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Improved gaussian2d estimator #37

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Improved gaussian2d estimator #37

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77e7d56
Using a most likelihood estimator to improve performance of the estim…
Geegee Nov 20, 2022
5b1d06c
Small bugfix in the determination in the stepsize in y.
Geegee Nov 21, 2022
cc8149d
Remove logging
Geegee Nov 21, 2022
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61 changes: 40 additions & 21 deletions src/qudi/util/fit_models/gaussian.py
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Original file line number Diff line number Diff line change
Expand Up @@ -28,6 +28,8 @@
from qudi.util.fit_models.helpers import estimate_double_peaks, estimate_triple_peaks
from qudi.util.fit_models.linear import Linear

from qudi.core.logger import get_logger
logger = get_logger(__name__)

def multiple_gaussian(x, centers, sigmas, amplitudes):
""" Mathematical definition of the sum of multiple gaussian functions without any bias.
Expand Down Expand Up @@ -351,29 +353,46 @@ def _model_function(xy, offset, amplitude, center_x, center_y, sigma_x, sigma_y,
@estimator('Peak')
def estimate_peak(self, data, xy):
# ToDo: Not properly implemented, yet
x_range = abs(np.max(xy[0]) - np.min(xy[0]))
y_range = abs(np.max(xy[1]) - np.min(xy[1]))
stepsize_x = xy[0][1,0] - xy[0][0,0]
stepsize_y = xy[1][0,1] - xy[1][0,0]
x_axis = xy[0].flatten()
y_axis = xy[1].flatten()

# TODO: Make good estimate for theta

amplitude = float(data.max() - data.min())

# By calculating the log likelihood of the 2D gaussian pdf, one obtain for
# the minimization of the center_x or center_y values the following formula
# (which are in fact just the expectation/mean value formula):
norm = np.sum(data)
center_x = np.sum(x_axis * data) / norm
center_y = np.sum(y_axis * data) / norm
exp_of_xsquared = np.sum(x_axis ** 2 * data) / norm
exp_of_ysquared = np.sum(y_axis ** 2 * data) / norm
sigma_x = np.sqrt(exp_of_xsquared - center_x ** 2)
sigma_y = np.sqrt(exp_of_ysquared - center_y ** 2)
xrange = x_axis.max() - x_axis.min()
yrange = y_axis.max() - y_axis.min()
theta = 0.0
offset = float(data.min())

# populate the parameter container:
params = self.make_params()
params['amplitude'].set(value=amplitude, min=100, max=1e7)
params['sigma_x'].set(value=sigma_x, min=1*stepsize_x,
max=3*xrange)
params['sigma_y'].set(value=sigma_y, min=1*stepsize_y,
max=3*yrange)
params['center_x'].set(value=center_x, min=center_x - xrange,
max=center_x + xrange)
params['center_y'].set(value=center_y, min=center_y - yrange,
max=center_y + yrange)
params['theta'].set(value=theta, min=0, max=np.pi)
params['offset'].set(value=offset, min=0, max=1e7)
return params

amplitude = np.max(data)
center_x = x_range / 2 + np.min(xy[0])
center_y = y_range / 2 + np.min(xy[1])
sigma_x = x_range / 10
sigma_y = y_range / 10
theta = 0

estimate = self.make_params()
estimate['offset'].set(value=np.mean(data), min=-np.inf, max=np.max(data))
estimate['amplitude'].set(value=amplitude, min=0, max=amplitude * 2)
estimate['center_x'].set(value=center_x,
min=np.min(xy[0]) - x_range / 2,
max=np.max(xy[0]) + x_range / 2)
estimate['center_y'].set(value=center_y,
min=np.min(xy[1]) - y_range / 2,
max=np.max(xy[1]) + y_range / 2)
estimate['sigma_x'].set(value=sigma_x, min=x_range / (xy[0].shape[0] - 1), max=x_range)
estimate['sigma_y'].set(value=sigma_y, min=y_range / (xy[0].shape[1] - 1), max=y_range)
estimate['theta'].set(value=theta, min=-np.pi, max=np.pi)
return estimate

@estimator('Dip')
def estimate_dip(self, data, xy):
Expand Down