Labeled destroys the log scales in "log" plots when notebook is re-opened

Question

Bug introduced in 10 or earlier and fixed in 11.1

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While testing this pdf export bug caused by Labeled, I noticed that this function also destroys the log scales in all "log" plots when you reopen the notebook in which the plots were created.

The problem not only concerns the plots generated by the different *Log* functions but also those obtained by setting the option ScalingFunctions to the "Log" mode (see examples below):

For example when you execute:

Labeled[LogLogPlot[x, {x, 10^-5, 1}], "Test"] 

it displays correctly

but once you save/close/reopen the notebook, this previous plot becomes:

Here are some other examples showing the same wrong behavior (for me with MMA v10.3.1, OSX):

LogLogPlot[x, {x, 10^-5, 1}]
Labeled[LogLogPlot[x, {x, 10^-5, 1}], "LogLogPlot"]

LogLinearPlot[Tanh[x], {x, 1, 100}]
Labeled[LogLinearPlot[Tanh[x], {x, 1, 100}], "LogLinearPlot"]

LogPlot[x^x, {x, 1, 5}]
Labeled[LogPlot[x^x, {x, 1, 5}], "LogPlot"]

ListLogPlot[Table[PartitionsQ[n], {n, 50}]]
Labeled[ListLogPlot[Table[PartitionsQ[n], {n, 50}]], "ListLogPlot"]

ListLogLogPlot[Range[20]^3]
Labeled[ListLogLogPlot[Range[20]^3], "ListLogLogPlot"]

Plot[Exp[x], {x, 1, 10}, ScalingFunctions -> "Log"]
Labeled[Plot[Exp[x], {x, 1, 10}, ScalingFunctions -> "Log"], "Plot"]

ListPlot[Fibonacci[Range[50]], ScalingFunctions -> "Log"]
Labeled[ListPlot[Fibonacci[Range[50]], 
  ScalingFunctions -> "Log"], "ListPlot"]

gh = Histogram[
  VertexDegree[RandomGraph[BarabasiAlbertGraphDistribution[10^4, 3]]],
   ColorFunction -> "Rainbow", ScalingFunctions -> {"Log", "Log"}, 
  PlotRange -> All]
Labeled[gh, "Histogram"]

In v10.4.0 however, the problem does not occur anymore for ListLogPlot, ListLogLogPlot and ListPlot. The problem was probably noticed while adding Labeled as a new possible wrapper for the datas (see the corresponding documentations), maybe involving a redesign of these functions ...

The only workaround (as originally proposed by @Algohi) seem to be to wrap the whole Labeled expression with Dynamic.

I also notice that:

• you can copy/paste the "wrong" plot, to get back the original correct plot.
• you can wrap the plot in GraphicsGrid (GraphicsRow, ...) to prevent the log scale to be destroyed. However this is not a very useful workaround as the final plot has extra margins which I was not able to get rid of.

Answer 1

LogLogPlot plots contain a dynamic objects which when you open the notebook, the security of Mathematica prevents the dynamic objects from being updated. Check this

What you can do is wrap your plot with dynamic and when opened again and when you click Enable Dynamic, you will get the correct plot.

Dynamic@Labeled[LogLogPlot[x, {x, 10^-5, 1}], "Test"]

Answer 2

The workaround suggested by Algohi works but it leads to reevaluation of the entire LogLogPlot each time you open a Notebook. The following workaround avoids this:

With[{g = Labeled[LogLogPlot[x, {x, 10^-5, 1}], "Test"]}, Dynamic@g]

Another workaround is to place this Graphics as Inset inside of another Graphics object:

pl = LogLogPlot[x, {x, 10^-5, 1}];
Labeled[Graphics[{Inset[pl, Center, Center, Scaled[1]]}, 
  Options[pl, {AspectRatio, ImageSize}]], "LogLogPlot"]

(the correct ticks will be generated only after you click the Enable Dynamics button after opening the Notebook).

The essence of the bug is that FrontEnd does not update functional (i.e. Dynamic) Ticks specification when Graphics is enclosed by Labeled. The bug doesn't reveal itself in older Mathematica versions seemingly because in those versions the BoxData of the output Cell in the Notebook contains cached explicit Ticks specification produced during first-time rendering of the output by the FrontEnd (the following is a truncated version of that specification generated by version 8.0.4):

Ticks -> FrontEndValueCache[{Charting`ScaledTicks[{Log, Exp}], 
    Charting`ScaledTicks[{Log, Exp}]}, {{{-13.122363377404328`, 
     FormBox[InterpretationBox[
       StyleBox[GraphicsBox[{}, ImageSize -> {0., 0.}, BaselinePosition -> Baseline], 
        "CacheGraphics" -> False], Spacer[{0., 0.}]], TraditionalForm], {0.005, 
      0.}, {Thickness[0.001]}}, 

When Graphics is wrapped by Labeled Mathematica 10 (as opposed to version 8.0.4) doesn't generate this cache. And it is still ignoring functional Ticks specification when Graphics is wrapped by Labeled.