two y-axes with different scaling
Joerg
I want to combine two 2-D plots into one.
However, I want to have two different
y-axes. One on the left and one two the right,
with different ticklabels, respectively.
How do I do that? I couln't find any
example in the help files.
Thanks,
joerg
Jaccard Florian
If you look in the archives, you will see that this question has often come around.
There are several ways of doing it.
For example "by hand" (to plot y=sin(x) and y=3cos(x) with same looking amplitude):
d1 = Plot[{Sin[x], Cos[x]}, {x, 0, 10}, PlotRange -> {{0, 10}, {-1, 1}},
PlotStyle -> {Blue, Red}, Epilog -> {Text[Style["Sin(x)", FontColor -> Blue],
{2, 0.8}, Background -> White], Text[Style["3 Cos(x)", FontColor -> Red],
{5.2, 0.8}, Background -> White]}, DisplayFunction -> Identity];
Show[FullGraphics[d1] /. {{GrayLevel[0.], AbsoluteThickness[0.125],
Line[{{0., b_}, {c_, d_}}]} -> {Red, AbsoluteThickness[0.125],
Line[{{10, b}, {10 + c, d}}]}, Text[a_, {b_, c_}, {1., 0.}] ->
{Text[Style[3*a, FontColor -> Red], {b + 10, c}, {-1.5, 0}],
Text[Style[a, FontColor -> Blue], {b, c}, {1, 0}]}},
Graphics[{Red, Line[{{10, -1}, {10, 1}}]}], PlotRange -> {{-1.5, 12}, {-1.1, 1.1}}]
Or using what was on http://support.wolfram.com/mathematica/graphics/2d/twoaxisgraph.html (but I can't find it anymore) :
TwoAxisPlot[{f_, g_}, {x_, min_, max_}, frange_, grange_, (opts___)?OptionQ] :=
Module[{old, new, scale, pts, gstuff, fstuff}, {fm, fM} = frange;
{gm, gM} = grange; scale[var_] = ((var - gm)*(fM - fm))/(gM - gm) + fm;
old = AbsoluteOptions[Plot[g, {x, min, max}, Frame -> True, PlotRange -> grange,
DisplayFunction -> Identity], FrameTicks][[1,2,2]];
new = (Prepend[Rest[#1], scale[First[#1]]] & ) /@ old;
Plot[{f, scale[g]}, {x, min, max}, Frame -> True,
PlotRange -> frange + {0, 0.05*(fM - fm)}, FrameTicks ->
{Automatic, Automatic, None, new}, PlotStyle ->
{{Thickness[0.01], RGBColor[1, 0, 0]}, {Thickness[0.01], RGBColor[0, 1, 0]}},
FrameStyle -> {{}, {RGBColor[1, 0, 0]}, {}, {RGBColor[0, 1, 0]}}, opts]]
Example :
v[t_] := 3*t - 2
s[t_] := (3/2)*t^2 - 2*t
TwoAxisPlot[{v[t], s[t]}, {t, -10, 12}, {-50, 50}, {-100, 200},
GridLines -> {Range[-10, 12, 2], None},
Epilog -> {Text["v(t)", {-5, -20}, Background -> White],
Text["s(t)", {-8, 20}, Background -> White]}]
Regards
F.Jaccard
________________________________
David Park
One method is to use Frame -> True, and FrameTicks -> tick specification,
and give your own specification for the ticks on the right hand side of the
plot. (Lookup Ticks to see how to make these specifications.) You can use
Automatic for the regular ticks and make a table for the right hand side.
However, sometimes this is a lot of work, especially if you want both the
major and minor ticks.
The curve that goes with the right hand side will also have to be scaled to
match the ticks.
The Presentations package from my web site has CustomTicks routines that
make it easy to produce any kind of tick scale that is a 1-1 mapping from
the underlying plot coordinates, with linear or log ticks. It also makes it
easy to combine curves from two or more plot types. (And many other
features.)
I think there is also a free TwoScalePlot package on the WRI MathSource that
may also be useful - but I don't know much about it.
David Park
djm...@comcast.net
http://home.comcast.net/~djmpark/
hayes...@gmail.com
The best thing I have found for customizing graphics is David Park's
Presentations package. It is hands down one of the best and most
practical third party applications.
Check out:
http://home.comcast.net/~djmpark/DrawGraphicsPage.html
http://blackbook.mcs.st-and.ac.uk/~Peter/djmpark/html/
Hope that helps. Unfortunately the TwoAxisListPLot is no longer
available (from what I understand) and extending ListPlot to include
an arbitrary number of differently scaled functions isn't readily
transparent to me using the standard plots.
Cheers,
t.
dimitris
Something like...
Plot[{Sin[x], Cos[x]}, {x, -Pi, Pi},
Frame -> {True, True, False, True}, Axes -> False,
FrameLabel -> {"x axis", "y1 axis", None, "y2 axis"},
FrameStyle -> {Automatic, Green, None, Orange},
FrameTicks -> {Range[-2*Pi, 2*Pi, Pi/2], Range[-1, 1, 0.5], None,
Range[-1, 1, 0.5]}]
???
Dimitris
Bob F
Found this on the www.advancedphysics.org web site from a jbiggs2: (at
http://www.advancedphysics.org/forum/showthread.php?t=9228 ) which
works when I tried it on my Mac version 7 of Mathematica:
TwoAxisPlot[{f_, g_}, {x_, x0_, x1_}, color1_, color2_,
opts : OptionsPattern[]] :=
Module[{f0, f1, g0, g1, gp, scale, gticks}, {f0, f1} =
Options[Plot[f, {x, x0, x1}, Frame -> True, opts], PlotRange][[1,
2, 2]];
{g0, g1} =
Options[gp = Plot[g, {x, x0, x1}, Frame -> True, opts],
PlotRange][[1, 2, 2]];
scale[y_] := f0 + ((f1 - f0) (y - g0))/(g1 - g0);
gticks =
Apply[{scale[#1], ##2} &,
AbsoluteOptions[gp, FrameTicks][[1, 2, 2]], {1}];
Plot[{f, scale[g]}, {x, x0, x1}, PlotRange -> 1.001 {f0, f1},
Frame -> True,
FrameTicks -> {{Automatic, gticks}, {Automatic, Automatic}},
PlotStyle -> {{color1}, {color2}},
FrameStyle -> {{color1, color2}, {{}, {}}}, opts]]
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][[1]],
Map[scale, Transpose[g][[2]], {1, 2}]}];
ListLinePlot[{f, newg}, Frame -> True,
FrameTicks -> {Automatic, Automatic, None, new},
PlotStyle -> {{color1}, {color2}},
FrameStyle -> {{}, {color1}, {}, {color2}},
PlotRange -> frange*(1 + .05 (fM - fm)), opts]]
for example, with
TwoAxisPlot[{Sin[x], 0.1 Cos[x]}, {x, -\[Pi], \[Pi]}, Red, Blue]
and
TwoAxisListPlot[Table[{x, Sin[x]}, {x, -\[Pi], \[Pi], .01}],
Table[{x, 0.1 Cos[x]}, {x, -\[Pi], \[Pi], .01}], {-1., 1}, {-0.2,
0.2}, Red, Blue]
-Bob
dh
Hi Joerg,
see e.g.:
http://groups.google.com/group/comp.soft-sys.math.mathematica/msg/90cbe68c4c78f9b0
Daniel
Tugrul Temel
Do I have to buy the "Presentations" package or is it available for free? If
free, could you please send me web address?
Regards,
Tugrul