**Course Title:** MATLAB Programming: Applications in Engineering, Data Science, and Simulation **Section Title:** Parallel Computing and Performance Optimization **Topic:** Speed up a computationally intensive problem using parallel computing techniques in MATLAB (Lab topic) **Objective:** In this lab topic, you will learn how to speed up a computationally intensive problem using parallel computing techniques in MATLAB. You will explore how to use MATLAB's built-in functions, such as `parfor` and `spmd`, to parallelize your code and take advantage of multi-core processors. By the end of this lab, you will be able to identify opportunities for parallelization, apply parallel computing techniques to improve performance, and demonstrate the benefits of parallel computing in MATLAB. **Pre-requisites:** Before starting this lab, you should have: 1. Completed the previous labs on parallel computing and performance optimization. 2. A basic understanding of MATLAB programming and data structures. 3. Access to a multi-core processor or a cluster of computers. **Lab Overview:** In this lab, you will work with a computationally intensive problem, such as a Monte Carlo simulation or a dense matrix multiplication. You will analyze the performance of the problem using profiling tools, identify opportunities for parallelization, and implement parallel computing techniques to speed up the computation. **Step 1: Analyze the Performance of the Problem** 1. Start by creating a simple MATLAB script that performs the computationally intensive task. For example, you can use the following code to perform a dense matrix multiplication: ```matlab % Define the size of the matrices n = 1000; % Generate two random matrices A = rand(n, n); B = rand(n, n); % Perform the matrix multiplication C = A * B; ``` 2. Use the MATLAB Profiler to analyze the performance of the code. You can access the Profiler by clicking on the "Profiler" button in the MATLAB toolbar or by typing `profile on` in the Command Window. Run the script several times to get an accurate measurement of the performance. **Step 2: Identify Opportunities for Parallelization** 1. Examine the Profiler output to identify the parts of the code that are computationally intensive. 2. Look for loops or functions that can be parallelized. In the example above, the matrix multiplication can be parallelized using the `parfor` loop. **Step 3: Implement Parallel Computing Techniques** 1. Use the `parfor` loop to parallelize the matrix multiplication. For example: ```matlab % Define the size of the matrices n = 1000; % Generate two random matrices A = rand(n, n); B = rand(n, n); % Perform the matrix multiplication using parfor parfor i = 1:n C(i, :) = A(i, :) * B(:, i); end ``` 2. Use the `spmd` function to parallelize the computation on a cluster of computers. For example: ```matlab % Define the size of the matrices n = 1000; % Generate two random matrices A = rand(n, n); B = rand(n, n); % Use spmd to parallelize the computation on a cluster spmd C = A * B; end ``` 3. Use distributed arrays to parallelize the computation on a cluster of computers. For example: ```matlab % Define the size of the matrices n = 1000; % Generate two random matrices A = rand(n, n); B = rand(n, n); % Use distributed arrays to parallelize the computation C = A .* B; ``` **Step 4: Compare the Performance** 1. Run the parallelized code and compare the performance with the serial code. 2. Use the Profiler to analyze the performance of the parallelized code. 3. Plot the results to visualize the speedup obtained using parallel computing techniques. **Conclusion:** In this lab, you learned how to speed up a computationally intensive problem using parallel computing techniques in MATLAB. You identified opportunities for parallelization, applied parallel computing techniques to improve performance, and demonstrated the benefits of parallel computing in MATLAB. **Additional Resources:** * MATLAB Parallel Computing Toolbox: <https://www.mathworks.com/products/parallel-computing.html> * MATLAB Distributed Computing Server: <https://www.mathworks.com/products/distrib-comp-server.html> * MATLAB Profiler: <https://www.mathworks.com/help/matlab/matlab_prog/profiling-for-improved-performance.html> **Exercise:** 1. Modify the example code to use the `parfor` loop to parallelize the computation of the matrix multiplication. 2. Use the `spmd` function to parallelize the computation on a cluster of computers. 3. Compare the performance of the parallelized code with the serial code. **Comments/Help:** If you have any questions or need help with this lab, please leave a comment below or contact the instructor. **Next Topic:** In the next topic, you will learn how to develop graphical user interfaces (GUIs) using MATLAB's App Designer. You will learn how to create a GUI, add controls and widgets, and respond to user events.