.67,295.63,293.40,352.19)
ckz=unp.uarray(np.average(ckz),np.std(ckz))
Tzm=np.average(Tzm)
print('Abweichung von ckz',ab(noms(ckz),0.23))
print('Abweichung von ckg',ab(ckg,0.715))
print('ckz',ckz)
print('ckg',ckg)
Cz=C(ckz,Molz,az,kz,rhoz,Tzm)
Cg=C(ckg,Molg,ag,kg,rhog,Tgm)
print('Cz',Cz)
print('Cg',Cg)
print('3R',3*8.3144598)
print('Abweichung von 3R z',ab(noms(Cz),3*8.3144598))
decay_rate_calculated = decay_rate(area_under_peak, angle_distribution,
prohability, efficency_calculated,
measurment_time)
print('Gemittelte Aktivität', decay_rate_calculated.mean())
# ########################################################################### #
# #### --- Speicherergebnisse Peak Eigenschaften in eine Tabelle --- ######## #
# ########################################################################### #
l.Latexdocument(
filename=abs_path('tabs/sb_or_ba/peak_fit_parameter.tex')).tabular(
data=[
peak_indexes[0],
unp.uarray(noms(amplitude_of_peaks), stds(amplitude_of_peaks)),
unp.uarray(noms(sigma_of_peaks), stds(sigma_of_peaks)),
unp.uarray(noms(offset_of_peak), stds(offset_of_peak))
],
header=[
'Kanal / ', r'Amplitude / None ', r'\sigma /\kilo\eV',
r'\mu / \kilo\eV'
],
places=[0, (1.2, 1.2), (1.2, 1.2), (2.2, 1.2)],
caption='Regressionsparameter der Peak-Anpassung.',
label='results_peaks')
l.Latexdocument(
filename=abs_path('tabs/sb_or_ba/peak_charakteristiken.tex')
).tabular(
data=[
B_1 = eichfunktion(current, *params)
print(f'\tB: {B_1}')
d_lambda = wellenlaengenAenderung(del_s, delta_s, d_lambda_D)
delta_mg = g_factor(d_lambda, B_1, lambda_1)
# print(f'\tWellenlängenänderung: {d_lambda}')
# print(f'\tDelta_mg: {delta_mg}')
# print(f'\tMittelwert: {sum(delta_mg)/len(delta_mg)}')
print(f'\tMittelwert Delta_mg: {sum(delta_mg)/len(delta_mg)}')
# save results
make_table(header= ['$\delta s$ / pixel', '$\Delta s$ / pixel', '$\delta\lambda$ / \pico\meter', '$g$'],
places= [3.0, 3.0, 2.2, (1.2, 1.2)],
data = [delta_s, del_s, d_lambda*1e12, delta_mg],
caption = 'Werte zur Bestimmung des Lande-Faktors für die rote Spektrallinie.',
label = 'tab:rot_sigma',
filename = 'build/rot_sigma.tex')
if __name__ == '__main__':
if not os.path.isdir('build'):
os.mkdir('build')
lambda_1 = 643.8e-9 # nano meter
lambda_2 = 480e-9 # nano meter
lande_factors()
d_lambda_1, d_lambda_2 = lummer_gehrke_platte()
p, e = eichung()
params = unp.uarray(p, e)
auswertung_blau(params, d_lambda_2)
auswertung_rot(params, d_lambda_1)
import math
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from pint import UnitRegistry
import latex as l
import result
#import pandas as pd
r = result.Results()
u = UnitRegistry()
Q_ = u.Quantity
#umrechnung einheiten mit var.to('unit')
# Einheiten für pint:dimensionless, meter, second, degC, kelvin
#beispiel:
a = ufloat(5, 2) * u.meter
b = Q_(unp.uarray([5, 4, 3], [0.1, 0.2, 0.3]), 'ohm')
c = Q_(0, 'degC')
#variabel_1,variabel_2=np.genfromtxt('name.txt',unpack=True)
#Standartabweichung und Mittelwert
def mittel_und_abweichung(messreihe):
messreihe_einheit = messreihe.units
mittelwert = sum(messreihe) / len(messreihe)
abweichung_des_mittelwertes = 1 / (np.sqrt(
len(messreihe))) * np.std(messreihe)
mittel_und_abweichung = Q_(
unp.uarray(mittelwert, abweichung_des_mittelwertes), messreihe_einheit)
return mittel_und_abweichung
#Einlesen der Daten
Ck_a_b_in_nF, Bäuche, fehler_bäuche, v_plus_in_kHz, v_minus_in_kHz, fehler_frequenzen = np.genfromtxt(
'messdaten_a_b.txt', unpack=True)
Ck_c_in_nF, Delta_t_1_in_ms, Delta_t_2_in_ms, fehler_zeiten = np.genfromtxt(
'messdaten_c.txt', unpack=True)
L_in_mH = 23.954
C_in_nF = 0.7932
Csp_in_nF = 0.028
f_start_in_kHz = 20.06
f_end_in_kHz = 68.97
f_resonanz_gemessen_in_kHz = 35.65
Fehler_Ck = 0.003
f_res_gemessen = ufloat(35.65, 0.02)
#Messgrößen mit Fehlern
Bäuche = unp.uarray(Bäuche, fehler_bäuche)
v_plus_in_kHz = unp.uarray(v_plus_in_kHz, fehler_frequenzen)
v_minus_in_kHz = unp.uarray(v_minus_in_kHz, fehler_frequenzen)
Delta_t_1_in_ms = unp.uarray(Delta_t_1_in_ms, fehler_zeiten)
Delta_t_2_in_ms = unp.uarray(Delta_t_2_in_ms, fehler_zeiten)
#Kapazitäten mit Fehlern (gerundet auf 3 signifikante Stellen)
Ck_a_b_Fehler_nF = unp.uarray(Ck_a_b_in_nF,
np.round(Ck_a_b_in_nF * Fehler_Ck, 3))
Ck_c_Fehler_nF = unp.uarray(Ck_c_in_nF, np.round(Ck_c_in_nF * Fehler_Ck, 3))
#Werte in SI
Ckab = Ck_a_b_Fehler_nF * 10**(-9)
Ckc = Ck_c_Fehler_nF * 10**(-9)
L = L_in_mH * 10**(-3)
C = C_in_nF * 10**(-9)