Represent Infinities in List Ploting

Question

I'm trying to plot a big imported list of data as a result of a simulation, however some of the values are Infinity (represented by "xxx" for example), currently I'm replacing those "xxx" with a "out of the range" numbers, like -1 ( supposing that all resultant data of the simulation is positive).

But this seems to be add-hoc, and problematic if the range of your plotting data covers this -1, is there any nice/professional way to represent Infinite values in Mathematica plots? (supposing that it is essential to show them on the plot).

Answer 1

If you have Mathematica version 10 how about using InfiniteLine?

First generate some dummy data:

d = Table[{x, Sin[x/3.1]}, {x, 0, 10}];

Set a y value to your "infinite" value:

d[[3, 2]] = "xxx";

ListPlot ignores your "xxx" values and we add InfiniteLines using the Epilog:

 ListPlot[d, Epilog -> {Dashed, Red, 
    InfiniteLine[{#1[[1]], 0}, {0, 1}] & /@ Cases[d, {_, "xxx"}]}]

Answer 2

Not that I knew such a built-in function. What about the following idea. Let this be the list in question:

lst = {{1, -0.44}, {2, -0.89}, {3, 0.74}, {4, xxx}, {5, 0.03}, {6, -0.17}, {7, 0.29}, {8, 0.48}, {9, 0.9}, {10, -0.9}};

Then this:

pos = Position[lst, {_, xxx}][[1, 1]];
rangeMin = -1;
rangeMax = 1;
Show[{
  ListPlot[Delete[lst, pos], PlotRange -> {rangeMin, rangeMax}],
  Graphics[{Red, 
    Arrow[{{lst[[pos, 1]], 0}, {lst[[pos, 1]], rangeMax}}]}]
  }]

gives a plot, in which the xxx outlier is shown by a red arrow, as it is shown below.

Have fun!