# Create a two axis plot with fixed y range? **URL:** \ **Category:** Questions\ **Tags:** graphics-and-visualization\ **Created:** [December 13, 2016, 1:09pm UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751 "2016-12-13T13:09:46Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![saraaasly](https://avatars.discourse-cdn.com/v4/letter/s/6f9a4e/32.png) [@saraaasly](https://community.wolfram.com/u/saraaasly)\ **Post date:** [December 13, 2016, 1:09pm UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751/1 "2016-12-13T13:09:46Z")
I have this code to plot with two y-axes, but the rage are automatically generated. I want the range to be fixed, so it always shows the y-axes with the same range independent of what I am plotting. Thank you in advance 🙂 The code can be found here as well: > **[Generate Plots with Two Vertical Scales—Wolfram Documentation](https://reference.wolfram.com/language/howto/GeneratePlotsWithTwoVerticalScales.html)** > > Suppose two functions have the same domain and different ranges. Plotting them together using Plot uses the same scale for the y values. To compare the functions, TwoAxisPlot plots them with different scales for the y values (on the left and right)... ``` TwoAxisPlot[{f_, g_}, {x_, x1_, x2_}] := Module[{fgraph, ggraph, frange, grange, fticks, gticks}, {fgraph, ggraph} = MapIndexed[ Plot[#, {x, x1, x2}, Axes -> True, PlotStyle -> ColorData[1][#2[[1]]]] &, {f, g}]; {frange, grange} = (PlotRange /. AbsoluteOptions[#, PlotRange])[[ 2]] & /@ {fgraph, ggraph}; fticks = N@FindDivisions[frange, 5]; gticks = Quiet@ Transpose@{fticks, ToString[NumberForm[#, 2], StandardForm] & /@ Rescale[fticks, frange, grange]}; Show[fgraph, ggraph /. Graphics[graph_, s___] :> Graphics[ GeometricTransformation[graph, RescalingTransform[{{0, 1}, grange}, {{0, 1}, frange}]], s], Axes -> False, Frame -> True, FrameStyle -> {ColorData[1] /@ {1, 2}, {Automatic, Automatic}}, FrameTicks -> {{fticks, gticks}, {Automatic, Automatic}}]] TwoAxisPlot[{Sin[x], 3 Sin[x] + 5 Cos[x]}, {x, 0, 4 Pi}] ``` ---
**Author:** ![henrikschachner](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/henrikschachner/32/32119_2.png) [@henrikschachner](https://community.wolfram.com/u/henrikschachner)\ **Post date:** [December 14, 2016, 8:59pm UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751/2 "2016-12-14T20:59:18Z")
I would like to help, but for _which one_ of the _two_ y-axes do you want to keep the range fixed? ---
**Author:** ![saraaasly](https://avatars.discourse-cdn.com/v4/letter/s/6f9a4e/32.png) [@saraaasly](https://community.wolfram.com/u/saraaasly)\ **Post date:** [December 14, 2016, 9:14pm UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751/3 "2016-12-14T21:14:58Z")
Thanks a lot! The right one (purple) ---
**Author:** ![henrikschachner](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/henrikschachner/32/32119_2.png) [@henrikschachner](https://community.wolfram.com/u/henrikschachner)\ **Post date:** [December 15, 2016, 8:09am UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751/4 "2016-12-15T08:09:14Z")
OK, here comes my slightly changed version (`GridLines` added, colors changed, function name changed): ``` twoAxisPlot[{f_, g_}, {x_, x1_, x2_}, gyRange : {gy1_, gy2_} : {Automatic, Automatic}] := Module[{fgraph, ggraph, frange, grange, fticks, gticks}, {fgraph, ggraph} = {Plot[f, {x, x1, x2}, Axes -> True, PlotStyle -> Blue, PlotRange -> Automatic, GridLines -> Automatic], Plot[g, {x, x1, x2}, Axes -> True, PlotStyle -> Red, PlotRange -> gyRange]}; {frange, grange} = (PlotRange /. AbsoluteOptions[#, PlotRange])[[2]] & /@ {fgraph, ggraph}; fticks = N@FindDivisions[frange, 5]; gticks = Quiet@Transpose@{fticks, ToString[NumberForm[#, 2], StandardForm] & /@ Rescale[fticks, frange, grange]}; Show[fgraph, ggraph /. Graphics[graph_, s___] :> Graphics[ GeometricTransformation[graph, RescalingTransform[{{0, 1}, grange}, {{0, 1}, frange}]], s], Axes -> False, Frame -> True, FrameStyle -> {ColorData[1] /@ {1, 2}, {Automatic, Automatic}}, FrameTicks -> {{fticks, gticks}, {Automatic, Automatic}}]] ``` The function now has an _optional_ argument `gyRange` which defines the right y-axis, i.e. it can be envoced like so (as before): ``` twoAxisPlot[{Sin[x], 3 Sin[x] + 5 Cos[x]}, {x, 0, 4 Pi}] ``` or (e.g.): ``` twoAxisPlot[{Sin[x], 3 Sin[x] + 5 Cos[x]}, {x, 0, 4 Pi}, {-10, 15}] ``` Regards – Henrik ---
