ParallelArray

ParallelArray[f,n]

generates in parallel a list of length n, with elements f[i], evaluated.

ParallelArray[f,{n1,n2,…}]

generates in parallel an array of nested lists, with elements f[i1,i2,…].

ParallelArray[f,{n1,n2,…},{r1,r2,…}]

generates in parallel a list using the index origins ri (default 1).

ParallelArray[f,dims,origin,h]

uses head h, rather than List, for each level of the array.

Details and Options

  • ParallelArray is a parallel version of Array, which automatically distributes different evaluations of expr among different kernels and processors.
  • ParallelArray will give the same results as Array, except for side effects during the computation.
  • Parallelize[Array[f,n]] is equivalent to ParallelArray[f,n].
  • If an instance of ParallelArray cannot be parallelized it is evaluated using Array.
  • The following options can be given:
  • MethodAutomaticgranularity of parallelization
    DistributedContexts$DistributedContextscontexts used to distribute symbols to parallel computations
    ProgressReporting$ProgressReportingwhether 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"->ebreak the computation into at most e pieces per kernel
    "ItemsPerEvaluation"->mbreak the computation into evaluations of at most m subunits each
    Automaticcompromise 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.

Examples

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Basic Examples  (3)

ParallelArray works like Array, but in parallel:

Generate a array:

Generate a array:

Use index origin 0 instead of 1:

Start with indices 0 and 4 instead of 1:

Options  (13)

Method  (6)

Break the computation into the smallest possible subunits:

Break the computation into as many pieces as there are available kernels:

Break the computation into at most 2 evaluations per kernel for the entire job:

Break the computation into evaluations of at most 5 elements each:

The default option setting balances evaluation size and number of evaluations:

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:

DistributedContexts  (5)

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:

ProgressReporting  (2)

Do not show a temporary progress report:

Use Method"FinestGrained" for the most accurate progress report:

Possible Issues  (2)

A function used that is not known on the parallel kernels may lead to sequential evaluation:

Define the function on all parallel kernels:

The function is now evaluated on the parallel kernels:

Definitions of functions in the current context are distributed automatically:

Definitions from contexts other than the default context are not distributed automatically:

Use DistributeDefinitions to distribute such definitions:

Alternatively, set the DistributedContexts option to include all contexts:

Wolfram Research (2008), ParallelArray, Wolfram Language function, https://reference.wolfram.com/language/ref/ParallelArray.html (updated 2010).

Text

Wolfram Research (2008), ParallelArray, Wolfram Language function, https://reference.wolfram.com/language/ref/ParallelArray.html (updated 2010).

CMS

Wolfram Language. 2008. "ParallelArray." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2010. https://reference.wolfram.com/language/ref/ParallelArray.html.

APA

Wolfram Language. (2008). ParallelArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ParallelArray.html

BibTeX

@misc{reference.wolfram_2021_parallelarray, author="Wolfram Research", title="{ParallelArray}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ParallelArray.html}", note=[Accessed: 16-May-2022 ]}

BibLaTeX

@online{reference.wolfram_2021_parallelarray, organization={Wolfram Research}, title={ParallelArray}, year={2010}, url={https://reference.wolfram.com/language/ref/ParallelArray.html}, note=[Accessed: 16-May-2022 ]}