This package consists of a small library of optimised tools for doing things that can roughly
be considered "group-indexing operations". The most prominent tool is aggregate
, which is
descibed in detail further down the page.
If you have pip
, then simply:
pip install numpy_groupies
Note that numpy_groupies
doesn't have any compulsory dependencies (even numpy
is optional)
so you should be able to install it fairly easily even without a package manager. If you just
want one particular implementation of aggregate
(e.g. aggregate_numpy.py
), you can download
that one file, and copy-paste the contents of utils.py
into the top of that file (replacing
the from .utils import (...)
line).
import numpy as np
import numpy_groupies as npg
group_idx = np.array([ 3, 0, 0, 1, 0, 3, 5, 5, 0, 4])
a = np.array([13.2, 3.5, 3.5,-8.2, 3.0,13.4,99.2,-7.1, 0.0,53.7])
npg.aggregate(group_idx, a, func='sum', fill_value=0)
# >>> array([10.0, -8.2, 0.0, 26.6, 53.7, 92.1])
aggregate
takes an array of values, and an array giving the group number for each of those values.
It then returns the sum (or mean, or std, or any, ...etc.) of the values in each group. You have
probably come across this idea before - see Matlab's accumarray
function, or
pandas
groupby concept, or
MapReduce paradigm, or simply the basic histogram.
A couple of implemented functions do not reduce the data, instead it calculates values cumulatively while iterating over the data or permutates them. The output size matches the input size.
group_idx = np.array([4, 3, 3, 4, 4, 1, 1, 1, 7, 8, 7, 4, 3, 3, 1, 1])
a = np.array([3, 4, 1, 3, 9, 9, 6, 7, 7, 0, 8, 2, 1, 8, 9, 8])
npg.aggregate(group_idx, a, func='cumsum')
# >>> array([3, 4, 5, 6,15, 9,15,22, 7, 0,15,17, 6,14,31,39])
The function accepts various different combinations of inputs, producing various different shapes of output. We give a brief description of the general meaning of the inputs and then go over the different combinations in more detail:
group_idx
- array of non-negative integers to be used as the "labels" with which to group the values ina
.a
- array of values to be aggregated.func='sum'
- the function to use for aggregation. See the section below for nore details.size=None
- the shape of the output array. IfNone
, the maximum value ingroup_idx
will set the size of the output.fill_value=0
- value to use for output groups that do not appear anywhere in thegroup_idx
input array.order='C'
- for multidimensional output, this controls the layout in memory, can be'F'
for fortran-style.dtype=None
- thedtype
of the output.None
means choose a sensible type for the givena
,func
, andfill_value
.axis=None
- explained below.ddof=0
- passed through into calculations of variance and standard deviation (see section on functions).
- Form 1 is the simplest, taking
group_idx
anda
of matching 1D lengths, and producing a 1D output. - Form 2 is similar to Form 1, but takes a scalar
a
, which is broadcast out to the length ofgroup_idx
. Note that this is generally not that useful. - Form 3 is more complicated.
group_idx
is the same length as thea.shape[axis]
. The groups are broadcast out along the other axis/axes ofa
, thus the output is of shapen_groups x a.shape[0] x ... x a.shape[axis-1] x a.shape[axis+1] x ... a.shape[-1]
, i.e. the output has two or more dimensions. - Form 4 also produces output with two or more dimensions, but for very different reasons to Form 3. Here
a
is 1D andgroup_idx
is exactly2D
, whereas in Form 3a
isND
,group_idx
is1D
, and we provide a value foraxis
. The length ofa
must matchgroup_idx.shape[1]
, the value ofgroup_idx.shape[0]
determines the number of dimensions in the ouput, i.e.group_idx[:,99]
gives the(x,y,z)
group indices for thea[99]
. - Form 5 is the same as Form 4 but with scalar
a
. As with Form 2, this is rarely that helpful.
Note on performance. The order
of the output is unlikely to affect performance of aggregate
(although it may affect your downstream usage of that output), however the order of multidimensional a
or group_idx
can affect performance: in Form 4 it is best if columns are contiguous in memory within group_idx
, i.e. group_idx[:, 99]
corresponds to a contiguous chunk of memory; in Form 3 it's best if all the data in a
for group_idx[i]
is contiguous, e.g. if axis=1
then we want a[:, 55]
to be contiguous.
