Using PlotLegends with Show messes up the graphics

Question

I have already obtained the plot that I want but am having trouble legending the graph correctly.

plot = ListLogLogPlot[Sort[depth4], PlotRange -> {{1, 50000}, {1, 50000}}, Joined -> True, 
PlotStyle -> {Purple}, BaseStyle -> {FontSize -> 14}];

line = LogLogPlot[11024 x^(-0.94232), {x, 1, 100000}, 
   PlotStyle -> {Orange, Dashed, Thick}];
line2 = LogLogPlot[31862 x^(-1.07076), {x, 1, 100000}, 
   PlotStyle -> {Green, Dotted, Thick}];

Show[plot, line, line2]

If I insert a legend command into the first plot, it doesn't work. I need to be able to legend my 3 curves in the graph. Thanks for your help!

Answer 1

When Show is used the legends use ShowLegend. Here is a demo:

depth4 = Range[20]^3;
plot = ListLogLogPlot[Sort[depth4], PlotRange -> {{1, 50000},
     {1, 50000}}, Joined -> True, PlotStyle -> {Purple},
   BaseStyle -> {FontSize -> 14}];
line = LogLogPlot[11024 x^(-0.94232), {x, 1, 100000},
   PlotStyle -> {Orange, Dashed, Thick}];
line2 = LogLogPlot[31862 x^(-1.07076), {x, 1, 100000},
   PlotStyle -> {Green, Dotted, Thick}];

Needs["PlotLegends`"]
ShowLegend[Show[plot, line, line2, ImageSize -> 500],
 {{{Graphics[{Purple, Line[{{0, 0}, {2, 0}}]}], "   depth4"},
   {Graphics[{Orange, Dashed, Line[{{0, 0}, {2, 0}}]}], "   line"},
   {Graphics[{Green, Dashed, Line[{{0, 0}, {2, 0}}]}], "   line2"}},
  LegendPosition -> {0.7, 0.2}, LegendSize -> {0.45, 0.4},
  LegendShadow -> False}]

Answer 2

While in many ways Mathematica's graphics is miles ahead of its competition, the supplied legend package looks like a hack that does not belong. In its own documentation, under Inset, you will find examples of better looking legends. Building on those examples, I have a simple legend function.

ClearAll[simpleLegend]
simpleLegend[legendItems__,pos_]:=Module[{legendLine,offset,legend},
  offset=Module[{s,o,insetpts=10},
    s=pos/.{Left->0,Right->1,Bottom->0,Top->1};
    o=insetpts pos/.{Left->1,Right->-1,Bottom->1,Top->-1};
    Offset[o,Scaled[s]]
  ];
  legendLine[{lbl_,lineStyle_}]:={
    Graphics[{lineStyle,Line[{{0,0.5},{1,0.5}}]},ImageSize->{20,10},AspectRatio->0.5],
    Style[lbl,FontFamily->"Tahoma",FontSize->11,TextAlignment->Left,LineBreakWithin->False]
  };
  legend=GraphicsGrid[legendLine/@legendItems,Alignment->Left];
  Graphics@Inset[legend,offset,pos]
];

which can be used like this

labels={"data","eq1","eq2"};
styles={Directive[Purple],Directive[Orange,Dashed,Thick],Directive[Green,Dotted,Thick]};

depth4=Table[{x,(11024 x^(-0.94232))*RandomReal[{0.4,1.6}]}/.x->10^n,{n,0,5,0.1}];

plot=ListLogLogPlot[Sort[depth4],
  PlotRange->{{1,50000},{1,50000}},Joined->True,PlotStyle->styles[[1]],
    BaseStyle->{FontSize->14}
];

line=LogLogPlot[11024 x^(-0.94232),{x,1,100000},PlotStyle->styles[[2]]];
line2=LogLogPlot[31862 x^(-1.07076),{x,1,100000},PlotStyle->styles[[3]]];

Show[plot,line,line2,simpleLegend[Thread@{labels,styles},{Right,Top}]]

Answer 3

You can also use Epilog->Inset[...] as follows:

For

  depth4 = Range[20]^3; 
  plot =  ListLogLogPlot[Sort[depth4], PlotRange -> {{1, 50000}, {1, 50000}}, 
  Joined -> True, PlotStyle -> {Purple}, BaseStyle -> {FontSize -> 14}]; 
  line = LogLogPlot[11024 x^(-0.94232), {x, 1, 100000}, 
  PlotStyle -> {Orange, Dashed, Thick}]; 
  line2 = LogLogPlot[31862 x^(-1.07076), {x, 1, 100000}, 
  PlotStyle -> {Green, Dotted, Thick}];

as in Chris's answer,

 Show[plot, line, line2, ImageSize -> 500, 
 Epilog -> 
 Inset[Panel[
 Grid[{{Graphics[{Purple, 
 Line[{{0, 0}, {2, 0}}]}, AspectRatio -> .1, ImageSize -> 30], 
   Style["depth4", FontFamily -> "SketchFlowPrint", Bold, FontColor -> Purple]}, 
  {Graphics[{Orange, Dashed, 
     Line[{{0, 0}, {2, 0}}]}, AspectRatio -> .1, ImageSize -> 30],
    Style["line", FontFamily -> "SketchFlowPrint", Bold, FontColor -> Orange]}, 
  {Graphics[{Green, Dotted, 
     Line[{{0, 0}, {2, 0}}]}, AspectRatio -> .1, ImageSize -> 30],
    Style["line2", FontFamily -> "SketchFlowPrint", Bold, FontColor -> Green]}}, 
 Alignment -> {{Left, Left}, {Left, Left}}], ImageSize -> Full], 
 Offset[{-2, -2}, Scaled[{1, 1}]], {Right, Top}]]

gives

Answer 4

In Mathematica 10.3 you can use LineLegend. I myself have never liked to have a legend within the plot, so I insert it in a grid.

