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I'm trying to adapt Nasser's method for using a control variable inside Manipulate to selectively choose what part of the code should be recalculated depending on the controls changed. I've also read his previous notes but the last version seems much more simple and something I can follow.

I need this functionality for a simulation I'm working on about the field lines of an electric dipole.

In the simulation it should be possible to move the two charges q1 and q2 generating the field and also to move a third point P. The point P only serves to see the field line passing through P.

Since the single field line originating from P should have different graphical parameters than the field lines of the "background field" I created two different Streamplots: "fieldlines" is for the general field and "fieldpoint" is for the single line through P. They are combined together with the "Show" command.

So my problem is similar to the one addressed in the first link. If I move the point P I don't want the Streamplot fieldlines of the electric field lines recalculated, but just the Streamplot fieldpoint (dealing with the single line through P). On the contrary both Streamplots should be recalculated when the two charges generating the field are moved or changed.

Up to now, following Nasser's model I've come up with the following "example" code (my intended simulation is much more complicated):

Manipulate[tick;
 Show[f1, f2],
 Grid[{
   {"q1pos", 
    Slider2D[
     Dynamic[q1pos, {q1pos = #; f1 = fieldlines[q1pos, q2pos]; 
        f2 = fieldpoint[q1pos, q2pos, pt];
        tick = Not[tick]} &], {{-6, -6}, {6, 6}}], Dynamic[q1pos]},
   {"q2pos", 
    Slider2D[
     Dynamic[q2pos, {q2pos = #; f1 = fieldlines[q1pos, q2pos]; 
        f2 = fieldpoint[q1pos, q2pos, pt];
        tick = Not[tick]} &], {{-6, -6}, {6, 6}}], 
    Dynamic[q2pos]}, {"pt", 
    Slider2D[Dynamic[pt, {pt = #; f2 = fieldpoint[q1pos, q2pos, pt];
        tick = Not[tick]} &], {{-6, -6}, {6, 6}}], Dynamic[pt]}
   }],
 {{tick, False}, None},
 {{q1pos, {-2, 0}}, None},
 {{q2pos, {2, 0}}, None},
 {{pt, {-2.5, 2}}, None},
 {{f1, fieldlines[{-2, 0}, {2, 0}]}, None},
 {{f2, fieldpoint[{-2, 0}, {2, 0}, {-2.5, 2}]}, None},
 TrackedSymbols :> {tick},
 Initialization :> (
   {
    field[x_Real, y_Real] := Module[{},
      (*heavy computation goes here*)
      {(2 (x - q1pos[[1]]))/
        EuclideanDistance[q1pos, {x, y}]^3 + (-2 (x - q2pos[[1]]))/
        EuclideanDistance[q2pos, {x, y}]^3, (2 (y - q1pos[[2]]))/
        EuclideanDistance[q1pos, {x, y}]^3 + (-2 (y - q2pos[[2]]))/
        EuclideanDistance[q2pos, {x, y}]^3}];
    fieldlines[q1pos_, q2pos_] := Module[{},
      (*heavy computation goes here*)
      StreamPlot[field[x, y], {x, -5, 5}, {y, -5, 5},
       StreamPoints -> pnts,
       StreamScale -> 1/20, ImageSize -> 600]];
    fieldpoint[q1pos_, q2pos_, pt_] := Module[{},
      (*heavy computation goes here*)
      StreamPlot[field[x, y], {x, -5, 5}, {y, -5, 5}, 
       StreamPoints -> {{{pt, {Thickness[0.005], RGBColor[1, 0, 0], 
            Arrowheads[0.02]}}}, Automatic, {ForwardBackward, 400}}, 
       ImageSize -> 600]];
    pnts = Tuples[{-3, -2, -1, 0, 1, 2, 3}, 2]
    }
   )
 ]

But there are problems with this code:

  1. The first run is very slow; the second run is ok (there must be some problem with the inizializaton).
  2. When I move the point P I can see that the Streamplot of the "background" field lines is not recalculated. That's fine and that's what I wanted. Anyway the single field line loses some of the specifications (arrows). The same thing happens when one of the charges q1 or q2 are moved.
  3. I'd like to use three Locator instead of three Slider2D for q1, q2 and P in my simulation, but I haven't found yet if that's possible and how to do that.

Any help?

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1 Answer

up vote 3 down vote accepted

You have few issues there. But nothing major. This runs much faster now. It also fixes the background field lines. Will add more comments later. For you third request, using Locators, needs more time. I'd actually suggest making a new question just for the locator question (your third question, i.e. changing Slider2D to Locator, since this is not related to this method itself and it is not a simple change as 1,2 questions you had).

This below addresses issue 1 and 2.

