I want to extract half of the non-zero element of a matrix

Hello, I have a matrix of the following form: [1,0,0,0;0,0,0,0;0,10,0,12;13,0,0,0], I need a mask that allows me to extract half of the data of each nonzero matrix of this form in this case for example I want the following result [1,0,0,0;0,0,0,0;0,10,0,0;0,0,0,0]

Answer 1

[Matt J]

idx=find(A);

A(idx(2:2:end))=0;

[BANI tita]

merci

Answer 2

[Andrei Bobrov]

ii = 1:fix(nnz(A)/2);
At = A';
jj = find(At);
At(jj(fix(nnz(A)/2)+1:end)) = 0;
out = At';

[BANI tita]

merci bien