Module score_opt 

Certified global optimization of one-dimensional scores on a bounded domain, together with the affine-pencil spectral profile shared by the Gaussian REML smoothing-parameter searches.

Point samples alone cannot prove that a smooth function has no narrow stationary pair between them. The search therefore requires two pieces of information from its caller:

• an exact point evaluation (value, first derivative, second derivative);
• an OUTER enclosure of both derivatives over every requested interval.

An interval is discarded only when its first-derivative enclosure excludes zero. A stationary point is refined only after the second-derivative enclosure excludes zero, proving that the first derivative is monotone and hence that a straddling interval contains exactly one root. Every other interval is subdivided. If floating-point spacing or the caller-requested resolution is reached before either fact is proved, the result is a typed ScoreSearchError::Unresolved rather than a best-effort optimum.

AffineRemlProfile supplies both the point jets and rigorous interval formulas for scores whose penalized Hessian has simultaneously diagonal affine modes h_i(lambda) = g_i + lambda s_i. This covers an ordinary Demmler–Reinsch eigensystem (g_i = 1) and a reference-Hessian pencil (g_i = 1 - lambda_0 mu_i, s_i = mu_i) without any matrix dependency in this crate.

Structs

AffineRemlProfile

Spectral REML/profile score with affine diagonal modes h_i(lambda) = g_i + lambda s_i.

ClosedInterval

Closed real interval [lo, hi].

DerivativeEnclosure

Outer derivative ranges supplied to the certified search.

ScoreJet

Value and the analytic derivatives at one abscissa.

ScoreSample

A point evaluation augmented with its abscissa.

ScoreSearchResult

Complete successful search result. Endpoints are retained explicitly so the global comparison is independently checkable by the caller.

StationaryPoint

One stationary point together with the final bracket that certifies its location. The bracket width is no larger than the requested resolution, unless the point was represented exactly (a zero-width bracket).

Enums

AffineRemlError

Static validation or evaluation failure for AffineRemlProfile.

ScoreOptimumLocation

ScoreSearchError

Failure of the generic certified search.

Functions

maximize_score_1d

Globally maximize a smooth score on [lo, hi] by certified stationary isolation.