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Re: ParallelTable slows down computation

• To: mathgroup at smc.vnet.net
• Subject: [mg105712] Re: [mg105692] ParallelTable slows down computation
• From: Patrick Scheibe <pscheibe at trm.uni-leipzig.de>
• Date: Wed, 16 Dec 2009 06:18:59 -0500 (EST)
• References: <200912151233.HAA15506@smc.vnet.net>

Hi,

Here (Ubuntu 64bit, 4 Cores, Mathematica 7.0.1) the timing is 53 for the
serial evaluation and 22 sec for the parallel computation.

If I try to minimize the data-transfer-overhead which arises when the
kernels return their result, then the speed-up is more visible.
Note the changed stepsize and the semicolon:

ClearSystemCache[];
AbsoluteTiming[
 Table[Integrate[
     Sin[ph]*1/(2 Pi)*Sin[nn*ph]*Cos[mm*ph], {ph, Pi/2, Pi}];, {nn, 0,
     15}, {mm, 0, 15, 1/2}];]

needs 145.314899 seconds

AbsoluteTiming[
 ParallelTable[
   Table[Integrate[
      Sin[ph]*1/(2 Pi)*Sin[nn*ph]*Cos[mm*ph], {ph, Pi/2, Pi}];, {nn, 
     0, 15}],
   {mm, 0, 15, 1/2}]
  ;]

needs 52.036152 seconds. Every call on a new Mathematica-session.

Cheers
Patrick

On Tue, 2009-12-15 at 07:33 -0500, K wrote:
> Hi,
> 
> I was trying to evaluate definite integrals of different product
> combinations of trigonometric functions like so:
> 
> ClearSystemCache[];
> AbsoluteTiming[
>    Table[Integrate[
>      Sin[ph]*1/(2 Pi)*Sin[nn*ph]*Cos[mm*ph], {ph, Pi/2, Pi}], {nn, 0,
>      15}, {mm, 0, 15}];]
> 
> I included ClearSystemCache[] to get comparable results for successive
> runs. Output of the actual matrix result is suppressed. On my dual
> core AMD, I got this result from Mathematica 7.0.1 (Linux x86 64-bit)
> for the above command:
> 
> {65.240614, Null}
> 
> Now I thought that this computation could be almost perfectly
> parallelized by having, e.g., nn = 0,...,7 evaluated by one kernel and
> nn=8, ..., 15 by the other and typed:
> 
> ParallelEvaluate[ClearSystemCache[]];
> AbsoluteTiming[
>   ParallelTable[
>     Integrate[
>      Sin[ph]*1/(2 Pi)*Sin[nn*ph]*Cos[mm*ph], {ph, Pi/2, Pi}], {nn, 0,
>      15}, {mm, 0, 15}, Method -> "CoarsestGrained"];]
> 
> The result, however, was disappointing:
> 
> {76.993888, Null}
> 
> By the way, Kernel[] returns:
> 
> {KernelObject[1,local],KernelObject[2,local]}
> 
> This seems to me that the parallel command should in fact have been
> evaluated by two kernels. With Method-> "CoarsestGrained", I hoped to
> obtain the data splitting I mentioned above. If I do the splitting and
> combining myself, it gets even a bit worse:
> 
> ParallelEvaluate[ClearSystemCache[]];
> AbsoluteTiming[
>    job1=ParallelSubmit[Table[Integrate[Sin[ph]*1/(2 Pi)*Sin[nn*ph]*Cos
> [mm*ph],{ph, Pi/2,Pi}],{nn,0,7},{mm,0,15}]];
>    job2=ParallelSubmit[Table[Integrate[Sin[ph]*1/(2 Pi)*Sin[nn*ph]*Cos
> [mm*ph],{ph, Pi/2,Pi}],{nn,8,15},{mm,0,15}]];
>    {res1,res2}=WaitAll[{job1,job2}];
>    Flatten[{{res1},{res2}},2];]
> 
> Result is here:
> 
> {78.669442,Null}
> 
> I can't believe that the splitting and combining overhead on a single
> machine (no network involved here) can eat up all the gain from
> distributing the actual workload to two kernels. Does anyone have an
> idea what is going wrong here?
> Thanks,
> K.
> 

• References:
  • ParallelTable slows down computation
    • From: K <kgspga@googlemail.com>