Some coding things fixed: need to make each function self contained. Do not reference Manipulate internal variables from the Initialization section functions. Pass all these via call parameters. Initialization section should not contain variables assignments. Only definitions (functions, and any other rules). Keep all variables inside Manipulate itself, or inside Modules inside Manipulate.

Added PerformanceGoal to Stream plots. few display changes.

One thing to note with this method, is that Manipulate variables needs to be explicitly initialized, this is the same as when using DynamicModule[{f=,b=},... where each symbol is initialized. This is needed, since Manipulate expression is evaluated first time, and it needs values for this variables. Other than this little house keeping, everything else is standard operating procedures.

enter image description here

Updated

This version has ContinuousAction -> option on each Dynamic. This way one can choose to make it false if needed. When it is true, it is much faster, but does not show the display as the mouse is being moved.

Manipulate[tick;
 Show[f2, f1, ImageSize -> 300],

 Text@Grid[{
    {Grid[{
       {"Q1"},
       {Slider2D[Dynamic[q1pos, {q1pos = #;
            f1 = fieldlines[q1pos, q2pos, pnts];
            f2 = fieldpoint[q1pos, q2pos, pt];
            tick = Not[tick]} &, SynchronousUpdating -> False], {{-6, -6}, {6, 6}}, 
             ContinuousAction -> True]},
       {Dynamic[q1pos]}
       }, Alignment -> Center]}
    ,
    {Grid[{{"Q2"},
       {Slider2D[Dynamic[q2pos, {q2pos = #;
            f1 = fieldlines[q1pos, q2pos, pnts];
            f2 = fieldpoint[q1pos, q2pos, pt];
            tick = Not[tick]} &, SynchronousUpdating -> False], {{-6, -6}, {6, 6}}, 
              ContinuousAction -> True]},
       {Dynamic[q2pos]}
       }, Alignment -> Center]}
    ,
    {Grid[{{"pt"},
       {Slider2D[Dynamic[pt, {pt = #;
            f2 = fieldpoint[q1pos, q2pos, pt];
            tick = Not[tick]} &, SynchronousUpdating -> False], {{-6, -6}, {6, 6}}, 
              ContinuousAction -> True]},
       {Dynamic[pt]}
       }, Alignment -> Center]}
    }, Spacings -> {.5, 1.5}, Alignment -> Center, Frame -> All
   ]
 ,
 {{tick, False}, None},
 {{q1pos, {-2, 0}}, None},
 {{q2pos, {2, 0}}, None},
 {{pt, {-2.5, 2}}, None},
 {{f1, fieldlines[{-2, 0}, {2, 0}, Tuples[{-3, -1, 0, 1, 3}, 2]]}, None},
 {{f2, fieldpoint[{-2, 0}, {2, 0}, {-2.5, 2}]}, None},
 (*{{pnts,Tuples[{-3,-2,-1,0,1,2,3},2]},None},*)
 {{pnts, Tuples[{-3, -1, 0, 1, 3}, 2]}, None},
 ControlPlacement -> Left,
 ContinuousAction -> False,
 SynchronousUpdating -> True,
 SynchronousInitialization -> False,
 TrackedSymbols :> {tick}, Initialization :> (

   field[x_, y_, q1pos_List, q2pos_List] := Module[{},
     {
      (2 (x - q1pos[[1]]))/EuclideanDistance[q1pos, {x, y}]^3 + 
        (-2 (x - q2pos[[1]]))/EuclideanDistance[q2pos, {x, y}]^3
      ,
      (2 (y - q1pos[[2]]))/EuclideanDistance[q1pos, {x, y}]^3 + 
         (-2 (y - q2pos[[2]]))/EuclideanDistance[q2pos, {x, y}]^3}
     ];

   fieldlines[q1pos_List, q2pos_List, pnts_List] := Module[{x, y},
     StreamPlot[field[x, y, q1pos, q2pos], {x, -5, 5}, {y, -5, 5},
      StreamPoints -> pnts, StreamScale -> Automatic , PerformanceGoal -> "Quality"]];

   fieldpoint[q1pos_List, q2pos_List, pt_List] := Module[{x, y},
     StreamPlot[field[x, y, q1pos, q2pos], {x, -5, 5}, {y, -5, 5},
      StreamPoints -> {
        {
         {pt, {Thickness[0.005], RGBColor[1, 0, 0], Arrowheads[0.02]}}
         }, Automatic, {ForwardBackward, 400}}, PerformanceGoal -> "Quality"]
     ]

   )
 ]

Original code

This version defaults to ContinuousAction -> true which makes it much slower, but does show the display as the mouse is being moved.

