bayespecon._ops.kron_solve_vec¶
- bayespecon._ops.kron_solve_vec(Lo, Ld, b, n)[source]¶
Solve \((L_o \otimes L_d)\,\eta = b\) via two \(n \times n\) sparse solves.
Uses the vec-permutation identity \((L_o \otimes L_d)\operatorname{vec}(H) = \operatorname{vec}(L_d H L_o^\top)\):
\(H' = L_d^{-1} H_b\)
\(Z = L_o^{-1} H'^{\,\top}\) (i.e. solve \(L_o Z = H'^\top\))
\(\eta = \operatorname{vec}(Z^\top)\)
- Parameters:¶
- Lo : scipy.sparse.csr_matrix, shape (n, n)¶
Factor matrices \(L_o = I_n - \rho_o W\) and \(L_d = I_n - \rho_d W\).
- Ld : scipy.sparse.csr_matrix, shape (n, n)¶
Factor matrices \(L_o = I_n - \rho_o W\) and \(L_d = I_n - \rho_d W\).
- b¶
- n : int¶
Number of spatial units.
- Returns:¶
eta
- Return type:¶
ndarray, shape (N,)