I am currently trying to improve the performance in the PR
https://github.com/sympy/sympy/pull/16509
To complete my gsoc proposal should i write the way i am trying to improve
the performance and how i have planned to proceed ?

Because the idea of benchmarking and performance mainly involves trying to
find suitable substitute for a bottleneck.

On Sat, Mar 30, 2019 at 1:29 AM Shiksha Rawat <[email protected]>
wrote:

> Okay, i have continued the discussion on the issue itself.
>
> On Sat, Mar 30, 2019 at 12:06 AM Aaron Meurer <[email protected]> wrote:
>
>> On Fri, Mar 29, 2019 at 12:07 PM Shiksha Rawat <[email protected]>
>> wrote:
>> >
>> > Thank you for the replies.
>> >
>> > As suggested by Aaron , I figured out ways to fix the performance of
>> https://github.com/sympy/sympy/issues/16249.
>> > One of the easy way is to disable _find_localzeros
>> > The function is creating a set of non-minimal(non-maximal) numbers and
>> to identify these it is making comparison between every two possible
>> combination of numbers.
>> > But these non-minimal values can be computed by sorting the values in
>> ascending or descending order.
>> > This sorting can be done by using algorithms like merge-sort with
>> complexity (nlogn) which is much better than currently used n**2.
>> > So second option is to use better algorithms.
>> >
>> > Which would be better or which one should i use to fix this issue?
>> >  Please suggest.
>>
>> It depends on what the performance is like, and what the tradeoffs
>> are. Often when trying to make something faster you may think that
>> something will improve performance, but after implementing it you'll
>> find that it doesn't change it at all, or it even makes it worse. So
>> you always have to try it out and profile it.
>>
>> It would be better to move the discussion of this specific issue to
>> the issue itself.
>>
>> Aaron Meurer
>>
>> >
>> > I am also trying to find regressions on which i could work in
>> https://github.com/sympy/sympy_benchmarks.
>> >
>> > On Thu, Mar 28, 2019 at 9:38 PM Jason Moore <[email protected]>
>> wrote:
>> >>
>> >> We have a benchmark repository that is run periodically:
>> https://github.com/sympy/sympy_benchmarks
>> >>
>> >> I recommend starting there. You can find a number of regressions that
>> can be investigated.
>> >>
>> >> Jason
>> >> moorepants.info
>> >> +01 530-601-9791
>> >>
>> >>
>> >> On Wed, Mar 27, 2019 at 5:17 PM Aaron Meurer <[email protected]>
>> wrote:
>> >>>
>> >>> I agree with Oscar. I would also add that it's usually not trivial to
>> >>> determine where the bottlenecks are in SymPy. So I would write more
>> >>> about how you intend to profile the code.
>> >>>
>> >>> Perhaps it would be useful to take an existing thing that is slow in
>> >>> SymPy (you can use the performance issue label as a guide, or find
>> >>> something yourself,
>> >>>
>> https://github.com/sympy/sympy/issues?q=is%3Aopen+is%3Aissue+label%3APerformance
>> ),
>> >>> and try to fix the performance, documenting how you went about finding
>> >>> the bottleneck and fixing it. This can be used as a case study in your
>> >>> application.
>> >>>
>> >>> Also I would note that currently the benchmarking infrastructure for
>> >>> SymPy is quite bad (basically nonexistent). See
>> >>>
>> https://github.com/sympy/sympy/wiki/GSoC-2019-Ideas#benchmarks-and-performance
>> .
>> >>> It's fine if you do not want to work on that specifically, but you
>> >>> should note that you will be running the benchmarks on your own
>> >>> computer to find performance regressions. Not all performance issues
>> >>> are regressions either (some things have always been slow), so you
>> >>> should consider absolute numbers as well as relative numbers.
