Skip to main content

plotting - Color vectors according to a user-defined function 


V[x_,z_]:=x/Sqrt[x^2+z^2];
Ex[x_,z_]=-D[V[x,z],x];
Ez[x_,z_]=-D[V[x,z],z];

The electric field components (Ex,Ez) are to be plotted as a vector field in the x-z plane. In addition, I would like to color the vectors according to |E|^2. The default option:


  VectorColorFunction -> "ThermometerColors"


does not suit here because it plots magnitude of the vectors, but my vectors only contain the real part of the field. Below is my attempt:


vectorplot = 
 VectorPlot[{Re[Ex[x, z]], Re[Ez[x, z]]}, {x, -2*R, 2*R}, {z, -2*R, 
2*R}, 
VectorColorFunction -> Function[{x, z, vx, vz, n}, ColorData["ThermometerColors"]
[Abs[Ex[x,z]]^2+Abs[Ez[x,z]]^2]],

VectorScale -> {0.03, Automatic, None}, 
VectorColorFunctionScaling -> True, VectorPoints -> 25, 
PlotLegends -> BarLegend[Automatic, 

LegendLabel -> HoldForm[Superscript["|E|", 2]], 
LabelStyle -> {FontFamily -> "Helvetica", FontSize -> 18, Black}], AspectRatio -> 1];

Would be grateful for your suggestions.



Answer



So there was nothing wrong with your user-defined color function, the only problem is that you paired it with VectorColorFunctionScaling->True. This means that the x and z values fed to the color function were scaled to lie between 0 and 1. What you really want to do is to scale the field intensity, not the coordinates.


Since your field intensity has a singularity at the origin, you need to choose some maximum intensity value for the color scale, otherwise the arrow at the origin will be red and every other arrow will be blue. Here I choose a maximum intensity of 2,


V[x_, z_] := x/Sqrt[x^2 + z^2];
Ex[x_, z_] = -D[V[x, z], x];
Ez[x_, z_] = -D[V[x, z], z];

R = 1;

With[{vectorscale = {0, 2}},
 Legended[
  VectorPlot[Re@{Ex[x, z], Ez[x, z]}, {x, -2*R, 2*R}, {z, -2*R, 2*R},
   VectorColorFunction ->
    Function[{x, z, vx, vz, n},
     ColorData[{"ThermometerColors", vectorscale}][
      Abs[Ex[x, z]]^2 + Abs[Ez[x, z]]^2]],
   VectorScale -> {0.03, Automatic, None},

   VectorColorFunctionScaling -> False,
   VectorPoints -> 25,
   AspectRatio -> 1],
  BarLegend[{ColorData[{"ThermometerColors", vectorscale}], 
    vectorscale}, LegendLabel -> HoldForm[Superscript["|E|", 2]], 
   LabelStyle -> {FontFamily -> "Helvetica", FontSize -> 18, Black}]
  ]
 ]

enter image description here



Also I moved your BarLegend outside because it seems that VectorPlot will not take a PlotLegends option. I would like to point out that you could write that a bit simpler since your field is real-valued, and therefore the intensity that you are coloring according to is simply the norm squared, and so you could replace Abs[Ex[x, z]]^2 + Abs[Ez[x, z]]^2 with n^2, but I left it like this to be most general, i.e. you could color the arrows according to any scalar field


Finally, you could also display this field using VectorDensityPlot


With[{vectorscale = {0, 5}},
 VectorDensityPlot[{{Re[Ex[x, z]], Re[Ez[x, z]]}, 
   Abs[Ex[x, z]]^2 + Abs[Ez[x, z]]^2}, {x, -2*R, 2*R}, {z, -2*R, 
   2*R},
  VectorScale -> {0.03, Automatic, None},
  VectorPoints -> 25,
  VectorStyle -> White,
  ColorFunction ->(*"ThermometerColors"*)

   Function[{x, z, vx, vz, n}, 
    ColorData["ThermometerColors"][Rescale[n^2, vectorscale]]],
  ColorFunctionScaling -> False,
  PlotLegends ->
   BarLegend[{ColorData[{"ThermometerColors", vectorscale}], 
     vectorscale},
    LegendLabel -> HoldForm[Superscript["|E|", 2]], 
    LabelStyle -> {FontFamily -> "Helvetica", FontSize -> 18, Black}]
  ]
 ]


enter image description here


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more