Opened 10 years ago
Closed 9 years ago
#9663 closed enhancement (fixed)
Fast computation of Stirling numbers of 2nd kind
Reported by: | fredrik.johansson | Owned by: | sage-combinat |
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Priority: | major | Milestone: | sage-4.6.1 |
Component: | combinatorics | Keywords: | |
Cc: | was | Merged in: | sage-4.6.1.alpha0 |
Authors: | Fredrik Johansson, Nathann Cohen | Reviewers: | Nathann Cohen, Nicolas Borie, Jeroen Demeyer |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Currently, Stirling numbers are computed by calling GAP. The patch provides fast Cython code for Stirling numbers of the second kind, and allows using GAP or Maxima as an optional algorithm.
By having less overhead, the Cython code is about 10000 times faster than GAP or Maxima for tiny inputs, and it remains much faster than GAP for larger inputs as well. Apparently Maxima uses a fast algorithm unlike GAP, but my code is still about twice as fast as Maxima for huge n due to an algorithmic optimization.
sage: %timeit stirling_number2(10,5) 625 loops, best of 3: 2.33 µs per loop sage: %timeit stirling_number2(10,5,algorithm='gap') 25 loops, best of 3: 20 ms per loop sage: %timeit stirling_number2(10,5,algorithm='maxima') 5 loops, best of 3: 40 ms per loop 625 loops, best of 3: 16.2 µs per loop sage: %timeit stirling_number2(100,50,algorithm='gap') 25 loops, best of 3: 20 ms per loop sage: %timeit stirling_number2(100,50,algorithm='maxima') 5 loops, best of 3: 40 ms per loop sage: %timeit stirling_number2(2000,1500) 25 loops, best of 3: 35.9 ms per loop sage: %timeit stirling_number2(2000,1500,algorithm='gap') 5 loops, best of 3: 348 ms per loop sage: %timeit stirling_number2(2000,1500,algorithm='maxima') 5 loops, best of 3: 210 ms per loop sage: %timeit stirling_number2(4000,3000) 5 loops, best of 3: 249 ms per loop sage: %timeit stirling_number2(4000,3000,algorithm='gap') 5 loops, best of 3: 2.96 s per loop sage: %timeit stirling_number2(4000,3000,algorithm='maxima') 5 loops, best of 3: 948 ms per loop sage: %time stirling_number2(20000,15000); CPU times: user 20.30 s, sys: 0.23 s, total: 20.53 s Wall time: 21.82 s sage: %time stirling_number2(20000,15000,algorithm='maxima'); CPU times: user 0.00 s, sys: 0.01 s, total: 0.01 s Wall time: 51.90 s
Mathematica seems to be about as slow as GAP (warning: timed on a different system):
In[1]:= Timing[StirlingS2[4000,3000];] Out[1]= {27.1809, Null}
Attachments (3)
Change History (20)
comment:1 Changed 10 years ago by
- Status changed from new to needs_review
comment:2 Changed 10 years ago by
comment:3 Changed 10 years ago by
Oops, my editor was set to "strip trailing whitespace when saving files".
comment:5 Changed 10 years ago by
- Milestone set to sage-4.5.3
- Reviewers set to Nathann Cohen
Nice one !!
I learned many things while reviewing this patch :-)
Would you mind adding this small doctest in the patch I attach ? If not, you can set this ticket to "positive_review" !
Thanksssssssssssss !!!
Nathann
Changed 10 years ago by
comment:6 Changed 9 years ago by
Are you around ? There's basically nothing to do on this patch :-)
Nathann
comment:7 Changed 9 years ago by
- Reviewers changed from Nathann Cohen to Nathann Cohen, Nicolas Borie
- Status changed from needs_review to positive_review
The two patch applied on 4.5.3 All tests pass, no warning in docbuild... Nice documentation, powerful implantation... Good job!
I give the two patch a positive review.
For the release manager, please apply :
- stirling2.patch
- trac_9663 - additional test.patch
comment:8 follow-up: ↓ 11 Changed 9 years ago by
- Milestone changed from sage-4.6 to sage-4.6.1
I think you should add a patch with a test for "unknown algorithm".
comment:9 Changed 9 years ago by
- Status changed from positive_review to needs_work
comment:10 Changed 9 years ago by
Also, please do not put spaces in patch filenames.
comment:11 in reply to: ↑ 8 ; follow-up: ↓ 12 Changed 9 years ago by
Replying to jdemeyer:
I think you should add a patch with a test for "unknown algorithm".
What do you mean ?
Nathann
comment:12 in reply to: ↑ 11 Changed 9 years ago by
comment:13 follow-up: ↓ 14 Changed 9 years ago by
- Status changed from needs_work to needs_review
Here is a new version of my patch with the requested doctest.
Nathann
comment:14 in reply to: ↑ 13 Changed 9 years ago by
- Reviewers changed from Nathann Cohen, Nicolas Borie to Nathann Cohen, Nicolas Borie, Jeroen Demeyer
- Status changed from needs_review to needs_work
Replying to ncohen:
Here is a new version of my patch with the requested doctest.
Nathann
On line 670, TESTS::
should be TESTS:
(the :: should precede a block of code, which is not the case here).
Changed 9 years ago by
comment:16 Changed 9 years ago by
- Status changed from needs_review to positive_review
comment:17 Changed 9 years ago by
- Merged in set to sage-4.6.1.alpha0
- Resolution set to fixed
- Status changed from positive_review to closed
Please explain the *massive* number of changes to module_list.py of the form: