Generating random 0/1 matrix with fixed features in R - r

Question

I want to generate a random M x N matrix with zeros and ones with the following special properties:
1) The ones are only in m of the M rows.
2) The ones are only in n of the N columns.
Suppose I am ONLY given that M=10, N=10, m=6 and n=4. One possible random matrix is given by
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 0 0 1 0 0 0 1 0 1 0
[2,] 0 0 1 0 0 0 1 0 1 0
[3,] 0 0 0 0 0 0 0 0 0 0
[4,] 0 0 0 0 0 0 0 0 0 0
[5,] 0 0 1 0 0 0 1 0 0 0
[6,] 0 1 0 0 0 0 0 0 0 0
[7,] 0 0 0 0 0 0 0 0 0 0
[8,] 0 0 1 0 0 0 0 0 0 0
[9,] 0 0 1 0 0 0 0 0 1 0
[10,] 0 0 0 0 0 0 0 0 0 0
For reproducibility, I've artificially generated the above "random" matrix using
ex <- matrix(0,10,10)
ex[1,3] <- ex[1,7] <- ex[1,9] <- ex[2,3] <- ex[2,7] <-
ex[2,9] <- ex[5,3] <- ex[5,7] <- ex[6,2] <- ex[8,3] <- ex[9,3] <- ex[9,9] <- 1
Note that
sum(rowSums(ex)>0)
[1] 6
sum(colSums(ex)>0)
[1] 4
which match exactly m and n above. The number of ones can be random. On one extreme I could have 6 ones spread out over 6 rows and 4 columns (2 columns will have 2 ones, while the rest have 1) or on the other extreme, I could have 24 ones (each of the 6 rows will have a 1 in the same 4 columns).
Question
I can generate this in a brute force manner, sampling over the rows and columns, but I need to do this over thousands of such matrices (because the m and n will be different each time) and these matrices are large (M=5000 and N=8000, typically). Is there a way to do this efficiently in R?

Answer 1

M=10 #total number rows
N=10 #total number columns
m=6 #number valid rows
n=4 #number valid columns
#number of cells to simulate
k=12
ex <- matrix(0,M,N)
#sample m valid rows and n valid columns from uniform
mi <- sample(1:M, m)
ni <- sample(1:N, n)
#get all valid cells (valid rows and columns)
mn_i <- expand.grid(mi, ni)
#sample k cells from valid cells
x <- mn_i[sample(1:nrow(mn_i), k), ]
#update sampled cells using matrix subet on ex
ex[as.matrix(x)] <- 1
# > ex
# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1,] 1 0 0 0 0 0 0 0 0 0
# [2,] 0 0 0 0 0 0 0 0 0 0
# [3,] 0 0 0 0 0 0 1 1 0 1
# [4,] 0 0 0 0 0 0 0 0 0 0
# [5,] 1 0 0 0 0 0 1 1 0 1
# [6,] 1 0 0 0 0 0 1 0 0 0
# [7,] 0 0 0 0 0 0 0 0 0 0
# [8,] 0 0 0 0 0 0 0 1 0 1
# [9,] 0 0 0 0 0 0 0 0 0 0
# [10,] 0 0 0 0 0 0 0 0 0 0
You might want to wrap in a function to call it something like
ex <- constrained_matrix_sample(M, N, m, n, k)

Answer 2

A dplyr variant
M = 10 # rows
N = 10 # columns
m = 6
n = 4
ni = sample(1:N, n)
mi = sample(1:M, m)
expand.grid(N = 1:N, M = 1:M) %>%
mutate(value = ifelse(N %in% ni & M %in% mi, 1, 0)) %>%
.$value %>%
matrix(., nrow = M, byrow = TRUE)