在Matlab中随机选择4D矩阵的元素

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