How to print a circulant matrix (toeplitz), in MATLAB, where each input is a 3D matrix of dimention m x m x 3?

Question

I know how to use toeplitz function in MATLAB to create a circulant matrix of 1 D vector. However, I am trying to create a circulant block

For example, I have 3 matrices of size (2,2,3) where third dimension is R,G, B: Below I am showing the sample values of row and column of each matrix. First Matrix:

# 01  02
# 03  04

Second Matrix:

# 05  06
# 07  08

Third Matrix:

# 09  10
# 11  12

Now I want to create a circulant matrix which looks like this

# 01  02  05  06  09  10
# 03  04  07  08  11  12
# 09  10  01  02  05  06
# 11  12  03  04  07  08
# 03  04  09  10  01  02
# 05  06  11  12  03  04

Note, I want to be able to move the entire block of the matrix to the right in the subsequent lines, and not just the first line of the matrix. Please note, i want to preserve the third dimensions of these matrices w(which has color dimension in them)

Can someone tell me how to go ahead with it? I thought of making an array I already have a 3D matrix, and don't know how to make an array of the array here, if it will help at all.

References:

• Toeplitz command in MATLAB: https://www.mathworks.com/help/matlab/ref/toeplitz.html
• A Stackoverflow I was trying to understand but couldn't: Matlab: How to convert a matrix into a Toeplitz matrix (not yet sure if i answers my question)

Answer 1

The following code builds a linear index as the sum of two parts:

• an "outer" pattern describing the structure of blocks (generated with repelem), and
• an "inner" pattern with the structure of a block repeated (using repmat).

Applying this index to the original matrix produces the desired result.

data = cat(3, [1 2; 3 4], [5 6; 7 8], [9 10; 11 12]); % example data
[L, M, N] = size(data);
ind_outer = repelem(mod(bsxfun(@minus, 0:N-1, (0:N-1).'), N), L, M);
ind_inner = repmat(reshape(1:L*M, L, M), N, N);
ind = ind_outer*L*M + ind_inner;
result = data(ind);

This gives

result =
     1     2     5     6     9    10
     3     4     7     8    11    12
     9    10     1     2     5     6
    11    12     3     4     7     8
     5     6     9    10     1     2
     7     8    11    12     3     4

To better understand how this works, see the outer and inner indexing patterns (and if needed read about linear indexing):

>> ind_outer
ind_outer =
     0     0     1     1     2     2
     0     0     1     1     2     2
     2     2     0     0     1     1
     2     2     0     0     1     1
     1     1     2     2     0     0
     1     1     2     2     0     0

>> ind_inner
ind_inner =
     1     3     1     3     1     3
     2     4     2     4     2     4
     1     3     1     3     1     3
     2     4     2     4     2     4
     1     3     1     3     1     3
     2     4     2     4     2     4