bayespecon._logdet.make_flow_separable_logdet¶

bayespecon._logdet.make_flow_separable_logdet(W_sparse, n, method=None, rho_min=-1.0, rho_max=1.0, cheb_order=20, trace_estimator='hutchpp', trace_k=None)[source]¶

Pre-compute logdet data for separable flow models and return a logdet callable.

For the separable constraint \(\rho_w = -\rho_d \rho_o\) the full system log-determinant factors exactly as

\[\log|L_o \otimes L_d| = n\,\log|I_n - \rho_d W| + n\,\log|I_n - \rho_o W|\]

This function pre-computes the required data once at model initialisation and returns a closure that evaluates the expression as a symbolic pytensor scalar, suitable for pm.Potential.

Parameters:¶

W_sparse : array-like or scipy.sparse matrix¶

Row-standardised \(n \times n\) spatial weights matrix.

n : int¶

Number of spatial units.

method=None¶

"eigenvalue" — exact O(n) per-step evaluation after O(n³) eigendecomposition. Exact for any rho. "chebyshev" — near-minimax Chebyshev polynomial; O(m) per step after O(n³) or O(R·n·m) precomputation via chebyshev(). Coefficients use exact eigenvalues when n is small, otherwise a stochastic trace estimator selected by trace_estimator.

rho_min : float, default -1.0¶

Lower bound of the rho domain ("chebyshev" only).

rho_max : float, default 1.0¶

Upper bound of the rho domain ("chebyshev" only).

cheb_order : int, default 20¶

Chebyshev polynomial order ("chebyshev" only).

trace_estimator : {"hutchinson", "hutchpp", "xtrace"}, default "hutchpp"¶

Stochastic trace estimator used to build Chebyshev coefficients when an eigendecomposition is unavailable.

trace_k : int, optional¶

Number of probe vectors for the trace estimator.

Returns:¶

Function fn(rho_d, rho_o) -> pt.TensorVariable evaluating \(n\,f(\rho_d) + n\,f(\rho_o)\) where \(f(\rho) = \log|I_n - \rho W|\).

Return type:¶

callable