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MathGroup Archive 2004

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Re: ListDensityPlot (solution, and critical comment))

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49790] Re: ListDensityPlot (solution, and critical comment))
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Sat, 31 Jul 2004 03:14:12 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 7/30/04 at 6:02 AM, siegman at stanford.edu (AES/newspost) wrote:

>Answering my own question on this:  Adding PlotRange->All as an
>option to ListDensityPlot makes it function as it should.

>But, some further, and critical, commentary:  Seems to me this
>should be the _default_ for this function.

This merely trades one problem for a different problem. But it is easy to arrange for PlotRange->All to be the default for your usage. Simply place in the init.m file that Mathematica executes when you begin a session SetSoptions[ListDensityPlot, PlotRange->All]. Once done, PlotRange->All will the the default for you. This can be repeated for other plot functions where you might like this behaviour.

>If you make a Plot3D or ListPlot3D and the function goes off scale
>in the z direction, you can tell this from the plot: the peaks that
>go off scale are visibly cut off, have an obviously truncated or
>chopped-off flat top, where they protrude through the top of the
>box.  You receive a visible warning.

>With ListDensityPlot, this is not nearly so obvious -- you don't
>get nearly as obvious a visual indication that the plot has been
>truncated. I would never have realized it was happening if I didn't
>have the ListPlot3D and ListDensityPlot side by side.

>Further, haven't rechecked this, but I believe the Help for
>ListDensityPlot says ColorFunctionScaling->True is the default.  My
>arrays were not unusual -- didn't have any wild outliers, just a
>central tallest gaussian-like "big peak" covering 10% to 15% of the
>plot area, with some lower (i.e., 30% to 50% of peak height)
>secondary peaks around it.  Default conditions for ListDensityPlot
>should have scaled and handled them properly.  Instead, it brought
>the secondary peaks up to full scale (they would have been
>perfectly visible without doing this), and truncated the "big peak"
>with no warning.  Not good.

Consider what would happen with different data if PlotRange->All were the default. For example, I have an experiment where I measue optical power in dBm. I expect data to vary over a range of about 10 dB. This particular instrument gives me a output value of 9E+037 when values are out of range. With the default settings in Mathematica's plotting routines, such values are ignored and I see useful plots. With PlotRange->All, I single overrange value would cause the trend in the valid values to become unobservable. And if the power was expected to be constant, this could be interpreted as expected behaviour with potential problems going unnoticed. A single overrange value would be one point which would likely be unnoticed.

The point is, no matter what is chosen for the default graphic settings, there will be some dataset prone to misinterpretation with those particular settings. The only way to avoid misinterpretation of plots is to plot the data in several different ways. 
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