#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: new
Priority: trivial | Milestone: sage-5.2
Component: group theory | 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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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: 929 µs per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13196>
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