sorting matrix by diagonal of submatrix

Hi,

I have a matrix of m x m^2 and I want to find the diagonals of the sub matrices m x m, then rearrange the matrix A such that the sub matrix with the largest diagonal is first and the sub matrix with the lowest diagonal is last

E.g. For the matrix A = [A1 A2 A3]

A =

     2     4     6     8     9     1     4     8     1
     4     1     2     3     6     1     2     3     4
     5     2     3     4     1     7     2     3    12

Sub matrix A1 has a diagnoal of 6 Sub matrix A2 has a diagonal of 21 Sub matrix A3 has a diagonal of 19

so the final output would be A = [A2 A3 A1]

A =

     8     9     1     4     8     1     2     4     6
     3     6     1     2     3     4     4     1     2
     4     1     7     2     3    12     5     2     3

Thanks in advance

[Cedric]

By largest diagonal you mean largest trace?

Answer 1

[Andrei Bobrov]

[~,ii] = sort(sum(reshape(A(repmat(eye(3),1,3)>0),3,[])),'descend');
A1 = reshape(A,3,[],3);
out = reshape(A1(:,:,ii),3,[]);

or

Ac = mat2cell(A,3,[3 3 3]);
[~,ii] = sort(cellfun(@trace,Ac),'descend');
out = cell2mat(Ac(ii));