I am experimenting with Parallelize and ParallelTable

This is the code I am using:

K[a_, b_, r_] = a*Exp[-r/b]/r;

T = D[K[10^5, 10^9, s], s]/299792^2 /. s -> 7.6

R = Range[0, 7, 0.01];
\[Theta] = Range[0, 2*Pi, 0.05];

RcG[d_, t_] = Sqrt[7.6^2 + d^2 - 2*7.6*d*Cos[t]];
f[a_?NumberQ, b_?NumberQ] := 
  1/299792^2*NIntegrate[K[10^5, 10^9, x], {x, 7.6 - a, b}];

tab = Parallelize[
      d*(K[10^5, 10^9, RcG[d, t]] - K[10^5, 10^9, 7.6] - d*T) + 
     f[d, RcG[d, t]], {d, R}, {t, \[Theta]}]];
p1 = ListPlot3D[tab, InterpolationOrder -> 4]

I want make a 3d plot using the complicated function defined in the table. When computing, Mathem. gives this error a lot of times:

NIntegrate::inumr: The integrand K[100000,1000000000,x] has evaluated to non-numerical values for all sampling points in the region with boundaries {{7.3,7.30039}}.

It doesn't happen without the Parallelize, so this means that I am using it wrongly, but I don't get where. I also used ParallelTable, with the same result.


1) K is a built-in symbol. Don't use this symbol.

2) Use DistributedContexts with ParallelTable

  tab = ParallelTable[1/299792^2*d*(K[10^5, 10^9, RcG[d, t]] - K[10^5, 10^9, 7.6] - d*T) + f[d, RcG[d, t]], {d, R}, {t, \[Theta]}, DistributedContexts -> All];
  • $\begingroup$ Thank you, it works now. Also I didn't know that K is built-in, thanks for that too. $\endgroup$
    – mattiav27
    May 22 '14 at 13:04
  • $\begingroup$ @mattiav27 DistributeContexts is in fact not necessary here and when set to All it can potentially cause problems ... the problem was (1), not (2). $\endgroup$
    – Szabolcs
    May 22 '14 at 16:36

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