How do I perform a loop on one matrix after the next?

A = [1 4 0 1 1; -1 -5 9 -20 2; 15 1 4 5 1; 2 2 -5 0 0; 0 2 -3 1 -9];
B = [9 3 3; 12 3 2; 1 3 5];
C = [1 13 2; 1 3 9; -12 2 -1];
D = [5 -2 4 2; 0 3 -1 -1; 3 3 9 -5; 1 1 1 5];

[maxrow, ind] = max(abs(A), [], 2);
if all(2 * maxrow > sum(abs(A), 2)) && isequal(sort(ind),(1:numel(ind))) 
    A(ind, :) = M_A
    disp('This matrix can be made diagonally dominant');
    M_A
else
    disp('This matrix can NOT be made diagonally dominant')
    M_A = A;
    M_A
end

Apologies is the question is worded badly.

So the code above checks if matrix A can be made diagonally dominant through row swaps, then the resultant matrix (in its diagonally dominant form, or in its initial form if it cannot be transformed into a diagonally dominant matrix) is stored as a new variable M_A (where the 2nd letter is the matrix being analysed - A in this case) .

However I want to carry out the analysis on all the matirces A - D either at once or one by one.

I cant think of a way to do this except copy and paste the code another 3 times and changing the matrix its analysing.

Any suggestions??

Answer 1

[Ameer Hamza]

Due to such issues, it is always recommended to create arrays for related data instead of creating several variables. In this case, creating a cell array will simplify the code

A = [1 4 0 1 1; -1 -5 9 -20 2; 15 1 4 5 1; 2 2 -5 0 0; 0 2 -3 1 -9];
B = [9 3 3; 12 3 2; 1 3 5];
C = [1 13 2; 1 3 9; -12 2 -1];
D = [5 -2 4 2; 0 3 -1 -1; 3 3 9 -5; 1 1 1 5];

M = {A,B,C,D};
M_A = cell(1,numel(M));
for i=1:numel(M)
    [maxrow, ind] = max(abs(M{i}), [], 2);
    if all(2 * maxrow > sum(abs(M{i}), 2)) && isequal(sort(ind),(1:numel(ind))) 
        M{i}(ind, :) = M_A{i};
        disp('This matrix can be made diagonally dominant');
        M_A{i}
    else
        disp('This matrix can NOT be made diagonally dominant')
        M_A{i} = M{i};
        M_A{i}
    end
end

Read more on this here: https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

[Andrei]

Thank you!!!

Works as intended, however all outputs are assigned to M_A. I need the output result for matrix B to be set to a new variable M_B, output for C set to M_C and so on.

I've tried to use arrays but with no success.

Any ideas will be helpful!

[Ameer Hamza]

Try the updated code. Now M_A is also a cell array.

[Stephen23]

"Any ideas will be helpful!"

Your code would be simpler, more generalized, and more efficient if you changed your approach a little bit: instead of having separate matrices with different names, you should just use one cell array (as Ameer Hamza has shown you) together with very efficient indexing. Then your code would trivially expand to any number of matrices, and you could trivially access any of them using basic indexing:

https://www.mathworks.com/help/matlab/matlab_prog/access-data-in-a-cell-array.html