On Thu, Sep 4, 2014 at 10:39 AM, Eelco Hoogendoorn < hoogendoorn.eelco@gmail.com> wrote:

On Thu, Sep 4, 2014 at 10:31 AM, Eelco Hoogendoorn < hoogendoorn.eelco@gmail.com> wrote:

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

On Wed, Sep 3, 2014 at 9:33 AM, Jaime Fernández del Río < jaime.frio@gmail.com> wrote:

On Wed, Sep 3, 2014 at 6:41 AM, Eelco Hoogendoorn < hoogendoorn.eelco@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 dataset.

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.

Oh I forgot to add: with an indexing mechanism based on sorting, unique values and counts also come 'for free', not counting the O(N) cost of actually creating those arrays. The only time an operating relying on an index incurs another nontrivial amount of overhead is in case its 'rank' or 'inverse' property is used, which invokes another argsort. But for the vast majority of grouping or set operations, these properties are never used.

That extra argsort is now gone from master: https://github.com/numpy/numpy/pull/5012 Even with this improvement, returning any index typically makes `np.unique` run at least 2x slower: In [1]: import numpy as np In [2]: a = np.random.randint(100, size=(1000,)) In [3]: %timeit np.unique(a) 10000 loops, best of 3: 37.3 us per loop In [4]: %timeit np.unique(a, return_inverse=True) 10000 loops, best of 3: 62.1 us per loop In [5]: %timeit np.unique(a, return_index=True) 10000 loops, best of 3: 72.8 us per loop In [6]: %timeit np.unique(a, return_counts=True) 10000 loops, best of 3: 56.4 us per loop In [7]: %timeit np.unique(a, return_index=True, return_inverse=True, return_coun ts=True) 10000 loops, best of 3: 112 us per loop -- (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial.