Randomly select Elements of 4D matrix in Matlab

Question

I have a 4D matrix with dimensions 7x4x24x10 (Lets call it main_mat). I want to get a matrix of size 7x4x24 (rand_mat) so that each element of this (rand_mat) matrix is actually a uniformly random draw from the main matrix (main_mat). I am sorry if I have not put the question clearly, so I try to explain:

I have a stack of 24 sheets of 7x4 elements, and I have 10 such stacks. What I want is that I get a single stack of 24 sheets of 7x4 elements in such a way that every element out of resultant single stack is uniformly randomly drawn from exactly same sheet number from within 10 stacks. How can I do it without using loops?

Answer 1

If I am interpreting what you want correctly, for each unique 3D position in this matrix of 7 x 4 x 24, you want to be sure that we randomly sample from one out of the 10 stacks that share the same 3D spatial position.

What I would recommend you do is generate random integers that are from 1 to 10 that is of size 7 x 4 x 24 long, then use sub2ind along with ndgrid. You can certainly use randi as you have alluded to in the comments.

We'd use ndgrid to generate a grid of 3D coordinates, then use the random integers we generated to access the fourth dimension. Given the fact that your 4D matrix is stored in A, do something like this:

rnd = randi(size(A,4), size(A,1), size(A,2), size(A,3));
[R,C,D] = ndgrid(1:size(A,1), 1:size(A,2), 1:size(A,3));
ind = sub2ind(size(A), R, C, D, rnd);
B = A(ind);

Bear in mind that the above code will work for any 4D matrix. The first line of code generates a 7 x 4 x 24 matrix of random integers between [1,10]. Next, we generate a 3D grid of spatial coordinates and then use sub2ind to generate column-major indices where we can sample from the matrix A in such a way where each unique 3D spatial location of the matrix A only samples from one chunk and only one chunk. We then use these column-major indices to sample from A to produce our output matrix B.

Answer 2

This problem might not be solvable without the use of loops. One way that could work is:

mainMatrix = ... (7x4x24x10 matrix)
randMatrix = zeros(mainMatrix(:,1,1,1), mainMatrix(1,:,1,1), mainMatrix(1,1,:,1))
for x = 1:length(mainMatrix(:,1,1,1))
  for y = 1:length(mainMatrix(1,:,1,1))
    for z = 1:length(mainMatrix(1,2,:,1))
      randMatrix(x,y,z) = mainMatrix(x,y,z,randi(10))
    end
  end
end