Re: plotminmax written/query for Jacobian functions

[Juhana Sadeharju <kouhia@nic.funet.fi>]

>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