filling a 2D numpy array in a pythonic way

Question

I am trying to populate a 2D numpy array. In my experience, the following is not going to scale up well with array sizes.

x=np.array([2,3,4])
y=np.array([1,3,9,13])
mat=np.zeros((x.size,y.size))
for i in range(nx):
 for j in range(ny):
   if x[i] > y[j]:
        mat[i,j] = 1
   else:
        mat[i,j] = -1

Ideally, I would like to use list comprehension like It would be simple if it was 1D only

mat=np.asarray([foo(x_) for x_ in x])

but how to generalize this to 2D np.arrays? Other numpy based solutions are also suitable, but efficiency is the key metric here

Are you looking for a general solution or specifically like in the example to populate triangular parts of the matrix? — MB-F
– MB-F, Commented Dec 13, 2017 at 8:01
my application case is the one of the example. However, a general solution would be probably useful to more SO users... It would be nice to have something which works with a generic foo(x_,y_) with two inputs similarly to the last code line — 00__00__00
– 00__00__00, Commented Dec 13, 2017 at 8:04

hpaulj · Accepted Answer · 2017-12-13 08:34:50Z

2

Your mat:

In [352]: mat
Out[352]: 
array([[ 1., -1., -1., -1.],
       [ 1., -1., -1., -1.],
       [ 1.,  1., -1., -1.]])

broadcasting x against y:

In [353]: x[:,None]>y
Out[353]: 
array([[ True, False, False, False],
       [ True, False, False, False],
       [ True,  True, False, False]], dtype=bool)

turn that boolean mask into 1/-1 array with where:

In [354]: np.where(x[:,None]>y,1,-1)
Out[354]: 
array([[ 1, -1, -1, -1],
       [ 1, -1, -1, -1],
       [ 1,  1, -1, -1]])

Or you could turn the boolean into a 0/1 array, and scale that to fit

(x[:,None]>y).astype(float)*2-1

A double loop over two 1d arrays or lists can often be cast as an outer operation like this.

edited Dec 13, 2017 at 8:34

answered Dec 13, 2017 at 8:23

hpaulj

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Comments

MB-F · Accepted Answer · 2017-12-13 08:17:02Z

2

It is possible to build 2 dimensional nested list comprehensions:

mat = np.array([[1 if x_ > y_ else -1 for y_ in y] for x_ in x])

However, this can become pretty unreadable, and is not much different from for loops as far performance scaling is concerned. Broadcasting and vectorization will usually work better with larger arrays:

mat = (x[:, None] > y[None, :]) * 2 - 1

edited Dec 13, 2017 at 8:17

answered Dec 13, 2017 at 8:12

MB-F

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Comments

zyun · Accepted Answer · 2017-12-13 08:40:49Z

1

try:

x=np.array([2,3,4])
y=np.array([1,3,9,13])
a = (x.reshape(x.shape[0], 1) - y) > 0  # a=(x.reshape(-1, 1) - y) > 0
a = a.astype(int)*2 -1

edited Dec 13, 2017 at 8:40

answered Dec 13, 2017 at 8:15

zyun

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1 Comment

MB-F Over a year ago

You can also pass -1 to reshape instead of x.shape[0].

Borian · Accepted Answer · 2017-12-13 09:12:15Z

1

If using numpy:

import numpy as np
nx = x.size
ny = y.size
mat = np.sign(x * np.atleast_2d(np.ones(ny)).T - np.ones(nx) * np.atleast_2d(y).T)
mat[np.where(mat==0)] = -1

numpy will take care regarding efficiency (whatever it means here).

answered Dec 13, 2017 at 9:12

Borian

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1 Comment

00__00__00 Over a year ago

in the end, you answer (without the last line) was the solution to my actual problem. However, since I made a mistake in the question by describing incorrectly the desired behavior with when x==y, I cannot accept it. but thanks :)

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