Manipulate[tick;
 Show[f2, f1, ImageSize -> 300],

 Text@Grid[{
    {Grid[{
       {"Q1"},
       {Slider2D[Dynamic[q1pos, {q1pos = #;
            f1 = fieldlines[q1pos, q2pos, pnts];
            f2 = fieldpoint[q1pos, q2pos, pt];
            tick = Not[tick]} &], {{-6, -6}, {6, 6}, {.1, .1}}]},
       {Dynamic[q1pos]}
       }, Alignment -> Center]}
    ,
    {Grid[{{"Q2"},
       {Slider2D[Dynamic[q2pos, {q2pos = #;
            f1 = fieldlines[q1pos, q2pos, pnts];
            f2 = fieldpoint[q1pos, q2pos, pt];
            tick = Not[tick]} &], {{-6, -6}, {6, 6}, {.1, .1}}]},
       {Dynamic[q2pos]}
       }, Alignment -> Center]}
    ,
    {Grid[{{"pt"},
       {Slider2D[Dynamic[pt, {pt = #;
            f2 = fieldpoint[q1pos, q2pos, pt];
            tick = Not[tick]} &], {{-6, -6}, {6, 6}, {.1, .1}}]},
       {Dynamic[pt]}
       }, Alignment -> Center]}
    }, Spacings -> {.5, 1.5}, Alignment -> Center, Frame -> All
   ]
 ,
 {{tick, False}, None},
 {{q1pos, {-2, 0}}, None},
 {{q2pos, {2, 0}}, None},
 {{pt, {-2.5, 2}}, None},
 {{f1, fieldlines[{-2, 0}, {2, 0}, Tuples[{-3, -2, -1, 0, 1, 2, 3}, 2]]}, None},
 {{f2, fieldpoint[{-2, 0}, {2, 0}, {-2.5, 2}]}, None},
 {{pnts, Tuples[{-3, -2, -1, 0, 1, 2, 3}, 2]}, None},
 ControlPlacement -> Left,
 ContinuousAction -> False,
 SynchronousInitialization -> False,
 TrackedSymbols :> {tick}, 
 Initialization :> (

   field[x_, y_, q1pos_List, q2pos_List] := Module[{},
     {
      (2 (x - q1pos[[1]]))/EuclideanDistance[q1pos, {x, y}]^3 + 
         (-2 (x - q2pos[[1]]))/EuclideanDistance[q2pos, {x, y}]^3
      ,
      (2 (y - q1pos[[2]]))/EuclideanDistance[q1pos, {x, y}]^3 + 
        (-2 (y - q2pos[[2]]))/EuclideanDistance[q2pos, {x, y}]^3}
     ];

   fieldlines[q1pos_List, q2pos_List, pnts_List] := Module[{x, y},
     StreamPlot[field[x, y, q1pos, q2pos], {x, -5, 5}, {y, -5, 5},
      StreamPoints -> pnts, StreamScale -> Automatic , PerformanceGoal -> "Quality"]];

   fieldpoint[q1pos_List, q2pos_List, pt_List] := Module[{x, y},
     StreamPlot[field[x, y, q1pos, q2pos], {x, -5, 5}, {y, -5, 5},
      StreamPoints -> {
        {
         {pt, {Thickness[0.005], RGBColor[1, 0, 0], Arrowheads[0.02]}}
         }, Automatic, {ForwardBackward, 400}}, PerformanceGoal -> "Quality"]
     ]

   )
 ]
share|improve this answer
    
Thanks Nasser! There are great improvements with your code. Anyway it seems that issue 1) is not really solved yet. The first run (just after starting Mathematica) is very slow, and there's a message saying "Formatting Notebook content". After that, if the Manipulate is run a second time everything is fine. –  Luca M Jan 12 at 9:47
    
Windows 8.1/Mathematica 9.0.1. If delete the Manipulate output, quit and restart the kernel the first run is slow (about 10s). It seems that Mathematica must do some heavy work to initialize the front end. –  Luca M Jan 12 at 10:15
    
@LucaM I was able to reproduce it now. Deleting the cell output, then restarting the kernel. But this is just the initialization part. If you just add SynchronousInitialization -> False then now you will see it come right away, and see it updating on the screen with a nice progress chart, instead of what was happening before. The computation in your initialization has to complete before manipulate display the first time. This only happens once. The above should make it more user friendly. I've added SynchronousInitialization -> False, to the code also. –  Nasser Jan 12 at 10:24
    
Yes that's much more better. Anyway I can't understand why, after the first run (and waiting for the initialization to complete), the controls are much unresponsive, unless the manipulate is run a second time. –  Luca M Jan 12 at 10:38
    
@LucaM making dynamics fast and optimized is something that has to be looked at in any method and that is not easy. There are few ways to make it is faster. You can for example make PerformanceGoal->"Speed", you can reduce the numbers/data used by StreamPlot? I am not familiar with StreamPlot and all its options. Also using ControlActive might help. –  Nasser Jan 12 at 11:04
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