#11837: Make Newton basin plotting fun and easy
---------------------------+------------------------------------------------
Reporter: kcrisman | Owner: jason, was
Type: enhancement | Status: new
Priority: major | Milestone:
Component: graphics | Keywords: fractal newton complex plot
Work_issues: | Upstream: N/A
Reviewer: | Author: Karl-Dieter Crisman, SImon King
Merged: | Dependencies:
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Changes (by newvalueoldvalue):
* author: Karl-Dieter Crisman => Karl-Dieter Crisman, SImon King
Comment:
I just attached [attachment:newton_basins_more_cython.spyx], which
improves the timing by a factor of almost 100:
With the original version of the code together with the `2./3`, I get
{{{
sage: %time basin_plot([-1,i,1],(-3,3),(-3,3),plot_points=100,figsize=7)
CPU times: user 13.70 s, sys: 0.00 s, total: 13.70 s
Wall time: 13.74 s
}}}
With the code that I just attached, I get
{{{
sage: %time basin_plot([-1,i,1],(-3,3),(-3,3),plot_points=100,figsize=7)
CPU times: user 0.15 s, sys: 0.00 s, total: 0.15 s
Wall time: 0.15 s
}}}
How is that done?
Apparently, the optimization should mainly take place in `which_root`.
Since it is not possible to turn it into a fast_callable, I cythonised it
instead. More precisely, I introduced a cdef'd class `RootFinder`, that
carries all relevant data (the list of roots, the function newtf and also
the cutoff 2/3) as a cdef'd attribute.
Originally, the function f1 is a lambda function (slow!) that calls the
Python function `which_root` (slow!) by providing two arguments, where the
first argument is always the same (redundant!). I replaced it by the
method `Finder.which_root`, where `Finder` is an appropriate instance of
`RootFinder`.
Inside `which_root`, further improvements happened:
* First of all, the list of roots is transformed into a list of complex
doubles (because, in your original example, the complex unit `i` is a
symbolic expression, not a complex double, which was responsible for the
slowness).
* Moreover, Cython is informed that the list of roots is a list, and that
both the root and "varia" are complex doubles.
* We know that all our complex doubles have the same parent. Hence, we
avoid the parental tests that are part of `__sub__` and call `_sub_`
instead (single underscore).
* Since the `counter` loop is rather tight, `counter` is declared as an
int.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11837#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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