#19340: Better interface for hadamard_matrix
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/19340 | a5a4bbff80f2aed2a5b549d6b64f215967bc5ec7
Dependencies: | Stopgaps:
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Comment (by dimpase):
Replying to [comment:21 fredrik.johansson]:
> That part of the tests amounts to approximately 0.000% of the total
running time.
>
> In any case, a constant factor anywhere in the code doesn't
fundamentally change the imbalance between testing and generating, as you
suggested above.
as you imagine, I didn't profile this change. Still, it removes `O(n^2)`
multiplications and comparisons. If you prefer to keep them in your code,
it is up to you.
>
> The reason testing is far slower is not a factor 2 inefficiency (or even
a factor 6 or whatever from not using BLAS) in the matrix multiplication,
but the fact that constructing a Hadamard matrix is only {{{O(n^2)}}}
while testing is {{{O(n^omega)}}}.
On a good BLAS, the speed-up is a function of the number of cores
available... Then, as we know, the devil is in the constants; if matrices
were optimised for the task at hand, you would only have started to notice
on 10000x10000 matrices, not on 1000x1000.
Anyhow, this is an academic discussion.
--
Ticket URL: <http://trac.sagemath.org/ticket/19340#comment:22>
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