jaxvacua.sampling.sample_in_ellipsoid

sample_in_ellipsoid(key, m, q, n)

Draw rounded integer points from a positive-definite ellipsoid.

A uniform draw x in the unit ball is mapped to u = sqrt(2*q) M^{-1/2} x. Before rounding this satisfies 1/2 u.T @ M @ u <= q. Rounding can move some points across the bound, so callers should reconstruct the full flux and re-check the signed tadpole.

Parameters:

• key (Array) – PRNG key.

• m (Array) – Symmetric positive-definite matrix of shape (d, d).

• q (float | Array) – Ellipsoid bound for the continuous draw.

• n (int) – Number of points to draw.

Returns:

• Array – Rounded integer-valued samples with shape (n, d) and

• the same real dtype as ``m``.

Return type:

Array

Note

This routine assumes positive-definite input. Eigenvalues are floored at machine resolution before the inverse square root to avoid NaNs from roundoff in numerically flat directions.