MATLAB: Reshaping a 2D matrix into a 3D matrix (layers of square matrices) with specific order (no loop)

Question

I have a 15 x 15 matrix(2D) (which is made of 9 blocks (3 x 3) of 5 x 5 matrices). I would like to reshape this matrix into a 3×3 x 25 matrix(3D); however the matrix elements of each 3×3 layer are chosen in a specific order from the original 2D matrix. The ordering is described below.

The elements of the 25 matrices are chosen from the elements of 5 x 5 matrices embedded in the original 2D matrix. I would like not to utilize "for" loops because the code becomes very inefficient as the dimensions of the original matrix grows. I have used the following code to reshape the 2D matrix, but this piece of code scrambles the rows and columns, and the order of 25 layers is not deterministic.

 A =[1     1     1     1     1     1     1     1     1     1     1     1     1     1     1
     1     1     1     1     1     1     1     1     1     1     1     1     1     1     1
     1     1     1     1     1     1     1     1     1     1     1     1     1     1     1
     1     1     1     1     1     1     1     1     1     1     1     1     1     1     1
     1     1     1     1     1     1     1     1     1     1     1     1     1     1     1
     4     8    13    19    26    34    43    53    64    76    89   103   118   134   151
     7    12    18    25    33    42    52    63    75    88   102   117   133   150   168
    11    17    24    32    41    51    62    74    87   101   116   132   149   167   186
    16    23    31    40    50    61    73    86   100   115   131   148   166   185   205
    22    30    39    49    60    72    85    99   114   130   147   165   184   204   225
    29    38    48    59    71    84    98   113   129   146   164   183   203   224   246
    37    47    58    70    83    97   112   128   145   163   182   202   223   245   268
    46    57    69    82    96   111   127   144   162   181   201   222   244   267   291
    56    68    81    95   110   126   143   161   180   200   221   243   266   290   315
    67    80    94   109   125   142   160   179   199   220   242   265   289   314   340];
permute(reshape(A', 25, 3, 3), [3 2 1])

This scheme, if figured out, helps calculating the determinant of 3 x 3 blocks inside very large 3N x 3M (or 3N x 3N) matrices.

Thanks

Answer 1

B = mat2cell(A,[5 5 5],[5 5 5]);
C = cat(3,B{:});
out = reshape(permute(C(1,1:3,:),[3 2 1]),3,[]);

or

[m,n] = size(A);
q = 3;
out = reshape(A((1:5:m)'+(0:5:n-1)*m + reshape(m*(0:q-1),1,1,[])),q,[]);