How to combine two loops - r

Question

In a tutorial on for() Loops came across the following exercise:
Exercise 4.4. Write a function to perform matrix-vector multiplication. It should take a matrix A and a vector b as arguments, and return the vector Ab. Use two loops to do this, rather than %*% or any vectorization.
Lets say I use a specific matrix A(dim:3,4) and vector b(length(3)).
> # Ex 4.4
> out<-c(1,1,1)
> Ab<-function(A,b) {
+ for(i in 1:dim(A)[1]) {
+
+ out[i]=sum(A[i,]*b)
+ }
+ out
+ }
> a = c(1,1,1)
> A
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 10
> a
[1] 1 1 1
> Ab(A,a)
[1] 12 15 19
This works for a very specific case, i.e. matrix with 3 rows and vector of length 3, but leaves much to be desired, i don't know what a good solution to this exercise would be but the question says 'use two loops'. Suggestions will be much appreciated.
thx

Answer 1

You are hiding the inner loop with A[i,]*b which is doing vectorized multiplication (ie. a hidden loop). So, if you expand that out explicitly you will have the two required loops.
Ab<-function(A,b) {
if (dim(A)[2] != NROW(b)) stop("wrong dimensions")
out <- matrix(, nrow(A), 1)
for(i in 1:dim(A)[1]) {
s <- 0
for (j in 1:dim(A)[2]) s <- s + A[i,j] * b[j]
out[i] <- s
}
out
}