## NumPy indexing peculiarities

Many scientific Python users are surprised when I tell them that ndarray.take is faster than __getitem__-based (a.k.a. “fancy” as I call it) indexing.

import numpy as np
import random

arr = np.random.randn(10000, 5)
indexer = np.arange(10000)
random.shuffle(indexer)

In [26]: timeit arr[indexer]
1000 loops, best of 3: 1.25 ms per loop

In [27]: timeit arr.take(indexer, axis=0)
10000 loops, best of 3: 127 us per loop

It’s actually kind of unbelievable when you think about it. What’s going on here that take is almost 10x faster? I really should take a closer at the internals of what __getitem__ does because this has always struck me as pretty bad. Maybe I shouldn’t be complaining? I mean, R 2.13′s indexing falls somewhere in the middle:

mat <- matrix(rnorm(50000), nrow=10000, ncol=5)
set.seed(12345)
indexer <- sample(1:10000)
> system.time(for (i in 1:1000) mat[indexer,])
user  system elapsed
0.460   0.197   0.656

So 656 microseconds per iteration. (In an earlier version of this post I used rpy2 to do the benchmark and got 1.05 ms, but there was apparently some overhead from rpy2)

Another peculiarity that I noticed with take is that performance gets worse when you use the out argument, which tells the function to use an array you pass in to write out the result:

out = np.empty_like(arr)

In [50]: timeit np.take(arr, indexer, axis=0, out=out)
10000 loops, best of 3: 200 us per loop

EDIT: I’ve been informed that using mode='clip' or mode='wrap' makes this run as fast as without the out argument.

Weird! I was dissatisfied by this, so I got curious how fast a hand-coded little Cython function can do this:

@cython.wraparound(False)
@cython.boundscheck(False)
def take_axis0(ndarray[float64_t, ndim=2] values,
ndarray[int32_t] indexer,
out=None):
cdef:
Py_ssize_t i, j, k, n, idx
ndarray[float64_t, ndim=2] outbuf

if out is None:
outbuf = np.empty_like(values)
else:
outbuf = out

n = len(indexer)
k = values.shape[1]
for i from 0 <= i < n:
idx = indexer[i]

if idx == -1:
for j from 0 <= j < k:
outbuf[i, j] = NaN
else:
for j from 0 <= j < k:
outbuf[i, j] = values[idx, j]

Don’t worry about the -1 thing– that’s a specialization that I’m using inside pandas. Curiously, this function is a lot faster than take using out but faster than the regular take by a handful of microseconds.

In [53]: timeit lib.take_axis0(arr, indexer)
10000 loops, best of 3: 115 us per loop

In [54]: timeit lib.take_axis0(arr, indexer, out)
10000 loops, best of 3: 109 us per loop

Very interesting.

### TL;DR

• Use take not []-based indexing to get best performance
• Cython is just as fast for my specific application and a lot faster if you’re passing an out array (which I will be for the application that I needed this for)
• R’s matrix indexing performance is better than NumPy’s fancy indexing, but about 5-6x slower than ndarray.take. This can probably be improved.