Suppose I have a list list0 of length D, where each element is a matrix N x T.
I am trying to create a Kronecker product, row by row that does the following.
for(i in 1:N){
dummy[,i] <- list0[[D]][i,] %x% ...( (list0[[2]][i,] %x% list0[[1]][i,]))
}
Does anyone know the smartest way to apply this function? The below is an example where I manually type it out, but I want this for arbitrary D.
set.seed(1)
N = 2
T = 3
D = 4
dummy = matrix(0,(T)^D,N)
list0 = list()
for(d in 1:D) {
list0[[d]] <- matrix(rnorm(N*T,0,1),N,T)
}
for(i in 1:N){
dummy[,i] <- list0[[4]][i,] %x% (list0[[3]][i,] %x% (list0[[2]][i,] %x% list0[[1]][i,]))
}
head(dummy)
[,1] [,2]
[1,] 0.15578313 -0.1783412
[2,] 0.20779959 -1.5492222
[3,] -0.08194020 0.7967800
[4,] 0.18402067 0.0737661
[5,] 0.24546573 0.6407946
[6,] -0.09679284 -0.3295669
The lapply gives a list of the ith row of the matrices and Reduce kroneckers them together. The sapply then assembles that into the final matrix.
N <- nrow(list0[[1]])
sapply(1:N, function(i) Reduce("%x%", init = 1, lapply(rev(list0), "[", i, TRUE)))