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`parfor`

A `parfor`

-loop in MATLAB^{®} executes
a series of statements in the loop body in parallel. The MATLAB client
issues the `parfor`

command and coordinates with MATLAB workers
to execute the loop iterations in parallel on the workers in a *parallel
pool*. The client sends the necessary data on which `parfor`

operates
to workers, where most of the computation is executed. The results
are sent back to the client and assembled.

A `parfor`

-loop can provide significantly
better performance than its analogous `for`

-loop,
because several MATLAB workers can compute simultaneously on
the same loop.

Each execution of the body of a `parfor`

-loop
is an *iteration*. MATLAB workers evaluate
iterations in no particular order and independently of each other.
Because each iteration is independent, there is no guarantee that
the iterations are synchronized in any way, nor is there any need
for this. If the number of workers is equal to the number of loop
iterations, each worker performs one iteration of the loop. If there
are more iterations than workers, some workers perform more than one
loop iteration; in this case, a worker might receive multiple iterations
at once to reduce communication time.

A `parfor`

-loop can be
useful if you have a slow `for`

-loop. Consider `parfor`

if
you have:

Some loop iterations that take a long time to execute. In this case, the workers can execute the long iterations simultaneously. Make sure that the number of iterations exceeds the number of workers. Otherwise, you will not use all workers available.

Many loop iterations of a simple calculation, such as a Monte Carlo simulation or a parameter sweep.

`parfor`

divides the loop iterations into groups so that each worker executes some portion of the total number of iterations.

A `parfor`

-loop might
not be useful if you have:

Code that has vectorized out the

`for`

-loops. Generally, if you want to make code run faster, first try to vectorize it. For details how to do this, see Vectorization (MATLAB). Vectorizing code allows you to benefit from the built-in parallelism provided by the multithreaded nature of many of the underlying MATLAB libraries. However, if you have vectorized code and you have access only to*local*workers, then`parfor`

-loops may run slower than`for`

-loops. Do not devectorize code to allow for`parfor`

; in general, this solution does not work well.Loop iterations that take a short time to execute. In this case, parallel overhead dominates your calculation.

You cannot use a `parfor`

-loop
when an iteration in your loop depends on the results of other iterations.
Each iteration must be independent of all others. For help dealing
with independent loops, see Ensure That parfor-Loop Iterations are Independent.
The exception to this rule is to accumulate values in a loop using Reduction Variables.

In deciding
when to use `parfor`

, consider parallel overhead.
Parallel overhead includes the time required for communication, coordination
and data transfer — sending and receiving data — from
client to workers and back. If iteration evaluations are fast, this
overhead could be a significant part of the total time. Consider two
different types of loop iterations:

`for`

-loops with a computationally demanding task. These loops are generally good candidates for conversion into a`parfor`

-loop, because the time needed for computation dominates the time required for data transfer.`for`

-loops with a simple computational task. These loops generally do not benefit from conversion into a`parfor`

-loop, because the time needed for data transfer is significant compared with the time needed for computation.

`parfor`

With Low Parallel OverheadIn this example, you start with a computationally demanding
task inside a `for`

-loop. The `for`

-loops
are slow, and you speed up the calculation using `parfor`

-loops
instead. `parfor`

splits the execution of `for`

-loop
iterations over the workers in a parallel pool.

This example calculates
the spectral radius of a matrix and converts a `for`

-loop
into a `parfor`

-loop. Find out how to measure the
resulting speedup and how much data is transferred to and from the
workers in the parallel pool.

In the MATLAB Editor, enter the following

`for`

-loop. Add`tic`

and`toc`

to measure the computation time.tic n = 200; A = 500; a = zeros(n); for i = 1:n a(i) = max(abs(eig(rand(A)))); end toc

Run the script, and note the elapsed time.

Elapsed time is 31.935373 seconds.

In the script, replace the

`for`

-loop with a`parfor`

-loop. Add`ticBytes`

and`tocBytes`

to measure how much data is transferred to and from the workers in the parallel pool.tic ticBytes(gcp); n = 200; A = 500; a = zeros(n); parfor i = 1:n a(i) = max(abs(eig(rand(A)))); end tocBytes(gcp) toc

Run the new script on four workers, and run it again. Note that the first run is slower than the second run, because the parallel pool takes some time to start and make the code available to the workers. Note the data transfer and elapsed time for the second run.

By default, MATLAB automatically opens a parallel pool of workers on your local machine.

TheStarting parallel pool (parpool) using the 'local' profile ... connected to 4 workers. ... BytesSentToWorkers BytesReceivedFromWorkers __________________ ________________________ 1 15340 7024 2 13328 5712 3 13328 5704 4 13328 5728 Total 55324 24168 Elapsed time is 10.760068 seconds.

`parfor`

run on four workers is about three times faster than the corresponding`for`

-loop calculation. The speed-up is smaller than the ideal speed-up of a factor of four on four workers. This is due to parallel overhead, including the time required to transfer data from the client to the workers and back. Use the`ticBytes`

and`tocBytes`

results to examine the amount of data transferred. Assume that the time required for data transfer is proportional to the size of the data. This approximation allows you to get an indication of the time required for data transfer, and to compare your parallel overhead with other`parfor`

-loop iterations. In this example, the data transfer and parallel overhead are small in comparison with the next example.

The current example has a low parallel overhead and benefits
from conversion into a `parfor`

-loop. Compare this
example with the simple loop iteration in the next example, see Example of parfor With High Parallel Overhead.

For another example of a `parfor`

-loop with
computationally demanding tasks, see Nested parfor-Loops and for-Loops

`parfor`

With High Parallel OverheadIn this example, you write a loop to create a simple sine wave.
Replacing the `for`

-loop with a `parfor`

-loop
does *not* speed up your calculation. This loop
does not have a lot of iterations, it does not take long to execute
and you do not notice an increase in execution speed. This example
has a high parallel overhead and does not benefit from conversion
into a `parfor`

-loop.

Write a loop to create a sine wave. Use

`tic`

and`toc`

to measure the time elapsed.tic n = 1024; A = zeros(n); for i = 1:n A(i,:) = (1:n) .* sin(i*2*pi/1024); end toc

Elapsed time is 0.012501 seconds.

Replace the

`for`

-loop with a`parfor`

-loop. Add`ticBytes`

and`tocBytes`

to measure how much data is transferred to and from the workers in the parallel pool.tic ticBytes(gcp); n = 1024; A = zeros(n); parfor (i = 1:n) A(i,:) = (1:n) .* sin(i*2*pi/1024); end tocBytes(gcp) toc

Run the script on four workers and run the code again. Note that the first run is slower than the second run, because the parallel pool takes some time to start and make the code available to the workers. Note the data transfer and elapsed time for the second run.

Note that the elapsed time is much smaller for the serialBytesSentToWorkers BytesReceivedFromWorkers __________________ ________________________ 1 13176 2.0615e+06 2 15188 2.0874e+06 3 13176 2.4056e+06 4 13176 1.8567e+06 Total 54716 8.4112e+06 Elapsed time is 0.743855 seconds.

`for`

-loop than for the`parfor`

-loop on four workers. In this case, you do not benefit from turning your`for`

-loop into a`parfor`

-loop. The reason is that the transfer of data is much greater than in the previous example, see Example of parfor With Low Parallel Overhead. In the current example, the parallel overhead dominates the computing time. Therefore the sine wave iteration does not benefit from conversion into a`parfor`

-loop.

This example illustrates why high parallel overhead calculations
do not benefit from conversion into a `parfor`

-loop.
To learn more about speeding up your code, see Convert for-Loops Into parfor-Loops

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