Why doesn't ParallelTable work while Table does in Mathematica 11?

Questions
1

I have written a heavy program that my computer is unable to process. Therefore, I decided to use both processor cores for data processing. My code is as follows: (Note that to test the program, set the value of p to a smaller number, such as 5.)

Open in Wolfram Cloud ↗

I used the function LaunchKernels[]; to activate both processor cores, and instead of the Table function, I used the ParallelTable function. However, the program does not produce any output. If I use the Table function, the program works correctly.

Can anyone explain why the program does not work with ParallelTable?

I am using version 11.

2

I mean you don’t store the results I think… normally you have:

 output = (Parallel)Table[…]

You want to do this:

data = ParallelTable[previous code followed by ;
   (Subscript[fdiag, r] - Re[Subscript[fSp, r]])/4
   ,
   {r, 0.01, 3.5, 0.01}
   ];

Here the last statement inside the Table comments is ‘collected’ and store in the data variable…

And then use:

ListLinePlot[data, …]

Btw, using subscripts is bound to fail at some point. You should use that as a typographic construct only.

And in the code you can remove all the subscripts and it will work…

3

Also the use of For loop is very awkward and can be much simplified for readability:

data = ParallelTable[
   pf = \[Rho][r];
   pf /= Tr[pf];
   ef = Chop[Eigenvalues[pf]];
   fdiag = 0;
   fSp = 0;
   Do[
    If[Chop[pf[[i, i]]] =!= 0,
     fdiag -= pf[[i, i]] Log2[pf[[i, i]]]
     ];
    If[ef[[i]] =!= 0,
     fSp -= ef[[i]] Log2[ef[[i]]]
     ];
    ,
    {i, 1, Length[\[Rho][r]]}
    ];
   (fdiag - Re[fSp])/4
   ,
   {r, 0.01, 3.5, 0.01}
   ];

But even these loops are not really needed as the entire thing can be handled in a vector manner:

ClearAll[NewLog2]
SetAttributes[NewLog2, Listable];
NewLog2[val_] := If[Chop[val] == 0, 0, Log2[val]]
data = ParallelTable[
   pf = \[Rho][r];
   pf /= Tr[pf];
   ef = Chop[Eigenvalues[pf]];
   fdiag = -Total[Diagonal[pf] NewLog2[Diagonal[pf]]];
   fSp = -Total[ef NewLog2[ef]];
   (fdiag - Re[fSp])/4
   ,
   {r, 0.01, 3.5, 0.01}
   ];