Re: Problem plotting high-order Laguerre polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg63868] Re: Problem plotting high-order Laguerre polynomials
- From: dh <dh at metrohm.ch>
- Date: Fri, 20 Jan 2006 04:32:21 -0500 (EST)
- Organization: Cablecom Newsserver
- References: <dqn7br$l3v$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Elinor,
plot the following:
Plot[LaguerreL[40, 2 q^2], {q, 2, 3}, PlotRange -> All]
Plot[Evaluate[LaguerreL[40, 2 q^2]], {q, 2, 3}, PlotRange -> All]
You will see that the second plot has numerical problems.
By default, Plot does not evaluate ist first argument (Attribute
HoldFirst). Therefore Plot gets the name of the function to evaluate
(LaguerreL) and then uses an appropriate algorithm to evaluate it.
On the other side, in the second example we force LaguerreL[40, 2 q^2]
to evaluate what gives a polynimial in q. Polynomial with high exponents
are numerically difficult and give errors (cancelation errors) as you
see in the example.
hope you succeed, Daniel
Elinor K. Irish wrote:
> 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
>