GSoC Week 9
Like I said in my last post, this was my first week in college after summer vacation. I had to reschedule my daily work according to my class timings (which are pretty arbitrary). Anyway, since I do not have a test anytime soon, things were manageable.
So Far
Ring Series
This week I worked on rs_series
in PR 9614.
As Donald Knuth succinctly said, ‘Premature optimisation is the root of all
evil’, my first goal was to write a function that used ring_series
to expand
Basic
expressions and worked in all cases. That has been achieved. The new
function is considerably faster than SymPy’s series
in most cases. eg.
In [9]: %timeit rs_series(sin(a)*cos(a)  exp(a**2*b),a,10)
10 loops, best of 3: 46.7 ms per loop
In [10]: %timeit (sin(a)*cos(a)  exp(a**2*b)).series(a,0,10)
1 loops, best of 3: 1.08 s per loop
However, in many cases the speed advantage is not enough, especially considering
that all elementary ring_series
functions are faster than SymPy’s series
functions by factors of 20100. Consider:
In [20]: q
Out[20]: (exp(a*b) + sin(a))*(exp(a**2 + a) + sin(a))*(sin(a) + cos(a))
In [21]: %timeit q.series(a,0,10)
1 loops, best of 3: 2.81 s per loop
In [22]: %timeit rs_series(q,a,10)
1 loops, best of 3: 3.99 s per loop
In this case, rs_series
is in fact slower than the current series
method!.
This means that rs_series
needs to be optimised, as expanding the same
expression directly with rs_*
functions is much faster.
In [23]: %timeit (rs_exp(x*y,x,10) + rs_sin(x,x,10))*(rs_exp(x**2+ x,x,10) + rs_sin(x,x,10))*(rs_sin(x,x,10) + rs_cos(x,x,10))
1 loops, best of 3: 217 ms per loop
I spent Friday playing with rs_series
. Since the function is recursive, I even
tried using a functional approach (with map, reduce, partial, etc). It was fun
exploring SymPy’s functional capabilities (which are quite decent, though
Haskell’s syntax is of course more natural). This didn’t make much difference in
speed. Code profiling revealed that rs_series
is making too many function
calls (which is expected). So, I plan to try a nonrecursive approach to see if
that makes much of a difference. Other than that, I will also try to make it
smarter so that it does not go through needless iterations (which it currently
does in many cases).
SymEngine
I had a discussion with Sumith about Polynomial wrappers. I am helping him
with constructors and multiplication. We both want the basic Polynomial
class
done as soon as possible, so that I can start with writing series expansion of
functions using it.
I also sent a PR 562 that adds C
wrappers for Complex
class. This will be especially helpful for Ruby wrappers
that Abinash is working on. FQA
is a nice place to read about writing C++/C wrappers and for some side
entertainment too.
Other than that, I also happened to have a discussion with
Harsh on the new solveset he and
Amit are working on. Their basic idea is that you
always work with sets (input and output) and that the user can choose what
domain he wants to work on. The latter idea is quite similar to what SymPy’s polys
does. Needless to say, their approach is much more powerful that solvers
’s. I
will be working with them.
Next Week
Targets for the next week are as modest as they are crucial:

Play with
rs_series
to make it faster. 
Finish Polynomial wrappers and start working on series expansion.
Cheers!
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