>> >>>
>> >>> Aaron Meurer
>> >>>
>> >>> On Wed, Mar 27, 2019 at 5:11 PM Oscar Benjamin
>> >>> <[email protected]> wrote:
>> >>> >
>> >>> > This looks like good work to do. I don't know how these applications
>> >>> > are evaluated but my thought if I was reviewing this would be that
>> it
>> >>> > seems quite vague. This would probably be a more enticing proposal
>> if
>> >>> > it had some specific suggestions of changes that would speed things
>> >>> > up.
>> >>> >
>> >>> > I can tell you now what is slow in the ODE module: currently even
>> for
>> >>> > the simplest ODEs all matching code is run for all the possible
>> >>> > methods even after a suitable method has been found. It would be
>> much
>> >>> > better to identify the most immediately usable solver and then use
>> >>> > that without matching all the others. This needs a refactor of the
>> >>> > module though and a redesign of the basic approach used by dsolve. I
>> >>> > want that to happen as an ultimate goal but I would like to see
>> better
>> >>> > test coverage first.
>> >>> >
>> >>> > On Wed, 27 Mar 2019 at 09:56, Shiksha Rawat <
>> [email protected]> wrote:
>> >>> > >
>> >>> > >
>> https://github.com/sympy/sympy/wiki/GSoC-2019-Application-SHIKSHA-RAWAT-:-Benchmarks-and-performance
>> >>> > >
>> >>> > > I have designed a proposal for Benchmarks and Perfromance idea,
>> though it is not complete yet.
>> >>> > >
>> >>> > > Can Jason Moore, Aaron and Oscar please review that and suggest
>> changes?
>> >>> > >
>> >>> > >
>> >>> > > On Tue, Mar 19, 2019 at 11:53 PM Shiksha Rawat <
>> [email protected]> wrote:
>> >>> > >>
>> >>> > >> I did further digging on the idea mentioned by Jason Moore.
>> >>> > >>
>> >>> > >> Figuring out the main bottlenecks for sympy : The best way to
>> figure out these bottlenecks would be to designing a typical problem for
>> each module for example mass spring damper for physics and computing time
>> taken by sympy to give the output.If it is greater then expected than or a
>> predefined threshold than analyzing the codebase of that module for
>> possible changes to decrease computation time. And the results of
>> predefined benchmarks could also be used.
>> >>> > >>
>> >>> > >> Creating benchmarks :
>> https://media.readthedocs.org/pdf/asv/v0.1.1/asv.pdf
>> >>> > >> I think this documentation could come in handy for creating the
>> benchmarks. The requirement of a particular benchmark could be made on the
>> basis of the bottlenecks which we will figure out.
>> >>> > >>
>> >>> > >> Improving performance:  I think the best way to improve
>> performance would be cleaning up the codebase first and then making changes
>> in the algorithms used according to the requirements.
>> >>> > >>
>> >>> > >> Future Scope: Figuring out a method by which each PR also has to
>> give information about the time the modules related to that PR will take to
>> give output of problems associated with that module. (those mentioned in
>> figuring out the bottlenecks point).
>> >>> > >>
>> >>> > >> I might be wrong about the ideas mentioned above. So I want
>> suggestions from the mentors.
>> >>> > >>
>> >>> > >> Thanks.
>> >>> > >>
>> >>> > >> On Fri, Mar 15, 2019 at 9:48 PM Shiksha Rawat <
>> [email protected]> wrote:
>> >>> > >>>
>> >>> > >>> I am really interested in taking up that idea. Can you suggest
>> where or how should I start from because up till now I was just focusing on
>> the physics module and benchmarks related to it?
>> >>> > >>> I am still trying to find how could we optimize matrix
>> operations.
>> >>> > >>>
>> >>> > >>>
>> >>> > >>> On Fri, Mar 15, 2019 at 8:46 PM Jason Moore <
>> [email protected]> wrote:
>> >>> > >>>>
>> >>> > >>>> The mechanics speedup idea is really just a narrow version of
>> the profiling and benchmarking idea (focuses on just a couple of packages).
