
Re: dark halo around gaussian peak in Plot3D?
Posted:
Mar 9, 2013 5:25 AM


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

