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[Help-gsl] Re: ODE IV Control and Variable Scale

From: Tuomo Keskitalo
Subject: [Help-gsl] Re: ODE IV Control and Variable Scale
Date: Mon, 22 Mar 2010 19:26:26 +0200
User-agent: Thunderbird (X11/20090817)


sorry, I did not understand your case correctly the first time. I often want to make sure that (fast) changes in variable values are followed precisely (my problems tend to be stiff) and therefore use eps_rel dominantly. You are right that eps_rel may well be 0. Depends on your problem.

On 03/22/2010 04:48 PM, Kevin H. Hobbs wrote:

On 03/20/2010 03:18 PM, Tuomo Keskitalo wrote:

about ODE solver error tolerances: you _never_ want to set eps_rel to
zero. It would mean that you allow no error for the ODE solver, which is
something no numerical method can give you.

The ODE example program sets eps_rel to 0.0.

As an example: gsl_odeiv_control_y_new (1e-12, 1e-8) means that if the
absolute value of a variable drops below 1e-12, you don't really care of
it's value any more (it is essentially zero for you).

Right now I'm setting eps_abs to something like 1.0e-3.

As far as I can tell from the documentation there's nothing special
about a variable value of 0.0 when eps_rel is 0.0. 1.0e-3 is the same as
0.0 and 100 + 1.0e-3 is the same as 100.

I want a constant error across the range of the variables.

eps_rel = 1e-8
means that you want at least 7 decimals of each variable to be accurate
on each ODE solver step. If you need to control the level of error with
more detail, then you can use a_y, a_dydt and scale_abs.

The trouble I have with these parameters is they depend on 0.0 being a
special value, but in my model there is nothing special about 0.0 for
most of the variables.

Voltage is the major example. Membrane voltage ranges from the reversal
potential for potassium E_K = -80 mV to the reversal potential of sodium
E_Na = 50 mV. The values of membrane voltage where the various membrane
currents turn on and off are the critical values, but there are many of
them and they are spread across the voltage range.

A practical way to choose tolerances is to make a test and compare
results calculated with "strict" and "loose" eps_abs and eps_rel (order
of magnitude difference between strict and loose). If you get nearly
same values as result, you are probably safe to use your loose
tolerances. Of course, this depends on your problem, so be sure to test
it with your final computation case again.

We have a whole graduate student devoted to this testing right now.

If you are not interested in optimizing the performance, I'd suggest you
simply try to use control_y_new and see how it works for you.

We are very much interested in performance since we're trying to
evaluate millions of models per day.

It appears that by using gsl_odeiv_control_scaled_new with scales
proportional to the range of each variable, eps_rel = 0.0, a_y = 0.0,
and a_dydt = 0.0 we can relax eps_abs and evaluate more models with
greater accuracy.


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