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Topic: dark halo around gaussian peak in Plot3D?
Replies: 9   Last Post: Mar 10, 2013 12:47 AM

 Messages: [ Previous | Next ]
 Bob Hanlon Posts: 906 Registered: 10/29/11
Re: dark halo around gaussian peak in Plot3D?
Posted: Mar 9, 2013 5:25 AM

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@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@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@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@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@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@alum.mit.edu
>> >> > ----------------------------------------------------------
>> >> >
>> >> >

>> >
>> >
>> >
>> >
>> > --
>> > ----------------------------------------------------------
>> > Michael B. Heaney
>> > 3182 Stelling Drive
>> > Palo Alto, CA 94303 USA
>> > mheaney@alum.mit.edu
>> > ----------------------------------------------------------
>> >

>
>
>
>
> --
> ----------------------------------------------------------
> Michael B. Heaney
> 3182 Stelling Drive
> Palo Alto, CA 94303 USA
> mheaney@alum.mit.edu
> ----------------------------------------------------------
>

Date Subject Author
3/8/13 Bob Hanlon
3/8/13 Michael B. Heaney
3/9/13 David Reiss
3/9/13 Bob Hanlon
3/9/13 Bob Hanlon
3/9/13 Michael B. Heaney
3/9/13 David Park
3/10/13 Michael B. Heaney