# How to sum all the diagonals of a matrix in parallel

Normally we can sum over any dimention of a tensor, like this:
1+2+3
4+5+6
7+8+9

My question is how to sum all of the diagonals efficiently:
0+0+3
0+2+6
1+5+9
4+8+0
7+0+0

An equivalent question would be how to roll a tensor like this:
1 2 3
4 5 6
7 8 9

1 2 3
5 6 4
9 7 8

And here is a naive solution:

``````a = torch.arange(1, 10).view(3,3)
b = torch.zeros_like(a)
for i in range(3)
b[i] = a[i].roll(shifts=i, dims=0)
``````

Obviously this will be slow because of the for loop, how should I get rid of the for loop?

EDIT:
see my other reply below for possible solution.

Interesting question!
Still thinking if it’s possible to get rid of the for loop, ill update if an idea comes up (currently testing it with einsum function but no solution so far)

In case ‘for loop’ will stay, I belive using sum+diagonal will be more readable:

``````a = torch.arange(1, 10).view(3,3)
b = torch.zeros(5) # 5 diagonals for 3x3 due to (2*3-1), for nxn, there are (2*n-1) diagonals
for i in range(5):
b[i] = torch.sum(torch.diagonal(a, offset=2-i))
``````

Would be nice if torch.diagonal could get a list of offsets output from code above:
`tensor([ 3., 8., 15., 12., 7.])`

Roy

Managed to solve it via conv2d:

``````import torch
import torch.nn.functional as F

dim = 3
num_diagonls = 2*dim-1
# need to unsqueeze twice for use in conv2d
x = torch.rand(dim, dim).unsqueeze(0).unsqueeze(0)

print('x:')
print(x)

expected = torch.zeros(num_diagonls)
for i in range(num_diagonls):
expected[i] = torch.sum(torch.diagonal(x, offset=dim-1-i))

print('expected diagonal sums:')
print(expected)

# need to unsqueeze twice for use in conv2d
w = torch.eye(dim).unsqueeze(0).unsqueeze(0)
# from after conv2d result, extract inner inner dim, then take the middle column
result = F.conv2d(x, w, padding=num_diagonls//2)[:, num_diagonls//2]
print('result diagonal sums:')
print(result)
``````

outputs:

``````x:
tensor([[[[0.5106, 0.9985, 0.6385],
[0.5529, 0.5057, 0.7685],
[0.0656, 0.4694, 0.0604]]]])
expected diagonal sums:
tensor([0.6385, 1.7670, 1.0767, 1.0223, 0.0656])
result diagonal sums:
tensor([0.6385, 1.7670, 1.0767, 1.0223, 0.0656])
``````

Roy