slmsuite.holography.toolbox.smallest_distance#

smallest_distance(vectors, metric='chebyshev')[source]#

Returns the smallest distance between pairs of points under a given metric.

Tip

This function supports a \(\mathcal{O}(N\log(N))\) divide and conquer algorithm and can handle large pointsets. An \(\mathcal{O}(N^2)\) brute force approach is implemented as a backup.

Caution

Vectors using unsigned datatypes can lead to unexpected results when evaluating a distance metric. Be sure that your vectors are signed.

Parameters:

vectors (array_like) – Points to compare. Cleaned with format_2vectors().
metric (str OR function) – Function to use to compare. Defaults to "chebyshev" which corresponds to scipy.spatial.distance.chebyshev(). The \(\mathcal{O}(N\log(N))\) divide and conquer algorithm is only compatible with string inputs allowed by scipy.spatial.distance.pdist(). Function arguments will fallback to the brute force approach.

Returns:

Minimum distance between any pair of points under the given metric. If fewer than two points are given, then np.inf is returned.

Return type:

float