#8096: Speed up parent creation for multiplication of square matrices
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Reporter: boothby | Owner: boothby
Type: enhancement | Status: needs_info
Priority: minor | Milestone:
Component: linear algebra | Keywords:
Work_issues: various doc test errors | Upstream: N/A
Reviewer: | Author: boothby, robertwb
Merged: | Dependencies:
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Comment(by malb):
One more data point.
Again, this is with #9562:
{{{
#!python
sage: MS = MatrixSpace(GF(64,'a'),5000,5000)
sage: %time A = MS.random_element()
CPU times: user 0.46 s, sys: 0.01 s, total: 0.46 s
Wall time: 0.47 s
sage: B = MS.random_element()
sage: %time C = A*B
CPU times: user 22.69 s, sys: 0.06 s, total: 22.75 s
Wall time: 22.84 s
}}}
Note that we only implemented Travolta for GF(2^6^) so far. With Karatsuba
we expect to get close to 4.5 seconds, because:
{{{
#!python
sage: A = random_matrix(GF(2),5000,5000)
sage: B = random_matrix(GF(2),5000,5000)
sage: %timeit C=A*B
5 loops, best of 3: 249 ms per loop
}}}
and the best known formula for degree 5 polynomials needs 17 such
multiplications:
http://www.csd.uwo.ca/~eschost/Exam/Montgomery
--Five_six_and_seven_terms_Karatsuba-like_formulae.pdf
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8096#comment:27>
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