Use different markers/colors in logarithmic plot depending on sign

Question

Suppose you have the dataset

xData = Table[i, {i, 1, 30}];
yData = RandomReal[{0.995, 1.005}, 30];

and want to plot the difference of yData-1 on a ListLogPlot.

ListLogPlot[Transpose[{xData, yData - 1}], Joined -> True, Mesh -> All]

Of course, there will be negative differences, hence not being plotted. If the differences' signs were unimportant one could just plot Abs[yData-1]. However, if the sign is important: What is a (I am sure there must be something) nice way to e.g. plot the Abs but use different markers for different signs. The only way I can come up with is pre-processing the data into two sets corresponding to the signs and then plot both seperately into the same graph.

Edit: I decided to accept MichaelE2's answer because I did not know anything about VertexColor and it could be very useful for future plotting issues. However, also all other answers are great solutions and I don't mean to depreciate their value by not accepting them - I just think that one answer should be accepted to "close" the question.

Answer 1

You can use VertexColors to color the individual points, since the points are all in a single Point in order.

ListLogPlot[Transpose[{xData, Abs[yData - 1]}], Joined -> True, Mesh -> All] /. 
 Point[p_] :> 
   Point[p, VertexColors -> (Sign[yData - 1] /. {1 -> Black, -1 -> Red, 0 -> Blue})]

Threw in the 0 case even though 0 won't be plotted by ListLogPlot. One could have it print a warning, too.

Answer 2

The colors can be determined by the sign separately like this:

colors = Sign[yData - 1] /. {1 -> Blue, -1 -> Red};

In order to change the color of the individual markers we have to change the Graphics object that ListLogPlot generates. We can view that expression using

plot = ListLogPlot[
 Transpose[{xData, Abs[yData - 1]}],
 Joined -> True, Mesh -> All
 ];
plot // FullForm

We notice that the points are drawn by using the Point graphics primitive, like this:

Point[{{x1,y1},{x2,y2},...}]

In order to define the colors of the markers separately we have to create one Point primitive for each marker. We can do that using Thread:

Thread@Point[{{x1,y1},{x2,y2},...}]
(* Out: {Point[{x1,y1}],Point[{x2,y2}],...} *)

Now we can use Riffle to insert the colors.

plot /. p : Point[_] :> Riffle[colors, Thread[p]]

Answer 3

Fundamentally this isn't much different than what you're suggesting, as far as splitting the data into positive and negative parts,

xData = Table[i, {i, 1, 30}];
yData = RandomReal[{0.995, 1.005}, 30];

ListLogPlot[
 {{#1, Abs@#2}} & @@@ Transpose@{xData, yData - 1},
 PlotStyle -> (yData - 1) /. {x_Real /; Sign[x] == -1 :> Red, 
   x_Real :> Black}
 ]

Answer 4

I propose the Epilog option

xData = Table[i, {i, 1, 30}];
yData = RandomReal[{0.995, 1.005}, 30];

(*Construct the colors and the point objects*)

pts = Point /@ Transpose[{xData, Log@Abs[yData - 1]}];
colors = Sign[yData - 1] /. {1 -> Blue, -1 -> Red};

(*visulization*)

ListLogPlot[
 Transpose[{xData, Abs[yData - 1]}], Joined -> True, 
  Epilog -> Prepend[Riffle[colors, pts], PointSize[Medium]]
]

Answer 5

Style can be used directly on elements of several different plot types.

ListPlot[
  Transpose[{xData, yData - 1}] /.
    {x_, y_?Negative} :> Style[{x, -y}, Red], 
  Joined -> True,
  Mesh -> All,
  ImageSize -> 500
]