Hello,
I'm still in my iteration challenges... I put pointers to itertools
wherever it is needed for speed (i.e. choose_nk, subset, subword) as
well as additional _fast_iterator in some combinatorial classes
(SetPartitions). But now, must of the iterator yield tuples and not
lists. The timing is better by a factor > 590 for the below example.
I think I will prepare a cleaned patch for this and submit it to Sage
trac, but you have to say to me if this is a problem that generators
(at least _fast_iterator versions of them) prefer tuples to lists.
Old versions timings
sage: S = SetPartitions(13,[5,4,4])
sage: x = S.__iter__()
sage: timeit('x.next()')
5 loops, best of 3: 1.77 ms per loop
New versions timings
sage: S = SetPartitions(19,[12,3,2,2])
sage: x = S._fast_iterator()
sage: y = S.__iter__()
sage: timeit('x.next()')
625 loops, best of 3: 124 µs per loop
sage: timeit('y.next()')
625 loops, best of 3: 710 µs per loop
And from this I get a reasonable iterator over conjugacy classes of
the symmetric group.
sage: x=conjugacy_class_iterator([3,3,3,3])
sage: timeit('x.next()')
625 loops, best of 3: 3.26 µs per loop
Just as a remark, the old version of SetPartitions was not able to
give me the FIRST element of SetPartitions(19, [12,3,3,2])...
Cheers,
Vincent
PS: As the speed gain is I think enough for my purpose, I won't go
further in iteration using the C/API and I put a #+experimental on the
corresponding patch. If you are interesting in going further in this
direction...
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