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This example shows how to solve an embarrassingly parallel problem with uneven work distribution using `for drange`. The `for drange` splits iterations equally. As a result it can do suboptimal load balancing, which is visible using the parallel profiler.
The procedures described here are also applicable to other work distribution problems.

**Prerequisites**:

Interactive Parallel Mode in Parallel Computing Toolbox™ (See

`pmode`in the user's guide.)

The plots in this example are produced from a 12-node MATLAB® cluster. If not otherwise specified, everything else is shown running on a 4-node local cluster. In particular, all text output is from a local cluster.

This example uses `for drange` to illustrate how you use the profiler to observe suboptimal load distribution. Let's look at this embarrassingly parallel
`for drange` loop.

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Enabling the Parallel Profiler's Data Collection Running the Parallel Profiler Graphical Interface Observing Uneven Work Distribution |

The objective in the `pctdemo_aux_proftaskpar` example is to calculate the `eig` of a random matrix of increasing size, and pick the maximum value from the resulting vector. The crucial issue is the increasing
matrix size based on the loop counter `ii`. Here is the basic iteration:

`v(ii) = max( abs( eig( rand(ii) ) ) )`;

The actual `for` loop can be seen in the example code.

The code for this example can be found in pctdemo_aux_proftaskparpctdemo_aux_proftaskpar.

**Enabling the Parallel Profiler's Data Collection**

A good practice is to reset the parallel profiler on the cluster before turning on mpiprofile in `pmode`. It makes sure the data is cleared and the profiler is off and in default -messagedetail setting.

P>> mpiprofile reset; P>> mpiprofile on;

Inside a `for drange` there cannot be any communication between labs so the `-messagedetail` can be set to simplified (see help `mpiprofile`). If you do not specify the `-messagedetail` option and you run a program with no communication, you get 0s in the communication fields.

```
P>> v = zeros( 1, 300, codistributor() );
P>> tic;pctdemo_aux_proftaskpar('drange');toc;
```

1 Start of for-drange loop. The computational complexity increases with the loop index. Done Elapsed time is 0.718183 seconds.

2 Start of for-drange loop. The computational complexity increases with the loop index. Done Elapsed time is 2.083491 seconds.

3 Start of for-drange loop. The computational complexity increases with the loop index. Done Elapsed time is 6.487598 seconds.

4 Start of for-drange loop. The computational complexity increases with the loop index. Done Elapsed time is 12.927539 seconds.

In this algorithm the elapsed time should always be longest on the last lab. We use `tic toc` here so that we can compare the longest running time to a `parfor`. The use of profiling inside a `parfor` loop with `mpiprofile` is currently not supported.

**Running the Parallel Profiler Graphical Interface**

To get the profiler interface, simply type `mpiprofile viewer` in `pmode`. You can also view data from a parallel job. See the help or documentation for information on how to do this.

```
P>> mpiprofile viewer; % The viewer action also turns off the profiler
```

1 Sending pmode lab2client to the MATLAB client for asynchronous evaluation.

When the profiler interface opens, by default the Function Summary Report is shown for lab 1. Click **Compare max vs min TotalTime** to see the difference in work distribution between the first and last lab for all the functions called. Look at the `pctdemo_aux_proftaskpar` function:

**Observing Uneven Work Distribution**

Here are a few steps for spotting uneven work distribution on the MATLAB workers. Uneven work distribution almost certainly prevents optimal speedup of serial algorithms.

Select

`max Time Aggregate`from the**Manual Comparison Selection**listbox (see Using the Parallel Profiler in Pmode). With this selection you can observe the effective total time for a parallel program.Click

**Compare max vs. min TotalTime**. As you can see, this loop takes much longer on the last MATLAB worker compared to the first one. The`for drange`is clearly not distributing the work correctly, at least on these two labs. To confirm this is true for all the labs, you can use the histogram feature of the Plot View page. Before doing so, click the`pctdemo_aux_proftaskpar`function to get more specific plots.Click

**Plot Time Histograms**to see how the computation time was distributed on the four local labs. Observe the total execution time histogram.

In the top figure of this page, only the first few labs take approximately the same amount of time; the others take significantly longer. This large difference in the total time distribution is an indicator of suboptimal load balancing.

**Using PARFOR for Better Work Distribution**

Optimal performance for this type of parallelism requires manual distribution of the iterations in `pmode` or the use of `parfor` with `parpool`. To get better work distribution (with pmode) in this type of a problem, you need to create a random distribution of the
tasks rather than rely on `for drange` to statically partition the iterations.

Using `parfor` is generally better suited to this type of task. With the `parfor (i=n:N)` construct you get dynamic work distribution which splits the iterations at execution time, across all labs. Thus the cluster
is better utilized. You can see this by running the same function outside of pmode using a `parfor` construct. This results in significantly higher speedup compared to the `for drange`.

To try this with parfor, run the following commands on the MATLAB client outside of `pmode`.

`pmode close;`

`parpool;`

`tic;pctdemo_aux_proftaskpar('parfor');toc;`

You should get an output that looks like: Done Elapsed time is 6.376887 seconds.

There is a significant speedup (it's nearly two times faster on the 4-node cluster) using `parfor` instead of `for drange`, with no change to the actual algorithm. Note that `parfor` operates as a standard `for` loop inside of `pmode`. Please ensure you try parfor outside of pmode to get the speedup. See help for `parpool` and `parfor`.

**Parallelizing Serial for Loops**

To make a serial (iteration independent) `for`-loop parallel you need to add the `drange` option when inside a parallel job, or replace `for` with a `parfor`. The `parfor` loop will only work as intended with `parpool`. You can view the different styles of for loop parallelism in the code shown in this example. See pctdemo_aux_proftaskparpctdemo_aux_proftaskpar. The `parfor` version is under the case `'parfor'` and the `drange` version is under the case `'drange'`.

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