Question

Use the Help Browser to look up information about the standard MATLAB function sortrows and compare the performance of sortrows with the sort-with-carry function created in the previous exercise. To do this, create two copies of a \(1000 \times 2\) element array containing random values, and sort column 1 of each array while carrying along column 2 using both functions. Determine the execution times of each sort function using tic and toe. How does the speed of your function compare with the speed of the standard function sorerows?

Short answer

To compare the performance of MATLAB's built-in 'sortrows' function and a custom 'sort-with-carry' function, create two identical \(1000 \times 2\) arrays filled with random values. Sort one array using 'sortrows' and the other using the 'sort-with-carry' function. Record execution times using 'tic' and 'toc' functions in MATLAB. Generally, the built-in 'sortrows' function will perform faster than the custom 'sort-with-carry' function due to optimization, but actual results can vary based on your computer's hardware and workload.

Step-by-step solution

Creation of Data

To begin, create two \(1000 \times 2\) arrays filled with random values. MATLAB's built-in function 'rand' can be used for this purpose. ```MATLAB A = rand(1000, 2); B = A; ``` Here, array 'A' is copied to 'B' so 'A' and 'B' are identical.

Sorting Array Using MATLAB's sortrows

The built-in function 'sortrows' is used here to sort one of the arrays in ascending order. ```MATLAB tic; % starts timer A_sort = sortrows(A,1); sortR_time = toc; % stops timer and stores execution time ``` In 'sortrows', the second parameter signifies the column by which to sort 'A'. The 'tic' and 'toc' functions are used to measure the execution time.

Create Sort-with-Carry Function

If you have not created a 'sort-with-carry' function before, it would look something like this: ```MATLAB function [sorted_array] = sort_with_carry(array_to_sort) % Sorts the first column in ascending order and carries along the second column [~,idx] = sort(array_to_sort(:,1)); sorted_array = array_to_sort(idx,:); end ``` This function takes an input array, sorts it based on the first column values while carrying along the corresponding values in the second column.

Sorting Array Using Sort-with-Carry Function

Use the custom 'sort-with-carry' function to sort the second array. ```MATLAB tic; % starts timer B_sort = sort_with_carry(B); sortC_time = toc; % stops timer and stores execution time ``` The 'tic' and 'toc' functions are used again to measure the execution time of the 'sort-with-carry' function.

Compare Execution Times

Finally, display and compare the execution times for both the sort function and the sort-with-carry function. ```MATLAB disp(['Execution time of sortrows: ', num2str(sortR_time)]); disp(['Execution time of sort_with_carry: ', num2str(sortC_time)]); ``` 'num2str' function is used here to convert numerical values of times to string so they can be printed using the 'disp' function.

Conclusion

The speed of the 'sortrows' compared with the speed of the 'sort-with-carry' function will be indicated by the execution times. The function with the shorter execution time is the faster one. Usually, built-in functions are optimized and work faster than custom user-defined functions. However, actual results can vary based on the computer's hardware and current workload.

Key concepts

Understanding the sortrows Function in MATLAB

When working with arrays in MATLAB, it is often necessary to sort data based on one or more columns. The sortrows function is a powerful tool for this purpose. It is specifically designed to sort the rows of a matrix based on the values in one or multiple columns. To use sortrows, you simply provide the array you want to sort and the column index by which sorting should be performed.

For instance, consider an array A that has multiple rows and columns. If you want to sort the array based on the values in the first column, you would use A_sorted = sortrows(A,1). This command ensures that all rows are sorted in ascending order, taking into account the values in the first column.

In an educational context, the simplicity of sortrows makes it ideal for students who are learning how to handle and manipulate large sets of data. When introducing this function, highlight practical examples such as sorting a list of students by their grades or organizing data entries based on timestamps. These real-world analogies can make the function's application and importance crystal clear.

Measuring Execution Time in MATLAB

Measuring the execution time of a function in MATLAB is critical, not just for performance analysis but also for optimizing code. Students learning to code often overlook this aspect. The common practice to assess the performance of any block of code is by using the tic and toc functions. You initiate tic before the code block and call toc immediately after it to measure the time elapsed.

To highlight the utility of this concept, present an example where students can compare the runtime of two functions performing the same task. This hands-on experience underlines the fact that efficiency is as paramount as functionality. Additionally, it is a good practice to demonstrate the impact of various operations on execution time, such as loops, large data manipulations, and complex calculations. By grasping the importance of performance metrics early on, students will develop a mindset for writing efficient code and utilizing resources effectively in their future engineering or data analysis roles.

Creating a Custom Sort-with-Carry Function

In MATLAB, creating customized functions adds flexibility to data manipulation tasks. A 'sort-with-carry' function is a classic example; it allows for sorting an array by one column while ensuring associated values in other columns follow the lead value—as if they're bound together or 'carried' with the sorting column. Although sortrows performs this inherently, understanding and implementing a custom version is an educational journey in programming logic and MATLAB functions.

To teach this concept, emphasize the steps of function creation, starting by accepting an array as an input, then using MATLAB's sort function to get sorting indices, and finally using these indices to rearrange the original array. These principles aren't just theoretical—they underpin many real-world algorithms in software that deals with complex data sets. An exercise to improve this could be to add functionality for descending order or to handle multi-column sorting. It's a practical lesson in algorithmic thinking and software customization that will serve students in their computational projects.