#18312: Construction of a sparse matrix from sparse vectors does not exploit
sparseness
---------------------------------------------+------------------------
Reporter: nthiery | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.7
Component: linear algebra | Resolution:
Keywords: sparse matrix constructor | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by nthiery):
* keywords: => sparse matrix constructor
Old description:
> {{{
> sage: n = 10^3
> sage: F = FreeModule(QQ, n, sparse=True)
> sage: v = F.an_element()
> sage: vectors = [v]*n
>
> sage: %time a = matrix(vectors, sparse=True)
> CPU times: user 2.01 s, sys: 38.4 ms, total: 2.05 s
> Wall time: 1.96 s
> }}}
>
> Compare with the construction of the same matrix through an
> intermediate dictionary:
>
> {{{
> sage: %time b = matrix(QQ, n, {(i,j): c for i,v in enumerate(vectors) for
> j,c in v.iteritems()}, sparse=True)
> CPU times: user 7.33 ms, sys: 124 µs, total: 7.46 ms
> Wall time: 6.06 ms
> sage: a == b
> True
> }}}
>
> Running `%prun` shows that the input vectors are converted to dense
> lists and back (gasp), which gives a complexity of `n^2` instead of
> linear in the number of nonzero entries as would be expected.
New description:
{{{
sage: n = 10^3
sage: F = FreeModule(QQ, n, sparse=True)
sage: v = F.an_element()
sage: vectors = [v]*n
sage: %time a = matrix(vectors, sparse=True)
CPU times: user 2.01 s, sys: 38.4 ms, total: 2.05 s
Wall time: 1.96 s
}}}
Compare with the construction of the same matrix through an
intermediate dictionary:
{{{
sage: %time b = matrix(QQ, n, {(i,j): c for i,v in enumerate(vectors) for
j,c in v.iteritems()}, sparse=True)
CPU times: user 7.33 ms, sys: 124 µs, total: 7.46 ms
Wall time: 6.06 ms
sage: a == b
True
}}}
Running `%prun` shows that the input vectors are converted to dense
lists and back (gasp!), which gives a complexity of `n^2` instead of
linear in the number of nonzero entries as would be expected.
See also: #10312
--
--
Ticket URL: <http://trac.sagemath.org/ticket/18312#comment:1>
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