How do I create subplots in Mathematica using LevelScheme?

Question

Consider the following arbitrary figure generated in MATLAB as an example. The basic idea is that I have a contour plot and I want to showcase selected slices from it in subplots on the right. Is there an equivalent of subplot in mma?

The work around that I have right now is to have just the contour plot with the slices and the arrows and the two slice-plots separately and then put them together in latex. However, I'd like to be able to do this within mma. How do I go about doing this?

An idea that I had is to generate a the contour plot with a full vertical & half horizontal aspect ratio, the two plots with half vertical & half horizontal aspect ratio, and then use GraphicsGrid to align them up. But this still gave me the plots as a list, not a composite figure. Is this the only way or is there a nicer, more elegant way of doing it?

Answer 1

I know that Multipanel in LevelScheme can probably let you do what you want - but I don't have much experience with it and the examples in the docs are fairly sparse. I've already pasted one of the examples into this SO answer, so have a look there and see what you think!

---

Here's my attempt with GraphicsGrid. The thing that Multipanel lets you do but GraphicsGrid doesn't is to let you use varying Column/Row sizes. This means that I struggled to get the arrows drawn in programmatically, and resorted to hand drawing them using the "Drawing Tools" panel ( :D )

With[{yslice1 = .5, yslice2 = -.8},
 GraphicsGrid[
  {{DensityPlot[Sin[15 x y], {x, -1, 1}, {y, -1, 1}, 
     ColorFunction -> "PlumColors", AspectRatio -> 2,
     Epilog -> {Dashed, White, Line[{{-1, yslice1}, {1, yslice1}}], 
       Line[{{-1, yslice2}, {1, yslice2}}]}],
    Plot[Sin[15 x yslice1], {x, -1, 1}, Axes -> False, Frame -> True]},
   {SpanFromAbove,
    Plot[Sin[15 x yslice2], {x, -1, 1}, Axes -> False, 
     Frame -> True]}},
  Spacings -> {Scaled[0.2], Scaled[0.0]}]]

---

Edit:

Here's the same thing using LevelScheme, note that the frames line up. It should be possible to add arrows - since LevelScheme has lots of new arrow directives - but I'll leave that as a homework problem!

<< "LevelScheme`"
{yslice1 = .5, yslice2 = -.8};
Figure[{
  SetOptions[Multipanel, 
   ShowTickLabels -> {True, False, False, True}, Background -> Wheat,
   PanelLetterFontSize -> 10, Margin -> {{40, 40}, {40, 0}}],
  Multipanel[{{0, 1}, {0, 1}}, {2, 2},
   XPlotRanges -> {-1, 1}, YPlotRanges -> {-1, 1},
   XFrameLabels -> textit["x"], YFrameLabels -> textit["y"],
   TickFontSize -> 10, XFrameTicks -> LinTicks[-1, 1, .5, 4], 
   YFrameTicks -> LinTicks[-1, 1, .5, 4],
   BufferL -> 1.5, BufferB -> 3, Order -> Vertical,
   XPanelSizes -> {1, 1}, XGapSizes -> 0.25, YGapSizes -> 0.2],
  FigurePanel[{1, 2}], 
  RawGraphics[
   Plot[Sin[15 x yslice1], {x, -1, 1}, Axes -> False, Frame -> True]],
  FigurePanel[{2, 2}], 
  RawGraphics[
   Plot[Sin[15 x yslice2], {x, -1, 1}, Axes -> False, Frame -> True]],
  FigurePanel[{2, 1}, PanelAdjustments -> {{0, 0}, {0, +1.2}}],
  RawGraphics[
   DensityPlot[Sin[15 x y], {x, -1, 1}, {y, -1, 1}, 
    ColorFunction -> "PlumColors", AspectRatio -> 2],
   Graphics[{Dashed, Thick, White, 
     Line[{{-1, yslice1}, {1, yslice1}}], 
     Line[{{-1, yslice2}, {1, yslice2}}]}]]},
 PlotRange -> {{0, 1}, {0, 1}}, ImageSize -> 2*72*{5, 3}
 ]

Answer 2

Re the OPs comment about GraphicsGrid, you can use FullGraphics@GraphicsGrid@{...} to get a single graphics object out. This is necessary to get copy as PDF to work also.

Answer 3

Here is a first pass at making Simon's solution dynamic. The arrows are hard coded for this particular image. Later I shall try to implement them more generally.

dp1 = DensityPlot[Sin[15 x y], {x, -1, 1}, {y, -1, 1}, 
   ColorFunction -> "PlumColors", AspectRatio -> 2, PlotPoints -> 30];
Manipulate[
 Show[
  GraphicsGrid[{{dp1 ~Append~
        (Epilog -> {Dashed, White, 
         Line[{{-1, yslice1}, {1, yslice1}}], 
         Line[{{-1, yslice2}, {1, yslice2}}]}), 
     Plot[Sin[15 x yslice1], {x, -1, 1}, Axes -> False, 
      Frame -> True]}, {SpanFromAbove, 
     Plot[Sin[15 x yslice2], {x, -1, 1}, Axes -> False, 
      Frame -> True]}}, Spacings -> {Scaled[0.2], Scaled[0.0]}],
  Graphics[{Red, {Arrowheads[Large],
     Arrow[{{380, Rescale[yslice1, {-1, 1}, {-646, -46}]}, {440, -170}}], 
     Arrow[{{380, Rescale[yslice2, {-1, 1}, {-646, -46}]}, {440, -530}}]
     }}],
  ImageSize -> 600
 ],
 {{yslice1, 0.5, "Slice 1"}, -1, 1},
 {{yslice2, -0.8, "Slice 2"}, -1, 1}
]

---

Here is a slightly different method that puts the arrows inside Epilog, which links their position to the left plot, perhaps easier to use.

dp1 = DensityPlot[Sin[15 x y], {x, -1, 1}, {y, -1, 1}, 
   ColorFunction -> "PlumColors", AspectRatio -> 2, PlotPoints -> 30, 
   PlotRangeClipping -> False, 
   ImagePadding -> {{Automatic, 100}, {Automatic, Automatic}}];
Manipulate[
 Show[
  GraphicsGrid[{{dp1~
      Append~(Epilog -> {{Dashed, White, 
          Line[{{-1, yslice1}, {1, yslice1}}], 
          Line[{{-1, yslice2}, {1, yslice2}}]}, {Red, 
          Arrowheads[Large],
          Arrow[{{1, yslice1}, {1.7, 0.88}}], 
          Arrow[{{1, yslice2}, {1.7, -0.9}}]
          }}), 
     Plot[Sin[15 x yslice1], {x, -1, 1}, Axes -> False, 
      Frame -> True]}, {SpanFromAbove, 
     Plot[Sin[15 x yslice2], {x, -1, 1}, Axes -> False, 
      Frame -> True]}}, Spacings -> {Scaled[-0.2], Scaled[0.0]}],
  ImageSize -> 600
  ],
 {{yslice1, 0.5, "Slice 1"}, -1, 1},
 {{yslice2, -0.8, "Slice 2"}, -1, 1}
 ]