How to exclude multiple ranges from the X-axis in ListPlot

Question

Here I have the codes for my Listplot.

α[δ_, s13_, s12_, θ12_, 
   c13_] := (-180/2 π  ) ArcTan[
    s13^2 s12^2 Sin[
       2 δ Degree]/(c13^2 Cos[2 θ12 Degree] s12^2 + 
        s13^2 s12^2 Sin[2 δ Degree])];

Tab1 = Table[{δ, α[δ, 
     Random[Real, {0.1363, 0.157}], Random[Real, {0.5, 0.595}], 
     Random[Real, {30.002, 36.6}], 
     Random[Real, {0.9906, 0.9875}]]}, {δ, 0, 190, 1 Degree}];

P1 = ListPlot[Tab1, PlotRange -> {-25, 25}, 
  FrameLabel -> {δ, α}, Frame -> True,  PlotStyle -> Red,]

Here I want to omit the points from the plot obtained for the ranges of delta {20,50} and {125,150}. Please suggest how do I do that.

Answer 1

One way is to change the construction of Tab1 in the first place, and simply Join together the ranges that you are going to keep.

Another is to use Select, Cases, or DeleteCases to modify Tab1. With Select, one could do that as

Select[Tab1, Not[20 <= #[[1]] <= 50] && Not[125 <= #[[1]] <= 150] &]

This applies the function in the second argument to each element of the list, and throws away the ones that give False, keeping ("selecting") only those that give True.

As @Louis B mentioned in a comment, you can also represent the interval as Interval[{20, 50}, {125, 150}], and test for membership via IntervalMemberQ. As @Louis B says, the corresponding function to use in the second argument would be Not @ IntervalMemberQ[Interval[{20,50}, {125,150}], First[#]] &.

With DeleteCases, one could do that as

DeleteCases[Tab1, {_?(20 <= # <= 50 || 125 <= # <= 150 &), _}]

This deletes all parts of the expression that match the pattern in the second argument, which matches any list of two expressions, the first of which yields true under the function enclosed in parentheses after ?. Another way to write that pattern is

DeleteCases[Tab1, {x_, _} /; (20 <= x <= 50 || 125 <= x <= 150)]

where x now names the first blank pattern, and /; can be read as "on the condition that".

Hope this helps; let me know if anything is unclear or mysterious!

Answer 2

thorimur's answer explains various ways to remove parts of input data before plotting.

An alternative approach is to hide (rather than remove) parts of the data. This can be done by constructing white rectangles with appropriate coordinates and combine them with the original plot using Show:

listplot = ListPlot[Tab1, PlotStyle -> Red, PlotRange -> {-25, 25}, 
   FrameLabel -> {δ, α}, Frame -> True];


hiddenranges = {{20, 50}, {125, 150}};

Show[listplot, Graphics @ {White, 
  Rectangle[Scaled[{0, -1}, {#, 0}], Scaled[{0, 1}, {#2, 0}]] & @@@ hiddenranges}]