>> Maybe a proposal that focuses on figuring out the main bottlenecks for
>> sympy, creating benchmarks for them, and then improving performance is a
>> good proposal idea that will ultimately help all the packages. I'm happy to
>> support and mentor on that idea if someone wants to submit.
>> >>> > >>>>
>> >>> > >>>> Jason
>> >>> > >>>> moorepants.info
>> >>> > >>>> +01 530-601-9791
>> >>> > >>>>
>> >>> > >>>>
>> >>> > >>>> On Thu, Mar 14, 2019 at 2:19 PM Aaron Meurer <
>> [email protected]> wrote:
>> >>> > >>>>>
>> >>> > >>>>> I agree. The biggest challenge with symbolic matrices is
>> expression
>> >>> > >>>>> blow up. In some cases it is unavoidable, for instance,
>> symbolic
>> >>> > >>>>> eigenvalues/eigenvectors use the symbolic solutions to
>> polynomials,
>> >>> > >>>>> which are complicated in the general case for n > 2.
>> >>> > >>>>>
>> >>> > >>>>> One thing I meant by "overhead" is that if the type of a
>> matrix's
>> >>> > >>>>> entries is known to all be rational numbers, for instance, we
>> can
>> >>> > >>>>> operate directly on those numbers, ideally using fast number
>> types
>> >>> > >>>>> like gmpy.mpq. If they are all rational functions, we can use
>> >>> > >>>>> polynomial algorithms that operate on rational functions.
>> These always
>> >>> > >>>>> keep rational functions in canonical form, and the zero
>> equivalence
>> >>> > >>>>> testing becomes literally "expr == 0" (no simplification
>> required).
>> >>> > >>>>> These can be more efficient than general symbolic
>> manipulation.
>> >>> > >>>>>
>> >>> > >>>>> This is how the polys module is structured. See
>> >>> > >>>>> https://docs.sympy.org/latest/modules/polys/internals.html.
>> It would
>> >>> > >>>>> be nice to have a similar structure in the matrices, where a
>> matrix
>> >>> > >>>>> can have a ground domain (or type) associated with its
>> underlying
>> >>> > >>>>> data.
>> >>> > >>>>>
>> >>> > >>>>> Aaron Meurer
>> >>> > >>>>>
>> >>> > >>>>> On Thu, Mar 14, 2019 at 2:52 PM Oscar Benjamin
>> >>> > >>>>> <[email protected]> wrote:
>> >>> > >>>>> >
>> >>> > >>>>> > (Replying on-list)
>> >>> > >>>>> >
>> >>> > >>>>> > On Thu, 14 Mar 2019 at 20:37, Alan Bromborsky <
>> [email protected]> wrote:
>> >>> > >>>>> > >
>> >>> > >>>>> > > Since most pc these days have multiple cores and threads
>> what not use
>> >>> > >>>>> > > parallel algorithyms.  For honesty I must state I have a
>> vested interest
>> >>> > >>>>> > > since I have a pc with a threadripper cpu with 16 cores
>> and 32 threads.
>> >>> > >>>>> >
>> >>> > >>>>> > Parallel algorithms can offer improvement. Your 16 cores
>> might amount
>> >>> > >>>>> > to a 10x speed up if used well for this kind of thing. The
>> >>> > >>>>> > double-threading probably can't be exploited in CPython.
>> >>> > >>>>> >
>> >>> > >>>>> > However I think that many of the things that SymPy is slow
>> for have
>> >>> > >>>>> > *really* bad asymptotic performance: think O(N!) rather
>> than O(N^2).
>> >>> > >>>>> > Many orders of magnitude improvements can be made by
>> spotting these
>> >>> > >>>>> > where more efficient methods are possible. It's not hard in
>> a CAS to
>> >>> > >>>>> > accidentally generate enormous expressions and end up
>> simplifying them
>> >>> > >>>>> > down again. This leads to many situations where it would be
>> vastly
>> >>> > >>>>> > more efficient to somehow take a more direct route.
>> >>> > >>>>> >
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