[Numpy-discussion] Does a `mergesorted` function make sense?
Jaime Fernández del Río
jaime.frio at gmail.com
Wed Sep 3 12:46:16 EDT 2014
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
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