Re: How to rescale the x-axis in an nonlinear way?

• To: mathgroup at smc.vnet.net
• Subject: [mg112464] Re: How to rescale the x-axis in an nonlinear way?
• From: "David Park" <djmpark at comcast.net>
• Date: Thu, 16 Sep 2010 06:00:48 -0400 (EDT)

```I don't know if I understand precisely what is wanted, but with the
Presentations package you could use CustomTicks. The problem is that one
needs the inverse function. Here is an example.

Needs["Presentations`Master`"]

x[t_] := 1 + 10^t - E^t

In the domain 0 < t < 2 this is monotonic so we can get the inverse function
with NDSolve.

Clear[t]
NDSolve[{t'[x] == 1/x'[t[x]], t[1] == 0}, t, {x, 1, 100}][[1, 1]];
t[x_] = t[x] /. %

Then a plot with the new x scale is:

xticks = CustomTicks[t, {0, 80, 10, 5}] // Quiet;
Draw2D[
{Draw[Tanh[x[t]], {t, 0, 2}, PlotRange -> All]},
Frame -> True,
AspectRatio -> 1,
PlotRange -> All,
FrameTicks -> {{Automatic, Automatic}, {xticks,
xticks // NoTickLabels}}]

I don't especially like it, but there it is.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Liyi Li [mailto:llybt.ebay at googlemail.com]

Hello, everyone,

I am trying to plot out some data and on the x-axis, which is a log-
like scale (acutally it is a different function).
For example, I want the x sacled like this: 1 + 10^x -  E^x, so as the
ticks.
How can I do that?

thank you.

```

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