def plot_and_fit(data: List,
title: str = '',
xlabel: str = 'Charge (pes)',
ylabel: str = 'Entries / bin',
num_bins: int = 100) -> Tuple[float, float, float]:
# Fitting function
def gauss(x, amplitude, mu, sigma):
return amplitude / (2 * np.pi)**.5 / sigma * np.exp(
-0.5 * (x - mu)**2. / sigma**2.)
# Plotting the data
fig = plt.figure(figsize=(8, 5))
mean = np.mean(data)
max_range = 0.1
plt_range = ((1. - max_range) * mean, (1. + max_range) * mean)
y, x, _ = plt.hist(data, bins=num_bins, range=plt_range)
x = shift_to_bin_centers(x)
# Fitting data
seed = 1000, mean, mean * 0.01
sigma = poisson_sigma(y)
max_range = 0.05
fit_range = ((1. - max_range) * mean, (1. + max_range) * mean)
f = fitf.fit(gauss, x, y, seed, fit_range=fit_range, sigma=sigma)
amplitude, mu, sigma = f.values[0], f.values[1], f.values[2]
mu_err, sigma_err = f.errors[1], f.errors[2]
fwhm = 2.35 * sigma / mu
# Plotting the gauss fit
mx = np.linspace(fit_range[0], fit_range[1], 1000)
legend = f"$\mu$ = {mu:.3f}\n"
legend += f"$\sigma$ = {sigma:.3f}\n"
legend += f"fwhm = {fwhm/units.perCent:.2f} %"
plt.plot(mx, f.fn(mx), 'r-')
plt.plot(mx, gauss(mx, amplitude, mu, sigma), 'r-', label=legend)
plt.title(title, size=14)
plt.xlabel(xlabel, size=14)
plt.ylabel(ylabel, size=14)
plt.legend(loc=1)
plt.show()
# Verbosing
print(f"DATA from {title} ...\n" + \
f"mu = {mu:10.3f} +- {mu_err:.3f}\n" +\
f"sigma = {sigma:10.3f} +- {sigma_err:.3f} -> " + \
f"fwhm = {fwhm/units.perCent:.3f} %\n"
f"Chi2 = {f.chi2:10.3f}\n")
return mu, sigma, fwhm
def compute_drift_v(zdata: np.array,
nbins: int = 35,
zrange: Tuple[float, float] = (500, 640),
seed: Tuple[float, float, float, float] = None,
detector: str = 'new') -> Tuple[float, float]:
"""
Computes the drift velocity for a given distribution
using the sigmoid function to get the cathode edge.
Parameters
----------
zdata: array_like
Values of Z coordinate.
nbins: int (optional)
The number of bins in the z coordinate for the binned fit.
zrange: length-2 tuple (optional)
Fix the range in z.
seed: length-4 tuple (optional)
Seed for the fit.
detector: string (optional)
Used to get the cathode position from DB.
plot_fit: boolean (optional)
Flag for plotting the results.
Returns
-------
dv: float
Drift velocity.
dvu: float
Drift velocity uncertainty.
"""
y, x = np.histogram(zdata, nbins, zrange)
x = shift_to_bin_centers(x)
if seed is None: seed = np.max(y), np.mean(zrange), 0.5, np.min(y)
z_cathode = DB.DetectorGeo(detector).ZMAX[0]
try:
f = fitf.fit(sigmoid,
x,
y,
seed,
sigma=poisson_sigma(y),
fit_range=zrange)
dv = z_cathode / f.values[1]
dvu = dv / f.values[1] * f.errors[1]
except RuntimeError:
print(
"WARNING: Sigmoid fit for dv computation fails. NaN value will be set in its place."
)
dv, dvu = np.nan, np.nan
return dv, dvu
def compute_drift_v(zdata: np.array,
nbins: int = 35,
zrange: Tuple[float, float] = (500, 640),
seed: Tuple[float, float, float, float] = None,
detector: str = 'new',
plot_fit: bool = False) -> Tuple[float, float]:
"""
Computes the drift velocity for a given distribution
using the sigmoid function to get the cathode edge.
Parameters
----------
zdata: array_like
Values of Z coordinate.
nbins: int (optional)
The number of bins in the z coordinate for the binned fit.
zrange: length-2 tuple (optional)
Fix the range in z.
seed: length-4 tuple (optional)
Seed for the fit.
detector: string (optional)
Used to get the cathode position from DB.
plot_fit: boolean (optional)
Flag for plotting the results.
Returns
-------
dv: float
Drift velocity.
dvu: float
Drift velocity uncertainty.
