Module stats 

Statistics through the shared reductions and matrix products. Means and norms use the ordinary parallel folds. Variance makes two passes, without an array-sized buffer of deviations. No compensated sums or reproducibility rules are imposed.

Structs

Axes

Groups the selected axes into one reduction axis, and keeps the other axes’ metadata. One axis, or consecutive axes, needs no copy. Nonconsecutive axes gather through the ordinary transpose plan.

Functions

average

Weighted means. The two mappings broadcast data and weights into an array of dims. Weights may be real or complex; a zero total weight gives the ordinary floating-point quotient.

covariance

The covariance or correlation of a row-major variables × observations matrix. The centered Gram product uses the same native/Accelerate product as linear algebra. Complex covariance conjugates the second variable.

histogram

Counts in increasing bin edges. Bins include their lower edge and exclude their upper edge, except that the last bin includes both. Values outside the edges and NaNs aren’t counted.

histogram_edges

Equally spaced histogram edges, from the data’s extrema where no range is given. Constant data expands by 0.5 on each side; empty data uses 0 to 1.

mean

Means along the middle axis of [outer, len, inner]. Empty lanes give NaN.

norm

The elementwise p-norm along the selected axes: 0 counts nonzero values, ±infinity selects the greatest/least magnitude, and a finite p gives (sum |x|^p)^(1/p). A pair of axes still gives this norm, not a matrix-induced norm. For p = 2, each square is computed and summed in f64, where an f32’s square neither overflows nor underflows.

stddev

Standard deviations, the square roots of variance.

variance

Two-pass variances, real for complex data, with denominator len - ddof. Empty lanes and nonpositive denominators give NaN.