evaluates in parallel the sum .
starts with .
uses steps .
uses successive values , , ….
evaluates in parallel the multiple sum .
Details and Options
- ParallelSum is a parallel version of Sum, which automatically distributes partial summations among different kernels and processors.
- ParallelSum will give the same results as Sum, except for side effects during the computation.
- Parallelize[Sum[expr,iter,…]] is equivalent to ParallelSum[expr,iter,…].
- If an instance of ParallelSum cannot be parallelized it is evaluated using Sum.
- The following options can be given:
Method Automatic granularity of parallelization DistributedContexts $DistributedContexts contexts used to distribute symbols to parallel computations ProgressReporting $ProgressReporting whether to report the progress of the computation
- The Method option specifies the parallelization method to use. Possible settings include:
"CoarsestGrained" break the computation into as many pieces as there are available kernels "FinestGrained" break the computation into the smallest possible subunits "EvaluationsPerKernel"->e break the computation into at most e pieces per kernel "ItemsPerEvaluation"->m break the computation into evaluations of at most m subunits each Automatic compromise between overhead and load balancing
- Method->"CoarsestGrained" is suitable for computations involving many subunits, all of which take the same amount of time. It minimizes overhead, but does not provide any load balancing.
- Method->"FinestGrained" is suitable for computations involving few subunits whose evaluations take different amounts of time. It leads to higher overhead, but maximizes load balancing.
- The DistributedContexts option specifies which symbols appearing in expr have their definitions automatically distributed to all available kernels before the computation.
- The default value is DistributedContexts:>$DistributedContexts with $DistributedContexts:=$Context, which distributes definitions of all symbols in the current context, but does not distribute definitions of symbols from packages.
- The ProgressReporting option specifies whether to report the progress of the parallel computation.
- The default value is ProgressReporting:>$ProgressReporting.
Examplesopen allclose all
Basic Examples (1)
By default, definitions in the current context are distributed automatically:
Do not distribute any definitions of functions:
Distribute definitions for all symbols in all contexts appearing in a parallel computation:
Distribute only definitions in the given contexts:
Restore the value of the DistributedContexts option to its default:
Do not show a temporary progress report:
Show a temporary progress report even if the default setting $ProgressReporting may be False:
Possible Issues (2)
Sums with trivial terms may be slower in parallel than sequentially:
Splitting the computation into as few pieces as possible decreases the parallel overhead:
Sum may employ symbolic methods that are faster than an iterative addition of all terms:
Wolfram Research (2008), ParallelSum, Wolfram Language function, https://reference.wolfram.com/language/ref/ParallelSum.html (updated 2010).
Wolfram Language. 2008. "ParallelSum." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2010. https://reference.wolfram.com/language/ref/ParallelSum.html.
Wolfram Language. (2008). ParallelSum. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ParallelSum.html