#16617: simple echelon matrix iterator
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.3
Component: linear algebra | Resolution:
Keywords: matrix | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/16617 | f3cc9b7a9979e164565df53fa11dd6f8647a6ee9
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:4 ncohen]:
> Helloooooooooooo !
>
> First of all, I don't get why you wrote this in Cython instead of
changing the old implementation... Does it change much to the performance
? I wonder if you wouldn't obtain the same crazy speedups simply caching
`m0` as you do and using itertools instead of `VectorSpace`.. Or is it
that you want to aviod the final matrix multiplication ?
The main speed up is to get rid of VectorSpaces. I do not want to use
them, so I need a `echelon_matrix_iterator`. Whether it is cython or not
is a matter of micro seconds, so I do not care that much (except that
using cython allows to set the cache of matrices with the pivot that can
be used later).
> Details:
>
> - It seems that what you do is iterate on *reduced* echelon form
it is!
> - Could you add a doctest like that ?
>
> {{{
> sage: q=71
> sage: F = GF(q)
> sage: len(list(echelon_matrix_iterator(F, 1, 3, copy=False))) ==
q**2+q+1
> True
> sage: len(list(echelon_matrix_iterator(F, 2, 3, copy=False))) ==
q**2+q+1
> True
> }}}
Of course.
> - I do not understand why you have to call {{{del}}} `O_o`
This is a crazy thing in the implementation of itertools. If the only
reference to the tuple is owned by the iterator then it is reused.
Otherwise you create a fresh one. What you gain is creation time of a
tuple...
{{{
sage: from itertools import product
sage: timeit("for p in product([0,1,2,3],[3,4,5,6],[1,2,3,4],[1,2,3,4]):
pass")
625 loops, best of 3: 21.9 µs per loop
sage: timeit("for p in product([0,1,2,3],[3,4,5,6],[1,2,3,4],[1,2,3,4]):
del p")
625 loops, best of 3: 7.81 µs per loop
}}}
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16617#comment:5>
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