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Slow ParallelDo

Posted 1 month ago
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Hello, I am trying to speed up my code with ParallelDo, but I ended up with a super slow case. Here is an artificial example of the case:

inits = RandomReal[{0, 5}, 10000];
sols = Table[
   NDSolve[{f'[t] == Sin[t], f[0] == inits[[j]]}, f[t], {t, 0, 10}],
   {j, 1, Length[inits]}];

Now, the parallel part

ParallelDo[
  qsol = sols[[1]];
  f[t] /. qsol /. t -> 4
  , {i, 1, 50}
  ] // AbsoluteTiming

this took {15.5051, Null}

qsol = sols[[1]];
ParallelDo[
  f[t] /. qsol /. t -> 4
  , {i, 1, 50}
  ] // AbsoluteTiming

this took {0.01021, Null}

The situation gets worse as the number of sols increases. What is the problem here?

I am guessing that inside the parallel block, sols is copied to each kernel and this copying slows down as the number of elements increases in sols. So, I tried

SetSharedVariable[sols[[1]]];
ParallelDo[
      qsol = sols[[1]];
      f[t] /. qsol /. t -> 4
      , {i, 1, 50}
      ] // AbsoluteTiming

This took {2.07197, Null} which is an improvement.

But when I tried

SetSharedVariable[sols];
ParallelDo[
  qsol = sols[[1]];
  f[t] /. qsol /. t -> 4
  , {i, 1, 50}
  ] // AbsoluteTiming

This took {125.364, Null}. This is ridiculusly long.

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