> Hopefully your maximum step size and your tabulation step size are much > larger than the step size sometimes used by the adaptive integrator. > Here forcing results to come back at a fixed spacing forces you not to > capture this signal properly in your graphs. This seems really > unfortunate, you may have correctly integrated a complicated action > potential and then you draw a graph which completely misses it! This > seems really bad. Isn't it much better is to concentrate your line > segments in your graph in exactly the same places where the adaptive > step size system found your solution to be complicated?
yes. unless you need simulation results at exact values for whatever reason. > If an integrator produces "different" results depending on the > tabulation step size then it sounds as if it hasn't converged and so the > adaptive step size isn't working, maybe your maximum step size needs to > be further reduced for the problems you point out about missing the > important part? If your tabulation is a multiple of your maximum step > size as you suggested then I can't understand how this can happen. > (I do realise that there are probably a number of models that are > dependent on not being converged.) Sorry, maybe I wasn't clear enough. Its not that your integration results are different or not converged (assuming your maximum step size is reasonable), the problem is the representation of the simulation results that you are left with following the integration will be different. I agree, ideally you want to have simulation data stored/drawn/whatever say every 10 steps so you get high resolution where it is needed. But depending on what you want to do with the simulation results you may also want to be able to get simulation results evenly spaced in the bound variable(s) domain. > And if your integration solution is affected by the tabulated result > spacing what if you don't want tabulated results? You just want the end > integration, then you have to tell your integrator to generate some > special tabulation just to get the same final state from your model? I think I answered this above. The tabulation interval should definitely not affect the actual results - only the maximum step size should do that - it just changes the representation of the results. For this example I'd imagine just setting the tabulation step size to take you to the end point in one step. > After thinking about where the interpolation should be performed, I > expect that most integrators will end up interpolating somehow to > generate values at the exact grid you specified, I do agree that the > integrator may be able to give a far more accurate interpolation, as > presumably it has a far finer set of values than the ones returned as > results, however requiring a grid, specified in the model metadata, > doesn't seem the best way to specify this. Certainly most of the integrators I use internally maintain a history of integration information to specifically allow such interpolation (within reason). I think the distinction here (which has only just started to occur to me, sorry for being a bit slow this morning) is that for the specification of the bound variable interval in a given simulation, the start, end, and maximum step size values control the actual numerical integration of the model. Whereas the tabulation information (however we want to specify it) governs the representation of the simulation results that you are left holding at the completion of the simulation. In general, the tabulation specification is probably not all that important for any given simulation. Where it does start to become crucial is in the comparison of simulation results, either in the comparison of different models or the comparison of results from the same simulation using different tools. So does this mean it shouldn't be in the simulation metadata specification? I still don't see where else it could be. Although given it is an optional property of a simulation and tools are not forced to obey it when it is present I see no harm having it present. This then allows tools to use that information if required to produce a very specific representation of the simulation results. > I didn't even bring this up yesterday as I was ignored last time I > brought it up, but it really seems wrong to me to be forcing your > integrator to give results on a grid in every case, and even more > concerning to me if as you suggest, the performance of your model is > dependent on this grid. See comments above. I think we are only forcing the integrator to give results on a grid if a specific representation of the simulation results is required. > However I am not a user or intended user of these ODE integrators. My > experience only comes from the ODE integrator that I maintain in CMGUI > which is for tracking streamlines and streaklines. > So if I am outvoted I'll just take my concerns back into my hole. you can't do that - you've convinced me now to stop blindly following the tabulation step size unless I need to for some reason....who knows what your next reply will accomplish? Andre. _______________________________________________ cellml-discussion mailing list [email protected] http://www.cellml.org/mailman/listinfo/cellml-discussion
