Parallelize

Parallelize[expr]

evaluates expr using automatic parallelization.

Details and Options

  • Parallelize[expr] automatically distributes different parts of the evaluation of expr among different available kernels and processors.
  • Parallelize[expr] normally gives the same result as evaluating expr, except for side effects during the computation.
  • Parallelize has attribute HoldFirst, so that expressions are not evaluated before parallelization.
  • The Method option for Parallelize 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 for Parallelize specifies which symbols appearing in expr have their definitions automatically distributed to all available kernels before the computation.
  • The default value is DistributedContexts:>$Context, which distributes definitions of all symbols in the current context, but does not distribute definitions of symbols from packages.

Examples

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Basic Examples  (3)

Map a function in parallel:

Generate a table in parallel:

Functions defined interactively can immediately be used in parallel:

Scope  (13)

Listable Functions  (1)

All listable functions with one argument will automatically parallelize when applied to a list:

Implicitly defined lists:

Structure-Preserving Functions  (3)

Many functional programming constructs that preserve list structure parallelize:

The result need not have the same length as the input:

Without a function, Parallelize simply evaluates the elements in parallel:

Reductions  (3)

Count the number of primes up to one million:

Check whether 93 occurs in a list of the first 100 primes:

Check whether a list is free of 5:

The argument does not have to be an explicit List:

Inner and Outer Products  (2)

Inner products automatically parallelize:

Outer products automatically parallelize:

Iterators  (4)

Evaluate a table in parallel, with or without an iterator variable:

Generate an array in parallel:

Evaluate sums and products in parallel:

The evaluation of the function happens in parallel:

The list of file names is expanded locally on the subkernels:

Associative Functions  (1)

Functions with the attribute Flat automatically parallelize:

Generalizations & Extensions  (3)

Listable functions of several arguments:

Only the right side of an assignment is parallelized:

Elements of a compound expression are parallelized one after the other:

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  (4)

Search for Mersenne primes:

Watch the results appear as they are found:

Compute a whole table of visualizations:

Search a range in parallel for local minima:

Choose the best one:

Use a shared function to record timing results as they are generated:

Set up a dynamic bar chart with the timing results:

Run a series of calculations with vastly varying runtimes:

Properties & Relations  (7)

For data parallel functions, Parallelize is implemented in terms of ParallelCombine:

Parallel speedup can be measured with a calculation that takes a known amount of time:

Define a number of tasks with known runtimes:

The time for a sequential execution is the sum of the individual times:

Measure the speedup for parallel execution:

Finest-grained scheduling gives better load balancing and higher speedup:

Scheduling large tasks first gives even better results:

Form the arithmetic expression 1⊗2⊗3⊗4⊗5⊗6⊗7⊗8⊗9 for ⊗ chosen from +, –, *, /:

Each list of arithmetic operations gives a simple calculation:

Evaluating it is easy:

Find all sequences of arithmetic operations that give 0:

Display the corresponding expressions:

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:

Set up a random number generator that is suitable for parallel use and initialize each kernel:

Possible Issues  (8)

Expressions that cannot be parallelized are evaluated normally:

Side effects cannot be used in the function mapped in parallel:

Use a shared variable to support side effects:

If no subkernels are available, the result is computed on the master kernel:

If a function used is not distributed first, the result may still appear to be correct:

Only if the function is distributed is the result actually calculated on the available 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:

Explicitly distribute the definition of a function:

Modify the definition:

The modified definition is automatically distributed:

Suppress the automatic distribution of definitions:

Symbols defined only on the subkernels are not distributed automatically:

The value of $DistributedContexts is not used in Parallelize:

Set the value of the DistributedContexts option of Parallelize:

Restore all settings to their default values:

Trivial operations may take longer when parallelized:

Neat Examples  (1)

Display nontrivial automata as they are found:

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