以pythonic方式填充2D numpy数组

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

Answer 1

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

Answer 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.

Answer 3

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 

Answer 4

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).