Should all possibilities of such a matrix be equally likely? Then it might be very quite tricky.
Here's a brute force approach, that might not always work for specific values of S, L, M and N:
M = 5 ; N = 6 ;
S = 3 ; L = 2 ;
% fix the number of 1's per row
X = zeros(M,N) ;
sumRow = ceil(S*rand(M,1)) ;
for k=1:M,
X(k,1:sumRow(k)) = 1 ;
end
ntries = 0 ;
while ntries < 1000 ;
ntries = ntries + 1 ;
% randomly swap columns, see RANDSWAP on the File Exchange
for k=1:M,
p = randperm(N) ;
X(k,:) = X(k,p) ;
end
if all(sum(X,1) <= L) && all(sum(X,1)>0)
break ;
end
end
if ntries < 1000
disp(X)
sumCol = sum(X,1)
sumRow = sum(X,2).'
else
disp('No matrix found within a reasonable time') ;
end