"""
y, x = np.histogram(zdata, nbins, zrange)
x = shift_to_bin_centers(x)
if seed is None: seed = np.max(y), np.mean(zrange), 0.5, np.min(y)
f = fitf.fit(sigmoid, x, y, seed, sigma=poisson_sigma(y), fit_range=zrange)
z_cathode = DB.DetectorGeo(detector).ZMAX[0]
dv = z_cathode / f.values[1]
dvu = dv / f.values[1] * f.errors[1]
if plot_fit:
plt.figure()
plt.hist(zdata, nbins, zrange)
xx = np.linspace(zrange[0], zrange[1], nbins)
plt.plot(xx, sigmoid(xx, *f[1]), color='red')
return dv, dvu
def energy_in_XYRange(kre: KrEvent, xr: Tuple[float], yr: Tuple[float],
ernb: ExyzNBins) -> KrFit:
sel = in_range(kre.X, *xr) & in_range(kre.Y, *yr)
e = kre.E[sel]
bins = ernb.E
frame_data = plt.gcf().add_axes((.1, .3, .8, .6))
y, b, _ = plt.hist(e,
bins=bins,
histtype='step',
edgecolor='black',
linewidth=1.5)
x = shift_to_bin_centers(b)
seed = gauss_seed(x, y)
fit_range = seed[1] - 2.0 * seed[2], seed[1] + 2.0 * seed[2]
x, y = x[in_range(x, *fit_range)], y[in_range(x, *fit_range)]
f = fitf.fit(fitf.gauss, x, y, seed, sigma=poisson_sigma(y))
yu = poisson_sigma(y)
plt.plot(x, f.fn(x), "r-", lw=4)
frame_data.set_xticklabels([])
labels("", "Entries", "Energy fit example")
lims = plt.xlim()
frame_res = plt.gcf().add_axes((.1, .1, .8, .2))
plt.errorbar(x, (f.fn(x) - y) / yu, 1, np.diff(x)[0] / 2, fmt="p", c="k")
plt.plot(lims, (0, 0), "g--")
plt.xlim(*lims)
plt.ylim(-5, +5)
kf = KrFit(par=np.array(f.values),
err=np.array(f.errors),
chi2=chi2(f, x, y, yu))
return kf
def gaussian_fit(x: np.array, y: np.array, seed: GaussPar,
n_sigma: int) -> Tuple[FitPar, FitResult]:
"""Gaussian fit to x,y variables, with fit range defined by n_sigma"""
mu = seed.mu.value
std = seed.std.value
amp = seed.amp.value
fit_range = mu - n_sigma * std, mu + n_sigma * std
x, y = x[in_range(x, *fit_range)], y[in_range(x, *fit_range)]
yu = poisson_sigma(y)
fseed = (amp, mu, std)
par, err = par_and_err_from_seed(seed)
fr = FitResult(par=par, err=err, chi2=NN, valid=False)
fp = None
with warnings.catch_warnings():
warnings.filterwarnings(
'error') # in order to handle fit failures here
try:
fp, fr = gfit(x, y, yu, fseed)
except RuntimeWarning: # this is the most usual failure, and usually solved trying fitx
# with a different seed
print(
f' fit failed for seed = {seed}, due to RunTimeWarning, retry fit '
)
fseed = (10 * fseed[0], fseed[1], fseed[2])
try:
fp, fr = gfit(x, y, yu, fseed)
except RuntimeWarning: # Give up on second failure
print(
f' fit failed for seed = {seed}, due to RunTimeWarning, give up '
)
except OptimizeWarning:
print(
f' OptimizeWarning was raised for seed = {seed} due to OptimizeWarning'
)
except RuntimeError:
print(f' fit failed for seed = {seed} due to RunTimeError')
except TypeError:
print(f' fit failed for seed = {seed} due to TypeError')
return fp, fr
def get_chi2_and_pvalue(ydata, yfit, ndf, sigma=None):
"""
Gets reduced chi2 and p-value
Parameters
----------
ydata : np.ndarray
Data points.
yfit : np.ndarray
Fit values corresponding to ydata array.
sigma : np.ndarray
Data errors. If sigma is not given, it takes the poisson case:
sigma = sqrt(ydata)
ndf : int
Number of degrees of freedom
(number of data points - number of parameters).
Returns
-------
chi2 : float
Reduced chi2 computed as:
chi2 = [sum(ydata - yfit)**2 / sigma**2] / ndf
pvalue : float
Fit p-value.
