How do I get the sum of values under a diagonal in numpy?

Question

Given a 2D rectangular numpy array:

a = np.array([
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
])

I would like to take the sum of all values under the lower left to upper right diagonal , I.E. 8, 9 and 6.

What is the best way to accomplish this?

The method should work for large arrays too.

What are you considering diagonal? I do not know why 9 is included. — msi_gerva, Jun 04 '19 at 15:08
"Diagonal" as in 'towards the right and downwards of the secondary diagonal', perhaps? — TrebledJ, Jun 04 '19 at 15:10
good point. Its the lower left to upper right diagonal. Edited the question. — Rutger Hofste, Jun 04 '19 at 16:11
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Austin · Answer 1 · 2019-06-04T15:17:23.213

2

import numpy as np

a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

print(np.sum(np.tril(np.flip(a, 1), -1)))
# 23

edited Jun 04 '19 at 15:17

answered Jun 04 '19 at 15:12

Austin

score 1 · Accepted Answer · answered Jun 04 '19 at 15:12

1

You can rotate, sum the upper triangle, and subtract the diagonal.

import numpy as np
a = np.array([[1,2,3],[4,5,6],[7,8,9]])
result = np.triu(np.rot90(a)).sum() - np.trace(a)
#Output: 23

answered Jun 04 '19 at 15:12

Paritosh Singh

score 0 · Answer 3 · answered Jun 04 '19 at 16:45

0

You can use scipy.spatial.distance.squareform to select your triangle of interest:

from scipy.spatial.distance import squareform
squareform(a[::-1], checks=False)
# array([8, 9, 6])
squareform(a[::-1], checks=False).sum()
# 23

answered Jun 04 '19 at 16:45

Paul Panzer

3 Answers3