Four Indexing of a two index matrix

Hallo, my problem is that i want to address each element of a matrix (2index) by a 4index number and vice versa.

for example, a typicall matlab matrix "A" has the 2 index addressing

11 12 13 14

21 22 23 24

31 32 33 34

41 42 43 44

I want to make matrix "A" to have four index addressing ie

1111 1112 1121 1122

1211 1212 1221 1222

2111 2112 2121 2122

2211 2212 2221 2222

... So instead of writting A(1,1) i would instead writte A(1,1,1,1) (The reshape command doesnt give me right results for the 36x36 matrices i use, i believe that it reshapes the matrix not the way of the example)

Thank you all in advance.

Answer 1

[Walter Roberson]

Doing that and being consistent with the rest of MATLAB would require that you write a new MATLAB Object class with its own subsref() and subsasgn() methods, and possibly reshape() as well. You are asking that data be stored in a different order than MATLAB normally stores it. All kinds of routines (such as sum() and mean()) expect data to be stored in the MATLAB order.

However, it is possible that for your intended use, you just need to know how to re-order a vector with (36 * 36) elements so that it fills memory in to a 4D array with your desired order. If so, that can be done with transpose() and flipud() and fliplr() and permute() and reshape() in combination. You might not need all of those in practice for this particular order. (I haven't yet worked out a good reordering sequence for this.)

[Nikolaos]

Thank you a lot, it seems like a lot of trouble so i might have to cope with the matlab's way. (i use matrix of different dimensions so its a trouble)

Answer 2

[Jan]

A = [1111 1112 1121 1122;
     1211 1212 1221 1222;
     2111 2112 2121 2122;
     2211 2212 2221 2222];
B = reshape(A, 2,2,2,2);
C = permute(B, [2,1,4,3]);

>> ans(:,:,1,1) =
      1111        1211
      2111        2211
   ans(:,:,2,1) =
      1121        1221
      2121        2221
   ans(:,:,1,2) =
      1112        1212
      2112        2212
   ans(:,:,2,2) =
      1122        1222
      2122        2222

Now the i.th index is equivalent to the i.th digit in the number. This works for the 4x4 matrix only and I cannot predict, what you need for your 36x36 matrix. But the method will be very similar.

[Nikolaos]

Thank you a lot, this is very usefull.