how can i extract this matrix ?

i have a square matrix M of size 12x12 containing the integers from 1 to 144 rows, i want to extract the submatrix containing the coefficients m(i,j) for i + j even, can anyone help me ?

Answer 1

[Image Analyst]

I offer two methods, one brute force, and one vectorized where the sum of the row index and the column index equals an even number. (Note, this extracts a totally different set of numbers than Guillaume.)

yourMatrix = randi(9, 12, 12) % Create sample data.

% Mathod 1: brute force method:
[rows, columns] = size(yourMatrix);
% See which rows and columns we'll extract out:
index = 1;
for i = 1 : rows
  for j = 1 : columns
    if rem(i+j, 2) == 0
      fprintf('Extracting i=%d, j=%d\n', i, j);
      out(index) = yourMatrix(i,j);
      index = index + 1;
    end
  end
end
out = reshape(out, [12,6])

% Method 2: vectorized:
checkerBoardPattern = logical(mod(toeplitz(1:12, 1:12), 2))
out2 = yourMatrix(checkerBoardPattern)
out2 = reshape(out, [12,6])
isequal(out, out2)  % Prove that out and out2 are the same.

Answer 2

[Walter Roberson]

indices_both_even = M(1:2:end,1:2:end)
indices_both_odd = M(2:2:end,2:2:end)

but then what? You have not defined the order of the output. Should it be 12 x 6? Should it be 6 x 12?

If you look at the submatrix [A B; C D] then A and D are both in positions where the sum of the indices is even, but you have not said whether this should result in [A, D] or in [A; D]