bayespecon._logdet.traceax_traces¶

bayespecon._logdet.traceax_traces(W_sparse, order, k, estimator='hutchpp', seed=0)[source]¶

Estimate tr(W^k) for k=1..order via variance-reduced stochastic trace estimation.

Uses pure-NumPy batched matmuls with scipy CSR matrices, matching the speed of _barry_pace_traces() while achieving lower variance via the Hutch++ correction.

Parameters:¶

W_sparse : scipy.sparse.csr_matrix¶

Row-standardised n×n spatial weights matrix.

order : int¶

Maximum trace power to estimate.

k : int¶

Number of matrix-vector products (probes) per trace estimate. Clamped to n if larger (QR constraint).

estimator='hutchpp'¶

Estimator to use: "hutchpp", "xtrace", or "hutchinson".

seed : int, default 0¶

NumPy random seed for reproducibility.

Returns:¶

Mean trace estimates: traces[i] ≈ tr(W^{i+1}). Entries 0 and 1 are overridden with exact values (tr(W) and tr(W²)), matching the convention of _barry_pace_traces().

Return type:¶

np.ndarray, shape (order,)

Notes

The variance-reduced Hutch++ estimator provides lower variance than the basic Hutchinson (Girard) estimator by splitting probes into a low-rank approximation (k//3) and a residual trace, reducing variance for matrices with decaying eigenvalue spectra (typical of spatial weights matrices).

The XTrace estimator (Epperly–Tropp–Webber 2024) refines Hutch++ via a leave-one-out construction that reuses every probe for both the low-rank basis and the residual estimate, at roughly 2× the matvec cost of Hutch++.

For spatial weights matrices with a few dominant eigenvalues (common for row-standardised contiguity weights), Hutch++ can achieve the same accuracy as Hutchinson with 2–5× fewer probes.

Raises:¶

ValueError – If estimator is not one of the supported values.