How to generate all binary matrix by permuting subdiagonal elements in Matlab -

i interested in considering changes the sub-diagonal entries let diagonal , upper-triangular entries zero. closed formula total number of permutations given 2^( n choose 2 ). n=4 case have

         d_1          x(2,1)   d_2    x=                 x(3,1)  x(3,2)  d_3             x(4,1)  x(4,2) x(4,3)  d_4 

where upper triangular entries , d_i's equal zero.

i know there 64 different matrices, how generate them n?

first, figure out how extract/emplace subdiagonal elements. how just:

sub_idx = find(~triu(ones(n))); 

now use vector of indices permanent mapping of binary values subdiagonal. now, need matrix of possible binary values:

num_combs = 2^length(sub_idx); binary_combs = dec2bin(0:num_combs-1).' - '0'; 

and k'th combination matrix is:

mtx = zeros(n); mtx(sub_idx) = binary_combs(:,k); 

(editing add single output matrix option)

if want them in 1 big 3d matrix, instead:

tmp = zeros(n*n, num_combs); tmp(sub_idx, :) = binary_combs; mtx = reshape(tmp, [n n num_combs]);