[SciPy-User] Trajectory Integration via scipy.integrate or PyDSTool?

Rob Clewley rob.clewley@gmail....
Mon May 14 15:28:56 CDT 2012


Sara,

Your Hamiltonian system really requires a symplectic integrator or
similar, as Lou mentions, that truly respects energy conservation. A
regular ODE integrator will create numerical error in the total
energy, as it is oblivious. In lieu of such a thing, at the very least
you can make a correction at those detected events in your loop to
restore the total energy.

Anyway, regarding your installation. You should change your PATH to
point to whichever version of python you are using, i.e. the version
that has numpy, scipy etc. installed through EPD. It looks like you
are using a Mac, so if you've installed EPD you should point to that
version of python with your PATH. /sw/ is not a valid directory with
EPD. If EPD installs outside of the Mac Framework then you will need
to change the path, but if it uses the Framework python then there is
nothing to change.

Also, and I haven't given this much thought, but in the absence of a
geometric integrator, you could possibly even solve the system more
accurately as a differential-algebraic system (DAE), using the energy
constant as the algebraic constraint. But there might be more
mathematical problems with that approach that I'm not seeing (I'm not
an expert). At least you could try setting such a thing with the Radau
integrator in PyDSTool, and there are DAE examples provided.

Feel free to share your equations and code in more detail if you're
still struggling. With small integration steps you might be fine using
RK4 with the energy correction at boundaries.

-Rob

On Mon, May 14, 2012 at 2:12 PM, Sara Gallian <sara2411@gmail.com> wrote:
> Dear Lou,
> I'm just moving a bunch of electrons in a static b field
> dv/dt = q/m v x B
> B depends on the position, in general
> They move in this field, without interacting, till they bounce off a wall,
> that specularly reflects them
> Yes, the dynamic is conservative.
> I could just write a RK4 and check the position at every ts, but I was
> hoping to be able to use a better tool
> Thanks
> Sara
>
> Sent from my iPhone
>
> On 14.05.2012, at 20:03, Lou Pecora <lou_boog2000@yahoo.com> wrote:
>
> Hi, Sara,
>
> Can you give more information?
>
> Are the particles in a potential or is it free flight between hard wall
> collisions?  Do the particles interact?  I assume the dynamics are
> conservative (Hamiltonian). Is that correct?
>
> -- Lou Pecora, my views are my own.
> ________________________________
> From: Rob Clewley <rob.clewley@gmail.com>
> To: SciPy Users List <scipy-user@scipy.org>
> Sent: Monday, May 14, 2012 1:22 PM
> Subject: Re: [SciPy-User] Trajectory Integration via scipy.integrate or
> PyDSTool?
>
> Hi Sara,
>
> I think you should use a tool that's appropriate for the task. With an
> hour of work and help on this list or the PyDSTool forum at
> http://sourceforge.net/projects/pydstool/forums/forum/472291 you
> should be able to get your problem working quickly with PyDSTool. I
> expect your problem is easy to solve in PyDSTool, and difficult to do
> with odeint.
>
> You can still use scipy's VODE in PyDSTool and you won't need any
> fancy installation. Check out the file vode_event_test1.py in the
> tests directory. Writing the vector field is simple, but in case you
> have specific problems setting up yours then you should send me your
> code on list so that I can help. I'd be interested to see what the
> equations look like.
>
> It's very simple to define a terminal event, just copy and adapt the
> code in the file. You can write a loop so that whenever integration
> has stopped because of an event, you reverse the velocity IC and
> restart.
>
> -Rob
>
> On Mon, May 14, 2012 at 12:59 PM, Sara Gallian <sara2411@gmail.com> wrote:
>> Hi all,
>> I'm trying to integrate particle trajectories in a finite domain, and I
>> need to make them "reflect" at the boundaries (i.e. reverse the velocity
>> perpendicular to the plane they collided with). I started by using
>>  scipy.integrate.odeint , but since the integration steps are variable,
>> simply checking the position and reversing the velocity won't work!
>> Can anyone suggest the quickest way to obtain this? would Vode be able to
>> handle this, or should I try to learn to use  PyDSTool?
>> I'm running pretty late on a deadline, so any suggestion is more than
>> appreciated :)
>> Thanks!
>> Sara
>> _______________________________________________
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>
>
>
> --
> Robert Clewley, Ph.D.
> Assistant Professor
> Neuroscience Institute and
> Department of Mathematics and Statistics
> Georgia State University
> PO Box 5030
> Atlanta, GA 30302, USA
>
> tel: 404-413-6420 fax: 404-413-5446
> http://www2.gsu.edu/~matrhc
> http://neuroscience.gsu.edu/rclewley.html
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-- 
Robert Clewley, Ph.D.
Assistant Professor
Neuroscience Institute and
Department of Mathematics and Statistics
Georgia State University
PO Box 5030
Atlanta, GA 30302, USA

tel: 404-413-6420 fax: 404-413-5446
http://www2.gsu.edu/~matrhc
http://neuroscience.gsu.edu/rclewley.html


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