By default, aggregate
assumes you want to sum the values within each group, however you can specify another
function using the func
kwarg. This func
can be any custom callable, however you will likely want one of
the following optimized functions. Note that not all functions might be provided by all implementations.
'sum'
- sum of items within each group (see example above).'prod'
- product of items within each group'mean'
- mean of items within each group'var'
- variance of items within each group. Useddof
kwarg for degrees of freedom. The divisor used in calculations isN - ddof
, whereN
represents the number of elements. By defaultddof
is zero.'std'
- standard deviation of items within each group. Useddof
kwarg for degrees of freedom (seevar
above).'min'
- minimum value of items within each group.'max'
- maximum value of items within each group.'first'
- first item ina
from each group.'last'
- last item ina
from each group.'argmax'
- the index ina
of the maximum value in each group.'argmin'
- the index ina
of the minimum value in each group.
The above functions also have a nan
-form, which skip the nan
values instead of propagating them to the result of the calculation:
'nansum'
,'nanprod'
,'nanmean'
,'nanvar'
,'nanstd'
,'nanmin'
,'nanmax'
,'nanfirst'
,'nanlast'
,nanargmax
,nanargmin
The following functions are slightly different in that they always return boolean values. Their treatment of nans is also different from above:
'all'
-True
if all items within a group are truethy. Note thatnp.all(nan)
isTrue
, i.e.nan
is actually truethy.'any'
-True
if any items within a group are truethy.'allnan'
-True
if all items within a group arenan
.'anynan'
-True
if any items within a gorup arenan
.
The following functions don't reduce the data, but instead produce an output matching the size of the input:
cumsum
- cumulative sum of items within each group.cumprod
- cumulative product of items within each group. (numba only)cummin
- cumulative minimum of items within each group. (numba only)cummax
- cumulative maximum of items within each group. (numba only)'sort'
- sort the items within each group in ascending order, use reverse=True to invert the order.
Finally, there are three functions which don't reduce each group to a single value, instead they return the full set of items within the group:
'array'
- simply returns the grouped items, using the same order as appeared ina
. (numpy only)
Compute sums of consecutive integers, and then compute products of those consecutive integers.
group_idx = np.arange(5).repeat(3)
# group_idx: array([0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4])
a = np.arange(group_idx.size)
# a: array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])
x = aggregate(group_idx, a) # sum is default
# x: array([ 3, 12, 21, 30, 39])
x = aggregate(group_idx, a, 'prod')
# x: array([ 0, 60, 336, 990, 2184])
Get variance ignoring nans, setting all-nan groups to nan
.
x = aggregate(group_idx, a, func='nanvar', fill_value=nan)
Count the number of elements in each group. Note that this is equivalent to doing np.bincount(group_idx)
, indeed that is how the numpy implementation does it.
x = aggregate(group_idx, 1)
Sum 1000 values into a three-dimensional cube of size 15x15x15. Note that in this example all three dimensions have the same size, but that doesn't have to be the case.
group_idx = np.random.randint(0, 15, size=(3, 1000))
a = np.random.random(group_idx.shape[1])
x = aggregate(group_idx, a, func="sum", size=(15,15,15), order="F")
# x.shape: (15, 15, 15)
# np.isfortran(x): True
Use a custom function to generate some strings.
group_idx = array([1, 0, 1, 4, 1])
a = array([12.0, 3.2, -15, 88, 12.9])
x = aggregate(group_idx, a,
func=lambda g: ' or maybe '.join(str(gg) for gg in g), fill_value='')
# x: ['3.2', '12.0 or maybe -15.0 or maybe 12.9', '', '', '88.0']
Use the axis
arg in order to do a sum-aggregation on three rows simultaneously.
a = array([[99, 2, 11, 14, 20],
[33, 76, 12, 100, 71],
[67, 10, -8, 1, 9]])
group_idx = array([[3, 3, 7, 0, 0]])
x = aggregate(group_idx, a, axis=1)
# x : [[ 34, 0, 0, 101, 0, 0, 0, 11],
# [171, 0, 0, 109, 0, 0, 0, 12],
# [ 10, 0, 0, 77, 0, 0, 0, -8]]
There are multiple implementations of aggregate
provided. If you use from numpy_groupies import aggregate
,
the best available implementation will automatically be selected. Otherwise you can pick a specific version directly
like from numpy_groupies import aggregate_nb as aggregate
or by importing aggregate from the implementing module
from numpy_groupies.aggregate_weave import aggregate
.
