Re: Problem plotting high-order Laguerre polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg63925] Re: Problem plotting high-order Laguerre polynomials
- From: Peter Pein <petsie at dordos.net>
- Date: Sun, 22 Jan 2006 00:52:42 -0500 (EST)
- References: <dqn7br$l3v$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hello Elinor, for plotting, Ted Ersek's PrecisionPlot-package http://library.wolfram.com/infocenter/MathSource/715/ does a very good job: << "PrecisionPlot`" func[n_] := LaguerreL[n, 2*#1^2]/(E^#1^2*Pi) & f40 = Compile[{{q, _Real}}, Evaluate[FunctionExpand[func[40][q]]]]; Show @@ Block[{$DisplayFunction = #1 & }, {Plot[f40[q], {q, 0, 11}, PlotRange -> {-0.1, 0.1}, PlotStyle -> Red], PrecisionPlot[f40[q], {q, 0, 11}, PlotRange -> {-0.1, 0.1}, PlotStyle -> Blue]}] Peter Elinor K. Irish schrieb: > Hi folks, > I'm doing some work which involves plotting fairly high-order Laguerre > polynomials, up to 200 or so. I've been getting some very strange and > obviously incorrect results which seem to have to do with the order of > evaluation. (I'm using Mathematica 5.0, but I've checked it in 5.2 and I > get the same problems.) Here are some examples with a simple form of the > type of function I'm working with: > > func = 1/Pi Exp[- q^2] LaguerreL[n, 2 q^2] > > These commands work, displaying the expected oscillatory result: > > Plot[func /. n -> 40, {q, 0, 30}, PlotRange -> All] > Plot[Evaluate[func] /. n -> 40, {q, 0, 30}, PlotRange -> All] > > This form, however, results in a big mess which isn't even bounded correctly: > > Plot[Evaluate[func /. n -> 40], {q, 0, 30}, PlotRange -> All] > > I don't know whether this is a bug or if there's a subtlety of > Plot/Evaluate/etc. which I don't understand. I would very much like to be > able to use Evaluate on my functions before plotting them, because my > actual calculations involve complicated sums over expressions like that > above and take a LONG time to plot. (With Evaluate, a single plot takes > about 20 minutes; without it the same plot takes nearly 4 hours.) > > Could anyone shed some light on this problem? I have more examples, > including some involving sums, which I can give if needed. I've been > fighting with this issue for a long time... > > Thanks, > Elinor > > > > ______________________________ > Elinor K. Irish > Dept. of Physics and Astronomy > University of Rochester > Rochester, NY 14627 USA > eirish at pas.rochester.edu >