# -*- coding: utf-8 -*-
"""
.. Copyright (c) 2021, the qudi developers. See the AUTHORS.md file at the top-level directory of this
.. distribution and on <https://github.com/Ulm-IQO/qudi-core/>
..
.. This file is part of qudi.
..
.. Qudi is free software: you can redistribute it and/or modify it under the terms of
.. the GNU Lesser General Public License as published by the Free Software Foundation,
.. either version 3 of the License, or (at your option) any later version.
..
.. Qudi is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
.. without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
.. See the GNU Lesser General Public License for more details.
..
.. You should have received a copy of the GNU Lesser General Public License along with qudi.
.. If not, see <https://www.gnu.org/licenses/>.
"""
__all__ = [
'ComplexLorentzian',
'DoubleLorentzian',
'Lorentzian',
'LorentzianLinear',
'TripleLorentzian',
'multiple_lorentzian',
'multiple_complex_lorentzian',
]
import numpy as np
from typing import Sequence
from qudi.util.fit_models.model import FitModelBase, estimator
from qudi.util.fit_models.helpers import (
correct_offset_histogram,
smooth_data,
sort_check_data,
)
from qudi.util.fit_models.helpers import estimate_double_peaks, estimate_triple_peaks
from qudi.util.fit_models.linear import Linear
[docs]
def multiple_lorentzian(x, centers, sigmas, amplitudes):
"""
Mathematical definition of the sum of multiple (physical) Lorentzian functions without any bias.
WARNING: Iterable parameters "centers", "sigmas", and "amplitudes" must have the same length.
Parameters
----------
x : float
The independent variable to calculate lorentz(x).
centers : iterable
Iterable containing center positions for all Lorentzians.
sigmas : iterable
Iterable containing width parameters (half-width at half-maximum) for all Lorentzians.
amplitudes : iterable
Iterable containing amplitudes for all Lorentzians.
Returns
-------
float
The result given x for lorentz(x).
"""
assert len(centers) == len(sigmas) == len(amplitudes)
return sum(
amp * sig**2 / ((x - c) ** 2 + sig**2)
for c, sig, amp in zip(centers, sigmas, amplitudes)
)
[docs]
def multiple_complex_lorentzian(
x: float,
centers: Sequence[float],
sigmas: Sequence[float],
amplitudes: Sequence[float],
thetas: Sequence[float],
):
"""Mathematical definition of the sum of multiple complex Lorentzian functions without any
bias.
WARNING: Values in "thetas" must be in deg (NOT rad).
WARNING: Sequence parameters "centers", "sigmas", "amplitudes" and "thetas" must have same
length.
"""
assert len(centers) == len(sigmas) == len(amplitudes) == len(thetas)
return sum(
np.exp(1j * np.deg2rad(th))
* amp
* (-1j * (x - c) * sig + sig**2)
/ (np.pi * sig * ((x - c) ** 2 + sig**2))
for c, sig, amp, th in zip(centers, sigmas, amplitudes, thetas)
)
[docs]
class Lorentzian(FitModelBase):
""" """
[docs]
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.set_param_hint('offset', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('amplitude', value=0.0, min=0.0, max=np.inf)
self.set_param_hint('center', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('sigma', value=0.0, min=0.0, max=np.inf)
@staticmethod
def _model_function(x, offset, center, sigma, amplitude):
return offset + multiple_lorentzian(x, (center,), (sigma,), (amplitude,))
[docs]
@estimator('Peak')
def estimate_peak(self, data, x):
data, x = sort_check_data(data, x)
# Smooth data
filter_width = max(1, int(round(len(x) / 20)))
data_smoothed, _ = smooth_data(data, filter_width)
data_smoothed, offset = correct_offset_histogram(
data_smoothed, bin_width=2 * filter_width
)
# determine peak position
center = x[np.argmax(data_smoothed)]
# calculate amplitude
amplitude = abs(max(data_smoothed))
# according to the derived formula, calculate sigma. The crucial part is here that the
# offset was estimated correctly, then the area under the curve is calculated correctly:
numerical_integral = np.trapz(data_smoothed, x)
sigma = abs(numerical_integral / (np.pi * amplitude))
x_spacing = min(abs(np.ediff1d(x)))
x_span = abs(x[-1] - x[0])
data_span = abs(max(data) - min(data))
estimate = self.make_params()
estimate['amplitude'].set(value=amplitude, min=0, max=2 * amplitude)
estimate['sigma'].set(value=sigma, min=x_spacing, max=x_span)
estimate['center'].set(
value=center, min=min(x) - x_span / 2, max=max(x) + x_span / 2
)
estimate['offset'].set(
value=offset, min=min(data) - data_span / 2, max=max(data) + data_span / 2
)
return estimate
[docs]
@estimator('Dip')
def estimate_dip(self, data, x):
