Use values from 2 matrices to index a third in R

Question

I'm optimizing a more complex code, but got stuck with this problem.

a<-array(sample(c(1:10),100,replace=TRUE),c(10,10))  
m<-array(sample(c(1:10),100,replace=TRUE),c(10,10))  
f<-array(sample(c(1:10),100,replace=TRUE),c(10,10))  
g<-array(NA,c(10,10)) 

I need to use the values in a & m to index f and assign the value from f to g
i.e. g[1,1]<-f[a[1,1],m[1,1]] except for all the indexes, and as optimally/fast as possible

I could obviously make a for loop to do this for me but that seems rather dumb and slow. It seems like I should be able to us something in the apply family, but I've had no luck with figuring out how to do that. I do need to keep the data structured as it is here so that I can use matrix operations in different parts of my code. I've been searching for an answer to this but haven't found anything particularly helpful yet.

Answer 1

g[] <- f[cbind(c(a), c(m))]

This takes advantage of the fact that matrices can be addressed as vectors and using a matrix as the index.