How to index and multiply two matrices efficiently?

Question

I have two matrices "A", "B", and a data frame "C". They are

A <- matrix(1:10, nrow = 2) 
colnames(A) <- letters[1:5]

B <- matrix(11:16, nrow = 2)
colnames(B) <- letters[6:8]

C <- data.frame(ix1 = c("a", "d"), ix2 = c("f", "h"))

I want to create a vector "vec" with length 2 and values

vec[1] = A[,"a"] %*% B[,"f"]
vec[2] = A[,"d"] %*% B[,"h"]

This can be done easily with a for loop, but it is time consuming when the sizes of "A", "B" and "C" grow. How to do it efficiently?

Answer 1

You can vectorize as follows, but I'm not sure how costly it would be to transpose A

(vec <- diag(crossprod(A[, as.character(C$ix1)], B[, as.character(C$ix2)])))
## [1]  35 233