MATLAB multidimensional array

Question

I have been trying to use the multidimensional array function to store NxN vectors of length n in each (i,j) entry of a 3d matrix of NxNxn dimensions. My code looks like:

    a=zeros(N,N,n);
    a(i,j,:)=v_ij; %here v is a vector of length n, which differs for each i,j

However when I try to extract each vector by typing e.g. a(1,1,:) I don't get a nice vector. Rather I get something like:

    ans(:,:,1) = ..
    ans(:,:,2) = ..
    ...

I don't understand why it says ans(:,:)...

Answer 1

That's because each vector v_ij is stored along the 3rd dimension of your matrix, so when you access a(1,1,:), you are looking for a multidimensional array consisting of every value at the location (1,1) along the 3rd dimension of a.

Let's consider a simple example:

N = 2;
n = 3;

a = zeros(N,N,n);

for k = 1:N

    for l = 1:N

        v_kl = randi([0 10],1,n);
        a(k,l,:) = v_kl;

    end
end

The randomly-generated matrix a is a 2x2x3 matrix that looks like this:

a(:,:,1) =

     4     1
     4    10


a(:,:,2) =

     0     2
     0     5


a(:,:,3) =

     2     2
     9     5

Therefore, using a(1,1,:) is equivalent to getting the element located at (1,1) for all 3 dimensions, here it would be 4,0 and 2.

Indeed, calling a(1,1,:) yields:

ans(:,:,1) =

     4


ans(:,:,2) =

     0


ans(:,:,3) =

     2

Answer 2

Benoit_11's answer plus squeeze should work, but I would like to propose a different solution.

Rather than creating a NxNxn array, why not make it nxNxN?

N = 2;
n = 3;

a = zeros(n,N,N);

for p = 1:N
    for q = 1:N
        v_pq = randi([0 10],1,n);
        a(:,p,q) = v_pq;
        if (p == 1) && (q == 1)
           v_pq   %// display vector at a(:,1,1)
        end
    end
end

a


v_pq =

   3   4   8

a =

ans(:,:,1) =

   3   3
   4   9
   8   7
ans(:,:,2) =

    5    6
   10    1
    9    5

Now the vectors are stored along the first dimension, so [3 4 8] shows up as the first column of ans(:,:,1). To access it you would use a(:,p,q) rather than a(p,q,:):

a(:,1,1)

ans =

   3
   4
   8