11
$\begingroup$

I want to plot 

Plot[{Exp[x],Sin[x]},{x,0,10}]

The issue is that Sin[x] and Exp[x] are not of the same order of magnitude, so we do not see Sin[x]. Therefore, I would like to set different y-axis but on the same graph. For Exp[x], the y axis would go from 0 to 25000 and for Sin[x] from -1 to 1. How can I do that ?

|improve this question
$\endgroup$
  • 2
    $\begingroup$ Why do you need to plot curves with widely-varying ranges together? $\endgroup$ – J. M. will be back soon♦ Oct 8 '18 at 9:02
  • 1
    $\begingroup$ I have a case when I want to visualize the data and the log of the data. The curve is supposed to be an exponential at the beginning and vary linearly at the end. I want to see a linear evolution at the beginning with the log of the data, a linear evolution at the end with the data, and a transition area. I asked my question in a simple way, since the data is pretty big and that it's a general question $\endgroup$ – J.A Oct 8 '18 at 9:13
  • $\begingroup$ How about LogPlot? $\endgroup$ – Αλέξανδρος Ζεγγ Oct 8 '18 at 11:42
  • 1
    $\begingroup$ @ΑλέξανδροςΖεγγ: That won't work so well for a function that becomes negative, like Sin[x] does. (There are ways around this, of course.) $\endgroup$ – Michael Seifert Oct 8 '18 at 12:39
  • $\begingroup$ @MichaelSeifert Actually, it is about data rescaling. Admittedly, log function is not "good at" dealing with non-positive values, but it is not difficult to find a proper rescaling function to use. $\endgroup$ – Αλέξανδρος Ζεγγ Oct 9 '18 at 4:44
1
$\begingroup$

Rescaling the y-coordinates:

rescaleShow[p1_, p2_] := Module[{g1, g2, pr1, pr2, rs1, rs2},
   {g1, g2} = Cases[{p1, p2}, _Graphics, Infinity];
   {pr1, pr2} = Last /@ PlotRange /@ {g1, g2};
   rs1 = With[{pr = Last@PlotRange[g1]}, Rescale[#, pr] &];
   rs2 = With[{pr = Last@PlotRange[g2]}, Rescale[#, pr] &];
   Show[
    p1 /. Line[p_] :> Line[Transpose@MapAt[rs1, Transpose@p, 2]],
    p2 /. Line[p_] :> Line[Transpose@MapAt[rs2, Transpose@p, 2]],
    PlotRange -> {0, 1}, Frame -> True,
    FrameTicks -> {{Charting`FindTicks[{0, 1}, pr1], 
       Charting`FindTicks[{0, 1}, pr2]}, {Automatic, Automatic}}
    ]
   ];

OP's example:

rescaleShow[
 Plot[Exp[x], {x, 0, 10},
  PlotStyle -> ColorData[97][1], PlotLegends -> {HoldForm@Exp[x]}, 
  Frame -> True, PlotRange -> All],
 Plot[Sin[x], {x, 0, 10},
  PlotStyle -> ColorData[97][2], PlotLegends -> {Sin[x]}]
 ]

Mathematica graphics

This method uses Plot so you get the Plot bells and whistles, like discontinuity processing, except for automatic coloring of the graphs: 

rescaleShow[
 Plot[Tan[x], {x, 0, 10},
  PlotStyle -> ColorData[97][1], PlotLegends -> {Tan[x]}, 
  Frame -> True],
 Plot[Sin[x], {x, 0, 10},
  PlotStyle -> ColorData[97][2], PlotLegends -> {Sin[x]}]
 ]

Mathematica graphics

|improve this answer
$\endgroup$
12
$\begingroup$

A slightly modified version using Overlay.

combine[data1_, data2_] := Overlay[{ListLinePlot[data1,
  Frame -> {True, True, False, False}, 
  FrameLabel -> {"x1", "y1"}, LabelStyle -> Directive[12, Blue], 
  PlotStyle -> Blue, PlotRange -> All, 
  ImagePadding -> {{50, 50}, {40, 40}}],
  ListLinePlot[data2, Frame -> {False, False, True, True}, 
  FrameTicks -> All, FrameLabel -> {{None, "y2"}, {None, "x2"}}, 
  LabelStyle -> Directive[12, Red], PlotStyle -> {Red, Dashed}, 
  PlotRange -> All, ImagePadding -> {{50, 50}, {40, 40}}]}, 
 Alignment -> Center]

data1 = Table[{x, Sin[x]}, {x, 0, 10, 0.01}];
data2 = Table[{x, Exp[x]}, {x, -5, 5, 0.01}];
combine[data1, data2]

enter image description here

One advantage here is that you can use any range for x and y.

You can use Plot as well in the combine and modify the appearance.

|improve this answer
$\endgroup$
  • $\begingroup$ +1 for the coding ingenuity, but honestly, for me this just reinforces the idea that a small multiple chart is often the way to go. $\endgroup$ – Michael Seifert Oct 8 '18 at 12:45
6
$\begingroup$

Multiply, Sin[x] by, say, 1000 and rescale the right axis:

Plot[{Exp[x], 1000 Sin[x]}, {x, 0, 10}, Frame -> True, 
  FrameTicks -> {{Automatic, Charting`FindTicks[{-1000, 1000}, {-1, 1}]}, 
    {Automatic, Automatic}},
  PlotLegends -> {HoldForm @ Exp[x], Sin[x]}]

enter image description here

|improve this answer
$\endgroup$
  • $\begingroup$ Not to nitpick, but both curves use the left axis (according to the legend). $\endgroup$ – Andreas Rejbrand Oct 8 '18 at 18:26
  • $\begingroup$ thank you @AndreasRejbrand; good catch. Fixed now. $\endgroup$ – kglr Oct 8 '18 at 18:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.