Re: Problem plotting high-order Laguerre polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg63864] Re: Problem plotting high-order Laguerre polynomials
- From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
- Date: Fri, 20 Jan 2006 04:32:18 -0500 (EST)
- Organization: Uni Leipzig
- References: <dqn7br$l3v$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
a) Plot[] need an evaluate around the full
argument, i. e.
Plot[Evaluate[func] /. n -> 40, {q, 0, 30},
PlotRange -> All]
is use less, because Plot[] need the Evaluate[]
and not
ReplaceAll[]
b) try a higher precision with
func[n_Integer, qin_?NumericQ] :=
With[{q = SetPrecision[qin, 200]}, 1/Pi Exp[-
q^2] LaguerreL[n, 2 q^2]
]
Plot[func[40, q], {q, 0, 30}, PlotRange -> All]
Regards
Jens
"Elinor K. Irish" <eirish at pas.rochester.edu>
schrieb im Newsbeitrag
news:dqn7br$l3v$1 at smc.vnet.net...
| 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
|