#13196: GL(n, GF(q)).random_element() is way too slow for what it does
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Reporter: Bouillaguet | Owner:
joyner
Type: enhancement | Status:
needs_review
Priority: major | Milestone:
sage-5.2
Component: performance | Resolution:
Keywords: matrix group, finite field, random element | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Charles Bouillaguet | Merged in:
Dependencies: | Stopgaps:
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Description changed by jlopez:
Old description:
> GL(32, GF(2)).random_element() takes more than 10s, which is ridiculous.
>
> Proposed solution : use simple rejection sampling (i.e. generate a random
> matrix, check if it invertible, if not try again). The result is
> uniformly distributed amongst invertible matrices.
>
> Before patch:
> {{{
> sage: %time GL(64, GF(2)).random_element()
> 5 loops, best of 3: 15.5 s per loop
> }}}
>
> After patch :
> {{{
> sage: %timeit GL(64, GF(2)).random_element()
> 625 loops, best of 3: 2ms per loop
> }}}
New description:
GL(32, GF(2)).random_element() takes more than 10s, which is ridiculous.
Proposed solution : use simple rejection sampling (i.e. generate a random
matrix, check if it invertible, if not try again). The result is uniformly
distributed amongst invertible matrices.
Before patch:
{{{
sage: %time GL(64, GF(2)).random_element()
5 loops, best of 3: 15.5 s per loop
}}}
After patch :
{{{
sage: %timeit GL(64, GF(2)).random_element()
625 loops, best of 3: 2ms per loop
}}}
Apply [attachment: gln_gfq_random.patch] and [attachment:
trac_13196.improvement.patch]
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13196#comment:18>
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