Is it possible to retrieve an automatically-generated plot range in Mathematica?
For example, if I were to do:
Plot[Sin[x], {x, 0, 2 \[Pi]}, PlotRange -> Automatic] then I'd like to know that the range of the Y axis was -1 to 1 and the range of the X axis was 0 to 2 pi.
p = Plot[Sin[x], {x, 0, 2*Pi}, PlotRange -> Automatic]; AbsoluteOptions is a bit of a lottery but works in this case
AbsoluteOptions[p, PlotRange] {PlotRange -> {{0., 6.28319}, {-1., 1.}}} Even though AbsoluteOptions superceded FullOptions sometimes it is also worth trying FullOptions if and when AbsoluteOptions fails because I have come across cases when AbsoluteOptions fails but FullOptions works. In this case FullOptions also works:
FullOptions[p, PlotRange] {{0., 6.28319}, {-1., 1.}} 
PlotRange in the FullForm of p? I have had trouble with AbsoluteOptions in the past (perhaps due to not understanding how it works), so I now tend to avoid using it in favour of brute-force pattern-matching as in my answer.
AbsoluteOptions is badly broken (see stackoverflow.com/questions/8717608/…) but in principle it provides a concise why of retrieving these values. So when it works I use it and when it doesn't, after first trying FullOptions, then I use some sort of pattern matching routine. But it is generally the first thing I try.Not pretty or general, but you can brute-force it likes this:
p = Plot[Sin[x], {x, 0, 2*Pi}, PlotRange -> Automatic]; First@Cases[p, List[___, Rule[PlotRange, x_], ___] -> x] giving
{{0., 6.28319}, {-1., 1.}} You can work this out by looking at FullForm[p]
Use the AbsoluteOptions function, q. v. in the docs.
In[56]:= x = Plot[Sin[x], {x, 0, 2 \[Pi]}, PlotRange -> Automatic]; AbsoluteOptions[x, PlotRange] Out[57]= {PlotRange -> {{0., 6.28319}, {-1., 1.}}} I can suggest the following Ticks hack:
pl = Plot[Sin[x], {x, 0, 10}]; Reap[Rasterize[Show[pl, Ticks -> {Sow[{##}] &, Sow[{##}] &}], ImageResolution -> 1]][[2, 1]] => {{-0.208333, 10.2083}, {-1.04167, 1.04167}} The trick is that real PlotRange is determined by the FrontEnd, not by the Kernel. So we must force the FrontEnd to render the graphics in order to get tick functions evaluated. This hack gives the complete PlotRange with explicit value of PlotRangePadding added.
More general solution taking into account a possibility that pl has non-standard value of DisplayFinction option and that it may have Axes option set to False:
completePlotRange[plot_] := Last@Last@ Reap[Rasterize[ Show[plot, Ticks -> (Sow[{##}] &), Axes -> True, DisplayFunction -> Identity], ImageResolution -> 1]] On the Documentation page for PlotRange under the "More information" one can read an important note about AbsoluteOptions: "AbsoluteOptions gives the explicit form of PlotRange specifications when Automatic settings are given" (highlighting is mine). So it seems that the Documentation does not guarantee that AbsoluteOptions will give correct values for PlotRange when it is not Automatic for all coordinates.
Like acl I often dig into the FullForm with Position to post-process graphics:
E.g. Finding and modifying PlotRange:
p = Plot[Sin[x], {x, 0, 2 \[Pi]}, PlotRange -> Automatic]; rpos = Position[p, PlotRange]; Print["Initial PlotRange"]; p[[Sequence @@ Most[First[rpos]]]] Print["Modified PlotRange"]; p[[Sequence @@ Most[First[rpos]]]] = PlotRange -> {{0, Pi}, {-1, 1}} Print[p] Or, modifying colours:
p = Plot[{Sin[x], Cos[x]}, {x, 0, 2 \[Pi]}, PlotRange -> Automatic]; hpos = Position[p, Hue]; Print["Initial colours"] p[[Sequence @@ Most[#]]] & /@ hpos Print["New colours"] MapThread[(p[[Sequence @@ Most[#1]]] = #2) &, {hpos, {Green, Orange}}] Print[p] 