Extract diagonal element from each frontal slice of tensor

Question

I have a p-by-p-by-n tensor. I want to extract diagonal element for each p-by-p slice. Are there anyone know how to do this without looping?

Thank you.

Answer 1

One suggestion I have is to create a p x p logical identity matrix, replicate this n times in the third dimension, and then use this matrix to access your tensor. Something like this, supposing that your tensor was stored in A:

ind = repmat(logical(eye(p)), [1 1 n]);
out = A(ind);

Example use:

>> p = 5; n = 3;
>> A = reshape(1:75, p, p, n)

A(:,:,1) =

     1     6    11    16    21
     2     7    12    17    22
     3     8    13    18    23
     4     9    14    19    24
     5    10    15    20    25


A(:,:,2) =

    26    31    36    41    46
    27    32    37    42    47
    28    33    38    43    48
    29    34    39    44    49
    30    35    40    45    50


A(:,:,3) =

    51    56    61    66    71
    52    57    62    67    72
    53    58    63    68    73
    54    59    64    69    74
    55    60    65    70    75

>> ind = repmat(logical(eye(p)), [1 1 n]);
>> out = A(ind)

out =

     1
     7
    13
    19
    25
    26
    32
    38
    44
    50
    51
    57
    63
    69
    75

You'll notice that we grab the diagonals of the first slice, followed by the diagonals of the second slice, etc. up until the last slice. These values are all concatenated into a single vector.