Reshape matrix by distributing submatrices to third dimension

Question

I have a long nx3 matrix. For eg, I take a 9x3 matrix

A =

 8     9     8
 9     2     9
 2     9     6
 9     9     1
 6     5     8
 1     8     9
 3     2     7
 5     4     7
 9     9     7

Now I want it reshaped, (taking successive 3x3 sub-matrix to the next dimension) such that,

out(:,:,1) = 
 8     9     8
 9     2     9
 2     9     6
out(:,:,2)
 9     9     1
 6     5     8
 1     8     9
out(:,:,3)
 3     2     7
 5     4     7
 9     9     7

I could do this with loops but I wanted to know how to vectorize this process.. Can i do it with reshape and permute alone?

Answer 1

Yes, you can use permute and reshape :

A = [...
 8     9     8
 9     2     9
 2     9     6
 9     9     1
 6     5     8
 1     8     9
 3     2     7
 5     4     7
 9     9     7
 3     2     7
 5     4     7
 9     9     7]

n = size(A,2);
B = permute( reshape(A.',n,n,[]), [2 1 3]) %'
%// or as suggested by Divakar
%// B = permute( reshape(A,n,n,[]), [1 3 2]) 

---

out(:,:,1) =

     8     9     8
     9     2     9
     2     9     6

out(:,:,2) =

     9     9     1
     6     5     8
     1     8     9

out(:,:,3) =

     3     2     7
     5     4     7
     9     9     7

out(:,:,4) =

     3     2     7
     5     4     7
     9     9     7

Answer 2

This could be one approach -

N = 3
out = permute(reshape(A,N,size(A,1)/N,[]),[1 3 2])

This one has the advantage of avoiding the transpose as used in the other answer by @thewaywewalk .

Sample run -

A =
     8     9     8
     9     2     9
     2     9     6
     9     9     1
     6     5     8
     1     8     9
     3     2     7
     5     4     7
     9     9     7
out(:,:,1) =
     8     9     8
     9     2     9
     2     9     6
out(:,:,2) =
     9     9     1
     6     5     8
     1     8     9
out(:,:,3) =
     3     2     7
     5     4     7
     9     9     7