[SciPy-User] odeint python and mathematica

[Mark P]

In the Python routine:
	- number of time step evaluations 	50,000
	- number of function evaluations 	120,000

In the Mathematica routine:
	- time steps 					231,770
	- function evaluations 			500,000

I'm not sure how to work out the relative and absolute error tolerances, but I did set the 'atol' in Python to a number just before the answer became inaccurate and it did speed it up 2.5x but still 4x slower than Mathematica.

Thank you,

Mark


On 2010-02-10, at 10:58 AM, Nasser Mohieddin Abukhdeir wrote:

> Hello Mark:
>     I am quite new to Python and Scipy, but I have some experience with SciPy's ODE functionality and it has been comparable to compiled code, depending on my implementation of the integrand. There are a few important parameters for the integrator that you should take into account in order to assure a fair comparison. Based upon odeint's default values, you should confirm that the relative and absolute error tolerances are the same for both computations. Something else that is important is the integration scheme, it looks like both methods use LSODA, so it should be an even comparison. Can you rerun both simulations and check the number of time steps and function evaluations from each implementation?
> 
> 
> Nasser Mohieddin Abukhdeir
> Postdoctoral Fellow (Vlachos Research Group)
> University of Delaware - Department of Chemical Engineering
> (Personal Web Page) http://udel.edu/~nasser/
> (Group Web Page)    http://www.dion.che.udel.edu/
> 
> On Wed, 2010-02-10 at 09:08 -0600, scipy-user-request at scipy.org wrote:
> 
>> Message: 5
>> Date: Wed, 10 Feb 2010 10:08:29 -0500
>> From: Mark P <m.perrin at me.com>
>> Subject: [SciPy-User] odeint (python vs mathematica)
>> To: Scipy <scipy-user at scipy.org>
>> Message-ID: <18B95518-6CA6-4C5F-BB57-3BBECC863C0B at me.com>
>> Content-Type: text/plain; charset="us-ascii"
>> 
>> Hello all,
>> 
>> (my first post to the list)
>> 
>> I have been performing modelling of ionic currents in Mathematica for the past three years as a student. I have recently passed into the hallowed halls of post-grad, and am keen to be done with Mathematica and use a free and open solution for my projects, hence Python and numpy/scipy. 
>> 
>> I've made some progress with the transition; the cookbooks are especially helpful. There is one in particular I have been looking at - the rabbit/fox model ( Lotka-Volterra Tutorial), that is helping me to understand odeint.
>> 
>> =====
>> from numpy import *
>> import pylab as p
>> # Definition of parameters
>> a = 1.
>> b = 0.1
>> c = 1.5
>> d = 0.75
>> def dX_dt(X, t=0):
>>     """ Return the growth rate of fox and rabbit populations. """
>>     return array([ a*X[0] -   b*X[0]*X[1] ,
>>                   -c*X[1] + d*b*X[0]*X[1] ]) 
>> 
>> from scipy import integrate
>> 
>> t = linspace(0, 10000,  10000)              # time
>> X0 = array([10, 5])                     		# initials conditions: 10 rabbits and 5 foxes
>> X = integrate.odeint(dX_dt, X0, t)
>> ===
>> 
>> A simple form of this code in Mathematica is:
>> 
>> ===
>> a = 1
>> b = 0.1
>> c = 1.5
>> d = 0.75
>> 
>> eqn1 := r'[t] == a * r[t] - b * r[t] * f[t]
>> eqn2 := f'[t] == -c * f[t] + d * b * r[t] * f[t]
>> 
>> solution = NDSolve[{eqn1, eqn2, r[0] == 10, f[0] == 5}, {r[t], f[t]}, {t, 0, 10000}, MaxSteps -> Infinity]
>> ===
>> 
>> My question is about speed. When computed in Mathematica 7 the code is roughly about 10x faster than odeint (I've increased t from 15 in the cookbook to 10000 to allow the measurement of speed to be made). But I know from the web that numpy/scipy can be of an equivalent or faster speed. I was wondering whether the solution can be sped up; and would that require the use of C or Fortran.
>> 
>> I see the inherent advantage of using Python with numpy/scipy and I do not expect the speeds of a compiled language but I was hoping for equivalent speeds to other interpreted solutions.
>> 
>> Thank you,
>> 
>> Mark Perrin
>> Electrophysiology Research Fellow
>> Ottawa
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