Indexing numpy array by a numpy array of coordinates

Question

Suppose we have

• an n-dimensional numpy.array A
• a numpy.array B with dtype=int and shape of (n, m)

How do I index A by B so that the result is an array of shape (m,), with values taken from the positions indicated by the columns of B?

For example, consider this code that does what I want when B is a python list:

>>> a = np.arange(27).reshape(3,3,3)
>>> a[[0, 1, 2], [0, 0, 0], [1, 1, 2]]
array([ 1, 10, 20])    # the result we're after
>>> bl = [[0, 1, 2], [0, 0, 0], [1, 1, 2]]
>>> a[bl]
array([ 1, 10, 20])   # also works when indexing with a python list
>>> a[bl].shape
(3,)

However, when B is a numpy array, the result is different:

>>> b = np.array(bl)
>>> a[b].shape
(3, 3, 3, 3)

Now, I can get the desired result by casting B into a tuple, but surely that cannot be the proper/idiomatic way to do it?

>>> a[tuple(b)]
array([ 1, 10, 20])

Is there a numpy function to achieve the same without casting B to a tuple?

Answer 1

One alternative would be converting to linear indices and then index with np.take or index into its flattened version -

np.take(a,np.ravel_multi_index(b, a.shape))
a.flat[np.ravel_multi_index(b, a.shape)]

Custom np.ravel_multi_index for performance boost

We could implement a custom version to simulate the behaviour of np.ravel_multi_index to boost the performance, like so -

def ravel_index(b, shp):
    return np.concatenate((np.asarray(shp[1:])[::-1].cumprod()[::-1],[1])).dot(b)

Using it, the desired output would be found in two ways -

np.take(a,ravel_index(b, a.shape))
a.flat[ravel_index(b, a.shape)]

Benchmarking

Additionall incorporating tuple based method from the question and map based one from @Kanak's post.

Case #1 : dims = 3

In [23]: a = np.random.randint(0,9,([20]*3))

In [24]: b = np.random.randint(0,20,(a.ndim,1000000))

In [25]: %timeit a[tuple(b)]
    ...: %timeit a[map(np.ravel, b)]  
    ...: %timeit np.take(a,np.ravel_multi_index(b, a.shape))
    ...: %timeit a.flat[np.ravel_multi_index(b, a.shape)]
    ...: %timeit np.take(a,ravel_index(b, a.shape))
    ...: %timeit a.flat[ravel_index(b, a.shape)]
100 loops, best of 3: 6.56 ms per loop
100 loops, best of 3: 6.58 ms per loop
100 loops, best of 3: 6.95 ms per loop
100 loops, best of 3: 9.17 ms per loop
100 loops, best of 3: 6.31 ms per loop
100 loops, best of 3: 8.52 ms per loop

Case #2 : dims = 6

In [29]: a = np.random.randint(0,9,([10]*6))

In [30]: b = np.random.randint(0,10,(a.ndim,1000000))

In [31]: %timeit a[tuple(b)]
    ...: %timeit a[map(np.ravel, b)]  
    ...: %timeit np.take(a,np.ravel_multi_index(b, a.shape))
    ...: %timeit a.flat[np.ravel_multi_index(b, a.shape)]
    ...: %timeit np.take(a,ravel_index(b, a.shape))
    ...: %timeit a.flat[ravel_index(b, a.shape)]
10 loops, best of 3: 40.9 ms per loop
10 loops, best of 3: 40 ms per loop
10 loops, best of 3: 20 ms per loop
10 loops, best of 3: 29.9 ms per loop
100 loops, best of 3: 15.7 ms per loop
10 loops, best of 3: 25.8 ms per loop

Case #3 : dims = 10

In [32]: a = np.random.randint(0,9,([4]*10))

In [33]: b = np.random.randint(0,4,(a.ndim,1000000))

In [34]: %timeit a[tuple(b)]
    ...: %timeit a[map(np.ravel, b)]  
    ...: %timeit np.take(a,np.ravel_multi_index(b, a.shape))
    ...: %timeit a.flat[np.ravel_multi_index(b, a.shape)]
    ...: %timeit np.take(a,ravel_index(b, a.shape))
    ...: %timeit a.flat[ravel_index(b, a.shape)]
10 loops, best of 3: 60.7 ms per loop
10 loops, best of 3: 60.1 ms per loop
10 loops, best of 3: 27.8 ms per loop
10 loops, best of 3: 38 ms per loop
100 loops, best of 3: 18.7 ms per loop
10 loops, best of 3: 29.3 ms per loop

So, it makes sense to look for alternatives when working with higher-dimensional inputs and with large data.