Log-Plots and PlotRange

Question

Why does the PlotRange option in

list=Table[{x,Exp[Sqrt[x]]},{x,0,25}];
ListLogLogPlot[list,PlotRange->{0,10},Joined->True]

not work although there is no error-output? The same holds for ListLogLogPlot.

Answer 1

This is because you gave 0 as the lower limit and $\log (0)=-\infty$. If you look at the implementation of ListLogLogPlot, you'll see that somewhere along the line, the limits are converted to {N@Log@min, N@Log@max} and then plotted with ListPlot and the tick labels are tidied up. This is the specific line in the implementation:

logYPlotRange[{min_?Positive, max_?Positive}, r_] :=  N[{Log[min], Log[max]}]

So an extreme plot range will automatically be converted to something more "reasonable" that displays the plot. However, I do agree that a warning should be included. For instance, if you use -∞ as a plot range in Plot, you get the following warning:

Plot::prng: Value of option PlotRange -> {-∞,1} is not All, Full, Automatic, a positive machine number, or an appropriate list of range specifications. >>

If you want to set the limits for the axes from within PlotRange, then avoid 0. For example:

list = Table[{x, Exp[Sqrt[x]]}, {x, 0, 25}];
ListLogLogPlot[list, Joined -> True, PlotRange -> {{1, 10}, {1, 50}}]

Answer 2

I've seen problems with this before but can't find the reference right now. So here is a solution:

list = Table[{x, Exp[Sqrt[x]]}, {x, 0, 25}];
ListLogLogPlot[list, Joined -> True, PlotRange -> {1, 10}]

or

list = Table[{x, Exp[Sqrt[x]]}, {x, 0, 25}];
ListLogLogPlot[list, Joined -> True, PlotRange -> {All, {1, 10}}]

The problem of course could be called a bug, but in some sense it's also understandable that the plot range specification breaks when you put in a value of 0 for the argument on the x or y axis in a log-log plot. After all, the logarithm isn't defined there. It would be better if the function could recognize this and warn you, instead of ignoring the input altogether.