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Re: dark halo around gaussian peak in Plot3D?

• To: mathgroup at smc.vnet.net
• Subject: [mg130102] Re: dark halo around gaussian peak in Plot3D?
• From: "Michael B. Heaney" <mheaney at alum.mit.edu>
• Date: Sat, 9 Mar 2013 05:27:04 -0500 (EST)
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• References: <20130308035122.485BC6797@smc.vnet.net>

Thanks!

On Fri, Mar 8, 2013 at 2:58 PM, Bob Hanlon <hanlonr357 at gmail.com> wrote:

> You don't really care about the tails, so use a Boole factor to suppress
> them.
>
> With[{r = 40},
>   Table[
>    Plot3D[
>     Evaluate[
>      PDF[BinormalDistribution[{m, 0}, {1, 1}, 0], {x, y}]*
>       Boole[(x - m)^2 + y^2 < 25]],
>     {x, -r, r}, {y, -r, r},
>     PlotRange -> {{-r, r}, {-r, r}, {0, 0.15}},
>     PlotPoints -> 100,
>     PlotLabel -> StringForm["m = ``", m],
>     ImageSize -> 300], {m, -40, 40, 10}]] // Column
>
>
> Bob Hanlon
>
>
> On Fri, Mar 8, 2013 at 5:38 PM, Michael B. Heaney <mheaney at alum.mit.edu>
> wrote:
> > Hi Bob,
> >
> > Thanks for your reply. I need results that far out on the tail because I
> am
> > making a series of figures where a travelling gaussian moves from one
> side
> > of the graph to the other side of the graph, and I want each figure to
> show
> > the entire graph. Are there any workarounds?
> >
> > Thanks,
> >
> > Michael
> >
> >
> > On Fri, Mar 8, 2013 at 2:19 PM, Bob Hanlon <hanlonr357 at gmail.com> wrote:
> >>
> >> Table[
> >>    Plot3D[
> >>     Evaluate[
> >>      PDF[BinormalDistribution[0], {x, y}]],
> >>     {x, -n, n}, {y, -n, n},
> >>     PlotRange -> All,
> >>     PlotPoints -> 50,
> >>     PlotLabel -> StringForm["n = ``", n],
> >>     ImageSize -> 300],
> >>    {n, {5, 10, 15, 20, 37, 40}}] //
> >>   Partition[#, 2] & // Grid
> >>
> >> The problem starts at about 20 standard deviations and stops at about
> >> 37 standard deviations out on the tail. These are really small values.
> >> Presumably, this is a precision issue that stops when the algorithms
> >> just give up and call the results zero.
> >>
> >> Table[
> >>  PDF[BinormalDistribution[0], {n, n}] // N,
> >>  {n, {20, 37, 40}}]
> >>
> >> {3.0480870817634576*^-175, \
> >> 4.494427778507250610367056211787865772187`15.954589770191005*^-596,
> >>    2.1411598269883908369272155013252852`15.954589770191005*^-696}
> >>
> >> However, even extreme WorkingPrecision does not appear to resolve the
> >> issue
> >>
> >> With[{n = 40},
> >>  Plot3D[
> >>   Evaluate[PDF[BinormalDistribution[0], {x, y}]],
> >>   {x, -n, n}, {y, -n, n},
> >>   PlotRange -> All,
> >>   PlotPoints -> 50,
> >>   PlotLabel -> StringForm["n = ``", n],
> >>   ImageSize -> 300,
> >>   WorkingPrecision -> 2000,
> >>   PerformanceGoal -> "Quality"]]
> >>
> >> Perhaps then the question is: why do you need results that far out on
> the
> >> tail?
> >>
> >> Or you could work with the Log of the function
> >>
> >> With[{n = 40},
> >>  Plot3D[
> >>   Evaluate[
> >>    Log[PDF[BinormalDistribution[0], {x, y}]] //
> >>     PowerExpand],
> >>   {x, -n, n}, {y, -n, n},
> >>   PlotRange -> All,
> >>   PlotPoints -> 50,
> >>   PlotLabel -> StringForm["n = ``", n],
> >>   ImageSize -> 600]]
> >>
> >>
> >> Bob Hanlon
> >>
> >>
> >> On Fri, Mar 8, 2013 at 11:06 AM, Michael B. Heaney <
> mheaney at alum.mit.edu>
> >> wrote:
> >> > Here is simple example that demonstrates the problem:
> >> >
> >> > Plot3D[PDF[BinormalDistribution[0], {x, y}], {x, -40, 40}, {y, -40,
> 40},
> >> >
> >> >  PlotRange -> All, PlotPoints -> 200]
> >> >
> >> > Thanks,
> >> >
> >> > Michael
> >> >
> >> >
> >> > On Thu, Mar 7, 2013 at 8:49 PM, Bob Hanlon <hanlonr357 at gmail.com>
> wrote:
> >> >>
> >> >> I don't see a "dark halo" with the following
> >> >>
> >> >> Plot3D[
> >> >>  PDF[BinormalDistribution[0], {x, y}],
> >> >>  {x, -3, 3}, {y, -3, 3}]
> >> >>
> >> >> Can you send a simple example that demonstrates the problem?
> >> >>
> >> >>
> >> >> Bob Hanlon
> >> >>
> >> >>
> >> >> On Thu, Mar 7, 2013 at 10:51 PM, Michael B. Heaney
> >> >> <mheaney at alum.mit.edu>
> >> >> wrote:
> >> >> >
> >> >> > Hi,
> >> >> >
> >> >> > When I plot a gaussian peak in Plot3D, there is a dark halo around
> >> >> > the
> >> >> > peak. Why is this? How can I get rid of it?
> >> >> >
> >> >> > Thanks,
> >> >> >
> >> >> > Michael
> >> >> >
> >> >> > --
> >> >> > ----------------------------------------------------------
> >> >> > Michael B. Heaney
> >> >> > 3182 Stelling Drive
> >> >> > Palo Alto, CA 94303 USA
> >> >> > mheaney at alum.mit.edu
> >> >> > www.linkedin.com/in/michaelbheaney
> >> >> > ----------------------------------------------------------
> >> >> >
> >> >> >
> >> >
> >> >
> >> >
> >> >
> >> > --
> >> > ----------------------------------------------------------
> >> > Michael B. Heaney
> >> > 3182 Stelling Drive
> >> > Palo Alto, CA 94303 USA
> >> > mheaney at alum.mit.edu
> >> > www.linkedin.com/in/michaelbheaney
> >> > ----------------------------------------------------------
> >> >
> >
> >
> >
> >
> > --
> > ----------------------------------------------------------
> > Michael B. Heaney
> > 3182 Stelling Drive
> > Palo Alto, CA 94303 USA
> > mheaney at alum.mit.edu
> > www.linkedin.com/in/michaelbheaney
> > ----------------------------------------------------------
> >
>



-- 
----------------------------------------------------------
Michael B. Heaney
3182 Stelling Drive
Palo Alto, CA 94303 USA
mheaney at alum.mit.edu
www.linkedin.com/in/michaelbheaney
----------------------------------------------------------

• References:
  • dark halo around gaussian peak in Plot3D?
    • From: "Michael B. Heaney" <mheaney@alum.mit.edu>