       Re: Multiple scales for Y axis of plot?

• To: mathgroup at smc.vnet.net
• Subject: [mg31110] Re: [mg31094] Multiple scales for Y axis of plot?
• From: BobHanlon at aol.com
• Date: Wed, 10 Oct 2001 03:43:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2001/10/9 3:01:33 AM, crcarle at sandia.gov writes:

>I have a typical multi-expression plot like this:
>
>Plot[ {f1, f2}, {x,a,b}, PlotStyle->{RGBColor[1,0,0], RGBColor[0,0,1]}
>].
>
>On the Y axis, I want to have a different scale for each of the two
>functions.  How can I generate another scaled Y axis adjacent to the
>default one, or in general acheive this sort of thing?  I anticipate a
>lengthy process of building up all the graphics primitives, but before
>I
>figure all that out, I'm wondering if there is a reasonably easy way.
>

This makes use of AbsoluteOptions so I believe it requires version 4 or later.

Needs["Graphics`Colors`"];

twoAxesPlot[{leftPlot_, rightPlot_},
{var_Symbol, varMin_?NumericQ, varMax_?NumericQ},
opts___] :=
Module[{lftPlt, rghtPlt, conv,
lftTicks, rghtTicks, tcks,
y, y1, y2, y3, y4},
lftPlt = Plot[leftPlot,
{var, varMin, varMax},
DisplayFunction -> Identity, opts];
lftTicks =
(Ticks /. AbsoluteOptions[lftPlt])[];
tcks = First /@ lftTicks;
y1 = Min[tcks];
y2 = Max[tcks];
rghtPlt = Plot[rightPlot,
{var, varMin, varMax},
DisplayFunction -> Identity, opts];
rghtTicks =
(Ticks /. AbsoluteOptions[rghtPlt])[];
tcks = First /@ rghtTicks;
y3 = Min[tcks];
y4 = Max[tcks];
rghtTicks = (rghtTicks /.
{y_?NumericQ, z__} :> {conv[y], z});
conv[y_] := (y-y3)*(y2-y1)/(y4-y3) + y1;
Plot[{leftPlot, conv[rightPlot]},
{var, varMin, varMax},
Frame -> True, Axes -> False,
PlotStyle -> {Blue, Red},
FrameStyle -> {{}, {Blue}, {}, {Red}},
FrameTicks ->
{Automatic, lftTicks, None, rghtTicks},
PlotRange ->
{y1-0.02(y2-y1), y2+0.02(y2-y1)},
DisplayFunction -> \$DisplayFunction,
opts]
];

twoAxesPlot[{x, Exp[x]}, {x, 0, 10}];

Bob Hanlon
Chantilly, VA  USA

```

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