def main():
"""Illustrate workflow for fitting a mono-exponential decay.
Example of fitting a convolved mono-exponential fluorescence
decay to a single measurement using iterative least squares
with Chi2 Statistic and Pearson variance approximation.
"""
file = np.loadtxt('../decay_1exp_5ns.txt', skiprows=1)
time, irf, decay = file[:, 0], file[:, 1], file[:, 2]
model_kwargs_e1 = {
'model_components': 1,
'model_parameters': {
'amplitude1': {'value': 0.06, 'vary': True},
'offset': {'value': 0.1, 'vary': True},
'tau1': {'value': 5, 'vary': True},
},
'fit_start': 2,
'fit_stop': None
}
# ConvolutionFitter C Statistic for comparison
cstat_fitter = \
make_lifetime_fitter(
model_kwargs_e1,
time,
decay,
instrument_response=irf,
fit_statistic='c_statistic'
)
cstat_fit = cstat_fitter.fit()
# ConvolutionFitter Chi2 Statistic for initialization
chi2stat_fitter = \
make_lifetime_fitter(
model_kwargs_e1,
time,
decay,
instrument_response=irf,
fit_statistic='chi_square_statistic'
)
n_iter = 20
fits = iterative_least_squares(chi2stat_fitter, n_iter)
# plot
plt.plot(time, decay, 'bo', label='decay')
plt.plot(time, irf, 'go', label='irf')
plt.plot(
cstat_fitter.independent_var['time'],
cstat_fit.best_fit,
label='C stat',
color='k'
)
for ith, fit in enumerate(fits):
plt.plot(
chi2stat_fitter.independent_var['time'],
fit.best_fit,
label='{}-ith iter'.format(ith),
color=CMAP(ith / n_iter)
)
plt.legend(loc='best')
plt.yscale('log')
plt.show()
def main():
"""Illustrate workflow for fitting a mono-exponential decay.
Example of fitting a convolved mono-exponential fluorescence
decay to a single measurement using C Statistic.
"""
file = np.loadtxt('../decay_1exp_5ns.txt', skiprows=1)
time, irf, decay = file[:, 0], file[:, 1], file[:, 2]
model_kwargs_e1 = {
'model_components': 1,
'model_parameters': {
'amplitude1': {
'value': 0.06,
'vary': True
},
'offset': {
'value': 0.1,
'vary': True
},
'tau1': {
'value': 5,
'vary': True
},
},
'fit_start': 2,
'fit_stop': None
}
# Convolution fit with Chi2 Statistic
cstat_fitter = \
make_lifetime_fitter(
model_kwargs_e1,
time,
decay,
instrument_response=irf,
fit_statistic='c_statistic'
)
cstat_fit = cstat_fitter.fit(report=True)
# exit(1)
# plot
plt.plot(time, decay, 'bo', label='decay')
plt.plot(time, irf, 'go', label='irf')
plt.plot(cstat_fitter.independent_var['time'],
cstat_fit.best_fit,
'r-',
label='fit')
plt.legend(loc='best')
plt.yscale('log')
plt.show()
def main():
"""Illustrate workflow for tail-fitting a mono-exponential decay.
Example of tail-fitting a mono-exponential fluorescence
decay to a single measurement using Chi2 Statistic.
"""
file = np.loadtxt('../decay_1exp_5ns.txt', skiprows=1)
time, irf, decay = file[:, 0], file[:, 1], file[:, 2]
model_kwargs_e1_tail = {
'model_components': 1,
'model_parameters': {
'amplitude1': {
'value': 7000,
'vary': True
},
'offset': {
'value': 0.1,
'vary': True
},
'tau1': {
'value': 5,
'vary': True
},
},
'fit_start': 12,
'fit_stop': None
}
# Tail fit with Chi2 Statistic
chi2stat_tail_fitter = \
make_lifetime_fitter(
model_kwargs_e1_tail,
time,
decay,
fit_statistic='chi_square_statistic'
)
chi2stat_tail_fit = chi2stat_tail_fitter.fit(report=True)
# plot
plt.plot(time, decay, 'bo', label='decay')
plt.plot(chi2stat_tail_fitter.independent_var['time'],
chi2stat_tail_fit.best_fit,
'r-',
label='fit')
plt.legend(loc='best')
plt.yscale('log')
plt.show()
def main():
"""Illustrate workflow for fitting a bi-exponential decay.
Example of fitting a convolved bi-exponential fluorescence
decay to a single measurement using Chi2 Statistic.
"""
file = np.loadtxt('../decay_2exp_1ns_02_4ns_08.txt', skiprows=1)
time, irf, decay = file[:, 0], file[:, 1], file[:, 2]
model_kwargs_e2 = {
'model_components': 2,
'model_parameters': {
'amplitude1': {
'value': 0.1,
'vary': True,
'min': 1E-6
},
'amplitude2': {
'value': 0.1,
'vary': True,
'min': 1E-6
},
'tau1': {
'value': 1,
'vary': True,
'min': 1E-6
},
'tau2': {
'value': 4,
'vary': True,
'min': 1E-6
},
'offset': {
'value': 0.1,
'vary': True,
'min': 1E-6
},
'shift': {
'value': 0.5,
'vary': True
}
},
'fit_start': 2,
'fit_stop': None
}
# Convolution fit with Chi2 Statistic
chi2stat_fitter = \
make_lifetime_fitter(
model_kwargs_e2,
time,
decay,
instrument_response=irf,
fit_statistic='chi_square_statistic'
)
chi2stat_fit = chi2stat_fitter.fit(report=True)
# plot
plt.plot(time, decay, 'bo', label='decay')
plt.plot(time, irf, 'go', label='irf')
plt.plot(chi2stat_fitter.independent_var['time'],
chi2stat_fit.best_fit,
'r-',
label='fit')
plt.legend(loc='best')
plt.yscale('log')
plt.show()
