Because NIntegrate[] does not support parallel computation out of the box, I'm doing a simplified version by breaking the integration limit into pieces and using ParallelTable[]. The following code is just a minimum working example in which I used Sinc[] as the integrated function.
iser[x_] := NIntegrate[Sinc[t + x], {t, 0, 100}];
ipar[x_] := Total[ParallelTable[
With[{xx = x}, NIntegrate[Sinc[t + xx], {t, ii*25, ii*25 + 25}]
], {ii, 0, 3}]
];
where iser[] is the usual serialize version, and ipar[] is the parallel version. Then I do DistributeDefinitions[ipar]. Passing a value to iser[] and ipar[] and both give the correct answer:
In[28]:= ipar[3]
Out[28]= -0.270322
But, when I try to run Plot[ipar[x], {x, 0, 10}] // Timing I get error messages that says
NIntegrate::inumr: The integrand Sinc[t+x] has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,25}}.
NIntegrate::inumr: The integrand Sinc[t+x] has evaluated to non-numerical values for all sampling points in the region with boundaries {{50,75}}.
NIntegrate::inumr: The integrand Sinc[t+x] has evaluated to non-numerical values for all sampling points in the region with boundaries {{75,100}}.
NIntegrate::inumr: The integrand Sinc[t+x] has evaluated to non-numerical values for all sampling points in the region with boundaries {{25,50}}.
NIntegrate::nlim: t = 25. ii is not a valid limit of integration.
General::stop: Further output of NIntegrate::nlim will be suppressed during this calculation.
$Aborted
I know I can just generate a table of values and use ListPlot[] instead, but it's not easy to do adaptive sampling as Plot[] does. How can this be fixed?
ipar[x_?NumberQ] := ...– wxffles Nov 9 '12 at 2:23ipar[3]returns the correct value without the query?NumberQ– david sedai Nov 9 '12 at 2:56