Currently the following implementations exist:
- numpy - This is the default implementation. It uses plain
numpy
, mainly relying onnp.bincount
and basic indexing magic. It comes without other dependencies exceptnumpy
and shows reasonable performance for the occasional usage. - numba - This is the most performant implementation in average, based on jit compilation provided by numba and LLVM.
- weave -
weave
compiles C-code on demand at runtime, producing binaries that get executed from within python. The performance of this implementation is comparable to the numba implementation. - pure python - This implementation has no dependencies and uses only the standard library. It's horribly slow and should only be used, if there is no numpy available.
- numpy ufunc - Only for benchmarking. This impelmentation uses the
.at
method of numpy'sufunc
s (e.g.add.at
), which would appear to be designed for perfoming excactly the same calculation thataggregate
executes, however the numpy implementation is rather incomplete and slow (as ofv1.14.0
). A numpy issue has been created to address this issue. - pandas - Only for reference. The pandas'
groupby
concept is the same as the task performed byaggregate
. However,pandas
is not actually faster than the defaultnumpy
implementation. Also, note that there may be room for improvement in the way thatpandas
is utilized here. Most notably, when computing multiple aggregations of the same data (e.g.'min'
and'max'
) pandas could potentially be used more efficiently.
All implementations have the same calling syntax and produce the same outputs, to within some floating-point error.
However some implementations only support a subset of the valid inputs and will sometimes throw NotImplementedError
.
Scripts for testing and benchmarking are included in this repository. For benchmarking, run python -m numpy_groupies.benchmarks.generic
from the root of this repository.
Below we are using 500,000
indices uniformly picked from [0, 1000)
. The values of a
are uniformly picked from
the interval [0,1)
, with anything less than 0.2
then set to 0 (in order to serve as falsy values in boolean operations).
For nan-
operations another 20% of the values are set to nan, leaving the remainder on the interval [0.2,0.8)
.
The benchmarking results are given in ms for an i7-7560U running at 2.40GHz:
function ufunc numpy numba weave
-----------------------------------------------------------------
sum 28.763 1.477 0.917 1.167
prod 29.165 29.162 0.919 1.170
amin 33.020 33.134 0.979 1.181
amax 33.150 33.156 1.049 1.216
len 28.594 1.260 0.755 1.023
all 33.493 3.883 0.995 1.214
any 33.308 6.776 1.003 1.216
anynan 28.938 2.472 0.930 1.182
allnan 29.391 5.929 0.931 1.201
mean ---- 2.100 0.972 1.216
std ---- 6.600 1.127 1.370
var ---- 6.684 1.109 1.388
first ---- 2.140 1.067 1.188
last ---- 1.545 0.818 1.086
argmax ---- 33.860 1.016 ----
argmin ---- 36.690 0.981 ----
nansum ---- 4.944 1.722 1.342
nanprod ---- 27.286 1.726 1.369
nanmin ---- 30.238 1.895 1.359
nanmax ---- 30.337 1.939 1.446
nanlen ---- 4.820 1.707 1.312
nanall ---- 9.148 1.786 1.380
nanany ---- 10.157 1.830 1.392
nanmean ---- 5.775 1.758 1.440
nanvar ---- 10.090 1.922 1.651
nanstd ---- 10.308 1.884 1.664
nanfirst ---- 5.481 1.945 1.295
nanlast ---- 4.992 1.735 1.199
cumsum ---- 144.807 1.455 ----
cumprod ---- ---- 1.371 ----
cummax ---- ---- 1.441 ----
cummin ---- ---- 1.340 ----
arbitrary ---- 237.252 79.717 ----
sort ---- 261.951 ---- ----
Linux(x86_64), Python 2.7.12, Numpy 1.16.0, Numba 0.42.0, Weave 0.17.0
This project was started by @ml31415 and the numba
and weave
implementations are by him. The pure
python and numpy
implementations were written by @d1manson.
The authors hope that numpy
's ufunc.at
methods will eventually be fast enough that hand-optimisation
of individual functions will become unneccessary. However even if that does happen, there may still be a
role for the aggregate
function as a light-weight wrapper around those functions.
Maybe at some point a version of aggregate
will make its way into numpy
itself (or at least scipy
).