Module log_strength 

Exact supported domain for logarithmic penalty strengths.

Every smoothing precision has the form lambda = exp(rho). The value, gradient, and Hessian with respect to rho agree only while that exponentiation is evaluated exactly: clamping rho or flooring/ceilinging lambda creates a constant tail with a fictitious nonzero derivative. The inclusive [-700, 700] interval deliberately stays inside binary64’s finite, normal exponential range: its lower face avoids subnormal-strength arithmetic and its upper face leaves overflow guard margin. It is a solver policy domain, not a claim about the widest representable binary64 input. This module owns the single domain used by all penalty implementations.

Structs

IndexedLogStrengthDomainError

Coordinate-aware failure returned when validating a vector of logarithmic strengths.

LogStrengthDomainError

A logarithmic strength is outside the exact supported solver contract.

PhysicalStrengthDomainError

Constants

LOG_STRENGTH_MAX

Largest supported logarithmic strength (inclusive).

LOG_STRENGTH_MIN

Smallest supported logarithmic strength (inclusive).

Functions

checked_exp_log_strength

Exponentiate a logarithmic strength on the exact closed solver domain.

checked_exp_log_strengths

Convert a complete vector atomically on the exact supported domain.

checked_log_strength

Recover a canonical logarithmic coordinate without flooring or ceilinging a physical strength.

log_gradient_resolution

ln √ε: the log of the relative resolution of a criterion gradient carried through an inverse whose conditioning is the strength ratio itself. Per direction the ρ-gradient is the effective degrees of freedom γ/(γ+λ) through (H+λS)⁻¹, whose condition in that direction is λ/γ once the penalty dominates; a quantity through an inverse of condition κ holds relative error εκ, and value and error cross at λ/γ = 1/√ε. Every derived ρ-domain edge (#2812) is this many e-folds from the spectrum.

precision_box

The precision box [ln √ε, ln(1/√ε)] around unit strength: the domain of a coordinate whose penalty geometry cannot be projected, and the envelope a seed is placed in before the domain is derived.

validate_log_strength

Validate a logarithmic strength without changing it.

validate_log_strengths

Validate a complete vector, reporting the deterministic smallest invalid coordinate before any caller-visible computation begins.