Module robust 

Robust M-estimation primitives for iteratively reweighted least squares.

These are the per-outer-iteration reweighting pieces of a Huber IRLS loop: a median-absolute-deviation scale estimate and the Huber weight function. They are deliberately pure f64 arithmetic (abs, compare, divide, sort by f64::total_cmp) with no fused-multiply-add and no contraction, so the per-iteration weight vector is bit-reproducible against an explicit outer-loop reference recipe. The trust-region linear-algebra step that consumes the weights is BLAS-bound and is NOT a 0-ULP target.

Enums

RobustError

Constants

HUBER_K

The default Huber tuning constant. Residuals scaled below this (in units of the robust scale) keep full weight; larger ones are down-weighted as k / |u|. 1.345 gives ~95% efficiency at the Gaussian model.

MAD_NORMAL_CONST

The MAD-to-sigma consistency constant for a normal distribution, 1 / Phi^-1(3/4). Multiplying the median absolute deviation by this makes it a consistent estimator of the standard deviation under normality.

Functions

huber_weight

The Huber weight for a scaled residual u = r / s.

mad_scale

The median-absolute-deviation scale of residuals, scaled to a normal-sigma estimate and floored at scale_floor.

median

The median of values, computed on a total_cmp sort so the order (and thus the result for an even count, which averages the two central values) is deterministic. An empty slice yields 0.0. The two central elements use (a + b) / 2.0 when its addition is finite, with a / 2.0 + b / 2.0 only as the overflow-safe fallback. Neither path uses FMA.