#4260: use LinBox as native matrix representation for dense matrices over GF(p)
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Reporter: malb | Owner: cpernet
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: linear algebra | Keywords: linbox, linear algebra,
sd32
Work_issues: extend documentation | Upstream: N/A
Reviewer: | Author: Burcin Erocal, Martin
Albrecht, Rob Beezer
Merged: | Dependencies:
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Comment(by malb):
I adapted the crossover from {{{float}}} to {{{double}}}. Around 2^11^
{{{Modular<float>}}}} is '''really''' slow because there are not enough
bits left to let ATLAS do it's magic, i.e., too many modular reductions.
On my computer using {{{Modular<float>}}} up to 2^8^ seems like a good
choice. On sage.math this choice isn't too bad (but not optimal).
Multiplying two 1,000 x 1,000 matrices over GF(p) (2nd column) which is
smaller than 2^i^ (1st column) and the time it takes:
{{{
2 3 0.22000
3 7 0.24000
4 13 0.24000
5 31 0.25000
6 61 0.26000
7 127 0.26000
8 251 0.62000
9 509 0.38000 <=== using Modular<double> now
10 1021 0.38000
11 2039 0.39000
12 4093 0.39000
13 8191 0.40000
14 16381 0.41000
15 32749 0.41000
16 65521 0.42000
17 131071 0.43000
18 262139 0.43000
19 524287 0.44000
20 1048573 0.44000
21 2097143 0.45000
22 4194301 0.66000
23 8388593 1.91000 <=== Generic matrices
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4260#comment:15>
Sage <http://www.sagemath.org>
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