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Change matrix bits depending on the rate (Matlab)

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Afluo Raoual
Afluo Raoual on 20 May 2021
Commented: AMO on 1 Jun 2021
Dear members
I have matrix A of dimensions s1*s2 where the number of ones in each column and row is equal
And I have to write a program that verify if the final bits depending on the rate are 0 or 1. If final bits depending on the rate is 0, I have to make permutation between rows and columns in order to obtain final bits 1 not 0 and save the equal number of ones in each row and column.
For example : I have a matrix 5*10, so the rate is 5/10=1/2 and the number of ones in each row is 6 and in each column is 3
The final bit depending on the rate 1/2 in the first row is 0, so here I have to make permutation between rows and columns to obtain 1 in place of 0 and the number of ones in each row and columns still the same. We obtain this matrix finally :
I tried to program the first part that calcul the rate of the matrix like that:
[s1, s2] = size(A);
d = gcd(s1, s2);
n1 = s1 / d;
n2 = s2 / d;
Can you help me to program the permutation please.
  4 Comments
Afluo Raoual
Afluo Raoual on 21 May 2021
@Jan Permutation means change the order of rows and/or columns randomly until that all the final bits (zeros) depending on the rate ( red bits in the matrix ) being all ones with condition that the number of ones in each column and row still the same. For example in this matrix we have 3 ones in each colulmn and 6 ones in each row. It must still the same.

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Accepted Answer

AMO
AMO on 21 May 2021
Edited: AMO on 21 May 2021
[s1, s2] = size(A);
d = gcd(s1, s2);
n1 = s1 / d;
n2 = s2 / d;
% rows and columns of final bits
rows = 1:s1;
cols = zeros(1,s1);
cOffset = 0;
for c = n2:n2:s2
cols((1:n1) + cOffset) = c;
cOffset = cOffset + n1;
end
% linear index of final bits
finalBits = sub2ind([s1,s2], rows, cols);
% untill all final bits are 1s
while any(A(finalBits) == 0)
% randomly select to swap either rows or colmns
if randi(2) == 1
% swap rows
rswap = randperm(s1,2);
A(rswap,:) = A(flip(rswap),:);
else
% swap columns
cswap = randperm(s2,2);
A(:,cswap) = A(:, flip(cswap));
end
end
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