       Re: ListLogLinearPlot with two y-axis

• To: mathgroup at smc.vnet.net
• Subject: [mg102575] Re: [mg102559] ListLogLinearPlot with two y-axis
• From: "David Park" <djmpark at comcast.net>
• Date: Sat, 15 Aug 2009 05:32:54 -0400 (EDT)
• References: <26148220.1250245897619.JavaMail.root@n11>

```Here is an example of a two-axis log-linear plot using Presentations. We
plot the two functions Sqrt[n] and n^2 over the domain 1 to 100 on a log
scale. n^2 is scaled to fit in the Sqrt[n] range and a custom tick scale is
generated for it on the right hand side of the frame. n^2 and its ticks are
shown in red. Since we are dealing with underlying graphics primitives we
also have to construct our own log tick scale for the n axis.

Needs["Presentations`Master`"]

The following generates two sets of data points for the functions.

domainpoints = Union[Range[2, 20, 1]/2, 10 Range/2] // N;
dataset1 = Table[{n, Sqrt[n]}, {n, domainpoints}];
dataset2 =
Table[{n, Rescale[n^2, {0, 10000}, {0, 10}]}, {n, domainpoints}];

The following specifies the custom tick scales we need. One is a log scale
specifying the power range and the list of labeled and unlabeled ticks. The
second is a linear scale going from 0 to 10000 in steps of 2000 with 4
unlabeled intervals between the labeled ticks. The values are shown in Red.

xticks = CustomTicks[Log, {0, 2, {1, 2, 5}, {3, 4, 6, 7, 8, 9}}];
yticksright =
CustomTicks[Rescale[#, {0, 10000}, {0, 10}] &, {0, 10000, 2000, 4},
CTNumberFunction -> (Style[#, Red] &)];

The following draws the plot with a text label within the plot.

Draw2D[
{Text[Style["Two-Scale Plot", 14, Bold], Scaled[{.1, .9}], {-1, 0}],
ListLogLinearDraw[dataset1, Joined -> True],
Red, ListLogLinearDraw[dataset2, Joined -> True]},
AspectRatio -> .7,
Frame -> True,
FrameTicks -> {{Automatic, yticksright}, {xticks,
xticks // NoTickLabels}},
FrameLabel -> {{Sqrt[n], Style[n^2, Red]}, {n, None}},
RotateLabel -> False,
ImageSize -> 400]

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

Hi everybody,

I came across a solution for the plotting of continuous functions with
two y-axis. I also found code to plot two lists with different ranges
into one figure with two y-axis, but the thing I need is to plot two
lists into one figure with two y-axis where the x-axis is in log.

So, the solution for the lists looks like:

TwoAxisListPlot[f_List, g_List, frange_, grange_, color1_, color2_,
opts___?OptionQ] :=
Module[{old, new, scale, fm, fM, gm, gM, newg}, {fm, fM} = frange;
{gm, gM} = grange;
scale[var_] := ((var - gm) (fM - fm))/(gM - gm) + fm;
old = AbsoluteOptions[
ListPlot[g, Frame -> True, PlotRange -> grange,
DisplayFunction -> Identity], FrameTicks][[1, 2, 2]];
new = (Prepend[Rest[#1], scale[First[#1]]] &) /@ old;
newg =
Transpose[{Transpose[g][],
Map[scale, Transpose[g][], {1, 2}]}];
ListLinePlot[{f, newg}, Frame -> True,
FrameTicks -> {Automatic, Automatic, None, new},
PlotStyle -> {{color1}, {color2}},
FrameStyle -> {{}, {color1}, {}, {color2}},
PlotRange -> frange*(1 + .00 (fM - fm)), opts]]

And to plot the lists:

Labeled[Labeled[
TwoAxisListPlot[data1, data2, {5, 8.3}, {450, 460}, Red, Blue,
Axes -> False, Joined -> {True, False},
PlotMarkers -> {Style[\[EmptyCircle], Red, Medium,
Background -> White],
Style[\[FilledUpTriangle], Blue, Medium]} ], {Style["X",
FontFamily -> Times],
Style["Y", Red, FontFamily -> Times]}, {Bottom, Left}],
Style["Y-alt", Blue, FontFamily -> Times], Right]

I'm really not that a Mathematica Pro to translate this for my
purpose. Can anyone of you help me with this?
I would really appreciate it.

Thanks,

Pascal

```

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