From: Joel VanderWerf <joelvanderwerf@...>
Date: 2010-05-29T05:08:35+09:00
Subject: Re: A better way to write this function?

Jason Lillywhite wrote:
> What if I needed more speed but still wanted it in Ruby?

Not quite pure ruby, but if it's acceptable to have a C backend, then 
you can use redshift. On my computer, if I create 20K of the objects 
below, they run (concurrently) at about "real" time, i.e. 1 sec process 
time per 1 sec simulation time. Also, it is more accurate than your 
integration algorithm, since it uses a higher-order Runge-Kutta 
integrator. Plus, there are other features suitable for 
discrete/continuous multi-agent simulation (algebraic equations, 
discrete state transitions, event synchronization, queues with 
pattern-matching like Erlang, dataflow ports like Simulink, link 
variables, delay flows, differentiation, interactive shell and 
debuggers, ...).

If you want to try this, unpack this tarball:

http://path.berkeley.edu/~vjoel/redshift/redshift-1.3.14.tgz

and put the lib dir on your RUBYLIB. Some of the examples expect gnuplot 
to be installed, but otherwise there are no deps.

However, you must be able to build extensions, i.e, have a working C 
compiler that is binary compatible with your ruby (gcc, msvc, and 
solaris work for me), so that redshift can translate the equations into 
C and compile them into ruby extensions. If native gems build on your 
system, you should be ok. Note that the first time you run a particular 
redshift program, there is a delay while this build happens (the build 
goes into a tmp dir under the current dir).

-----

require 'redshift'

class Thing < RedShift::Component
   continuous :v, :x
   constant :m, :c, :G # per-instance constants

   flow do
     # "differential" means Runge-Kutta 4th order integration; if
     # you replace that word with "euler", it uses forward Euler
     # integration, which gives exactly the same results as the
     # original poster's example. Usually, RK4 is significantly
     # more accurate than Euler.
     differential " v' = G - c/m * v "

     # just for fun, let's keep track of distance traveled
     differential " x' = v "
   end
end

world = RedShift::World.new
world.time_step = 0.1

thing = world.create Thing
thing.m = 10
thing.c = 0.01
thing.v = 0
thing.x = 0
thing.G = 9.8

p thing
world.evolve 5.0 do
   p thing
end

__END__

Output:

<<Thing 0>: Enter; G = 9.8, c = 0.01, m = 10.0; v = 0.0, x = 0.0>
<<Thing 0>: Enter; G = 9.8, c = 0.01, m = 10.0; v = 0.979951001633293, x 
= 0.0489983667075>
<<Thing 0>: Enter; G = 9.8, c = 0.01, m = 10.0; v = 1.95980401306601, x 
= 0.195986933986642>
...
...
<<Thing 0>: Enter; G = 9.8, c = 0.01, m = 10.0; v = 47.9025429248678, x 
= 117.457075132208>
<<Thing 0>: Enter; G = 9.8, c = 0.01, m = 10.0; v = 48.8777039117133, x 
= 122.296088286671>