Changing particular cells of a Matrix iteratively in R - r

Question

Suppose that we have a (4,4) matrix. My goal is to change iteratively that cells (1,1),(2,1),(3,1),(1,2),(2,2),(1,3)
I wrote the following
for(i in 1:3){
for(j in 1:3){
if(i>j){
A[i,j] = A[i,j] + sample(c(-1,1),prob=c(0.5,0.5))
}
}
However, it doesn't change the correct cells and misses cells that have to be changed.
The matrix A can be of the form
A = matrix(c(1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0),4,4,byrow=T)
I think that the following chunk of code might be the solution, at least it gives the correct answer for a few runs that I did.
A = matrix(c(1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0),4,4,byrow=T)
k = 0
for(i in 1:3){
for(j in 1:(3-k)){
A[i,j] = A[i,j] + sample(c(-1,1),prob=c(0.5,0.5), size = 1)
}
k = k + 1
}

Answer 1

I think you simple forgot to set the size= parameter of sample to get one draw of the Rademacher universe.
set.seed(42)
for (i in 1:3) {
for (j in 1:3) {
if (i > j) {
A[i, j] <- A[i, j] + sample(c(-1, 1), size=1, prob=c(0.5, 0.5))
}
}
}
A
# [,1] [,2] [,3] [,4]
# [1,] 1 1 1 1
# [2,] 0 1 1 0
# [3,] 0 2 0 0
# [4,] 1 0 0 0
Another idea is to use a permutation matrix, which you may subset to your needs, and over which you may loop.
id <- RcppAlgos::permuteGeneral(ncol(B) - 1, ncol(B) - 2, repetition=T)
(id <- id[c(1, 4, 7, 2, 5, 3), ])
# [,1] [,2]
# [1,] 1 1
# [2,] 2 1
# [3,] 3 1
# [4,] 1 2
# [5,] 2 2
# [6,] 1 3
set.seed(42)
for (i in 1:nrow(id)) {
A[id[i, 1], id[i, 2]] <- A[id[i, 1], id[i, 2]] +
sample(c(-1, 1), size=1, prob=c(0.5, 0.5))
}
A
# [,1] [,2] [,3] [,4]
# [1,] 0 0 0 1
# [2,] 0 0 1 0
# [3,] 2 1 0 0
# [4,] 1 0 0 0

Answer 2

We can create a row/column index (vectorized approach) by cbinding the vector of index. Use the index to subset the cells of the matrix and assign (<-) after adding the sample output to those elements
n <- 3
j1 <- rep(seq_len(n), rev(seq_len(n)))
i1 <- ave(j1, j1, FUN = seq_along)
ind <- cbind(i1, j1)
ind
# i1 j1
#[1,] 1 1
#[2,] 2 1
#[3,] 3 1
#[4,] 1 2
#[5,] 2 2
#[6,] 1 3
A[ind] <- A[ind] + sample(c(-1,1),prob=c(0.5,0.5),
size = nrow(ind), replace= TRUE)