Fast NumPy array functions written in Cython

## Project description

Bottleneck is a collection of fast NumPy array functions written in Cython:

===================== =======================================================
NumPy/SciPy ``median, nanmedian, rankdata, nansum, nanmin, nanmax,
nanmean, nanstd, nanargmin, nanargmax``
Functions ``nanrankdata, nanvar``
Moving window ``move_sum, move_nansum, move_mean, move_nanmean,
move_std, move_nanstd, move_min, move_nanmin, move_max,
move_nanmax``
===================== =======================================================

Let's give it a try. Create a NumPy array::

>>> import numpy as np
>>> arr = np.array([1, 2, np.nan, 4, 5])

Find the nanmean::

>>> import bottleneck as bn
>>> bn.nanmean(arr)
3.0

Moving window nanmean::

>>> bn.move_nanmean(arr, window=2)
array([ nan, 1.5, 2. , 4. , 4.5])

Fast
====

Bottleneck is fast::

>>> arr = np.random.rand(100, 100)
>>> timeit np.nanmax(arr)
10000 loops, best of 3: 90 us per loop
>>> timeit bn.nanmax(arr)
100000 loops, best of 3: 12.6 us per loop

Let's not forget to add some NaNs::

>>> arr[arr > 0.5] = np.nan
>>> timeit np.nanmax(arr)
10000 loops, best of 3: 133 us per loop
>>> timeit bn.nanmax(arr)
100000 loops, best of 3: 12.6 us per loop

Bottleneck comes with a benchmark suite. To run the benchmark::

>>> bn.bench(mode='fast', dtype='float64', axis=0)
Bottleneck performance benchmark
Bottleneck 0.4.0
Numpy (np) 1.5.1
Scipy (sp) 0.8.0
Speed is NumPy or SciPy time divided by Bottleneck time
NaN means one-third NaNs; float64 and axis=0 are used
High-level functions used (mode='fast')

no NaN no NaN no NaN NaN NaN NaN
(10,10) (100,100) (1000,1000) (10,10) (100,100) (1000,1000)
median 9.34 14.40 7.29 8.27 3.64 2.84
nanmedian 219.65 127.95 8.21 226.79 176.69 8.10
nansum 12.16 6.40 1.72 12.10 7.34 1.71
nanmax 12.78 6.29 1.69 13.56 10.45 1.69
nanmean 21.97 13.98 3.00 21.93 28.89 4.99
nanstd 30.06 9.69 2.69 30.61 17.62 3.71
nanargmax 10.68 6.05 2.68 10.85 9.04 2.88
rankdata 23.11 12.51 8.33 22.71 14.09 9.36
move_sum 11.13 8.71 14.53 12.15 8.63 14.11
move_nansum 29.39 19.52 29.45 28.00 25.40 29.83
move_mean 11.11 4.25 14.43 11.23 8.36 14.30
move_nanmean 31.65 11.81 29.86 32.81 14.41 30.93
move_std 17.33 3.33 22.82 22.30 20.77 29.94
move_nanstd 34.82 6.18 34.94 40.44 7.06 36.09
move_max 4.06 3.61 9.26 4.71 5.54 11.65
move_nanmax 22.16 5.95 19.57 24.74 14.69 27.07

Reference functions:
median np.median
nanmedian local copy of sp.stats.nanmedian
nansum np.nansum
nanmax np.nanmax
nanmean local copy of sp.stats.nanmean
nanstd local copy of sp.stats.nanstd
nanargmax np.nanargmax
rankdata scipy.stats.rankdata based (axis support added)
move_sum sp.ndimage.convolve1d based, window=a.shape[0]/5
move_nansum sp.ndimage.convolve1d based, window=a.shape[0]/5
move_mean sp.ndimage.convolve1d based, window=a.shape[0]/5
move_nanmean sp.ndimage.convolve1d based, window=a.shape[0]/5
move_std sp.ndimage.convolve1d based, window=a.shape[0]/5
move_nanstd sp.ndimage.convolve1d based, window=a.shape[0]/5
move_max sp.ndimage.maximum_filter1d based, window=a.shape[0]/5
move_nanmax sp.ndimage.maximum_filter1d based, window=a.shape[0]/5

Faster
======

Under the hood Bottleneck uses a separate Cython function for each combination
of ndim, dtype, and axis. A lot of the overhead in bn.nanmax(), for example,
is in checking that the axis is within range, converting non-array data to an
array, and selecting the function to use to calculate the maximum.

You can get rid of the overhead by doing all this before you, say, enter
an inner loop::

>>> arr = np.random.rand(10,10)
>>> func, a = bn.func.nanmax_selector(arr, axis=0)
>>> func
<built-in function nanmax_2d_float64_axis0>

Let's see how much faster than runs::

>>> timeit np.nanmax(arr, axis=0)
10000 loops, best of 3: 24.7 us per loop
>>> timeit bn.nanmax(arr, axis=0)
100000 loops, best of 3: 2.1 us per loop
>>> timeit func(a)
100000 loops, best of 3: 1.47 us per loop

Note that ``func`` is faster than Numpy's non-NaN version of max::

>>> timeit arr.max(axis=0)
100000 loops, best of 3: 4.78 us per loop

So adding NaN protection to your inner loops comes at a negative cost!