depth4 = Range[20]^3;
style1 = Directive[Purple];
plot = ListLogLogPlot[Sort[depth4], 
   PlotRange -> {{1, 50000}, {1, 50000}}, Joined -> True, 
   PlotStyle -> style1, BaseStyle -> {FontSize -> 14}];
style2 = Directive[Orange, Dashed, Thick];
line = LogLogPlot[11024 x^(-0.94232), {x, 1, 100000}, 
   PlotStyle -> style2];
style3 = Directive[Green, Dotted, Thick];
line2 = LogLogPlot[31862 x^(-1.07076), {x, 1, 100000}, 
   PlotStyle -> style3];
temp = Grid[{{
    Show[{plot, line, line2}, ImageSize -> 300]
    , LineLegend[{style1, style2, style3}, {"plot", "line", "line2"}]
    }}]
Export[NotebookDirectory[] <> "plot_linelegend.png", temp]

If you save the notebook somewhere, you will obtain directly a png image of the plot with the legend as this one

Answer 5

I'm using version 10.2, and it seems that the legends from the initial plots work just fine with Show

depth4 = Range[20]^3;
plot = ListLogLogPlot[Sort[depth4], 
   PlotRange -> {{1, 50000}, {1, 50000}}, Joined -> True, 
   PlotStyle -> {Purple}, BaseStyle -> {FontSize -> 14}, 
   PlotLegends -> {"plot"}];

line = LogLogPlot[11024 x^(-0.94232), {x, 1, 100000}, 
   PlotStyle -> {Orange, Dashed, Thick}, PlotLegends -> {"line"}];
line2 = LogLogPlot[31862 x^(-1.07076), {x, 1, 100000}, 
   PlotStyle -> {Green, Dotted, Thick}, PlotLegends -> {"line2"}];

Show[plot, line, line2]

You'll notice that the purple line is smaller, because for some reason Mathematica makes the legend line longer if there is dashing. If we make the purple line dashed (but not really dashed), then they are consistent.

plot = ListLogLogPlot[Sort[depth4], 
   PlotRange -> {{1, 2 50000}, {1, 50000}}, Joined -> True, 
   PlotStyle -> {Purple,Dashing[{1, 0}]}, 
   BaseStyle -> {FontSize -> 14}, PlotLegends -> {"plot"}];
Show[plot, line, line2]

Answer 6

You can extract Line directives (color, thickness, dashing, etc. specifications) from the plot itself. This means that you don't have to call for a second time for the style specifications explicitly. For complex graphics (with e.g. plot markers) it might not be this simple though.

depth4 = Range[20]^3;
plot = ListLogLogPlot[Sort[depth4], 
   PlotRange -> {{1, 50000}, {1, 50000}}, Joined -> True, 
   PlotStyle -> {Purple}, BaseStyle -> {FontSize -> 14}];
line = LogLogPlot[11024 x^(-0.94232), {x, 1, 100000}, 
   PlotStyle -> {Orange, Dashed, Thick}];
line2 = LogLogPlot[31862 x^(-1.07076), {x, 1, 100000}, 
   PlotStyle -> {Green, Dotted, Thick}];

data = Show[plot, line, line2];
styles = Cases[data, {dir__, l_Line} :> {dir}, \[Infinity]]

{{Hue[0.67, 0.6, 0.6], RGBColor[0.5, 0, 0.5]}, {Hue[0.67, 0.6, 0.6], 
  RGBColor[1, 0.5, 0], Dashing[{Small, Small}], 
  Thickness[Large]}, {Hue[0.67, 0.6, 0.6], RGBColor[0, 1, 0], 
  Dashing[{0, Small}], Thickness[Large]}}

Row@{
  Show[plot, line, line2, ImageSize -> 300],
  Grid[Table[{Graphics[Append[styles[[i]], Line[{{0, 0}, {1, 0}}]], 
      ImageSize -> 50, AspectRatio -> 1/5], "plot" <> ToString@i}, {i,
      3}], Spacings -> {1, 2}]
  }

Answer 7

I don't know of a direct way to do that once the individual graphs have been plotted and legended. You can, however, use ListLogLogPlot on a table containing values from your functions, so as to have a single call to a Plot function, which can thus take a PlotLegend option:

Needs["PlotLegends`"];
ListLogLogPlot[{
  Sort[depth4],
  Table[{x, 11024 x^(-0.94232)} /. x -> 10^n, {n, 0, 5, 0.1}],
  Table[{x, 31862 x^(-1.07076)} /. x -> 10^n, {n, 0, 5, 0.1}]
  },
 PlotRange -> {{1, 50000}, {1, 50000}},
 Joined -> True,
 PlotStyle -> {Purple, Directive[Orange, Dashed, Thick], 
   Directive[Green, Dotted, Thick]},
 BaseStyle -> {FontSize -> 14},
 PlotLegend -> {"data", "eq1", "eq2"}]

---

PS: you were missing the definitio for depth4, so I took:

depth4 = Table[{x, (11024 x^(-0.94232))*RandomReal[{0.4, 1.6}]} /. x -> 10^n, {n, 0, 5, 0.1}];