#7730: hessenberg_form hangs (or is *very* slow)
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Reporter: spancratz | Owner: spancratz
Type: defect | Status: new
Priority: minor | Milestone:
Component: algebra | Keywords: matrices, hessenberg form
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by spancratz):
I spent some more time on this. The attached file `x2.sage` as before a
method `test_problem()`. To find out when things turn from acceptably
slow to ridiculously slow, I added one term after the other to the
numerator polynomial of ``a`` (in the notation as before). I think the
two elements ``b`` and ``c`` display the problem quite well, exhibiting
vastly different timings despite ``c`` only including one additional
monomial term:
{{{
sage: x,a,b,c,y = test_problem()
sage: timeit('_ = b*y', number=1, repeat=1)
1 loops, best of 1: 1.5 s per loop
sage: timeit('_ = c*y', number=1, repeat=1)
1 loops, best of 1: 1.79e+13 ns per loop
}}}
By the way, the second timing is about 4.97 hours and the output
``1.79e+13 ns`` should perhaps be improved. Is the ``timeit`` command
something imported from an outside package (and thus _perhaps_ difficult
to change), or something that can easily be changed within the Sage code?
Anyway, I am a little puzzled about this problem at the moment as I don't
quite see how the implementation of this should be this sensitive to the
input. I'll try to break it down to the level of multiplications and GCDs
next.
Finally, regarding the computation of ``a*y``, which I had started on
another machine, well, I terminated it this morning after running for 180
hours and a peak memory usage of over 1.1GB.
Sebastian
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7730#comment:5>
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