ParallelSum

ParallelSum[expr,{i,i_max}]

evaluates in parallel the sum .

ParallelSum[expr,{i,i_min,i_max}]

starts with .

ParallelSum[expr,{i,i_min,i_max,di}]

uses steps .

ParallelSum[expr,{i,{i₁,i₂,…}}]

uses successive values , , …..

ParallelSum[expr,{i,i_min,i_max},{j,j_min,j_max},…]

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.
ParallelSum takes the same Method option as Parallelize.
ParallelSum takes the same DistributedContexts option as ParallelTable.

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Calculations with vastly differing runtimes should be parallelized as finely as possible:

A large number of simple calculations should be distributed into as few batches as possible:

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:

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:

Introduced in 2008

(7.0)

Updated in 2010

(8.0)

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