ParallelMap works like Map, but in parallel:

ParallelMap can work with any function:

Use explicit pure functions:

Functions defined interactively can immediately be used in parallel:

Map at level 1 (default):

Map down to level 2:

Map at level 2:

Map down to level 3:

Map on all levels, starting at level 1:

Negative levels:

Positive and negative levels can be mixed:

Different heads at each level:

Not all levels can be parallelized:

ParallelMap can be used on expressions with any head:

Functions with attribute Listable are mapped automatically:

Watch the results appear as they are found:

Solve the arithmetic puzzle:

Write it in symbolic form:

Assign a single-digit number to each letter:

And interpret each word as a number in base 10:

Automate the checking for a particular digit assignment:

To systematically solve this assignment, first get the list of letters:

The puzzle can be solved by considering all permutations of all subsets of eight digits:

Parallelize it:

Only the solutions with are usually considered:

The search can be stopped as soon as a nontrivial solution is found using ParallelTry:

The parallelization happens at the outermost level used:

Map can be parallelized automatically, effectively using ParallelMap:

Show the effect of load balancing with tasks of known size:

Define a number of tasks with known runtimes:

Measure the time for parallel execution:

The speedup obtained (more is better):

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

Scheduling large tasks first gives even better results:

A function of several arguments can be mapped with MapThread:

Get a parallel version by using Parallelize:

MapIndexed passes the index of an element to the mapped function:

Get a parallel version by using Parallelize:

Scan does the same as Map, but without returning a result:

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:

Get the size of all Wolfram Language files in an installation of Mathematica in parallel:

If a level specification prevents parallelization, ParallelMap evaluates like Map:

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

Use a shared variable to support side effects:

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:

Measure the minimum parallel communication overhead:

Compare with a simple calculation done on the master kernel itself:

Functions may simplify short argument lists, but not longer ones:

Such simplification of partial expressions may make parallel mapping impossible:

Prevent simplification of partial expressions and apply the desired function only at the end: