[Numpy-discussion] Does a `mergesorted` function make sense?

Eelco Hoogendoorn hoogendoorn.eelco at gmail.com
Thu Sep 4 04:31:01 EDT 2014

On Wed, Sep 3, 2014 at 6:46 PM, Jaime Fernández del Río <
jaime.frio at gmail.com> wrote:

> On Wed, Sep 3, 2014 at 9:33 AM, Jaime Fernández del Río <
> jaime.frio at gmail.com> wrote:
>> On Wed, Sep 3, 2014 at 6:41 AM, Eelco Hoogendoorn <
>> hoogendoorn.eelco at gmail.com> wrote:
>>>  Not sure about the hashing. Indeed one can also build an index of a set
>>> by means of a hash table, but its questionable if this leads to improved
>>> performance over performing an argsort. Hashing may have better asymptotic
>>> time complexity in theory, but many datasets used in practice are very easy
>>> to sort (O(N)-ish), and the time-constant of hashing is higher. But more
>>> importantly, using a hash-table guarantees poor cache behavior for many
>>> operations using this index. By contrast, sorting may (but need not) make
>>> one random access pass to build the index, and may (but need not) perform
>>> one random access to reorder values for grouping. But insofar as the keys
>>> are better behaved than pure random, this coherence will be exploited.
>> If you want to give it a try, these branch of my numpy fork has hash
>> table based implementations of unique (with no extra indices) and in1d:
>>  https://github.com/jaimefrio/numpy/tree/hash-unique
>> A use cases where the hash table is clearly better:
>> In [1]: import numpy as np
>> In [2]: from numpy.lib._compiled_base import _unique, _in1d
>> In [3]: a = np.random.randint(10, size=(10000,))
>> In [4]: %timeit np.unique(a)
>> 1000 loops, best of 3: 258 us per loop
>> In [5]: %timeit _unique(a)
>> 10000 loops, best of 3: 143 us per loop
>> In [6]: %timeit np.sort(_unique(a))
>> 10000 loops, best of 3: 149 us per loop
>> It typically performs between 1.5x and 4x faster than sorting. I haven't
>> profiled it properly to know, but there may be quite a bit of performance
>> to dig out: have type specific comparison functions, optimize the starting
>> hash table size based on the size of the array to avoid reinsertions...
>> If getting the elements sorted is a necessity, and the array contains
>> very few or no repeated items, then the hash table approach may even
>> perform worse,:
>> In [8]: a = np.random.randint(10000, size=(5000,))
>> In [9]: %timeit np.unique(a)
>> 1000 loops, best of 3: 277 us per loop
>> In [10]: %timeit np.sort(_unique(a))
>> 1000 loops, best of 3: 320 us per loop
>> But the hash table still wins in extracting the unique items only:
>> In [11]: %timeit _unique(a)
>> 10000 loops, best of 3: 187 us per loop
>> Where the hash table shines is in more elaborate situations. If you keep
>> the first index where it was found, and the number of repeats, in the hash
>> table, you can get return_index and return_counts almost for free, which
>> means you are performing an extra 3x faster than with sorting.
>> return_inverse requires a little more trickery, so I won;t attempt to
>> quantify the improvement. But I wouldn't be surprised if, after fine tuning
>> it, there is close to an order of magnitude overall improvement
>> The spped-up for in1d is also nice:
>> In [16]: a = np.random.randint(1000, size=(1000,))
>> In [17]: b = np.random.randint(1000, size=(500,))
>> In [18]: %timeit np.in1d(a, b)
>> 1000 loops, best of 3: 178 us per loop
>> In [19]: %timeit _in1d(a, b)
>> 10000 loops, best of 3: 30.1 us per loop
>> Of course, there is no point in
> Ooops!!! Hit the send button too quick. Not to extend myself too long: if
> we are going to rethink all of this, we should approach it with an open
> mind. Still, and this post is not helping with that either, I am afraid
> that we are discussing implementation details, but are missing a broader
> vision of what we want to accomplish and why. That vision of what numpy's
> grouping functionality, if any, should be, and how it complements or
> conflicts with what pandas is providing, should precede anything else. I
> now I haven't, but has anyone looked at how pandas implements grouping?
> Their documentation on the subject is well worth a read:
> http://pandas.pydata.org/pandas-docs/stable/groupby.html
> Does numpy need to replicate this? What/why/how can we add to that?
> Jaime
> --
> (\__/)
> ( O.o)
> ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes
> de dominación mundial.
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> I would certainly not be opposed to having a hashing based indexing
mechanism; I think it would make sense design-wise to have a HashIndex
class with the same interface as the rest, and use that subclass in those
arraysetops where it makes sense. The 'how to' of indexing and its
applications are largely orthogonal I think (with some tiny performance
compromises which are worth the abstraction imo). For datasets which are
not purely random, have many unique items, and which do not fit into cache,
I would expect sorting to come out on top, but indeed it depends on the

Yeah, the question how pandas does grouping, and whether we can do better,
is a relevant one.

>From what I understand, pandas relies on cython extensions to get
vectorized grouping functionality. This is no longer necessary since the
introduction of ufuncs in numpy. I don't know how the implementations
compare in terms of performance, but I doubt the difference is huge.

I personally use grouping a lot in my code, and I don't like having to use
pandas for it. Most importantly, I don't want to go around creating a
dataframe for a single one-line hit-and-run association between keys and
values. The permanent association of different types of data and their
metadata which pandas offers is I think the key difference from numpy,
which is all about manipulating just plain ndarrays. Arguably, grouping
itself is a pretty elementary manipulating of ndarrays, and adding calls to
DataFrame or Series inbetween a statement that could just be
simply group_by(keys).mean(values) feels wrong to me. As does including
pandas as a dependency just to use this small piece of
functionality. Grouping is a more general functionality than any particular
method of organizing your data.

In terms of features, adding transformations and filtering might be nice
too; I hadn't thought about it, but that is because unlike the currently
implemented features, the need has never arose for me. Im only a small
sample size, and I don't see any fundamental objection to adding such
functionality though. It certainly raises the question as to where to draw
the line with pandas; but my rule of thumb is that if you can think of it
as an elementary operation on ndarrays, then it probably belongs in numpy.
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