R - Given a matrix and a power, produce multiple m

问题:

Given a matrix mat (of size N by M) and a power, p (e.g., 4), produce p matrices, where each p-th matrix contains all possible combinations of the columns in mat at that degree.

In my current approach, I generate the p-th matrix and then use it in the next call to produce the p+1th matrix. Can this be 'automated' for a given power p, rather than done manually?

I am a novice when it comes to R and understand that there is likely a more efficient and elegant way to achieve this solution than the following attempt...

N = 5
M = 3
p = 4
mat = matrix(1:(N*M),N,M)
mat_1 = mat
mat_2 = t(sapply(1:N, function(i) tcrossprod(mat_1[i, ], mat[i, ])))
mat_3 = t(sapply(1:N, function(i) tcrossprod(mat_2[i, ], mat[i, ])))
mat_4 = t(sapply(1:N, function(i) tcrossprod(mat_3[i, ], mat[i, ])))

Can anyone provide some suggestions? My goal is to create a function for a given matrix mat and power p that outputs the p different matrices in a more 'automated' fashion.

Related question that got me started: How to multiply columns of two matrix with all combinations

回答1:

You can do something like this

N = 5
M = 3
p = 4
mat = matrix(1:(N*M),N,M)

res_mat <- list()
res_mat[[1]] <- mat
for(i in 2:p) {
     res_mat[[i]] <- t(sapply(1:N, function(j) tcrossprod(res_mat[[i-1]][j, ], res_mat[[1]][j, ])))
}

回答2:

This solves your problem.

N = 5
M = 3
p = 4
mat = matrix(1:(N*M),N,M)
f=function(x) matrix(apply(x,2,"*",mat),nrow(x))
rev(Reduce(function(f,x)f(x), rep(c(f), p-1), mat, T,T))