**Author:** ![saraaasly](https://avatars.discourse-cdn.com/v4/letter/s/6f9a4e/32.png) [@saraaasly](https://community.wolfram.com/u/saraaasly)\ **Post date:** [December 15, 2016, 9:09am UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751/5 "2016-12-15T09:09:52Z")
Thank you so much for helping me, now my plots looks way better. Cheers, Sara ---
**Author:** ![dlkeith](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/dlkeith/32/31494_2.png) [@dlkeith](https://community.wolfram.com/u/dlkeith)\ **Post date:** [December 15, 2016, 5:51pm UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751/6 "2016-12-15T17:51:26Z")
Hi Henrik, This looks very useful. But I think there is a scaling problem. (In the first plot (no y range option), where does the 10^-6 come from?) Also, did you mean for the color of the axes tick labels to match color of the plots? ``` twoAxisPlot[{f_, g_}, {x_, x1_, x2_}, gyRange : {gy1_, gy2_} : {Automatic, Automatic}] := Module[{fgraph, ggraph, frange, grange, fticks, gticks}, {fgraph, ggraph} = {Plot[f, {x, x1, x2}, Axes -> True, PlotStyle -> Blue, PlotRange -> Automatic, GridLines -> Automatic], Plot[g, {x, x1, x2}, Axes -> True, PlotStyle -> Red, PlotRange -> gyRange]}; {frange, grange} = (PlotRange /. AbsoluteOptions[#, PlotRange])[[2]] & /@ {fgraph, ggraph}; fticks = N@FindDivisions[frange, 5]; gticks = Quiet@ Transpose@{fticks, ToString[NumberForm[#, 2], StandardForm] & /@ Rescale[fticks, frange, grange]}; Show[fgraph, ggraph /. Graphics[graph_, s___] :> Graphics[ GeometricTransformation[graph, RescalingTransform[{{0, 1}, grange}, {{0, 1}, frange}]], s], Axes -> False, Frame -> True, FrameStyle -> {ColorData[1] /@ {1, 2}, {Automatic, Automatic}}, FrameTicks -> {{fticks, gticks}, {Automatic, Automatic}}]] twoAxisPlot[{Sin[x], 3 Sin[x] + 5 Cos[x]}, {x, 0, 4 Pi}] ``` ![Twoaxisplot1.png](https://global.discourse-cdn.com/wolfram/original/2X/9/9ca89b46e986a0f80187c1740fcd6674c9e20b06.png) ``` twoAxisPlot[{Sin[x], 3 Sin[x] + 5 Cos[x]}, {x, 0, 4 Pi}, {-10, 15}] ``` ![Twoaxisplot2.png](https://global.discourse-cdn.com/wolfram/original/2X/2/2b66c20d9d5d7914fb18d1970ba790b5daf0981c.png) ---
**Author:** ![henrikschachner](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/henrikschachner/32/32119_2.png) [@henrikschachner](https://community.wolfram.com/u/henrikschachner)\ **Post date:** [December 15, 2016, 7:30pm UTC](https://community.wolfram.com/t/create-a-two-axis-plot-with-fixed-y-range/9751/7 "2016-12-15T19:30:00Z")
Hi David, yes, you are absolutely right - this was not carefully done, thanks for spotting! Here comes a hopefully improved version: ``` twoAxisPlot[{f_, g_}, {x_, x1_, x2_}, gyRange : {gy1_, gy2_} : {Automatic, Automatic}] := Module[{fgraph, ggraph, frange, grange, fticks, gticks, plotColors}, plotColors = {Blue, Red}; {fgraph, ggraph} = {Plot[f, {x, x1, x2}, Axes -> True, PlotStyle -> plotColors[[1]], PlotRange -> Automatic, GridLines -> Automatic], Plot[g, {x, x1, x2}, Axes -> True, PlotStyle -> plotColors[[2]], PlotRange -> gyRange]}; {frange, grange} = (PlotRange /. AbsoluteOptions[#, PlotRange])[[2]] & /@ {fgraph, ggraph}; fticks = N@FindDivisions[frange, 5]; gticks = Quiet[Transpose@{fticks, ToString[NumberForm[#, 2], StandardForm] & /@ (Threshold[#, Abs[Subtract @@ MinMax[#]]/1000] &@ Rescale[fticks, frange, grange])}]; Show[fgraph, ggraph /. Graphics[graph_, s___] :> Graphics[ GeometricTransformation[graph, RescalingTransform[{{0, 1}, grange}, {{0, 1}, frange}]], s], Axes -> False, Frame -> True, FrameStyle -> {plotColors, {Automatic, Automatic}}, FrameTicks -> {{fticks, gticks}, {Automatic, Automatic}}]] ``` And now we get: ![ToAxisPlot.png](https://global.discourse-cdn.com/wolfram/original/3X/6/2/62bb6bc4ae563e0bde278e6e32c7ca882d13623e.png) Best regards – Henrik