UQ sampling

Draw seeded multivariate-normal samples over a caller-supplied covariance block and compare sample moments.

Seeded MVN sampling in the SANDY role starts from a covariance block: given a mean vector and a covariance matrix, draw $n$ samples $x \sim N(\mu, C)$ and check the sample moments recover the inputs. (SANDY itself factorises with SVD; this kernel uses Cholesky-with-eigen-clip — same distribution, moment estimators agree.) The demo below runs the verified nucleide-linalg kernel over caller-supplied arrays — there are no vendored covariance stores anywhere in this path:

Cholesky factors positive-definite blocks (method reads cholesky).
Eigen-clip takes over for positive-semidefinite but singular blocks (method reads eigen_clip with the unclipped extremes reported).

Seeded sampling

Set the mean, the row-major covariance, the draw count, and the seed, then press Run sampling. The defaults replay the synthetic block from fixtures/uq/cov_2x2.json (variances 0.25/0.16, covariance 0.10, seed 20260913 — round numbers, no evaluated data). Draws are capped at 5000 to keep the demo slice cheap; identical inputs always yield identical samples.

LHS mode keeps the same inputs and result shape but swaps the normal source for stratified draws — one jittered uniform per stratum per dimension (Fisher–Yates permutation, inverse-normal CDF), then the shared factor path — so the IID $k$ -SE standard-error null is the wrong benchmark: stratified draws have smaller variance than IID by construction. The kernel’s separate correctness checks (G1/G2 on the theory page) therefore require stratification-exactness (each dimension hits each of the $n$ strata exactly once at the pinned seed) and use the IID standard errors as an upper bound on the sample mean/covariance, never an equality null. LHS is a draw mode, not a perturbation convention.

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