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

Examples

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Basic Examples  (5)

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:

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  (11)

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:

Applications  (6)

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:

Tabulate histograms of word lengths in various languages:

Show the results in a grid:

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:

Introduced in 2008
 (7.0)
 |
Updated in 2010
 (8.0)