Numpy:多个轴上的 argmax 没有循环 [英] Numpy: argmax over multiple axes without loop

问题描述

我有一个 N 维数组(命名为 A).对于 A 的第一轴的每一行，我想获取沿 A 其他轴的最大值的坐标.然后我将返回一个二维数组，其中包含第一轴每一行的最大值的坐标A.

I have a N-dimensional array (Named A). For each row of the first axis of A, I want to obtain the coordinates of the maximum value along the other axes of A. Then I would return a 2-dimensional array with the coordinates of the maximum value for each row of the first axis of A.

我已经使用循环解决了我的问题，但我想知道是否有更有效的方法来做到这一点.我目前的解决方案(例如数组 A)如下:

I already solved my problem using a loop, but I was wondering whether there is a more efficient way of doing this. My current solution (for an example array A) is as follows:

import numpy as np

A=np.reshape(np.concatenate((np.arange(0,12),np.arange(0,-4,-1))),(4,2,2))
maxpos=np.empty(shape=(4,2))
for n in range(0, 4):
    maxpos[n,:]=np.unravel_index(np.argmax(A[n,:,:]), A[n,:,:].shape)

在这里，我们会:

A: 
[[[ 0  1]
  [ 2  3]]

 [[ 4  5]
  [ 6  7]]

 [[ 8  9]
  [10 11]]

 [[ 0 -1]
  [-2 -3]]]

maxpos:
[[ 1.  1.]
 [ 1.  1.]
 [ 1.  1.]
 [ 0.  0.]]

如果有多个最大化器，我不介意选择哪个.

If there are multiple maximizers, I don't mind which is chosen.

我尝试使用 np.apply_over_axes，但我没有设法让它返回我想要的结果.

I have tried to use np.apply_over_axes, but I haven't managed to make it return the outcome I want.

推荐答案

你可以这样做 -

# Reshape input array to a 2D array with rows being kept as with original array.
# Then, get idnices of max values along the columns.
max_idx = A.reshape(A.shape[0],-1).argmax(1)

# Get unravel indices corresponding to original shape of A
maxpos_vect = np.column_stack(np.unravel_index(max_idx, A[0,:,:].shape))

样品运行 -

In [214]: # Input array
     ...: A = np.random.rand(5,4,3,7,8)

In [215]: # Setup output array and use original loopy code
     ...: maxpos=np.empty(shape=(5,4)) # 4 because ndims in A is 5
     ...: for n in range(0, 5):
     ...:     maxpos[n,:]=np.unravel_index(np.argmax(A[n,:,:,:,:]), A[n,:,:,:,:].shape)
     ...:     

In [216]: # Proposed approach
     ...: max_idx = A.reshape(A.shape[0],-1).argmax(1)
     ...: maxpos_vect = np.column_stack(np.unravel_index(max_idx, A[0,:,:].shape))
     ...: 

In [219]: # Verify results
     ...: np.array_equal(maxpos.astype(int),maxpos_vect)
Out[219]: True

推广到 n-dim 数组

我们可以概括来解决 n-dim 数组以获得最后 N 个轴的 argmax 结合类似这样的东西 -

Generalize to n-dim array

We could generalize to solve for n-dim array to get argmax for last N axes combined with something like this -

def argmax_lastNaxes(A, N):
    s = A.shape
    new_shp = s[:-N] + (np.prod(s[-N:]),)
    max_idx = A.reshape(new_shp).argmax(-1)
    return np.unravel_index(max_idx, s[-N:])

结果将是一个索引数组的元组.如果您需要将最终输出作为数组，我们可以使用 np.stack 或 np.concatenate.

The result would a tuple of arrays of indices. If you need the final output as an array, we can use np.stack or np.concatenate.

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