# Take the matrix product of all the elements in an array in R?

How can one take the matrix product of all the elements in an array in R?

``````n <- 3
ARRAY <- array(NA, dim = c(4, 4, n))
for (i in 1:4) {
for (j in 1:4) {
ARRAY[i, j, ] <- rnorm(n)
}
}

# this gives me a 1x1 matrix, which is wrong
Reduce("%*%", ARRAY)
mapply("%*%", ARRAY[,,1], ARRAY[,,2])

# this works, but I'd like a generalizable option
ARRAY[,,1]%*%ARRAY[,,2]%*%ARRAY[,,3]
``````

### >Solution :

We may use asplit to split by the third dimension into a `list` and then use `Reduce`

``````out2 <-  Reduce(`%*%`, asplit(ARRAY, 3))
``````

-testing

``````> out1 <- ARRAY[,,1]%*%ARRAY[,,2]%*%ARRAY[,,3]
> identical(out1, out2)
[1] TRUE
``````

Or may also loop over the last `dim` sequence, extract the elements in a `list`

``````out2 <- Reduce("%*%", lapply(seq(dim(ARRAY)[3]), function(i) ARRAY[,, i]))
``````

Or may also use `array_branch` from `purrr`

``````library(purrr)
library(magrittr)
out3 <- array_branch(ARRAY, 3) %>%
reduce(`%*%`)
> identical(out1, out3)
[1] TRUE
``````