How does the permute function in matlab work

Question

This is a somewhat silly question but I can't seem to figure out how permute works in matlab. Take the documentation example:

A = [1 2; 3 4]; permute(A,[2 1])
ans =
 1     3
 2     4

What is going on? How does this tell matlab that the 3 and 2 need to be swapped?

Answer 1

Wow, this is one of the hardest functions to figure out among all the different SDKs I have used up to now. Therefore, I used the F*ck word many times during " my journey of understanding the permute function" . Here are some examples to prevent you from suffering a similar excruciating pain:

First, let's remember the dimensions' names of matrix in matlab: A = zeros(4,5,7) , matrix A has 4 rows, 5 columns and 7 pages. And if you don't specify a dimension, its default count is set to 1. ( i.e. B=zeros(10,3) has 10 rows, 3 columns and 1 page, this order is important!)

order argument passed to permute swap these dimensions in the matrix and produce an awkward combination of arrays, I think permute is a misnomer for this effect.

Now let's move to the examples, Finally:

% A has 4 rows, 2 columns and 1 page
A =[     5     6
         8     2
         2     2
         1     3];
    % (numbers in the order argument of permute function indicates dimensions,
    % 3 = page , 2 = column and 1 = row dimensions):  

    B = permute(A,[3,2,1]); % [3,2,1] means [ page,column,row]
    C = permute(A,[3,1,2]); % [3,1,2] means [ page,row,column]
    D = permute(A,[1,3,2]); % [1,3,2] means [ row,page,column]
    E = permute(A,[2,3,1]); % [2,3,1] means [ column,page,row]
    F = permute(A,[2,1,3]); % [2,1,3] means [ column,row,page]
    G = permute(A,[1,2,3]); % [1,2,3] means [ row,column,page]

EXPLANATIONS:

B = permute(A,[3,2,1]);

1x2x4 ( page(3) dimension of A = 1, column(2) dimension of A = 2, row(1) dimension of A = 4; 1 is row dimension, 2 is column dimension and 4 is page dimension for the generated B. Keep reading here until you understand) So, there will be 4 1x2 (1x2x4) row matrixes. As in:

ans(:,:,1) =    
     5     6

ans(:,:,2) =    
     8     2 

ans(:,:,3) =    
     2     2

ans(:,:,4) =    
     1     3

*

C = permute(A,[3,1,2]);

1x4x2 ( page(3) dimension of A = 1, row(1) dimension of A = 4, column(2) dimension of A = 2; 1 is row dimension, 4 is column dimension and 2 is page dimension for the generated C) So, there will be 2 1x4 (1x4x2) row matrixes. As in:

ans(:,:,1) =    
      5     8     2     1

ans(:,:,2) =    
      6     2     2     3

*

D = permute(A,[1,3,2]);

4x1x2 ( row(1) dimension of A = 4, page(3) dimension of A = 1, column(2) dimension of A = 2; 4 is row dimension, 1 is column dimension and 2 is page dimension for the generated D) So, there will be 2 4x1 (4x1x2) column matrixes. As in:

ans(:,:,1) =

     5
     8
     2
     1


ans(:,:,2) =

     6
     2
     2
     3

*

E = permute(A,[2,3,1]);

2x1x4 ( column(2) dimension of A = 2, page(3) dimension of A = 1, row(1) dimension of A = 4; 2 is row dimension, 1 is column dimension and 4 is page dimension for the generated E) So, there will be 4 2x1 (2x1x4) column matrixes. As in:

ans(:,:,1) =

     5
     6

ans(:,:,2) =

     8
     2

ans(:,:,3) =

     2
     2

ans(:,:,4) =

     1
     3

*

F = permute(A,[2,1,3]); % this is transpose and same as [2,1]

2x4x1 ( column(2) dimension of A = 2, row(1) dimension of A = 4, page(3) dimension of A = 1; 2 is row dimension, 4 is column dimension and 1 is page dimension for the generated F) So, there will be 1 2x4 (2x4x1) matrix. As in:

 ans =

     5     8     2     1
     6     2     2     3

*

G = permute(A,[1,2,3]); % this makes no difference,  using to show the reasoning

4x2x1 ( row(1) dimension of A = 4, column(2) dimension of A = 2, page(3) dimension of A = 1; 4 is row dimension, 2 is column dimension and 1 is page dimension for the generated G) So, there will be 1 4x2 (4x2x1) matrix(itself!). As in:

 ans =

 5     6
 8     2
 2     2
 1     3

Yes, this looks hard and it is indeed hard! To check if you understand thoroughly, try predicting a square Matrix's similar different permutations. Have fun, I mean have less pain :)