Norm of a arrays of vectors in python

Question

I have this array

   A = array([[-0.49740509, -0.48618909, -0.49145315],
   [-0.48959259, -0.48618909, -0.49145315],
   [-0.49740509, -0.47837659, -0.49145315],
   ..., 
   [ 0.03079315, -0.01194593, -0.06872366],
   [ 0.03054901, -0.01170179, -0.06872366],
   [ 0.03079315, -0.01170179, -0.06872366]])

which is a collection of 3D vector. I was wondering if I could use a vectorial operation to get an array with the norm of each of my vector.

I tried with norm(A) but it didn't work.

I think it is yes. [`numpy.array`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html) is different from the [`array`](http://docs.python.org/library/array.html) class in Python. I assume that you want answers related to `numpy.array`? — Mark Byers, May 20 '12 at 14:56
FYI: In the next release of numpy (1.8.0), you will be able to use the `axis` argument: `norm(A, axis=1)`. — Warren Weckesser, Jul 18 '13 at 22:04

DSM · Accepted Answer · 2012-05-20T15:18:48.640

Doing it manually might be fastest (although there's always some neat trick someone posts I didn't think of):

In [75]: from numpy import random, array

In [76]: from numpy.linalg import norm

In [77]: 

In [77]: A = random.rand(1000,3)

In [78]: timeit normedA_0 = array([norm(v) for v in A])
100 loops, best of 3: 16.5 ms per loop

In [79]: timeit normedA_1 = array(map(norm, A))
100 loops, best of 3: 16.9 ms per loop

In [80]: timeit normedA_2 = map(norm, A)
100 loops, best of 3: 16.7 ms per loop

In [81]: timeit normedA_4 = (A*A).sum(axis=1)**0.5
10000 loops, best of 3: 46.2 us per loop

This assumes everything's real. Could multiply by the conjugate instead if that's not true.

Update: Eric's suggestion of using math.sqrt won't work -- it doesn't handle numpy arrays -- but the idea of using sqrt instead of **0.5 is a good one, so let's test it.

In [114]: timeit normedA_4 = (A*A).sum(axis=1)**0.5
10000 loops, best of 3: 46.2 us per loop

In [115]: from numpy import sqrt

In [116]: timeit normedA_4 = sqrt((A*A).sum(axis=1))
10000 loops, best of 3: 45.8 us per loop

I tried it a few times, and this was the largest difference I saw.

`**0.5` will always be slower than `math.sqrt` – Eric May 20 '12 at 15:14 — Eric, May 20 '12 at 15:14

score 2 · Answer 2 · answered May 13 '20 at 09:35

2

just had the same prob, maybe late to answer but this should help others. You can use the axis argument in the norm function

norm(A, axis=1)

answered May 13 '20 at 09:35

Shade

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Thanks! Works great. – Bret Hess Jul 28 '23 at 21:51

score 0 · Answer 3 · edited May 20 '12 at 15:57

0

How about this method? Also you might want to add a [numpy] tag to the post.

edited May 20 '12 at 15:57

Joel Cornett

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answered May 20 '12 at 14:55

Junuxx

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Initially I thought you couldn't find the `linalg.norm` method as you said norm(A) "didn't work", but after reading Eric's answer I guess it's more likely that you did try `linalg.norm` but it didn't give you what you wanted. – Junuxx May 20 '12 at 15:02
@JoelCornett: As a result of the OP being vague with "it didn't work". He might have explained what he tried and how it didn't work. Like I explained in my comment above. – Junuxx May 20 '12 at 15:24
You're right. This is more of a case of OP being obscure. Redacted. – Joel Cornett May 20 '12 at 15:57

Eric · Answer 4 · 2012-05-20T15:07:17.337

0

Having never used numpy, I'm going to guess:

normedA = array(norm(v) for v in A)

edited May 20 '12 at 15:07

answered May 20 '12 at 14:57

Eric

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`map(norm, A)` might be faster in this situation. – Joel Cornett May 20 '12 at 15:03
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@Joel: Yeah, but it doesn't return a numpy array, so you'd at least have to wrap it in `np.array()` – Niklas B. May 20 '12 at 15:04
@Matteo What about if I use it as a generator? – Eric May 20 '12 at 15:07
@Matteo: what size is your dataset and how slow is it? – Joel Cornett May 20 '12 at 15:10
Unfortunately this won't work as written: it will give something like `array( at 0x102d88f50>, dtype=object)`. You'd need to use `fromiter`, I think. – DSM May 20 '12 at 15:20

Norm of a arrays of vectors in python

4 Answers4