The example performs a parameter sweep on the Lorenz system of ordinary differential equations, on the parameters $\sigma $ and $\rho $, and shows the chaotic nature of this system.

**Create Parameter Grid**

Define the range of parameters that you want to explore in the parameter sweep.

Create a 2-D grid of parameters by using the `meshgrid`

function.

Create a figure object, and set `'Visible'`

to `true`

so that it opens in a new window, outside of the live script. To visualize the results of the parameter sweep, create a surface plot. Note that initializing the `Z`

component of the surface with `NaN`

creates an empty plot.

**Set Up Parallel Environment**

Create a pool of parallel workers by using the `parpool`

function.

Starting parallel pool (parpool) using the 'local' profile ...
Connected to the parallel pool (number of workers: 6).

To send data from the workers, create a `DataQueue`

object. Set up a function that updates the surface plot each time a worker sends data by using the `afterEach`

function. The `updatePlot`

function is a supporting function defined at the end of the example.

**Perform Parallel Parameter Sweep**

After you define the parameters, you can perform the parallel parameter sweep.

`parfeval`

works more efficiently when you distribute the workload. To distribute the workload, group the parameters to explore into partitions. For this example, split into uniform partitions of size `step`

by using the colon operator (`:`

). The resulting array `partitions`

contains the boundaries of the partitions. Note that you must add the end point of the last partition.

partitions = *1×17*
1 101 201 301 401 501 601 701 801 901 1001 1101 1201 1301 1401 1501 1601

For best performance, try to split into partitions that are:

To represent function executions on parallel workers and hold their results, use future objects.

Offload computations to parallel workers by using the `parfeval`

function. `parameterSweep`

is a helper function defined at the end of this script that solves the Lorenz system on a partition of the parameters to explore. It has one output argument, so you must specify `1`

as the number of outputs in `parfeval`

.

`parfeval`

does not block MATLAB, so you can continue working while computations take place. The workers compute in parallel and send intermediate results through the `DataQueue`

as soon as they become available.

If you want to block MATLAB until `parfeval`

completes, use the `wait`

function on the future objects. Using the `wait`

function is useful when subsequent code depends on the completion of `parfeval`

.

After `parfeval`

finishes the computations, `wait`

finishes and you can execute more code. For example, plot the contour of the resulting surface. Use the `fetchOutputs`

function to retrieve the results stored in the future objects.

If your parameter sweep needs more computational resources and you have access to a cluster, you can scale up your `parfeval`

computations. For more information, see Scale up from Desktop to Cluster.

**Define Helper Functions**

Define a helper function that solves the Lorenz system on a partition of the parameters to explore. Send intermediate results to the MATLAB client by using the `send`

function on the `DataQueue`

object.

Define another helper function that updates the surface plot when new data arrives.