numpy: fill offset diagonal with different values

Question

I need to make a n*n matrix m whose elements follow m(i,i+1)=sqrt(i) and 0 otherwise. For example, for n=5, we should have

[0 a 0 0 0]
[0 0 b 0 0]
[0 0 0 c 0]
[0 0 0 0 d]
[0 0 0 0 0]

where {a,b,c,d}=sqrt({1,2,3,4}). Here is a solution for a constant tri-diagonal matrix, but my case is a bit more complicated than that. I know I can do that with a loop or with list comprehension, but are there other ways? n can be potentially big.

e.g. (list comprehension code)

ele=lambda i,j:sqrt(i+1) if j-i==1 else 0

[[ele(i,j) for j in range(0,6)] for i in range(0,6)]

score 14 · Answer 1 · answered Dec 24 '17 at 20:35

You can straightforwardly use np.diag:

>>> d = np.sqrt(1 + np.arange(4))
>>> np.diag(d, 1)
array([[ 0.        ,  1.        ,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  1.41421356,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  1.73205081,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  2.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ]])

The second argument of np.diag specifies the diagonal in question.

This is ingenious, there should be an example in the [documentation](https://numpy.org/doc/stable/reference/generated/numpy.diag.html)! — Scriddie, Jun 02 '22 at 17:51

Alex Riley · Accepted Answer · 2015-05-27T16:14:32.037

One way could be to create the array of zeros and then use indexing to select and fill the desired indices with the square-root values.

For example:

>>> z = np.zeros((5,5))
>>> rng = np.arange(4)
>>> z[rng, rng+1] = np.sqrt(rng+1)
>>> z
array([[ 0.        ,  1.        ,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  1.41421356,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  1.73205081,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  2.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ]])

second line should be `rng = np.arange(4)` – egwene sedai May 27 '15 at 16:13 — egwene sedai, May 27 '15 at 16:13

score 2 · Answer 3 · answered Jun 03 '20 at 05:59

2

A bit late obviously but i want to introduce numpy diagflat method in this question. It can be done in this way:

import numpy as np

n = 5

aux = np.arange(1 , n)
aux = np.sqrt(aux)

A = np.diagflat(aux , 1)

answered Jun 03 '20 at 05:59

HernanBailo

101
3

In what way is this different from just using `np.diag(aux, 1)`? – Eknoma Feb 01 '23 at 16:27

numpy: fill offset diagonal with different values

3 Answers3