如何选择具有(n-1)D个轴索引的nD阵列轴上的值? [英] How can I select values along an axis of an nD array with an (n-1)D array of indices of that axis?

问题描述

这是由激发的.

给出形状为(n0，n1)的数组A和形状为(n0)的数组J，我想创建形状为(n0)的数组B，以使

Given array A with shape (n0,n1), and array J with shape (n0), I'd like to create an array B with shape (n0) such that

B[i] = A[i,J[i]]

我也想将其推广到k维数组，其中A的形状为(n0,n1,...,nk)，J的形状为(n0,n1,...,n(k-1))

I'd also like to be able to generalize this to k-dimensional arrays, where A has shape (n0,n1,...,nk) and J has shape (n0,n1,...,n(k-1))

有一些混乱的，扁平化的方法可以对索引顺序进行假设:

There are messy, flattening ways of doing this that make assumptions about index order:

import numpy as np
B = A.ravel()[   J+A.shape[-1]*np.arange(0,np.prod(J.shape)).reshape(J.shape) ]

问题是，有没有一种方法不依赖于展平数组和手动处理索引?

The question is, is there a way to do this that doesn't rely on flattening arrays and dealing with indexes manually?

推荐答案

对于2d和1d情况，此索引有效:

For the 2 and 1d case, this indexing works:

A[np.arange(J.shape[0]), J]

通过重塑为2d(并返回)可以将其应用于更多尺寸:

Which can be applied to more dimensions by reshaping to 2d (and back):

A.reshape(-1, A.shape[-1])[np.arange(np.prod(A.shape[:-1])).reshape(J.shape), J]

对于3d A，此方法有效:

For 3d A this works:

A[np.arange(J.shape[0])[:,None], np.arange(J.shape[1])[None,:], J]

其中第1 2个arange索引的广播尺寸与J相同.

where the 1st 2 arange indices broadcast to the same dimension as J.

对于lib.index_tricks中的函数，可以表示为:

With functions in lib.index_tricks, this can be expressed as:

A[np.ogrid[0:J.shape[0],0:J.shape[1]]+[J]]
A[np.ogrid[slice(J.shape[0]),slice(J.shape[1])]+[J]]

或用于多个维度:

A[np.ix_(*[np.arange(x) for x in J.shape])+(J,)]
A[np.ogrid[[slice(k) for k in J.shape]]+[J]]

---

对于较小的A和J(例如2 * 3 * 4)，J.choose(np.rollaxis(A,-1))更快.所有额外的时间都在准备索引元组中. np.ix_比np.ogrid快.

---

For small A and J (eg 2*3*4), J.choose(np.rollaxis(A,-1)) is faster. All of the extra time is in preparing the index tuple. np.ix_ is faster than np.ogrid.

np.choose具有大小限制.在上端，它比ix_慢:

np.choose has a size limit. At its upper end it is slower than ix_:

In [610]: Abig=np.arange(31*31).reshape(31,31)
In [611]: Jbig=np.arange(31)
In [612]: Jbig.choose(np.rollaxis(Abig,-1))
Out[612]: 
array([  0,  32,  64,  96, 128, 160, ... 960])

In [613]: timeit Jbig.choose(np.rollaxis(Abig,-1))
10000 loops, best of 3: 73.1 µs per loop
In [614]: timeit Abig[np.ix_(*[np.arange(x) for x in Jbig.shape])+(Jbig,)]
10000 loops, best of 3: 22.7 µs per loop
In [635]: timeit Abig.ravel()[Jbig+Abig.shape[-1]*np.arange(0,np.prod(Jbig.shape)).reshape(Jbig.shape) ]
10000 loops, best of 3: 44.8 µs per loop

我在 https://stackoverflow.com/a/28007256/901925 上做了类似的索引测试，发现对于更大的数组(例如n0=1000)，flat索引编制更快.那是我了解choice的32个限制的地方.

I did similar indexing tests at https://stackoverflow.com/a/28007256/901925, and found that flat indexing was faster for much larger arrays (e.g. n0=1000). That's where I learned about the 32 limit for choice.

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