# From a matrix, Pick one element from each row and not from same column for all possibilities. Only for non zero elements.

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MeMariah on 8 Jul 2020
Commented: MeMariah on 20 Sep 2020
Hi, From a matrix, I would like to pick one element from each row and not from same column for all possibilities.
Only for non zero elements.
Example, from A = [1 2 0; 1 2 0; 0 0 3], I want to obtain (1 2 3 and 2 1 3).
Thank you

Puru Kathuria on 22 Jul 2020
Hi,
Your requirements are answered in a similar question mentioned in this link. Also, selecting set of elements from a matrix such that each element comes from distinct row and column can also be modeled as a Matching problem. (graph theory)
MeMariah on 23 Jul 2020
Thank you Puru Kathuria.

Bruno Luong on 23 Jul 2020
Edited: Bruno Luong on 23 Jul 2020
A dynamic programming for fun
function p = nzperm(A,c)
if nargin < 2
c = 1;
end
r = find(A(:,c));
if isempty(r)
p = [];
elseif c==size(A,2)
p = A(r,c); % p = r(:);
else
p = [];
for i=r.'
Ai = A;
Ai(i,:) = 0;
q = nzperm(Ai,c+1);
a = A(i,c); % a = i
q = [a+zeros(size(q,1),1) q];
p = [p; q]; %#ok
end
end
Result
>> A=rand(5); A = A.*(rand(size(A))>0.6)
A =
0 0.6468 0.7881 0.5598 0.8008
0.5607 0 0 0 0.8961
0 0 0 0.9394 0.5975
0 0.4756 0.1335 0 0
0 0.3625 0.0216 0 0.9437
>> nzperm(A)
ans =
0.5607 0.6468 0.1335 0.9394 0.9437
0.5607 0.4756 0.7881 0.9394 0.9437
0.5607 0.4756 0.0216 0.5598 0.5975
0.5607 0.4756 0.0216 0.9394 0.8008
0.5607 0.3625 0.1335 0.5598 0.5975
0.5607 0.3625 0.1335 0.9394 0.8008
Note: this code will be slow on large array, since MATLAB make copies of matrix at every step. This algorithm could be implemented without copy using C mex.
MeMariah on 20 Sep 2020
@Bruno, you are right. large array take long. Unfortunately, I keep getting error when I try to generate the C mex file. Am using this app for the first time. Are able to help? error points to the line with
for i= r.'
Thanks.