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

