基于2d掩模数组的numpy 3d到2d变换

Question

If I have an ndarray like this:

>>> a = np.arange(27).reshape(3,3,3)
>>> a
array([[[ 0,  1,  2],
        [ 3,  4,  5],
        [ 6,  7,  8]],

       [[ 9, 10, 11],
        [12, 13, 14],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23],
        [24, 25, 26]]])

I know I can get the maximum along a certain axis using np.max(axis=...) :

>>> a.max(axis=2)
array([[ 2,  5,  8],
       [11, 14, 17],
       [20, 23, 26]])

Alternatively, I could get the indices along that axis which correspond to the maximum values from:

>>> indices = a.argmax(axis=2)
>>> indices
array([[2, 2, 2],
       [2, 2, 2],
       [2, 2, 2]])

My question -- Given the array indices and the array a , is there an elegant way to reproduce the array the array returned by a.max(axis=2) ?

This would probably work:

import itertools as it
import numpy as np
def apply_mask(field,indices):
    data = np.empty(indices.shape)

    #It seems highly likely that there is a more numpy-approved way to do this.
    idx = [range(i) for i in indices.shape]
    for idx_tup,zidx in zip(it.product(*idx),indices.flat):
        data[idx_tup] = field[idx_tup+(zidx,)]
    return data

But, it seems pretty hacky/inefficient. It also doesn't allow for me to use this with any axis other than the "last" axis. Is there a numpy function (or some use of magical numpy indexing) to make this work? The naive a[:,:,a.argmax(axis=2)] doesn't work.

UPDATE :

It seems the following also works (and is a little nicer):

import numpy as np
def apply_mask(field,indices):
    data = np.empty(indices.shape)

    for idx_tup,zidx in np.ndenumerate(indices):
        data[idx_tup] = field[idx_tup+(zidx,)]

    return data

---

I would like to do this because I would like to extract the indices based on the data in 1 array (typically using argmax(axis=...) ) and use those indices to pull data out of a bunch of other (equivalently shaped) arrays. I'm open to alternative ways to accomplish this (eg using boolean masked arrays). However, I like the "safety" that I get using these "index" arrays. With this I am guaranteed to have the right number of elements to create a new array which looks like a 2d "slice" through the 3d field.

Answer 1

Here is some magic numpy indexing that will do what you want, but unfortunately it's pretty unreadable.

def apply_mask(a, indices, axis):
    magic_index = [np.arange(i) for i in indices.shape]
    magic_index = np.ix_(*magic_index)
    magic_index = magic_index[:axis] + (indices,) + magic_index[axis:]
    return a[magic_index]

or equally unreadable:

def apply_mask(a, indices, axis):
    magic_index = np.ogrid[tuple(slice(i) for i in indices.shape)]
    magic_index.insert(axis, indices)
    return a[magic_index]

Answer 2

I use index_at() to create the full index:

import numpy as np

def index_at(idx, shape, axis=-1):
    if axis<0:
        axis += len(shape)
    shape = shape[:axis] + shape[axis+1:]
    index = list(np.ix_(*[np.arange(n) for n in shape]))
    index.insert(axis, idx)
    return tuple(index)

a = np.random.randint(0, 10, (3, 4, 5))

axis = 1
idx = np.argmax(a, axis=axis)
print a[index_at(idx, a.shape, axis=axis)]
print np.max(a, axis=axis)