Fast 1D and 2D histogram functions in Python

About

Sometimes you just want to compute simple 1D or 2D histograms with regular bins. Fast. No nonsense. Numpy's histogram functions are versatile, and can handle for example non-regular binning, but this versatility comes at the expense of performance.

The fast-histogram mini-package aims to provide simple and fast histogram functions for regular bins that don't compromise on performance. It doesn't do anything complicated - it just implements a simple histogram algorithm in C and keeps it simple. The aim is to have functions that are fast but also robust and reliable. The result is a 1D histogram function here that is 7-15x faster than numpy.histogram, and a 2D histogram function that is 20-25x faster than numpy.histogram2d.

To install:

pip install fast-histogram

or if you use conda you can instead do:

conda install -c conda-forge fast-histogram

The fast_histogram module then provides two functions: histogram1d and histogram2d:

from fast_histogram import histogram1d, histogram2d

Example

Here's an example of binning 10 million points into a regular 2D histogram:

In [1]: import numpy as np

In [2]: x = np.random.random(10_000_000)

In [3]: y = np.random.random(10_000_000)

In [4]: %timeit _ = np.histogram2d(x, y, range=[[-1, 2], [-2, 4]], bins=30)
935 ms ± 58.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [5]: from fast_histogram import histogram2d

In [6]: %timeit _ = histogram2d(x, y, range=[[-1, 2], [-2, 4]], bins=30)
40.2 ms ± 624 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

(note that 10_000_000 is possible in Python 3.6 syntax, use 10000000 instead in previous versions)

The version here is over 20 times faster! The following plot shows the speedup as a function of array size for the bin parameters shown above:

as well as results for the 1D case, also with 30 bins. The speedup for the 2D case is consistently between 20-25x, and for the 1D case goes from 15x for small arrays to around 7x for large arrays.

Q&A

Why don't the histogram functions return the edges?

Computing and returning the edges may seem trivial but it can slow things down by a factor of a few when computing histograms of 10^5 or fewer elements, so not returning the edges is a deliberate decision related to performance. You can easily compute the edges yourself if needed though, using numpy.linspace.

Doesn't package X already do this, but better?

This may very well be the case! If this duplicates another package, or if it is possible to use Numpy in a smarter way to get the same performance gains, please open an issue and I'll consider deprecating this package :)

One package that does include fast histogram functions (including in n-dimensions) and can compute other statistics is vaex, so take a look there if you need more advanced functionality!

Are the 2D histograms not transposed compared to what they should be?

There is technically no 'right' and 'wrong' orientation - here we adopt the convention which gives results consistent with Numpy, so:

numpy.histogram2d(x, y, range=[[xmin, xmax], [ymin, ymax]], bins=[nx, ny])

should give the same result as:

fast_histogram.histogram2d(x, y, range=[[xmin, xmax], [ymin, ymax]], bins=[nx, ny])

Why not contribute this to Numpy directly?

As mentioned above, the Numpy functions are much more versatile, so they could not be replaced by the ones here. One option would be to check in Numpy's functions for cases that are simple and dispatch to functions such as the ones here, or add dedicated functions for regular binning. I hope we can get this in Numpy in some form or another eventually, but for now, the aim is to have this available to packages that need to support a range of Numpy versions.

Why not use Cython?

I originally implemented this in Cython, but found that I could get a 50% performance improvement by going straight to a C extension.

What about using Numba?

I specifically want to keep this package as easy as possible to install, and while Numba is a great package, it is not trivial to install outside of Anaconda.

Could this be parallelized?

This may benefit from parallelization under certain circumstances. The easiest solution might be to use OpenMP, but this won't work on all platforms, so it would need to be made optional.

Couldn't you make it faster by using the GPU?

Almost certainly, though the aim here is to have an easily installable and portable package, and introducing GPUs is going to affect both of these.

Why make a package specifically for this? This is a tiny amount of functionality

Packages that need this could simply bundle their own C extension or Cython code to do this, but the main motivation for releasing this as a mini-package is to avoid making pure-Python packages into packages that require compilation just because of the need to compute fast histograms.

Can I contribute?

Yes please! This is not meant to be a finished package, and I welcome pull request to improve things.