ListDensityPlot - Ticks on axis

Question

I have a table of data of dimensions 150x51, each of the 150 points (frequency of a wave) corresponds to to 51 angles. I want to make a ListDensityPlot, and while the command on its own gives me the plot I want, I cannot understand how to change the value points of the axes.

DataRange kind does the job, but I want it to show more names of points. Ticks doesn't seem to work on ListDensityPlot . This is my command:

 ListDensityPlot[1 - RLfrl, ColorFunction -> "TemperatureMap", Frame -> True, PlotLegends -> BarLegend[{"TemperatureMap", {0, 1}}], DataRange -> {{0, Pi/2}, {0, 10^6}}, FrameLabel -> {"Angle of incidence [rad]", "Wave frequency  \[Omega] [\!\(\*SuperscriptBox[\(10\), \(6\)]\) \1/s]"}]    

and this is the picture I get:

Basically I want to refine the x-axis to show more points, and while we're at it, how can I tell him to show me the angles in rad, I.e instead of 1.57 to write π/2 ?

Answer 1

You can use FindDivisions to find ticks that are integer multiples of Pi/2:

• FindDivisions[{$x_{min}$, $x_{max}$}, $n$] finds a list of about $n$ "nice" numbers that divide the interval around $x_{min}$ to $x_{max}$ into equally spaced parts.
• FindDivisions[{$x_{min}$, $x_{max}$, $dx$}, $n$] makes the parts always have lengths that are integer multiples of $dx$.

Example:

data = Table[Sin[x] Cos[ y/200], {y, 0, 1000, 1}, {x, 0, 4 Pi, 4 Pi/ 50}];
ListDensityPlot[data, DataRange -> {{0, 4 Pi}, {0, 1000}}, 
  FrameTicks -> {{Automatic, Automatic}, {FindDivisions[{0, 4 Pi, Pi/2}, 10], Automatic}}]

Compare with Range:

FindDivisions[{0, 2 Pi, Pi/4}, 7]

{0, π/2, π, (3 π)/2, 2 π}

Range[0, 2 Pi, Pi/4]

{0, π/4, π/2, (3 π)/4, π, (5 π)/4, (3 π)/2, (7 π)/4, 2 π}