**Course Title:** MATLAB Programming: Applications in Engineering, Data Science, and Simulation **Section Title:** Functions and Scripts in MATLAB **Topic:** Using anonymous and nested functions in MATLAB **Introduction** In MATLAB, functions are useful for grouping executable code together to create procedural code. So far in this course, we've covered working with arrays and matrices, controlling the flow of our program using control structures, and writing and calling our own functions. However, in our function definitions, each function had a name assigned to it. MATLAB does support another type of function definition in which we do not need to give the function a name. This is called an anonymous function (not strictly anonymous since it has a placeholder name). We also have the option to define functions within another function where they are known as nested functions. In this topic, we will be discussing these two types of functions in MATLAB and how they can be used to simplify our code. **Anonymous Functions** An anonymous function, in MATLAB, is a function definition which lacks a name. Anonymous functions can accept input arguments and return output values like any other function. They are very useful for creating very simple or even complex functions in a single line. **Declaring Anonymous Functions** Declaring anonymous functions follows the following syntax in MATLAB: _functionalForm = @(inputArguments)expression_ Where inputArguments is the set of input arguments and expression is the operation that you want to apply. Let's say we want to create an anonymous function for f(x) = x^2. f = @(x) x^2; Now you can use the f for calculations f(4) The above function will return 16 Another example, say, g(x) = 20 - x^2: g = @(x) 20-x^2; Now, if you run g(4), MATLAB will return 0 as the value for expression g(x) Anonymous functions can also operate on arrays in MATLAB (just like regular functions) Here is a sample anonymous function operating on the vector A. A = [1 2 3 4 5 6 7 8 9] anonfunc = @(n, m) (A.^n).*m; result = anonfunc(2, 6) When you run the result command, MATLAB will return a vector [6 24 54 96 150 216 294 384 486]. This comes from squaring the vector A and then multiplying each of them by six. In anonymous functions, the input variables are limited to 20 characters. Hence the choice between a regular function (m-file), nested functions, or an anonymous function, is the problem complexity --- **Example Exercise:** Write two anonymous functions that represents these: 1. f(x) = 4x - 5 2. g(x,y) = x + y Try calling each of these functions with specific values. **Solution:** 1) f = @(x) 4*x-5 Now when you call, say f(5), MATLAB will return the value 15. 2) g = @(x, y) x+y Now you can call g(5,7), and MATLAB will return 12. The output is case insensitive when called. Now you see why we need to be cautious of variables created or modified inside of control statements within MATLAB —- it can be used globally until they go out of scope. --- **Nested Functions** A nested function is a function that is defined within another function. When a function is nested in a different function, it means a function has a child function. These are particularly useful when we want to break down long, complex functions into smaller functions to increase readibility. **Examples Using Nested Functions** To demonstrate how nested functions can simplify our code, we can use them to define temporary helper functions used in the main function and hide them from our workspace, keeping our workspace free of clutter. We can also have nested functions where they all share data with the parent. An example nested function which could also show shared variables between parent and the nested function. One of their major applications is when used for memory efficiency for solving multiple function input arguments calling parent function for solutions which is also demonstrated below is when calling the parent function a few times solving multiple values. Here is a sample: ```matlab function result = parent(x) m = 2; result = nested(x,m); function fresult = nested(x, m) fresult = m * x; end end A = 20; B = [1 2 3 4]; resultA = parent(A); %%parent result for 20 times m - which is 2 resultB = parent(B); %%parent result for array B times m - which is 2 ``` When calling A which is single result - we return a scalar value of m*x (2*20=40) When calling B [1 2 3 4] we return solution values of m*x -which is in this example(m has value of 2) resultB-[2 4 6 8] This means this function can return scalar value for single scalar input or result array values if array solution is requested by the input argument. At this point you can find an example code of some standard use cases [Example of standard use cases](https://uk.mathworks.com/help/matlab/matlab_prog/nested-functions.html) They have their downsides which include: They also require variables that the nested function uses but are defined before the nested function to be defined before it is called. If the nested function wants to use variables inside the parent function, those variables should have the keyword called **persistent** assigned to them between consecutive calls. **Remember**: Always create an example and call the function with a variable(s) assigned if you are debugging to get answer for yourself why an error may arise from your modified created function. In other terms - Try use examples to create function. At this stage, you should understand when and how nested functions and/or an anonymous function (also known as "lambda functions")-where it can be suitable to define the function of interest - most of which will be mainly and only useful when simplifying larger functions defining nested operation in your solution. We hope you now have the know-how of selecting when the use of these functions should be sought after in selecting how to approach your code from this page. To take this knowledge further, you can look at a couple of documentations listed below for some other function-uses-in problem-solving: * [Anonymous Functions Documentation](https://uk.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html) * [Nested Functions Documentation](https://uk.mathworks.com/help/matlab/matlab_prog/nested-functions.html) At this point, you can give us feedback by leaving a comment below for any part of the course. Should you require further explanations or need help with some function exercises please leave a comment. Next, we move on to the [next topic, introduction to 2D plotting: Line plots, scatter plots, bar graphs, and histograms](https://uk.mathworks.com/help/matlab/2d-plotting.html).