ParallelTable

ParallelTable[expr,{imax}]

generates in parallel a list of imax copies of expr.

ParallelTable[expr,{i,imax}]

generates in parallel a list of the values of expr when i runs from 1 to imax.

ParallelTable[expr,{i,imin,imax}]

starts with i=imin.

ParallelTable[expr,{i,imin,imax,di}]

uses steps di.

ParallelTable[expr,{i,{i1,i2,…}}]

uses the successive values i1, i2, ….

ParallelTable[expr,{i,imin,imax},{j,jmin,jmax},…]

gives a nested list. The list associated with i is outermost.

Details and Options

  • ParallelTable is a parallel version of Table that automatically distributes different evaluations of expr among different kernels and processors.
  • ParallelTable will give the same results as Table, except for side effects during the computation.
  • Parallelize[Table[expr,iter, …]] is equivalent to ParallelTable[expr,iter,…].
  • If an instance of ParallelTable cannot be parallelized, it is evaluated using Table.
  • The following options can be given:
  • Method Automaticgranularity of parallelization
    DistributedContexts $DistributedContextscontexts used to distribute symbols to parallel computations
    ProgressReporting $ProgressReportingwhether to report the progress of the computation
  • The Method option specifies the parallelization method to use. Possible settings include:
  • "CoarsestGrained"break the computation into as many pieces as there are available kernels
    "FinestGrained"break the computation into the smallest possible subunits
    "EvaluationsPerKernel"->ebreak the computation into at most e pieces per kernel
    "ItemsPerEvaluation"->mbreak the computation into evaluations of at most m subunits each
    Automaticcompromise between overhead and load balancing
  • Method->"CoarsestGrained" is suitable for computations involving many subunits, all of which take the same amount of time. It minimizes overhead, but does not provide any load balancing.
  • Method->"FinestGrained" is suitable for computations involving few subunits whose evaluations take different amounts of time. It leads to higher overhead, but maximizes load balancing.
  • By default, a nested table is parallelized at the innermost level. With Method->"CoarsestGrained", it is parallelized at the outermost level. With Method->"FinestGrained", it is parallelized at the innermost level.
  • The DistributedContexts option specifies which symbols appearing in expr have their definitions automatically distributed to all available kernels before the computation.
  • The default value is DistributedContexts:>$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

open allclose all

Basic Examples  (6)

ParallelTable works like Table, but in parallel:

A table of the first 10 squares:

A table with i running from 0 to 20 in steps of 2:

Make a 4×3 matrix:

Plot a table:

Longer computations display information about their progress and estimated time to completion:

Scope  (5)

The index in the table can run backward:

Make a triangular array:

Make a 3x2x4 array, or tensor:

Iterate over an existing list:

Make an array from existing lists:

Generalizations & Extensions  (1)

The table index can have symbolic values:

Options  (14)

Method  (7)

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:

By default, a nested table is parallelized fully at the innermost level:

To parallelize only at the first level, use Method"CoarsestGrained":

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:

Applications  (5)

Solve and plot a differential equation for many initial conditions and animate the results:

Explore different parameter values for the sine-Gordon equation in two spatial dimensions:

Apply different algorithms to the same set of data:

Apply a list of different filters to the same image and display the result:

Or apply a list of effects:

Generate 10 frames from an animation and save them to individual files:

Run several batches in parallel:

Each run returns one frame which can be used for checking the correctness:

Remove the generated files:

Quickly show the evaluation of several nontrivial cellular automata:

Properties & Relations  (10)

Parallelization happens along the outermost (first) index:

Using multiple iteration specifications is equivalent to nesting Table functions:

ParallelDo evaluates the same sequence of expressions as ParallelTable:

ParallelSum effectively applies Plus to results from ParallelTable:

ParallelArray iterates over successive integers:

Map applies a function to successive elements in a list:

Table can substitute successive elements in a list into an expression:

ParallelTable iterating over a given list is equivalent to ParallelCombine:

ParallelTable can be implemented with WaitAll and ParallelSubmit:

Parallelization at the innermost level of a multidimensional table:

Functions defined interactively are automatically distributed to all kernels when needed:

Distribute definitions manually and disable automatic distribution:

For functions from a package, use ParallelNeeds rather than DistributeDefinitions:

Possible Issues  (3)

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:

Trivial operations may take longer when parallelized:

Neat Examples  (2)

Visualize the Mandelbrot set:

Calculate and display the Feigenbaum (or bifurcation) diagram of the logistics map:

Wolfram Research (2008), ParallelTable, Wolfram Language function, https://reference.wolfram.com/language/ref/ParallelTable.html (updated 2021).

Text

Wolfram Research (2008), ParallelTable, Wolfram Language function, https://reference.wolfram.com/language/ref/ParallelTable.html (updated 2021).

CMS

Wolfram Language. 2008. "ParallelTable." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ParallelTable.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_paralleltable, author="Wolfram Research", title="{ParallelTable}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/ParallelTable.html}", note=[Accessed: 30-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_paralleltable, organization={Wolfram Research}, title={ParallelTable}, year={2021}, url={https://reference.wolfram.com/language/ref/ParallelTable.html}, note=[Accessed: 30-June-2025 ]}