Averaging upper and lower triangle of a matrix

1

Hello, I have a tensor of shape N * X * Y where N is the number of subjects. I want to average the upper and lower triangle for each matrix i in N. For example if subject 1 has the matrix:

tensor([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
Then the output should be:

tensor([[1, 3, 5],
[3, 5, 7],
[5, 7, 9]])
So, adding upper and lower triangle and dividing each value of two, the main diagonal remains same as you add each number with itself and divide by 2. I know I can loop through each subject, get the upper and lower triangle using torch. triu and torch. tril, add them together and take average and put them back in the array.
But I am looking for a faster method , specially without the loop.
Thank you

2

@ptrblck Any help on this?

3

Hi Usman!

Probably the most direct approach is to average the matrix with its
transpose. Here is an illustration for the 3-dimensional-tensor use
case you mention:

>>> torch.__version__
'1.7.1'
>>> t = torch.tensor ([[[1, 2, 3], [4, 5, 6], [7, 8, 9]], [[10, 20, 30], [40, 50, 60], [70, 80, 90]]])
>>> (t + t.transpose (1, 2)) / 2
tensor([[[ 1.,  3.,  5.],
         [ 3.,  5.,  7.],
         [ 5.,  7.,  9.]],

        [[10., 30., 50.],
         [30., 50., 70.],
         [50., 70., 90.]]])

Best.

K. Frank