Function rayleigh
pub fn rayleigh(cov: &[Vec<f64>], direction: &[f64]) -> f64Expand description
The Rayleigh quotient uᵀ C u / uᵀu — how much variance the covariance C
carries along the direction u.
1 for C = I whatever u is, so the quotient reads directly as “how many
times more (or less) than an isotropic distribution”. This is what turns
“CMA-ES scored better” into “CMA-ES stretched its search distribution along
the landscape’s flat axis”, which is the mechanism the headline claims.
The covariance lives in the unit hypercube while
Landscape::flat_direction is in problem coordinates — but every
landscape gives all its coordinates the same [low, high], so the two frames
differ by a single global scale factor, which the quotient’s own
normalization cancels. A direction can therefore be handed straight across.