IterativeGeneralizedGaussian.fit¶
giant.point_spread_functions.gaussians:
- classmethod IterativeGeneralizedGaussian.fit(x, y, z)[source]¶
This fits a 2d gaussian function to a surface using iterative non-linear least squares estimation.
The fit assumes that z = f(x, y) where f is the gaussian function (and thus z is the “height” of the gaussian function).
The fit performed is for a 2D gaussian function of the form
\[z = f(x, y) = A e^{\left(-\left[a(x-x_0)^2 + 2b (x-x_0)(y-y_0) + c (y-y_0)^2\right]\right)}\]The estimation in this function is performed iteratively. First, a transformed fit is performed using the
Gaussian.fit()method. This initial fit is then refined using iterative non-linear least squares to remove biases that can be introduced in the transformed fit.If the fit is unsuccessful due to a rank deficient matrix or a fit of a hyperbolic surface the resulting data will be set to np.nan.
- Parameters:
x (Sequence | ndarray) – The x values underlying the data the gaussian surface is to be fit to
y (Sequence | ndarray) – The y values underlying the data the gaussian surface is to be fit to
z (Sequence | ndarray) – The z or “height” values for the gaussian surface
- Returns:
The initialized PSF with values according to the fit
- Return type: