#7742: add a compose function to sage
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Reporter: was | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.6.1
Component: basic arithmetic | Keywords:
Author: Christopher Olah, Felix Lawrence | Upstream: N/A
Reviewer: Paul Zimmermann | Merged:
Work_issues: |
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Comment(by jrp):
Replying to [comment:19 flawrence]:
> With normal python functions (such as those in the doctest), the powers-
of-two provides a major speedup for large n over the other techniques I
tried, both for the function composition and for the evaluation of the
resulting function (benchmarked using "timeit"). In fact, without a
powers-of-two-type algorithm, the self_compose function regularly hit the
recursion limit and crashed for large n (above 500 or 1000).
I ran the following:
{{{
sage: def f(x):
....: return x + 1
....:
sage: g = self_compose(f,10000)
sage: g
<function <lambda> at 0xb0aa80c>
sage: timeit('g(0)')
25 loops, best of 3: 9.41 ms per loop
sage: timeit('nest(f,10000,0)')
125 loops, best of 3: 6.35 ms per loop
}}}
Since nest just loops through xrange and doesn't use powers of two, maybe
the slowdown before was due to the recursion. But in any case, it
definitely helps with the symbolic ones.
> The compose functions in the patch use lambda functions, which may or
may not break symbolic functions.
I'm attaching a patch to check for symbolic functions and (hopefully) do
the right thing. I also make self_compose(f,0) return the identity.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7742#comment:20>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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