#12499: The density() function of a sparse matrix looks at every matrix entry
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Reporter: jason | Owner: jason, was
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: linear algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Changes (by ppurka):
* status: new => needs_review
Comment:
Replying to [ticket:12499 jason]:
> The implementation of the density method for a sparse matrix is insane.
It loops through every single index possible and asks if each entry is
zero or nonzero:
>
> {{{
> sage: A=matrix(5000,5000,{(1,2): 1})
> sage: A.density()
> 1/25000000
> }}}
Thanks for the idea. An implementation is in [attachment:trac_12499
-faster-sparse-matrix-density.patch]. It passes all doctests in
`devel/sage/sage/matrix`.
> An implementation that instead relied on `A.nonzero_positions()` would
be orders of magnitude faster.
The ''orders of magnitude'' turns out to be `10^7` (or 1 billion % in
market-speak ;)) for the above example:
{{{
sage: A=matrix(5000,5000,{(1,2): 1})
sage: timeit('A.density()')
5 loops, best of 3: 11.3 s per loop
sage: timeit('QQ(len(A.nonzero_positions()))/QQ(A.nrows()*A.ncols())')
625 loops, best of 3: 15.6 µs per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12499#comment:1>
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