How to transform a matrix into a 3D array (tensor) ?

Say I have B, a matrix which looks like this:

B =
     1    10   100     2    20   200
     3    30   300     4    40   400

And I created a tensor specifically like down below, because I want those elements in that exact order:

   A(:,:,1) = [B(1,1) B(1,4); B(2,1) B(2,4)];
   A(:,:,2) = [B(1,2) B(1,5); B(2,2) B(2,5)];
   A(:,:,3) = [B(1,3) B(1,6); B(2,3) B(2,6)];   

So I obtained this:

A(:,:,1) =
     1     2
     3     4

A(:,:,2) =
    10    20
    30    40


A(:,:,3) =
   100   200
   300   400

Is there a way that I could automatize those 3 lines of code? To be able to create a tensor like that from a matrix of different dimensions, not manually telling it each element it needs to take?

B is the result of unfolding the tensor A, so I want to code the inverse operation.

LE:

I've read somewhere on here an algorithm that works for the mode-2 unfolding, which means B looks like this:

B2 =
     1     3    10    30   100   300
     2     4    20    40   200   400
     

the code:

x=2; y=2; z=3;     
    slice = size(B2,2)/x; %6:2=3
    part = size(B2,2)/z;  %6:3=2
    start=1;
    A=zeros(x,y,z);
    for i=1:slice
       A(:,:,i)=B2(:,start:start+part-1)';
       start=start+part;
    end

I also adapted it for B matrix but I am trying to adapt it to the other type of unfolding, for the matrix B3:

B3 =
     1     2     3     4
    10    20    30    40
   100   200   300   400

and the problem is now the 'part' variable would be 4/3 which isn't too convenient, and I also can't seem to fit the first line into the tensor without causing an error. I've tried manually something like this:

 for i=1:3
       A(:,:,i)=B3(i,1:4);
    end

and I am not sure how to break the first 2 elements of B3 so the next 2 ones can go to the second row of the tensor.

Answer 1

[Matt J]

 A=[1,2;3 4].*reshape([1,10,100], 1,1,[])

Answer 2

[Adam]

permute( reshape( reshape( B', 3, 4 )', [2 2 3] ), [2 1 3] )

gives the answer you want, but I'm sure there is a tidier way that someone will come up with!

[snowflake]

Thank you, I modified it a bit so that it works on different dimensions of a matrix and also for other types of foldings. I've tried to play with reshape and permute before and I couldn't find the perfect match, how did you manage to think of this line of code?

[Adam]

I just played around on the command line with reshape and permute, using knowledge of what order the data gets reshaped in.

I solve a large number of my problems by just trying stuff on command line, knowing what components I likely need, but not necessarily in what combination or order until I just try it. I don't find it worth trying to commit all these things to memory when I have the command line at my disposal to test things so quickly!