How can I make a grid of plots with no spacing, and have the plots line up perfectly?

Question

I am making a bunch of two dimensional plots and I would like to have them arranged in a grid with no space in between them. That is, I want their frames touching each other.

My problem is twofold. First I don't know how to get the plots to have a consistent size. When I try to give the plots the same size via ImageSize, it applies the size to the overall image, including the tick marks and labels. But when I have two different plots, one with tick labels and one without, giving the same value to ImageSize doesn't give the result I'm looking for.

Secondly, I want to get rid of any white space around the images such that when I give Grid the option Spacings ->{0,0} there really is no visible space between the plots.

In the example code I use the CustomTicks package.

(*an example of what I might plot, simple sum of two dimensional \
Lorentzians*)
lzn[x_, w_, g_] := (x - w + I g)^-1;
exampledata2D = 
  Table[Re[lzn[w1, .2, .1] lzn[w2, .3, .2] + 
     lzn[w1, .4, .1] lzn[w2, .8, .1] + 
     lzn[w1, .8, .2] lzn[w2, .4, .2]], {w1, 0, 1, .01}, {w2, 0, 
    1, .01}];
<< "CustomTicks`";  
standardticks = LinTicks[0, 1, .2, 4];
(*I don't want the last tick label for one plot overlapping with the \
first tick label of the plot right next to it.*)
ticks2 = LinTicks[0, 1, .2, 4, ShowLast -> False];
(*Custom plotting function so I don't have to reprint the same \
options over and over *)
plottingfunction[list_, plotopts : OptionsPattern[]] := 
  ListContourPlot[list, 
   Evaluate[FilterRules[{plotopts}, Options[ListContourPlot]]], 
   Contours -> 30, PlotRange -> All, DataRange -> {{0, 1}, {0, 1}}, 
   BaseStyle -> 18, 
   ColorFunction -> (Blend[{Red, Orange, Yellow, Green, Blue, 
        Darker[Blue]}, #] &)];

bottomleft = 
  plottingfunction[exampledata2D, 
   FrameTicks -> {{ticks2, StripTickLabels[standardticks]}, {ticks2, 
      StripTickLabels[standardticks]}}];
bottomright = 
  plottingfunction[exampledata2D, 
   FrameTicks -> {{StripTickLabels[standardticks], 
      StripTickLabels[standardticks]}, {standardticks, 
      StripTickLabels[standardticks]}}];
topleft = 
  plottingfunction[exampledata2D, 
   FrameTicks -> {{ticks2, 
      StripTickLabels[standardticks]}, {StripTickLabels[
       standardticks], StripTickLabels[standardticks]}}];
topright = 
  plottingfunction[exampledata2D, 
   FrameTicks -> {{StripTickLabels[standardticks], 
      StripTickLabels[standardticks]}, {StripTickLabels[
       standardticks], StripTickLabels[standardticks]}}];

Grid[{{topleft, topright}, {bottomleft, bottomright}}, 
 BaseStyle -> ImageSizeMultipliers -> 1, Spacings -> {0, 0}]

Answer 1

Another way to do this is to use the SciDraw package (LevelScheme successor). (Note: I'm still learning to use this package and I may not be doing things in the most efficient way. Also, the package is still in beta as of November 2013.)

This is the plot we're going to have in the grid:

plot = plottingfunction[exampledata2D];

First, load the package:

<<SciDraw`

A very simple way to construct the grid, exploiting the fact that all nine subplots are identical, is the following:

Figure[
 Multipanel[
  {
   FigurePanel[{FigGraphics[plot]}, All, (* "All" means evaluate this for all subplots *)
     PanelLetterTextColor -> White];
  },

  Dimensions -> {3, 3}  (* a 3 by 3 grid *)
 ],

 CanvasSize -> 8 {1, 1} (* the canvas aspect ratio sets the subplot aspect ratio too *)
]

Of course in practical situations the subplots are all different. Here's a more realistic way to do it which is convenient if the subplots are different but have the same plot range:

DefineStyle["ContourArray",
 {
  FigurePanel -> {
    XPlotRange -> {0, 1}, (* these need to be set if different from {0,1} *)
    YPlotRange -> {0, 1},
    YTickLabelRange -> {0.2, 1},
    XTickLabelRange -> {0.2, 1},
    PanelLetterTextColor -> White }
 }
]

Figure[
 Multipanel[
  {
   FigurePanel[{FigGraphics[plot]}, {1, 1}];
   FigurePanel[{FigGraphics[plot]}, {1, 2}];
   FigurePanel[{FigGraphics[plot]}, {1, 3}];
   FigurePanel[{FigGraphics[plot]}, {2, 1}];
   FigurePanel[{FigGraphics[plot]}, {2, 2}];
   FigurePanel[{FigGraphics[plot]}, {2, 3}];
   FigurePanel[{FigGraphics[plot]}, {3, 1}, XTickLabelRange -> All];
   FigurePanel[{FigGraphics[plot]}, {3, 2}];
   FigurePanel[{FigGraphics[plot]}, {3, 3}];       
  },

  Dimensions -> {3, 3}
 ],

 Style -> "ContourArray",
 CanvasSize -> 8 {1, 1}
]

Note how the tick label overlap was solved: the default tick range was set to $0.2 - 1.0$ and it was overridden on the bottom left panel only.