"""
if sigma is None:
sigma = poisson_sigma(ydata)
chi2 = np.sum(((ydata - yfit) / sigma)**2)
pvalue = scipy.stats.chi2.sf(chi2, ndf)
if ndf > 0:
return chi2 / ndf, pvalue
else:
print(f'Warning in fit_functions_ic:chi2: ndf =0: chi2 = {chi2}')
return chi2, pvalue
peaks_dark = find_peaks_cwt(dar, np.arange(2, 20), min_snr=2)
if len(peaks_dark) == 0:
## Try to salvage in case not a masked channel
## Masked channels have al entries in one bin.
if led[led > 0].size == 1:
outData.append([channs[ich], [0, 0, 0, 0], [0, 0, 0, 0], 0, 0])
print('no peaks in dark spectrum, spec ', ich)
continue
else:
peaks_dark = np.array([dar.argmax()])
## Fit the dark spectrum with a Gaussian (not really necessary for the conv option)
gb0 = [(0, -100, 0), (1e99, 100, 10000)]
sd0 = (dar.sum(), 0, 2)
sel = np.arange(peaks_dark[0] - 5, peaks_dark[0] + 5)
errs = poisson_sigma(dar[sel], default=0.1)
gauss_fit_dark = fitf.fit(fitf.gauss,
bins[sel],
dar[sel],
sd0,
sigma=errs,
bounds=gb0)
outDict[cpio.generic_params[2]] = (gauss_fit_dark.values[1],
gauss_fit_dark.errors[1])
outDict[cpio.generic_params[3]] = (gauss_fit_dark.values[2],
gauss_fit_dark.errors[2])
## Scale just in case we lost a different amount of integrals in dark and led
## scale = led.sum() / dar.sum()
scale = 1.5
def measureDriftVelocity(run, drift_field, z, zrange_dv, bins_dv, buffersize,
z_cathode, el_time):
"""
Given a Z distribution, returns the drift velocity with its error.
The drift velocity is obtained through an smooth Heavyside fit or logistic function (https://en.wikipedia.org/wiki/Logistic_function).
Parameters:
run = Run number, to add it to the figure title
drift_field = Drift field of the run, to add it to the figure title.
groupDST = Grouped DST (by event id).
zrange_dv = Range in drift time for the fit.
bins_dv = Bins for plotting the region of interest.
buffersize = Buffersize of the run, to plot the drift time distribution.
z_cathode = Cathode z-position in mm.
"""
fig, axes = plt.subplots(1, 3, figsize=(24, 6))
st = fig.suptitle(
"Run {0} (drift field = {1:.0f} V/cm/bar) Z distribution".format(
run, drift_field[0]),
fontsize=16)
axes[0].hist(z, 100, [0, buffersize], rasterized=True)
axes[0].set_xlabel("Z (mm)")
axes[0].set_ylabel("")
axes[1].hist(z, 100, [0, buffersize], rasterized=True)
axes[1].set_xlabel("Z (mm)")
axes[1].set_ylabel("")
axes[1].set_yscale('log')
plt.axes(axes[2])
y, x = h1d(z, bins_dv, zrange_dv, "Z (mm)", "Number of events", ax=axes[2])
axes[2].set_yscale('log')
sigmoid = lambda x, A, B, C, D: A / (1 + np.exp(-C * (x - B))) + D
seed = np.max(y), np.mean(zrange_dv), np.diff(zrange_dv)[0] / 100, np.min(
y)
f = fitf.fit(sigmoid,
x,
y,
seed,
fit_range=zrange_dv,
sigma=statf.poisson_sigma(y))
plt.plot(x, f.fn(x), "r", lw=1.25, rasterized=True)
histFun.labels("Drift time ($\mu$s)", "Number of events", "")
dv = z_cathode[0] / (f.values[1] - el_time[0])
dv_e_stat = z_cathode[0] / (
(f.values[1] - el_time[0])**
2) * f.errors[1] # Statistic error derived from fit.
dv_e_syst = (z_cathode[0]/((f.values[1] - el_time[0])**2) * 1.)**2 + \
(z_cathode[1]/(f.values[1] - el_time[0]))**2 + \
(z_cathode[0]/((f.values[1] - el_time[0])**2) * el_time[1])**2 # Systematic error derived from drift time measurement (asumed to be 1 mus), drift length and drifted time in EL.
dv_e_syst = np.sqrt(dv_e_syst)
dv = np.array([dv, dv_e_stat, dv_e_syst])
print("Max drift time = {:.3f} +- {:.3f}".format(f.values[1], f.errors[1]))
print(
"Drift velocity = {:.5f} +- {:.5f} (stat.) +- {:.5f} (syst.)".format(
dv[0], dv[1], dv[2]))
print("======================================")
axes[2].annotate("Drift time = \n{:.3f} $\pm$ {:.3f}".format(
f.values[1], f.errors[1]),
xy=(0.665, 0.9),
xycoords='axes fraction',
color="black") #, fontsize = 14)
extent = axes[0].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("DriftVel_R{}.pdf".format(run), bbox_inches=extent)
extent = axes[1].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("DriftVel_Log_R{}.pdf".format(run), bbox_inches=extent)
extent = axes[2].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("DriftVel_LogZoom_R{}.pdf".format(run), bbox_inches=extent)
plt.close(fig)
return dv