Sparse prior precision for q-th order random walk on a K x K lattice (d-dimensional)

Builds sparse 1D RW(q) precision Q1D = t(Dq) then constructs 2D lattice precision via Kronecker sum: Q2D = kron(Q1D, I_K) + kron(I_K, Q1D), and replicates across d independent processes: Q_U = lambda * kron(Q2D, I_d).

make_lattice_rwq_precision_sparse(K, d, q = 1, lambda = 1, ridge = 0)

Arguments

K

integer lattice side length (total sites = K^2).

d

integer number of independent processes.

q

integer RW order (1 <= q < K).

lambda

nonnegative scalar multiplier.

ridge

nonnegative ridge added to Q1D (and thus Q2D) for conditioning.

Value

sparse Matrix of size (d*K^2) x (d*K^2).