取数组中所有元素的矩阵积在R?

Question

如何在R中取数组中所有元素的矩阵积?我搜索了stack exchange，没有找到任何结果。

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]

Answer 1

我们可以使用asplit将第三维拆分为list，然后使用Reduce

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

测试

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

---

Or也可以循环最后一个dim序列，提取list中的元素

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

---

或者也可以从purrr使用array_branch

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