Sparse prior precision for q-th order random walk on K time points (d-dimensional)

Builds the q-th forward-difference matrix D (size (K-q) x K) with coefficients (-1)^(q-j) * choose(q, j), then returns: Q_U = lambda * (t(D)

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

Arguments

K

integer number of time points.

d

integer dimension per time point.

q

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

lambda

nonnegative scalar multiplier.

ridge

nonnegative scalar ridge added to Q1D.

Value

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