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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 ]
 Michael B. Heaney Posts: 16 Registered: 1/10/11
Re: dark halo around gaussian peak in Plot3D?
Posted: Mar 9, 2013 5:26 AM

Thanks!

On Fri, Mar 8, 2013 at 2:58 PM, Bob Hanlon <hanlonr357@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@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
> > ----------------------------------------------------------
> >

>

--
----------------------------------------------------------
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