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
el 8 de Jul. de 2020
Comentada: MeMariah
el 20 de Sept. de 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
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Respuesta aceptada
Puru Kathuria
el 22 de Jul. de 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)
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Bruno Luong
el 23 de Jul. de 2020
Editada: Bruno Luong
el 23 de Jul. de 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.
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