Creating Random Binary Asymmetric Square Matrices in R

Question

I am trying to create random binary square matrices. However, there are some constraints. I would like the diagonal to = 0. Also, the upper and lower triangles need to be inverse transpositions of each other.

To be clear, what I am looking for would look the below for a random example 5 x 5 matrix. If you look at any row/column pair e.g. 3&5, 1&4, the upper and lower triangles for those pairs have opposite results.

      [,1] [,2] [,3] [,4] [,5]
[1,]    0    0    0    1    0
[2,]    1    0    0    0    0
[3,]    1    1    0    1    0
[4,]    0    1    0    0    1
[5,]    1    1    1    0    0

I am running into some problems in making my random matrices asymmetric.

Here's what I have thus far for creating a random binary 12x12 matrix:

function1 <- function(m, n) {
matrix(sample(0:1, m * n, replace = TRUE), m, n)
}
A<-function1(12,12)
A #check the matrix
diag(A)<-0

My attempt at putting the transposed upper triangle into the lower triangle:

A[lower.tri(A)] <- t(A[upper.tri(A)])
A #rechecking the matrix - doesn't seem to do it.

I have tried some variations to see if I got my upper/lower triangles mixed up, but none seem to work.

Hope this question is understandable.

Answer 1

fun <- function(n){
  vals <- sample(0:1, n*(n-1)/2, rep = T)
  mat <- matrix(0, n, n)
  mat[upper.tri(mat)] <- vals
  mat[lower.tri(mat)] <- 1 - t(mat)[lower.tri(mat)]
  mat
}

And testing it out...

> fun(5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    0    0    1    0    1
[2,]    1    0    1    0    1
[3,]    0    0    0    0    0
[4,]    1    1    1    0    1
[5,]    0    0    1    0    0
> out <- fun(5)
> out + t(out)
     [,1] [,2] [,3] [,4] [,5]
[1,]    0    1    1    1    1
[2,]    1    0    1    1    1
[3,]    1    1    0    1    1
[4,]    1    1    1    0    1
[5,]    1    1    1    1    0