Extract upper or lower triangular part of a numpy matrix

Question

I have a matrix A and I want 2 matrices U and L such that U contains the upper triangular elements of A (all elements above and not including diagonal) and similarly for L(all elements below and not including diagonal). Is there a numpy method to do this?

e.g

A = array([[ 4.,  9., -3.],            [ 2.,  4., -2.],            [-2., -3.,  7.]]) U = array([[ 0.,  9., -3.],            [ 0.,  0., -2.],            [ 0.,  0.,  0.]]) L = array([[ 0.,  0.,  0.],            [ 2.,  0.,  0.],            [-2., -3.,  0.]]) 

Answer 1

Try numpy.triu (triangle-upper) and numpy.tril (triangle-lower).

Answer 2

To extract the upper triangle values to a flat vector, you can do something like the following:

import numpy as np  a = np.array([[1,2,3],[4,5,6],[7,8,9]]) print(a)  #array([[1, 2, 3], #       [4, 5, 6], #       [7, 8, 9]])  a[np.triu_indices(3)] #or list(a[np.triu_indices(3)])  #array([1, 2, 3, 5, 6, 9]) 

---

Similarly, for the lower triangle, use np.tril.

---

IMPORTANT

If you want to extract the values that are above the diagonal (or below) then use the k argument. This is usually used when the matrix is symmetric.

import numpy as np  a = np.array([[1,2,3],[4,5,6],[7,8,9]])  #array([[1, 2, 3], #       [4, 5, 6], #       [7, 8, 9]])  a[np.triu_indices(3, k = 1)]  # this returns the following array([2, 3, 6]) 

---

EDIT (on 11.11.2019):

To put back the extracted vector into a 2D symmetric array, one can follow my answer here: https://stackoverflow.com/a/58806626/5025009