Skip to main content

differential equations - Clicking phase plane with mouse


Here is what I have thus far:


SetOptions[VectorPlot,
  VectorScale -> {0.045, .9, None},
  Axes -> True,

  AxesLabel -> {x, y},
  VectorPoints -> 16,
  VectorStyle -> {GrayLevel[0.8]}];
SetOptions[ContourPlot,
  ContourStyle -> {Orange, Green}];
SetOptions[ParametricPlot,
  PlotStyle -> Blue];

I made the above an initialization cell. Next, I have this:


Manipulate[

 Module[{f, g, tmin, tmax, xmin, xmax, ymin, ymax},
  tmin = -2; tmax = 2;
  xmin = -2; xmax = 4;
  ymin = -4; ymax = 2;
  f[x_, y_] = 2 x - y + 3 (x^2 - y^2) + 2 x y;
  g[x_, y_] = x - 3 y - 3 (x^2 - y^2) + 3 x y;
  ptRules = NSolve[{f[x, y] == 0, g[x, y] == 0}, {x, y}];
  z = NDSolveValue[{{x'[t], y'[t]} == {f[x[t], y[t]], 
         g[x[t], y[t]]}, {x[0], y[0]} == #}, {x[t], y[t]}, {t, tmin, 
       tmax}] & /@ u;

  Show[
   VectorPlot[{f[x, y], g[x, y]}, {x, xmin, xmax}, {y, ymin, ymax}],
   ContourPlot[{f[x, y] == 0, g[x, y] == 0}, {x, xmin, xmax}, {y, 
     ymin, ymax}],
   Graphics[{Red, PointSize[Large], Point[{x, y}] /. ptRules}],
   ParametricPlot[z, {t, tmin, tmax}]]],
 {{u, {}}, Locator, Appearance -> None, LocatorAutoCreate -> All},
 {z, {}, None}, Paneled -> False]

Running the manipulate gives this image.



enter image description here


Now use your mouse to click anywhere in the phase plane vector field and a solution trajectory will be drawn.


Now my question. Each time I click in the vector field, it shrinks, then expands, then draws. Can anything be done to stop this motion (shrink, expand on each click)?


Second question: The cell indicators on the right margin are blinking. What's up with that?




Comments

Post a Comment

Popular posts from this blog

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

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

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more