# Change matrix bits depending on the rate (Matlab)

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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.
Jan on 21 May 2021
I still do not understand, what "permutation between rows and columns" means. Do you exchange some transposed columns with rows or the other way around? Do you want to permute the elements of a specific row and column? Do you want to change the order of rows and/or columns? Should the permutation randomly or do you want to swap the specific value with any (or the last) matching different value of the row (or column)?
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.

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
Afluo Raoual on 1 Jun 2021
@AMO It works now. Thank you
AMO on 1 Jun 2021
@Afluo Raoual You're welcome.