How to create multiple matrices based on a formula using two data frames and sum those matrices up in one go?

I'm fairly new to R and am thus not that knowledgeable yet about its different functionalities. I'm wondering if there is a more efficient way to replicate the following other than writing and running 230 lines of code.

I have two matrices, Z and E, which contain continuous numerical data and have the dimensions 7x229 and 17x229 respectively. For each column (so 229 times) I want to create a new 119x119 matrix by using the (repeated) formula below

ZZEE1 <- kronecker((Z[,1] %*% t(Z[,1])), (E[,1] %*% t(E[,1]))) ZZEE2 <- kronecker((Z[,2] %*% t(Z[,2])), (E[,2] %*% t(E[,2]))) ZZEE3 <- kronecker((Z[,3] %*% t(Z[,3])), (E[,3] %*% t(E[,3]))) ZZEE4 <- kronecker((Z[,4] %*% t(Z[,4])), (E[,4] %*% t(E[,4]))) #... ZZEE228 <- kronecker((Z[,228] %*% t(Z[,228])), (E[,228] %*% t(E[,228]))) ZZEE229 <- kronecker((Z[,229] %*% t(Z[,229])), (E[,229] %*% t(E[,229]))) 

After this is done, I want to add all 229 matrices up into one matrix like this (not complete)

Sum_ZZEE <- ZZEE1 + ZZEE2 + ZZEE3 + ZZEE4 + ZZEE228 + ZZEE229 #Sum of all matrices from ZZEE1 to ZZEE229 

Is there a quicker fix out there that will do exactly this? I have tried to find an answer online but did not find something that worked or something that I understood to the extent that I could modify it to my own data/code. As far as I understood it, there might be a fix with the function() function, but I would not know how to code it correctly. Getting the 'Sum_ZZEE' matrix is the final goal, I do not necessarily need the individual matrices stored in the workspace. Much obliged!

1 Answer

First construct a list of matrices: the following two code chunks are equivalent, use whichever is clearer to you.

ZZ_list <- lapply(1:229, function(i) kronecker((Z[,i] %*% t(Z[,i])), (E[,i] %*% t(E[,i]))) ) 

or

ZZ_list <- list() for (i in 1:229) { ZZ_list[[i]] <- kronecker((Z[,i] %*% t(Z[,i])), (E[,i] %*% t(E[,i]))) } 

Then use Reduce() (unfortunately sum() doesn't work the way you want):

answer <- Reduce("+", ZZ_list) 

There might be some super-clever answer that works in pure linear algebra (e.g. with stacking/unstacking operators) ...