>> you >> have a function of two variables that you can explicitly evaluate >> using your favourite route finding mechanism, and then use an >> approximation to avoid evaluating this at run time. This 2D >> approximation is pretty efficient and will be enough to solve this >> very basic case. But each non-linearity that is added increases the >> space by at least one dimension, so your function gets big very >> quickly and you have to start using a non-linear mapping into the >> space to keep things under control. > > > i haven't been able to decode what you just wrote.
This is important to understand if you want to use massive tables to model this stuff. Perhaps read Yeh's thesis paper? I have already posted this to another thread, but here it is again: "... but missed David Yeh's dissertation https://ccrma.stanford.edu/~dtyeh/papers/DavidYehThesissinglesided.pdf which contains a great description of MNA and how it relates to the DK-method. I highly recommend everyone read it, thanks David!! I really hope that an improved DK-method that handles multiple nonlinearities more elegantly that it currently does. A couple of things to note here, in general, this method uses multi-dimensional tables to pre-calculate the difficult implicit equations to solve the non-linearities, but as the number of non-linearities increases so does the size of your table as noted in 6.2.2: "The dimension of the table lookup for the stored nonlinearity in K-method grows with the number of nonlinear devices in the circuit. A straightforward table lookup is thus impractical for circuits with more than two transistors or vacuum tubes. However, function approximation approaches such as neural networks or nonlinear regression may hold promise for efficiently providing means to implement these high-dimensional lookup functions." " As you add more non-linearities to the circuit it becomes less practical to pre-calculate tables to handle the situation. Also changes caused by things like potentiometers add extra dimensions, and you will spend all your time doing very high dimensional table interpolation and completely blow the cache. > <sigh> it's a function. given his parameters, g and s, then x[n] goes in, > iterate the thing 50 times, and an unambiguous y[n] comes out. doesn't > matter what the initial guess is (start with 0, what the hell). i am saying > that *this* net function is just as deserving a candidate for modeling as is > the original tanh() or whatever. just run an offline program using MATLAB > or python or C or the language of your delight. get the points of that > function defined with a dense look-up-table. then consider ways of modeling > *that* directly. maybe leave it as a table lookup. whatever. but at least > you can see what you're dealing with and use that net function to help you > decide how much you need to upsample. <sigh> <sigh> <sigh> please at least try and understand what I wrote before sighing at me! Yes, I agree that for low dimensional cases this is a good approach, but for any realistic circuit things get complicated and inefficient really quickly and you are better off with other methods. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
