       Re: dark halo around gaussian peak in Plot3D?

• To: mathgroup at smc.vnet.net
• Subject: [mg130098] Re: dark halo around gaussian peak in Plot3D?
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 9 Mar 2013 05:25:43 -0500 (EST)
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• References: <20130308035122.485BC6797@smc.vnet.net>

```Table[
Plot3D[
Evaluate[
PDF[BinormalDistribution, {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, {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, {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, {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, {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, {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
>> > ----------------------------------------------------------
>> >
>> >
>
>
>
>
> --
> ----------------------------------------------------------
> Michael B. Heaney
> 3182 Stelling Drive
> Palo Alto, CA 94303 USA
> mheaney at alum.mit.edu