built-in range or numpy.arange: which is more efficient?

Question

When iterating over a large array with a range expression, should I use Python's built-in range function, or numpy's arange to get the best performance?

My reasoning so far:

range probably resorts to a native implementation and might be faster therefore. On the other hand, arange returns a full array, which occupies memory, so there might be an overhead. Python 3's range expression is a generator, which does not hold all the values in memory.

Luckless

arange probably resorts to ==> range probably resorts to. Seems to be a typo. – Galley

Answer 1

For large arrays, a vectorised numpy operation is the fastest. If you must loop, prefer xrange/range and avoid using np.arange.

In numpy you should use combinations of vectorized calculations, ufuncs and indexing to solve your problems as it runs at C speed. Looping over numpy arrays is inefficient compared to this.

(Something like the worst thing you could do would be to iterate over the array with an index created with range or np.arange as the first sentence in your question suggests, but I'm not sure if you really mean that.)

import numpy as np
import sys

sys.version
# out: '2.7.3rc2 (default, Mar 22 2012, 04:35:15) \n[GCC 4.6.3]'
np.version.version
# out: '1.6.2'

size = int(1E6)

%timeit for x in range(size): x ** 2
# out: 10 loops, best of 3: 136 ms per loop

%timeit for x in xrange(size): x ** 2
# out: 10 loops, best of 3: 88.9 ms per loop

# avoid this
%timeit for x in np.arange(size): x ** 2
#out: 1 loops, best of 3: 1.16 s per loop

# use this
%timeit np.arange(size) ** 2
#out: 100 loops, best of 3: 19.5 ms per loop

So for this case numpy is 4 times faster than using xrange if you do it right. Depending on your problem numpy can be much faster than a 4 or 5 times speed up.

The answers to this question explain some more advantages of using numpy arrays instead of python lists for large data sets.

Yeld

It's worth mentioning that, there is no xrange in Python3.x, and range is the same with xrange on it. – Venosity

Also, I tested for x in np.arange(size): x ** 2 which was faster than for x in range(size): x ** 2 in numpy==1.16.4 and python 3.6 – Venosity

Answer 2

First of all, as written by @bmu, you should use combinations of vectorized calculations, ufuncs and indexing. There are indeed some cases where explicit looping is required, but those are really rare.

If explicit loop is needed, with python 2.6 and 2.7, you should use xrange (see below). From what you say, in Python 3, range is the same as xrange (returns a generator). So maybe range is as good for you.

Now, you should try it yourself (using timeit: - here the ipython "magic function"):

%timeit for i in range(1000000): pass
[out] 10 loops, best of 3: 63.6 ms per loop

%timeit for i in np.arange(1000000): pass
[out] 10 loops, best of 3: 158 ms per loop

%timeit for i in xrange(1000000): pass
[out] 10 loops, best of 3: 23.4 ms per loop

Again, as mentioned above, most of the time it is possible to use numpy vector/array formula (or ufunc etc...) which run a c speed: much faster. This is what we could call "vector programming". It makes program easier to implement than C (and more readable) but almost as fast in the end.

Enzymolysis

There is a standard python 'timeit' module which allows to do the same without IPython. But it is just much more easy to use this magic function. – Enzymolysis

I fully agree, but the question was about "iterating over a large array". In some situation, it is not possible to use the numpy vectorized, ufunc or indexing. On example I encountered is to compute the eigenvectors of a list of matrices (>= 3x3) – Enzymolysis

I don't know if np.arange has been made more efficient since 2012, but it's main interest compared to the built-in range is that you can use float number as start:stop:step. – Bandur

np.arange is useful when we have non integer step size – Emad

Answer 3

First of all: range returns an iterator, np.arange returns a np.array with allocated memory (as OP already mentioned). To make both approaches comparable, we need to allocate a list for the iterator:

list(range(n))

When it comes to performance, it depends: For smaller (allocated) ranges, Python's range(...) is faster. However, numpy's np.arange(...) scales nicely and outperforms for larger ranges:

Please find the benchmark code here. Run on MacBook Pro M1 with Python 3.11 and numpy 1.23.5

This question is very driven from a performance perspective (which is completely valid). However, I find the usability/maintainability viewpoint equally important: Importing numpy for creating just a range would be terrible. Also, vice-versa: A heavily numpy-driven code using range feels wrong.

Also keep in mind, that np.arange has a better support for non-integer step sizes.

To summarize: It depends. :-)

Burletta