calculate_distance_weights

sofia_redux.toolkit.resampling.calculate_distance_weights(coordinates, reference, alpha)

Returns a distance weighting based on coordinate offsets.

Given a set of \(K\) dimensional coordinates (\(x\)), a single reference position (\(x_{ref}\)), and the scaling factor alpha (\(\alpha\)), returns the weighting factor:

\[w(x) = exp \left( \sum_{k=1}^{K}{\frac{-(x_{ref, k} - x_k)^2}{\alpha_k}} \right)\]

Parameters:

coordinatesnumpy.ndarray (n_dimensions, N)

An array of N coordinates in n_dimensions.

referencenumpy.ndarray (n_dimensions,)

The reference position from which to determine distance offsets for the weighting function.

alphanumpy.ndarray (1 or n_dimensions,)

The distance scaling factor. If an array of size 1 is supplied, it will be applied over all dimensions. Otherwise, a value must be provided for each dimension.

Returns:

weightsnumpy.ndarray (N,)

The distance weighting factors.

Notes

alpha relates to the standard deviation (\(\sigma\)) in a normal distribution as \(\alpha = 2\sigma^2\).