#16296: Speed improvements for categories with axioms
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Reporter: SimonKing | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.3
Component: categories | Resolution:
Keywords: cython | Merged in:
performance categories | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | d7f8250a1defbad2c5f3acb89d8f152a45d53523
u/SimonKing/ticket/16296 | Stopgaps:
Dependencies: #10963, #15801, |
#16309 |
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Comment (by SimonKing):
I switched `sage.categories.category` and
`sage.categories.category_with_axiom` back to Python. Instead, I created a
module with helper functions. Fortunately, `_sort_uniq` is a static
method, and thus it is no problem to replace it with a cpdef function
imported from the helper module.
The current timings:
{{{
sage: from sage.categories.category_with_axiom import canonicalize_axioms,
all_axioms
sage: canonicalize_axioms(all_axioms, ["Commutative", "Connected",
"Commutative", "WithBasis", "Finite"])
('Finite', 'Connected', 'WithBasis', 'Commutative')
sage: %timeit canonicalize_axioms(all_axioms, L)
100000 loops, best of 3: 3.83 µs per loop
sage: L = [Coalgebras(QQ), Sets().Finite(), Algebras(ZZ),
SimplicialComplexes()]
sage: %timeit Category._sort(L)
100000 loops, best of 3: 6.25 µs per loop
sage: %timeit Category._sort_uniq(L)
100000 loops, best of 3: 15.9 µs per loop
sage: %timeit Category.join(L)
10000 loops, best of 3: 816 µs per loop
}}}
Note: Since I want to keep `all_axioms` in
`sage.categories.category_with_axiom`, I need to provide it to
`canonicalize_axioms` (now defined in the helper module) as an argument.
__Evaluation__
- `canonicalize_axioms` is still fast, and so is (almost) `_sort_uniq`.
- I kept `_sort` in for now, but it isn't used, and I'd simply remove it.
- The join is now slow again, since it is Python.
__Concerning join__
Perhaps one could create another helper function for the join. It is
static, hence, a cpdef function won't be a problem. However, it uses a
cache. This cache should be local to `sage.categories.category.Category`,
but when defining the `join` in the helper module, we'd like to have
cython-speed access to it. OTOH, we could define the cache in the helper
module, and then assign it as an attribute to `Category`, if we think that
the cache is needed outside of the helper.
--
Ticket URL: <http://trac.sagemath.org/ticket/16296#comment:41>
Sage <http://www.sagemath.org>
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