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plotting - Aborts and beeps without error warning


I have a piece of code that generates a figure, performing a calculation to generate each pixel. At a certain resolution it runs fine, but after a high enough resolution it fails. Mathematica beeps (sounds more line a 'dong') and just stops after a few seconds with no error warnings. How can I run some diagnostics on my code to try and figure out the problem?


I assume it's a memory problem, but when I use the MaxMemoryUsed[] command it was only ~20Mb which doesn't seem that much.


The code is shown below. I adjust the parameter 'res'. Up to res=12 it runs fine but thereafter it fails.


Clear["Global`*"];
startTime = AbsoluteTime[];

f[{rx_, ry_}] := 
 Module[{e1, e2, e3, d1, d2, d3, a, b, c, sol1, sol2, data, round, 
   rArray},
  {e1, e2, e3} = # & /@ {{0, -1}, {Sqrt[3]/2, 1/2}, {-Sqrt[3]/2, 1/2}};
  If[
   Norm[{rx, ry} - e1] <= 1/3 || Norm[{rx, ry} - e2] <= 1/3 || 
    Norm[{rx, ry} - e3] <= 1/3,
   Null,
   {d1, d2, d3} = # - {rx, ry} & /@ {e1, e2, e3};
   {a, b, c} = Norm[#]^-3 & /@ {d1, d2, d3};

   round = 0.000001;
   sol1 =
    If[0 <= ((b + c)^2 - a^2)/(4 b c) <= 1, 0,
     Re[{x, y} /. Solve[
        Round[a b (d2 - d1), round] Sin[{x, y}.(d1 - d2)]
          + Round[b c (d3 - d2), round] Sin[{x, y}.(d2 - d3)]
          + Round[a c (d3 - d1), round] Sin[{x, y}.(d1 - d3)]
         == 0, {x, y}]]];
   sol2 = 
    Sqrt[a^2 + b^2 + c^2 + 2 a b Cos[#.(d1 - d2)] + 

        2 b c Cos[#.(d2 - d3)] + 2 a c Cos[#.(d1 - d3)]] & /@ sol1;
   Min[sol2]
   ]
  ]
res = 20;
rArray = Table[{rx, ry}, {rx, -Sqrt[3]/2, Sqrt[3]/2, 
    Sqrt[3]/res}, {ry, 3/4, -3/4, -3/(2 res)}];
diagram = Map[f, rArray, {2}];
ArrayPlot[diagram, ColorFunction -> "Rainbow", 
 ColorRules -> {0 -> White, Null -> Gray}]

endTime = AbsoluteTime[] - startTime

Answer



Get this code working


You can get the code running under Mma v9, by adding options to Solve:
Adding


VerifySolutions -> False

should work.
And also


VerifySolutions -> True, WorkingPrecision -> MachinePrecision


works on my PC, if res isn't too big.
For bigger res (tested for 50)


VerifySolutions -> False, WorkingPrecision -> MachinePrecision

will make the code working.



Parallelization


You didn't ask for this, but if you execute


ParallelEvaluate[Off[Solve::ifun]]


before the posted code, the Solve::ifun messages will be switched off.
And replacing Map with ParallelMap:


diagram=ParallelMap[f,rArray,{2}];

will speed up the code significantly, if you have more than one core.


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