Fast Kronecker-product matrix-vector multiply (times vary fastest)

In plain terms: multiplies a big covariance \(K = \mathrm{space} \otimes \mathrm{time}\) by a vector without ever forming K, using a reshape-multiply-reshape trick.

Usage

kron_mv(v, space, time)

Arguments

v: Numeric vector of length nrow(space) * nrow(time), ordered with times varying fastest within site.
space: Spatial kernel matrix (size \(n \times n\)). Must be symmetric (kernels are, by construction) – the implementation relies on t(space) == space.
time: Temporal kernel matrix (size \(nt \times nt\)).

Value

A numeric vector the same length as v.

Details

Technically: for \(v = \mathrm{vec}(X^\top)\) with times varying fastest, computes \((space \otimes time)\,v = \mathrm{vec}\!\big((space\,X\,time^\top)^\top\big)\).