#10763: Speedup of matrix multiplication
------------------------------+---------------------------------------------
Reporter: SimonKing | Owner: jason, was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6.2
Component: linear algebra | Keywords: matrix multiplication
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* status: new => needs_review
* author: => Simon King
Comment:
I did not run the doc test yet, but I think it already ready for review.
Here are timings. Note that the reduced overhead is most visible when the
multiplication itself is trivial.
Without the patch:
{{{
sage: def test(M):
....: for i in xrange(10^6):
....: M*=M
....: return M
....:
sage: m = matrix(GF(3),[[1]])
sage: %time test(m)
CPU times: user 51.36 s, sys: 0.16 s, total: 51.52 s
Wall time: 51.67 s
[1]
sage: m = matrix(GF(2),[[1]])
sage: %time test(m)
CPU times: user 39.16 s, sys: 0.20 s, total: 39.36 s
Wall time: 39.47 s
[1]
sage: m = matrix(ZZ,[[1]])
# apparently there is no overhead for matrices over ZZ
sage: %time test(m)
CPU times: user 7.81 s, sys: 0.15 s, total: 7.96 s
Wall time: 7.99 s
[1]
}}}
With the patch
{{{
sage: def test(M):
....: for i in xrange(10^6):
....: M*=M
....: return M
....:
sage: m = matrix(GF(3),[[1]])
sage: %time test(m)
CPU times: user 33.65 s, sys: 0.30 s, total: 33.95 s
Wall time: 34.05 s
[1]
sage: m = matrix(GF(2),[[1]])
sage: %time test(m)
CPU times: user 25.41 s, sys: 0.10 s, total: 25.51 s
Wall time: 25.58 s
[1]
sage: m = matrix(ZZ,[[1]])
sage: %time test(m)
CPU times: user 7.62 s, sys: 0.16 s, total: 7.78 s
Wall time: 7.80 s
[1]
}}}
Thus, over `GF(3)` and `GF(2)` the overhead is clearly reduced.
I don't know how the patch could be doc-tested, as it only concerns the
performance.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10763#comment:1>
Sage <http://www.sagemath.org>
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