Re: Want to plot list with modified x-axis.

• To: mathgroup at smc.vnet.net
• Subject: [mg20526] Re: [mg20440] Want to plot list with modified x-axis.
• From: "Wolf, Hartmut" <hwolf at debis.com>
• Date: Sat, 30 Oct 1999 00:13:48 -0400
• Organization: debis Systemhaus
• References: <199910260433.AAA05990@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```I. Ioannou schrieb:
>
> Hi all,
>
> I've been trying to plot a list which comes out of a table (a string of
> 10K numbers basically) with modified x-axis. If I were to "listplot", I'd
> get the x-axis to go from 0 to 10,000. I want to scale that by a physical
> factor and plot that way instead.
>
---x---

Well, John, ListPlot can alternatively accept a List of {x,y} pairs. So
if you specifiy for every y the corresponding 'physical' x-value, you'll
get what you want.

---x---
>
> Back to my original question, how can I generate these plots? I also tried
> the standard Plot function. However, my function has a lot of sharp
> (resonant) features (Bessel functions) and I don't seem to be able to tell
> Mathematica to plot it properly. I need to fiddle with MaxBend,
> PlotPoints, PlotDivision. Any clarification on these would be wellcome, as
> the help files don't seem entirely clear to me.
>
> Thanks, John

This feature allows you to deal with different densities for sampling
points at interesting regions (e.g. if for some cause you are
unsatisfied with Plot's build-in sampling algorithm (but that -- to my
experience -- is very good), or for performance reasons or for whatever
reason. Let's make up an example:

In[17]:=
tab0 = Chop[Table[With[{x = i*Pi/10},
y /. FindRoot[x == -Sqrt[y*(2 - y)] +
ArcCos[1 - y], {y, x}]], {i, 0, 10}], 10^(-7)]

In[18]:=
tab1 = Join[Reverse[tab0], tab0];

This is with an aequidistant spacing of x-samples.

In[27]:=
showTab = Function[tab,
Show[Apply[ListPlot[tab, ##1, DisplayFunction ->
Identity] & ,
{{PlotStyle -> PointSize[0.015]},
{PlotStyle -> GrayLevel[0.5], PlotJoined ->
True}}, {1}], DisplayFunction ->
\$DisplayFunction]];

In[29]:=
showTab[tab1]

This may be a graph you're unsatisfied with, due to unhappy spacing of
the sampling points and missing accuracy. But if you define your points
in a parametrical fashion...

In[34]:=
tab2 = N[Table[{t - Sin[t], 1 - Cos[t]}, {t, -Pi, Pi, Pi/10}]]

...you'll get something much better (with no more sampling points).

In[35]:=
showTab[tab2]

Kind regards, Hartmut

```

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