Take value from list and use it as index - r

Question

I have a matrix (A) like this (the names of row and column are identification codes (ID):
1 3 10 38 46
1 0 0.4 0 0 0
3 0 0 0 0 0
10 0 0 0.9 0.8 0
38 0 0 0 0 0
46 0 0.1 0 0 0
And another matrix (B) like this:
a b c
1 2.676651e-04 4.404911e-06 9.604227e-06
3 6.073389e-10 3.273222e-05 3.360321e-04
10 4.156392e-08 1.269607e-06 7.509217e-06
38 4.200699e-08 3.227431e-02 8.286920e-11
46 9.352353e-05 3.318948e-20 8.694981e-06
I would like to take the index of the elements of the A matrix >0, therefore I used this command:
temp <- apply(A,1, FUN=function(x) which(x>0))
it returned a list with the correct index of the elements >0.
After that I would like to multiply the element of the matrix B using the index. In particular, I would like to do something like these for each row:
1: 6.073389e-10*3.273222e-05*3.360321e-04
I have used the information of the matrix A (in the second column of the first row I have a value >0) as index to take the element in the matrix B for the first row.
For the second row, I obtained 0 because there aren't element in A[2,]>0
For the third row, I would like to obtain something like the first row, but I should sum the two products
10: 4.156392e-08*1.269607e-06*7.509217e-06 +4.200699e-08*3.227431e-02*8.286920e-11
I have tried to unlist the list but in this way I obtained a vector losing the corresponding between the ID

Answer 1

A <-
matrix(
c(0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.9, 0.8, 0, 0, 0, 0, 0, 0, 0, 0.1, 0, 0, 0),
nrow = 5,
ncol = 5,
byrow = T
)
B <-
matrix(
c(
2.676651e-04, 4.404911e-06, 9.604227e-06,
6.073389e-10, 3.273222e-05, 3.360321e-04,
4.156392e-08, 1.269607e-06, 7.509217e-06,
4.200699e-08, 3.227431e-02, 8.286920e-11,
9.352353e-05, 3.318948e-20, 8.694981e-06
),
nrow = 5,
ncol = 3,
byrow = T
)
idx<-which(A>0, arr.ind = T)
result <- 0;
for (i in 1:nrow(idx)) {
cat(A[idx[i,1],idx[i,2]], sep="\n")
cat(B[idx[i,2], ], sep="\n")
result = result + sum(A[idx[i,1],idx[i,2]] * B[idx[i,2],])
}
cat("result=")
cat(result)