skg.ngauss_fit¶

skg.ngauss_fit(x, y, axis=-1, weights=None, scaling=False)[source]¶

An N-dimensional Gaussian fit.

$S(\vec{x}) = a e^{-\frac{1}{2} \left(\vec{x} - \vec{\mu}\right)^T \Sigma^{-1} \left(\vec{x} - \vec{\mu}\right)}$

This implementation is based on an extension of [AnthonyGranick] and the first of two passes described in [Wan-Wang-Wei-Li-Zhang].

A weighing function must be applied to the data to avoid having the low-SNR data dominate the fit. The default is to weight the measurements by their intensity, as per _[Wan-Wang-Wei-Li-Zhang]. However, other schemes are possible, such as the one proposed by _[Anthony-Granick]. The latter scheme can be used by passing in a callable returned by anthony_weights as the weights parameter.

Parameters:

x (array-like) – The x-values of the data points. The fit will be performed on a version of the array raveled across all dimensions except axis.
y (array-like) – The y-values of the data points corresponding to x. Must be the same size as x except at axis. The fit will be performed on a raveled version of this array.
axis (int) – The axis containing the vectors of x. The dimension of the Gaussian is x.shape[axis]. The default is -1.
weights (array-like or callable, optional) – Either an array with the same number of elements as y (it will be raveled), or a callable that accepts reshaped versions of x and y and returns an array of weights.
scaling (bool, optional) – If True, scale and offset the data to a bounding box of -1 to +1 in each axis during computations for numerical stability. Default is False.

Returns:

a (float) – The amplitude of the Gaussian.
mu (~numpy.ndarray) – The mean of the Gaussian, as an N-element array.
sigma (~numpy.ndarray) – The covariance of the Gaussian, as an NxN positive definite matrix.