From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 7667 invoked by alias); 22 Mar 2010 17:26:35 -0000 Received: (qmail 7658 invoked by uid 22791); 22 Mar 2010 17:26:34 -0000 X-SWARE-Spam-Status: No, hits=-0.5 required=5.0 tests=AWL,BAYES_50,SARE_MILLIONSOF X-Spam-Check-By: sourceware.org Received: from filtteri1.pp.htv.fi (HELO filtteri1.pp.htv.fi) (213.243.153.184) by sourceware.org (qpsmtpd/0.43rc1) with ESMTP; Mon, 22 Mar 2010 17:26:29 +0000 Received: from localhost (localhost [127.0.0.1]) by filtteri1.pp.htv.fi (Postfix) with ESMTP id 4CF4718B3C3; Mon, 22 Mar 2010 19:26:27 +0200 (EET) Received: from smtp5.welho.com ([213.243.153.39]) by localhost (filtteri1.pp.htv.fi [213.243.153.184]) (amavisd-new, port 10024) with ESMTP id WYVGoYRNT-aM; Mon, 22 Mar 2010 19:26:26 +0200 (EET) Received: from [192.168.0.102] (cs27094158.pp.htv.fi [89.27.94.158]) by smtp5.welho.com (Postfix) with ESMTP id BFE9C5BC005; Mon, 22 Mar 2010 19:26:26 +0200 (EET) Message-ID: <4BA7A842.3020708@iki.fi> Date: Mon, 22 Mar 2010 17:26:00 -0000 From: Tuomo Keskitalo User-Agent: Thunderbird 2.0.0.23 (X11/20090817) MIME-Version: 1.0 To: "Kevin H. Hobbs" CC: gsl-discuss@sourceware.org, help-gsl@gnu.org Subject: Re: ODE IV Control and Variable Scale References: <4BA2707F.50105@ohiou.edu> <4BA51F85.4070305@iki.fi> <4BA78346.5060303@ohiou.edu> In-Reply-To: <4BA78346.5060303@ohiou.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org X-SW-Source: 2010-q1/txt/msg00065.txt.bz2 Hi, 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: >> Hi, >> >> 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. > -- Tuomo.Keskitalo@iki.fi http://iki.fi/tuomo.keskitalo