def mapm_spe(x, eped, eped_sigma, spe, spe_sigma, lambda_):
"""
Fit for the SPE spectrum of a MAPM
Parameters
----------
x : ndarray
The x values to evaluate at
eped : float
Distance of the zeroth peak from the origin
eped_sigma : float
Sigma of the zeroth peak, represents electronic noise of the system
spe : float
Signal produced by 1 photo-electron
spe_sigma : float
Spread in the number of photo-electrons incident on the MAPMT
lambda_ : float
Poisson mean (average illumination in p.e.)
Returns
-------
spectrum : ndarray
The y values of the total spectrum.
"""
# Obtain pedestal peak
p_ped = exp(-lambda_)
spectrum = p_ped * normal_pdf(x, eped, eped_sigma)
pk_max = 0
# Loop over the possible total number of cells fired
for k in range(1, 100):
p = poisson(k, lambda_) # Probability to get k avalanches
# Skip insignificant probabilities
if p > pk_max:
pk_max = p
elif p < 1e-4:
break
# Combine spread of pedestal and pe peaks
pe_sigma = sqrt(k * spe_sigma**2 + eped_sigma**2)
# Evaluate probability at each value of x
spectrum += p * normal_pdf(x, eped + k * spe, pe_sigma)
return spectrum
def _get_spectra(n_illuminations, data_x, lookup, *parameter_values):
spectra = []
for i in range(n_illuminations):
spectrum = normal_pdf(
data_x,
parameter_values[lookup[i]['mean']],
parameter_values[lookup[i]['std']],
)
spectra.append(spectrum)
return spectra
def _get_likelihood(n_illuminations, data_x, data_y, lookup,
*parameter_values):
likelihood = 0
for i in range(n_illuminations):
spectrum = normal_pdf(
data_x,
parameter_values[lookup[i]['mean']],
parameter_values[lookup[i]['std']],
)
likelihood += np.nansum(-2 * poisson_logpmf(data_y[i], spectrum))
return likelihood
def test_normal_pdf():
x = np.linspace(-10, 10, 100, dtype=np.float32)
mean = 0
std = 5
assert_allclose(normal_pdf(x, mean, std),
scipy_stats.norm.pdf(x, mean, std))
def sipm_gentile_spe(x, eped, eped_sigma, spe, spe_sigma, opct, lambda_):
"""
Fit for the SPE spectrum of a SiPM
Parameters
----------
x : ndarray
The x values to evaluate at
eped : float
Distance of the zeroth peak from the origin
eped_sigma : float
Sigma of the zeroth peak, represents electronic noise of the system
spe : float
Signal produced by 1 photo-electron
spe_sigma : float
Spread in the number of photo-electrons incident on the MAPMT
opct : float
Optical crosstalk probability
lambda_ : float
Poisson mean (average illumination in p.e.)
Returns
-------
spectrum : ndarray
The y values of the total spectrum.
"""
# Obtain pedestal peak
p_ped = exp(-lambda_)
spectrum = p_ped * normal_pdf(x, eped, eped_sigma)
pk_max = 0
# Loop over the possible total number of cells fired
for k in range(1, 100):
pk = 0
for j in range(1, k + 1):
pj = poisson(j, lambda_) # Probability for j initial fired cells
# Skip insignificant probabilities
if pj < 1e-4:
continue
# Sum the probability from the possible combinations which result
# in a total of k fired cells to get the total probability of k
# fired cells
pk += pj * pow(1 - opct, j) * pow(opct, k - j) * binom(
k - 1, j - 1)
# Skip insignificant probabilities
if pk > pk_max:
pk_max = pk
elif pk < 1e-4:
break
# Combine spread of pedestal and pe peaks
pe_sigma = sqrt(k * spe_sigma**2 + eped_sigma**2)
# Evaluate probability at each value of x
spectrum += pk * normal_pdf(x, eped + k * spe, pe_sigma)
return spectrum