estimate = self.estimate_peak(-data, x)
estimate['offset'].set(
value=-estimate['offset'].value,
min=-estimate['offset'].max,
max=-estimate['offset'].min,
)
estimate['amplitude'].set(
value=-estimate['amplitude'].value,
min=-estimate['amplitude'].max,
max=-estimate['amplitude'].min,
)
return estimate
[docs]
@estimator('Peak (no offset)')
def estimate_peak_no_offset(self, data, x):
estimate = self.estimate_peak(data, x)
estimate['offset'].set(value=0, min=-np.inf, max=np.inf, vary=False)
return estimate
[docs]
@estimator('Dip (no offset)')
def estimate_dip_no_offset(self, data, x):
estimate = self.estimate_dip(data, x)
estimate['offset'].set(value=0, min=-np.inf, max=np.inf, vary=False)
return estimate
[docs]
class DoubleLorentzian(FitModelBase):
"""ToDo: Document"""
[docs]
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.set_param_hint('offset', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('amplitude_1', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('amplitude_2', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('center_1', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('center_2', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('sigma_1', value=0.0, min=0.0, max=np.inf)
self.set_param_hint('sigma_2', value=0.0, min=0.0, max=np.inf)
@staticmethod
def _model_function(
x, offset, center_1, center_2, sigma_1, sigma_2, amplitude_1, amplitude_2
):
return offset + multiple_lorentzian(
x, (center_1, center_2), (sigma_1, sigma_2), (amplitude_1, amplitude_2)
)
[docs]
@estimator('Peaks')
def estimate_peaks(self, data, x):
data, x = sort_check_data(data, x)
data_smoothed, filter_width = smooth_data(data)
leveled_data_smooth, offset = correct_offset_histogram(
data_smoothed, bin_width=2 * filter_width
)
estimate, limits = estimate_double_peaks(leveled_data_smooth, x, filter_width)
params = self.make_params()
params['amplitude_1'].set(
value=estimate['height'][0],
min=limits['height'][0][0],
max=limits['height'][0][1],
)
params['amplitude_2'].set(
value=estimate['height'][1],
min=limits['height'][1][0],
max=limits['height'][1][1],
)
params['center_1'].set(
value=estimate['center'][0],
min=limits['center'][0][0],
max=limits['center'][0][1],
)
params['center_2'].set(
value=estimate['center'][1],
min=limits['center'][1][0],
max=limits['center'][1][1],
)
params['sigma_1'].set(
value=estimate['fwhm'][0] / 2.3548,
min=limits['fwhm'][0][0] / 2.3548,
max=limits['fwhm'][0][1] / 2.3548,
)
params['sigma_2'].set(
value=estimate['fwhm'][1] / 2.3548,
min=limits['fwhm'][1][0] / 2.3548,
max=limits['fwhm'][1][1] / 2.3548,
)
return params
[docs]
@estimator('Dips')
def estimate_dips(self, data, x):
estimate = self.estimate_peaks(-data, x)
estimate['offset'].set(
value=-estimate['offset'].value,
min=-estimate['offset'].max,
max=-estimate['offset'].min,
)
estimate['amplitude_1'].set(
value=-estimate['amplitude_1'].value,
min=-estimate['amplitude_1'].max,
max=-estimate['amplitude_1'].min,
)
estimate['amplitude_2'].set(
value=-estimate['amplitude_2'].value,
min=-estimate['amplitude_2'].max,
max=-estimate['amplitude_2'].min,
)
return estimate
[docs]
class TripleLorentzian(FitModelBase):
"""ToDo: Document"""
[docs]
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.set_param_hint('offset', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('amplitude_1', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('amplitude_2', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('amplitude_3', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('center_1', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('center_2', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('center_3', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('sigma_1', value=0.0, min=0.0, max=np.inf)
self.set_param_hint('sigma_2', value=0.0, min=0.0, max=np.inf)
self.set_param_hint('sigma_3', value=0.0, min=0.0, max=np.inf)
@staticmethod
def _model_function(
x,
offset,
center_1,
center_2,
center_3,
sigma_1,
sigma_2,
sigma_3,
amplitude_1,
amplitude_2,
amplitude_3,
):
return offset + multiple_lorentzian(
x,
(center_1, center_2, center_3),
(sigma_1, sigma_2, sigma_3),
(amplitude_1, amplitude_2, amplitude_3),
)
[docs]
@estimator('Peaks')
def estimate_peaks(self, data, x):
data, x = sort_check_data(data, x)
data_smoothed, filter_width = smooth_data(data)
leveled_data_smooth, offset = correct_offset_histogram(
data_smoothed, bin_width=2 * filter_width
)
estimate, limits = estimate_triple_peaks(leveled_data_smooth, x, filter_width)
params = self.make_params()
params['amplitude_1'].set(
