def local_fit(x, y, errors, mu, sigma):
func = lambda x, mu, sigma, A, a0, a1: GAUSS(x, mu, sigma, A) + a0 + a1 * x
fit = Fit(func)
fit.mu = _simple_peak(y, mu, sigma)
fit.sigma = sigma
fit.A = y[fit.mu]
fit.a0 = 0
fit.a1 = 0
for i in range(5):
lower = max(fit.mu - 5 * fit.sigma, 0)
upper = min(fit.mu + 5 * fit.sigma, len(x))
lx = x[lower:upper]
ly = y[lower:upper]
lerrors = errors[lower:upper]
if i <= 2:
fit.fit(lx, ly, lerrors, solver="curve_fit")
else:
fit.fit(lx, ly, lerrors, solver="minuit", method="migrad")
return fit
def energieaufloesung(calibration, plot=True):
print("##### ENERGY RESOLUTION #####")
energies = []
widths = []
sigma_energies = []
sigma_widths = []
for filename, meta in kalib.items():
experiment = Experiment("data/" + filename,
title=meta["title"],
calibration=calibration)
for peak in meta["peaks"]:
mu0, sigma0 = peak[0], peak[1]
fit = experiment.find_peak(mu0, sigma0, plot=False)
energies.append(experiment.channel2energy(fit.mu))
widths.append(experiment.channelwidth2energywidth(fit.sigma))
sigma_energies.append(
experiment.channelwidth2energywidth(fit.sigma_mu))
sigma_widths.append(
experiment.channelwidth2energywidth(fit.sigma_sigma))
for filename, meta in data.items():
experiment = Experiment("data/" + filename,
title=filename,
calibration=calibration)
experiment.subtract_empty("data/G20_Leer.mca", 0.5)
for peak in meta["peaks"]:
mu0, sigma0 = peak[0], peak[1]
fit = experiment.find_peak(mu0, sigma0, plot=False)
energies.append(experiment.channel2energy(fit.mu))
widths.append(experiment.channelwidth2energywidth(fit.sigma))
sigma_energies.append(
experiment.channelwidth2energywidth(fit.sigma_mu))
sigma_widths.append(
experiment.channelwidth2energywidth(fit.sigma_sigma))
energies = np.array(energies)
widths = np.array(widths)
sigma_energies = np.array(sigma_energies)
sigma_widths = np.array(sigma_widths)
X = energies
Y = np.power(widths, 2)
SX = sigma_energies
SY = 2 * widths * sigma_widths
func = lambda x, a0, a1, : a0 + x * a1 #+np.power(x,2)*a2
fit = Fit(func)
fit.a0 = 1
fit.a1 = 1
for _ in range(10):
err = fit.combine_errors(X, SX, SY)
fit.fit(X, Y, err)
if plot:
plt.clf()
plt.errorbar(X, Y, xerr=SX, yerr=SY, fmt=',')
fit.plot(np.min(X),
np.max(X),
box='br',
units={
'a0': 'keV',
'a1': r'\sqrt{keV}'
})
plt.xlabel(r"$ E $ / keV")
plt.ylabel(r"$ \Delta E^2 / keV^2$")
plt.title(r'Energieauflösung: Fit zu $ \Delta E^2 = a_0 + a_1 E $'
) # \oplus \frac{c}{E}
plt.savefig("out/energyresolution_fit." + SAVETYPE)
plt.clf()
err = fit.combine_errors(X, SX, SY)
fit.plot_residuums(X, Y, err, box='tr', fmt=",")
plt.xlabel(r"$ E $ / keV")
plt.ylabel(r"$ \Delta E^2 / keV^2$")
plt.title("Energieauflösung: Residuen")
plt.savefig("out/energyresolution_residuum." + SAVETYPE)
with LatexTable("out/energyresolution.tex") as table:
table.header("Parameter", "Wert")
table.row("$a_0$", format_error(fit.a0, fit.sigma_a0, unit="keV^2"))
table.row("$a_1$", format_error(fit.a1, fit.sigma_a1, unit="keV"))
table.hline()
a = math.sqrt(fit.a0)
b = math.sqrt(fit.a1)
sa = 0.5 * fit.sigma_a0 / a
sb = 0.5 * fit.sigma_a1 / b
table.row("$a$", format_error(a, sa, unit="keV"))
table.row("$b$", format_error(b, sb, unit="\sqrt{keV}"))
with LatexTable("out/energyresolution_examples.tex") as table:
energies = np.linspace(10, 60, 6)
sigmas = np.sqrt(fit.apply(energies))
deltas = sigmas * 2 * math.sqrt(2 * math.log(2))
table.header("Energie",
"Auflösung",
"Relative Auflösung",
"FWHM",
lineafter=0)
table.row("$E$", "$\sigma$", "$\sigma / E$",
"$2 \sqrt{2 \ln{2}} \sigma$")
table.hline(2)
for energy, sigma, delta in zip(energies, sigmas, deltas):
e = "%d keV" % energy
s = _n(sigma * 1000) + " eV"
d = "%d eV" % (delta * 1000)
table.row(e, s, _n(sigma / energy * 100) + r"\%", d)