To disable the automatic panel lettering, use PanelLetter -> None in the style.

Answer 2

Thanks to Kuba and Szabolcs for pointing out many related posts. I recognize that LevelScheme is probably the best way to go here, but at the moment I don't have the time to learn everything I need in order to use it.

I am going to use Jens's solution from this page, but I have to remove the certain tick labels so that they don't overlap each other.

(*an example of what I might plot, simple sum of two dimensional \
Lorentzians*)
lzn[x_, w_, g_] := (x - w + I g)^-1;
exampledata2D = 
  Table[Re[lzn[w1, .2, .1] lzn[w2, .3, .2] + 
     lzn[w1, .4, .1] lzn[w2, .8, .1] + 
     lzn[w1, .8, .2] lzn[w2, .4, .2]], {w1, 0, 1, .01}, {w2, 0, 
    1, .01}];
<< "CustomTicks`";  
tickbottom = LinTicks[-1, 1, .5, 5, ShowLast -> False];
ticktop = LinTicks[-1, 1, .5, 5, ShowFirst -> False];
tickmiddle = 
  LinTicks[-1, 1, .5, 5, ShowFirst -> False, ShowLast -> False];
standardticks = LinTicks[-1, 1, .5, 5];
plottingfunction[list_, horizontalposition_, verticalposition_, 
   plotopts : OptionsPattern[]] := 
  ListContourPlot[list, 
   Evaluate[FilterRules[{plotopts}, Options[ListContourPlot]]], 
   Contours -> 30, DataRange -> {{-1, 1}, {-1, 1}}, BaseStyle -> 18, 
   ColorFunction -> (Blend[{Red, Orange, Yellow, Green, Blue, 
        Darker[Blue]}, #] &), PlotRangePadding -> None, 
   PlotRange -> All, 
   FrameTicks -> {{Which[verticalposition == "Top", ticktop, 
       verticalposition == "Middle", tickmiddle, 
       verticalposition == "Bottom", tickbottom], 
      StripTickLabels[standardticks]}, {If[
       verticalposition == "Bottom", 
       Which[horizontalposition == "Right", ticktop, 
        horizontalposition == "Middle", tickmiddle, 
        horizontalposition == "Left", tickbottom], 
       StripTickLabels[standardticks]], 
      StripTickLabels[standardticks]}}];

Options[plotGrid] = {ImagePadding -> 40};
plotGrid[l_List, w_, h_, opts : OptionsPattern[]] := 
 Module[{nx, ny, sidePadding = OptionValue[plotGrid, ImagePadding], 
   topPadding = 0, widths, heights, dimensions, positions, 
   frameOptions = 
    FilterRules[{opts}, 
     FilterRules[Options[Graphics], 
      Except[{ImagePadding, Frame, FrameTicks}]]]}, {ny, nx} = 
   Dimensions[l];
  widths = (w - 2 sidePadding)/nx Table[1, {nx}];
  widths[[1]] = widths[[1]] + sidePadding;
  widths[[-1]] = widths[[-1]] + sidePadding;
  heights = (h - 2 sidePadding)/ny Table[1, {ny}];
  heights[[1]] = heights[[1]] + sidePadding;
  heights[[-1]] = heights[[-1]] + sidePadding;
  positions = 
   Transpose@
    Partition[
     Tuples[Prepend[Accumulate[Most[#]], 0] & /@ {widths, heights}], 
     ny];
  Graphics[
   Table[Inset[
     Show[l[[ny - j + 1, i]], 
      ImagePadding -> {{If[i == 1, sidePadding, 0], 
         If[i == nx, sidePadding, 0]}, {If[j == 1, sidePadding, 0], 
         If[j == ny, sidePadding, topPadding]}}, AspectRatio -> Full],
      positions[[j, i]], {Left, Bottom}, {widths[[i]], 
      heights[[j]]}], {i, 1, nx}, {j, 1, ny}], 
   PlotRange -> {{0, w}, {0, h}}, ImageSize -> {w, h}, 
   Evaluate@Apply[Sequence, frameOptions]]]

plotGrid[Table[
  plottingfunction[exampledata2D, h, 
   v], {v, {"Top", "Middle", "Bottom"}}, {h, {"Left", "Middle", 
    "Right"}}], 1000, 1000]

I'm not 100% happy with the way it looks, with the missing tick labels, but it is better than having the labels overlap or get cut off.