IterativeGeneralizedGaussian.fit

giant.point_spread_functions.gaussians:

classmethod IterativeGeneralizedGaussian.fit(x, y, z)

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 (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str]) – The x values underlying the data the gaussian surface is to be fit to

• y (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str]) – The y values underlying the data the gaussian surface is to be fit to

• z (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str]) – The z or “height” values for the gaussian surface

Returns:

The initialized PSF with values according to the fit

Return type:

Self