Module continuous_area 

Continuous-prior loss integration for spatial / area-based optimization (expected value, worst-case, CVaR over a continuous_area::Prior). Continuous-prior loss integration for spatial / area-based optimization.

Generic over dimension via const generics: D=1 for a line of seats, D=2 for a listening rectangle, D=3 for a head-volume sweep, and so on.

Three building blocks

• Prior — the probability distribution π(p) over positions p ∈ R^D. Currently Uniform over an axis-aligned box and axis-aligned Gaussian are first-class; Custom accepts an arbitrary density.
• Quadrature — how to discretise the integral into Q evaluation points. Supports Sobol (low-discrepancy QMC), Latin-Hypercube, and Gauss–Legendre tensor-product. Sobol/LH are seeded for determinism.
• AreaScalarisation — what to do with the Q losses: expected value, worst-case (max), or CVaR (mean of the worst α-tail).

The high-level call

evaluate_area_loss takes a base loss L(params, p), a Prior, a Quadrature, and a AreaScalarisation and returns one scalar that an outer optimizer can minimise. The outer optimizer never sees the quadrature; it just sees a robust scalar objective.

Cost model

Each outer fitness call costs Q base-loss evaluations for ExpectedValue and CVaR. WorstCase runs a small inner DE search per outer call — callers should be aware this is more expensive (typically 10×–50× a single base-loss eval).

use math_audio_optimisation::continuous_area::{
    AreaScalarisation, Prior, Quadrature, evaluate_area_loss,
};

// Minimise expected value of (params[0] - p)^2 with p ~ Uniform([-1,1])
let prior: Prior<1> = Prior::Uniform { bounds: [(-1.0, 1.0)] };
let quadrature: Quadrature<1> = Quadrature::Sobol {
    num_points: 128,
    seed: 0,
};
let loss = |params: &[f64], p: [f64; 1]| (params[0] - p[0]).powi(2);
let value = evaluate_area_loss(&loss, &[0.0], &prior, &quadrature, AreaScalarisation::ExpectedValue);
assert!((value - 1.0 / 3.0).abs() < 0.05);

Enums

AreaError

Errors raised by continuous-area evaluation.

AreaScalarisation

How to scalarise the Q per-point losses into one outer-loop loss.

Prior

Probability density / sampling region over R^D.

Quadrature

Quadrature scheme for discretising the prior integral into Q sample points.

Functions

build_quadrature_points

Generate the quadrature points and corresponding integration weights.

evaluate_area_loss

Evaluate a continuous-area loss.

try_evaluate_area_loss

Fallible version of evaluate_area_loss: returns errors instead of panicking.