Juhana Sadeharju on Sun, 2 Sep 2001 22:31:55 +0300 |
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Re: plotminmax written/query for Jacobian functions |
>From: Ilya Zakharevich <ilya@math.ohio-state.edu> > >Then plotminmax() also shows a wrong graph. There is no way to find a >correct graph. > >The difference is that plot() *always* shows the correct *values* at >the grid points; while plotminmax() *time to time* shows a usable >*C^O-approximation to the graph* of the function. I actually took the idea to minmax plot from audio signal editors where it is important to identify the peaks of the signal. If editors would not use minmax drawing, user would not have any idea about the true signal, because aliasing is so heavy. Yes, plotminmax() would show weird graphs when we are looking at high frequency sine wave (screen would have full of *'s), but in otherhand that would be perfectly correct graph if we are interested in finding what values the function gets, not where they are got. I hope you will find minmax plot useful too. I guess I could implement minmax plot to X and PS functions as well. >need more parameters). The agressive oversampling (64x) you use does >not help with "correctness", but would disable this usage. 64 was just random selection. It could be a parameter in plotminmax() but I wasn't sure how to add parameters to GP functions. I just replaced plot() when I tested the function; it was easier that way. Sure an automatic method for oversampling would be better. But I'm out of ideas. minmax mode converges to a fixed graph without recomputation, but the check of convergence should be local for best results. For example, the oversampling value 64 is global even only narrow peaks needs it. Anyway, the routine may still miss narrow peaks. Regards, Juhana