Benchmarks for the low-level Cython functions::

>>> bn.bench(mode='faster', dtype='float64', axis=0)
Bottleneck performance benchmark
Bottleneck 0.4.0
Numpy (np) 1.5.1
Scipy (sp) 0.8.0
Speed is NumPy or SciPy time divided by Bottleneck time
NaN means one-third NaNs; float64 and axis=0 are used
Low-level functions used (mode='faster')

no NaN no NaN no NaN NaN NaN NaN
(10,10) (100,100) (1000,1000) (10,10) (100,100) (1000,1000)
median 14.72 14.75 7.09 11.90 3.64 2.83
nanmedian 337.43 133.27 8.92 352.73 182.65 8.20
nansum 20.75 6.72 1.73 20.61 7.96 1.72
nanmax 20.03 6.58 1.72 22.44 11.11 1.69
nanmean 38.55 14.44 3.00 39.35 30.52 5.00
nanstd 41.78 9.85 2.70 44.16 18.17 3.71
nanargmax 17.97 6.33 2.70 18.50 9.64 2.91
rankdata 24.43 12.43 8.37 24.37 14.06 9.21
move_sum 18.29 8.60 14.52 18.13 8.87 13.62
move_nansum 45.98 20.80 29.33 48.56 26.25 29.29
move_mean 16.33 4.35 14.33 16.21 8.64 14.15
move_nanmean 50.79 11.92 29.36 51.63 14.93 30.32
move_std 23.45 3.36 22.88 33.20 20.18 29.18
move_nanstd 48.02 6.16 34.61 57.20 7.03 36.13
move_max 5.82 3.63 9.31 6.70 5.62 11.77
move_nanmax 29.09 6.02 19.55 36.57 14.83 27.02

Reference functions:
median np.median
nanmedian local copy of sp.stats.nanmedian
nansum np.nansum
nanmax np.nanmax
nanmean local copy of sp.stats.nanmean
nanstd local copy of sp.stats.nanstd
nanargmax np.nanargmax
rankdata scipy.stats.rankdata based (axis support added)
move_sum sp.ndimage.convolve1d based, window=a.shape[0]/5
move_nansum sp.ndimage.convolve1d based, window=a.shape[0]/5
move_mean sp.ndimage.convolve1d based, window=a.shape[0]/5
move_nanmean sp.ndimage.convolve1d based, window=a.shape[0]/5
move_std sp.ndimage.convolve1d based, window=a.shape[0]/5
move_nanstd sp.ndimage.convolve1d based, window=a.shape[0]/5
move_max sp.ndimage.maximum_filter1d based, window=a.shape[0]/5
move_nanmax sp.ndimage.maximum_filter1d based, window=a.shape[0]/5

Slow
====

Currently only 1d, 2d, and 3d input arrays with data type (dtype) int32,
int64, float32, and float64 are accelerated. All other ndim/dtype
combinations result in calls to slower, unaccelerated functions.

=======

Scipy and numpydoc, all of which have BSD licenses, are included in
Bottleneck. See the LICENSE file, which is distributed with Bottleneck, for
details.

URLs
====

=================== ========================================================
docs http://berkeleyanalytics.com/bottleneck
code http://github.com/kwgoodman/bottleneck
mailing list 2 http://mail.scipy.org/mailman/listinfo/scipy-user
=================== ========================================================

Install
=======

Requirements:

======================== ====================================================
Bottleneck Python, NumPy 1.5.1
Unit tests nose
Compile gcc or MinGW
Optional SciPy 0.8.0 (portions of benchmark)
======================== ====================================================

Directions for installing a *released* version of Bottleneck (i.e., one
obtained from http://pypi.python.org/pypi/Bottleneck) are given below. Cython
is not required since the Cython files have already been converted to C source
files. (If you obtained bottleneck directly from the repository, then you will
need to generate the C source files using the included Makefile which requires
Cython.)

**GNU/Linux, Mac OS X, et al.**

To install Bottleneck::

\$ python setup.py build
\$ sudo python setup.py install

Or, if you wish to specify where Bottleneck is installed, for example inside
``/usr/local``::

\$ python setup.py build
\$ sudo python setup.py install --prefix=/usr/local

**Windows**

You can compile Bottleneck using the instructions below or you can use the
Windows binaries created by Christoph Gohlke:
http://www.lfd.uci.edu/~gohlke/pythonlibs/#bottleneck

In order to compile the C code in Bottleneck you need a Windows version of the
gcc compiler. MinGW (Minimalist GNU for Windows) contains gcc.

Install MinGW and add it to your system path. Then install Bottleneck with the
commands::

python setup.py build --compiler=mingw32
python setup.py install

**Post install**

After you have installed Bottleneck, run the suite of unit tests::

>>> import bottleneck as bn
>>> bn.test()
<snip>
Ran 46 tests in 41.457s
OK
<nose.result.TextTestResult run=46 errors=0 failures=0>

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