value=estimate['height'][0],
min=limits['height'][0][0],
max=limits['height'][0][1],
)
params['amplitude_2'].set(
value=estimate['height'][1],
min=limits['height'][1][0],
max=limits['height'][1][1],
)
params['amplitude_3'].set(
value=estimate['height'][2],
min=limits['height'][2][0],
max=limits['height'][2][1],
)
params['center_1'].set(
value=estimate['center'][0],
min=limits['center'][0][0],
max=limits['center'][0][1],
)
params['center_2'].set(
value=estimate['center'][1],
min=limits['center'][1][0],
max=limits['center'][1][1],
)
params['center_3'].set(
value=estimate['center'][2],
min=limits['center'][2][0],
max=limits['center'][2][1],
)
params['sigma_1'].set(
value=estimate['fwhm'][0] / 2.3548,
min=limits['fwhm'][0][0] / 2.3548,
max=limits['fwhm'][0][1] / 2.3548,
)
params['sigma_2'].set(
value=estimate['fwhm'][1] / 2.3548,
min=limits['fwhm'][1][0] / 2.3548,
max=limits['fwhm'][1][1] / 2.3548,
)
params['sigma_3'].set(
value=estimate['fwhm'][2] / 2.3548,
min=limits['fwhm'][2][0] / 2.3548,
max=limits['fwhm'][2][1] / 2.3548,
)
return params
[docs]
@estimator('Dips')
def estimate_dips(self, data, x):
estimate = self.estimate_peaks(-data, x)
estimate['offset'].set(
value=-estimate['offset'].value,
min=-estimate['offset'].max,
max=-estimate['offset'].min,
)
estimate['amplitude_1'].set(
value=-estimate['amplitude_1'].value,
min=-estimate['amplitude_1'].max,
max=-estimate['amplitude_1'].min,
)
estimate['amplitude_2'].set(
value=-estimate['amplitude_2'].value,
min=-estimate['amplitude_2'].max,
max=-estimate['amplitude_2'].min,
)
estimate['amplitude_3'].set(
value=-estimate['amplitude_3'].value,
min=-estimate['amplitude_3'].max,
max=-estimate['amplitude_3'].min,
)
return estimate
[docs]
class LorentzianLinear(FitModelBase):
""" """
[docs]
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.set_param_hint('offset', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('slope', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('amplitude', value=0, min=-np.inf, max=np.inf)
self.set_param_hint('center', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('sigma', value=0.0, min=0.0, max=np.inf)
@staticmethod
def _model_function(x, offset, slope, center, sigma, amplitude):
x0 = x - min(x)
return (
offset
+ x0 * slope
+ multiple_lorentzian(x, (center,), (sigma,), (amplitude,))
)
[docs]
@estimator('Peak')
def estimate_peak(self, data, x):
data, x = sort_check_data(data, x)
data_span = abs(max(data) - min(data))
# Perform a normal Lorentzian peak fit and subtract the result from data
model = Lorentzian()
gauss_fit = model.fit(data, model.estimate_peak(data, x), x=x)
data_sub = data - gauss_fit.best_fit
# Perform a linear fit in subtracted data in order to estimate slope
model = Linear()
linear_fit = model.fit(data_sub, model.estimate(data_sub, x), x=x)
offset = linear_fit.params['offset'].value + min(x) * linear_fit.params['slope'].value
# Merge fit results into parameter estimates
estimate = self.make_params()
estimate['offset'].set(value=offset,
min=min(data) - data_span / 2,
max=max(data) + data_span / 2,
vary=True)
estimate['slope'].set(value=linear_fit.params['slope'].value, min=-np.inf, max=np.inf, vary=True)
estimate['amplitude'].set(value=gauss_fit.params['amplitude'].value,
min=gauss_fit.params['amplitude'].min,
max=gauss_fit.params['amplitude'].max,
vary=True)
estimate['center'].set(value=gauss_fit.params['center'].value,
min=gauss_fit.params['center'].min,
max=gauss_fit.params['center'].max,
vary=True)
estimate['sigma'].set(value=gauss_fit.params['sigma'].value,
min=gauss_fit.params['sigma'].min,
max=gauss_fit.params['sigma'].max,
vary=True)
return estimate
[docs]
@estimator('Dip')
def estimate_dip(self, data, x):
estimate = self.estimate_peak(-data, x)
estimate['offset'].set(
value=-estimate['offset'].value,
min=-estimate['offset'].max,
max=-estimate['offset'].min,
)
estimate['amplitude'].set(
value=-estimate['amplitude'].value,
min=-estimate['amplitude'].max,
max=-estimate['amplitude'].min,
)
return estimate
[docs]
class ComplexLorentzian(FitModelBase):
"""ToDo: Implement estimators"""
[docs]
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.set_param_hint('amplitude', value=0.0, min=0.0, max=np.inf)
self.set_param_hint('center', value=0.0, min=-np.inf, max=np.inf)
self.set_param_hint('sigma', value=1e-15, min=0, max=np.inf)
self.set_param_hint('theta', value=0.0, min=-180.0, max=180.0)
@staticmethod
def _model_function(x, center, sigma, amplitude, theta):
return multiple_complex_lorentzian(
x, (center,), (sigma,), (amplitude,), (theta,)
)