5. Control flow and operators

MATLAB is also a programming language. Like other computer programming languages, MATLAB has some decision making structures for control of command execution. These decision making or control flow structures include for loops, while loops, and if-else-end constructions. Control flow structures are often used in script M-files and function M-files. By creating a file with the extension .m, we can easily write and run programs. We do not need to compile the program since MATLAB is an interpretative (not compiled) language. MATLAB has thousands of functions, and you can add your own using m-files. MATLAB provides several tools that can be used to control the flow of a program (script or function). In a simple program as shown in the previous Chapter, the commands are executed one after the other. Here we introduce the flow control structure that makes possible to skip commands or to execute a specific group of commands.

This chunk introduces the concept of control flow in MATLAB, which refers to how the program decides which command to execute based on certain conditions. Unlike many other programming languages, MATLAB automatically interprets programs without needing compilation, which simplifies the process of writing and executing code. Control flow is essential as it allows a programmer to write more complex programs that can make decisions and repeat actions based on conditions, rather than simply executing commands in a straight line.

Think of control flow as a traffic signal. The light can change based on specific conditions (like time of day or traffic density). Just like how traffic signals control the flow of vehicles based on these conditions, control flow structures in MATLAB decide the flow of commands based on specific criteria.

MATLAB has four control flow structures: the if statement, the for loop, the while loop, and the switch statement.

This overview outlines the four main types of control flow structures in MATLAB. The 'if statement' allows for conditional execution of code, meaning specific code blocks only run if particular conditions are met. The 'for loop' repeats a section of code a predetermined number of times, while the 'while loop' continues executing as long as a specified condition remains true. Lastly, the 'switch statement' is useful for executing different code blocks based on the value of a particular variable. Understanding these structures allows developers to write more efficient and logical programs.

Consider a chef who has different recipes for various types of pasta. The chef checks what ingredients are available ('if statement'), prepares a specific dinner for a set number of guests ('for loop'), or keeps cooking until a dish is ready ('while loop'). The 'switch statement' is like making a meal choice based on what guests want from the available options.

MATLAB supports the variants of 'if' construct.

if ... end

• if ... else ... end

• if ... elseif ... else ... end

The simplest form of the if statement is:

if expression statements end

Here are some examples based on the familiar quadratic formula.

1. discr = bb - 4a*c; if discr < 0 disp('Warning: discriminant is negative, roots are imaginary'); end

2. discr = bb - 4a*c; if discr < 0 disp('Warning: discriminant is negative, roots are imaginary'); else disp('Roots are real, but may be repeated') end

3. discr = bb - 4a*c; if discr < 0 disp('Warning: discriminant is negative, roots are imaginary'); elif discr == 0 disp('Discriminant is zero, roots are repeated') else disp('Roots are real') end

The 'if...end' structure allows you to execute specific commands based on conditions. The simplest form runs a block of statements only if a condition evaluates to true. The 'if...else' variant adds a fallback that executes if the condition is false, while 'if...elseif...else' provides multiple pathways for different outcomes. This flexibility is vital for decision-making in programming.

Imagine a student deciding what to wear based on the weather. If it is raining ('if' condition), they choose a raincoat. If it's sunny ('else'), they pick sunglasses. If it’s cloudy ('elseif'), they might wear a light jacket. This decision-making process mirrors the structure of if-statements.

A relational operator compares two numbers by determining whether a comparison is true or false. Relational operators are:

Relational operators in MATLAB are used to compare values. They can evaluate conditions to determine the truthfulness of a statement. For example, if you want to check if the value of 'x' is greater than 10, you would use the '>' operator. Logical operators like AND (&), OR (|), and NOT (~) allow for complex conditions that can combine multiple expressions—essential for more intricate decision-making processes.

Think of relational operators like asking questions to determine eligibility. If you’re checking if a person is eligible for a discount, you might ask if they are a member ('x > 10'). If they are both a member and a student, you would use the AND operator to check both conditions together. This logical comparison helps in making decisions based on multiple factors.

In the for ... end loop, the execution of a command is repeated at a fixed and predetermined number of times. The syntax is:

for variable = expression statements end

Usually, expression is a vector of the form i:s:j. A simple example of for loop is:

for ii=1:5 x=ii*ii end

It is a good idea to indent the loops for readability, especially when they are nested. Note that MATLAB editor does it automatically.

The 'for...end' loop allows programming repetitive tasks by executing code a set number of times, defined by a specific range. The variable iterates through each value in this range, executing the included statements for each value. This simplifies repetitive calculations and is often used in tasks like calculating sums, generating sequences, or operating on arrays.

Consider a factory producing daily widgets. Each day, the line runs through the same steps to produce a set number of widgets, say five. The 'for' loop is like the machine that's programmed to follow a specific procedure five times daily. This automation increases efficiency and consistency in production.

This loop is used when the number of passes is not specified. The looping continues until a stated condition is satisfied. The while loop has the form:

while expression statements end

The statements are executed as long as expression is true.

The 'while...end' loop is designed for scenarios where you want to continue executing commands as long as a certain condition holds true. Unlike the 'for' loop, it doesn't rely on a predetermined number of iterations, making it flexible for tasks where the end condition can only be known during execution. However, it’s critical to ensure that the condition will eventually become false; otherwise, you may create an infinite loop.

Think of a runner training for a marathon. They will keep running ('while' the runner feels good) until they feel tired or reach a destination. If there's no limit to stop (like a bad condition), they could hypothetically keep running indefinitely. The 'while' loop behaves similarly when conditions aren't carefully defined.

The break statement. A while loop can be terminated with the break statement, which passes control to the first statement after the corresponding end. The break statement can also be used to exit a for loop. The continue statement can also be used to exit a for loop to pass immediately to the next iteration of the loop, skipping the remaining statements in the loop.

In MATLAB, the 'break' statement is crucial for controlling loop execution. By using 'break', you can stop the loop entirely when a certain condition is met, while 'continue' skips the remaining code in the current iteration and moves to the next one. This allows for dynamic control of flow within loops, enabling more complex and efficient program designs.

Think about a driver on a long highway trip. If they approach a town ('break'), they’ll exit to explore. If they see a service station ('continue') but don’t need service, they just drive past to the next destination without stopping. Loops operate similarly, providing you with control over your journey through the code.

We can build expressions that use any combination of arithmetic, relational, and logical operators. Precedence rules determine the order in which MATLAB evaluates an expression. The precedence rules for MATLAB are shown in this list (ordered from highest to lowest):

1. Parentheses ()
2. Transpose, power, matrix power
3. Unary plus, unary minus, logical negation
4. Multiplication, right division, left division, matrix multiplication, matrix right division, matrix left division
5. Addition, subtraction
6. Colon operator
7. Less than, less than or equal to, greater than, greater than or equal to, equal to, not equal to
8. Element-wise AND
9. Element-wise OR

Understanding operator precedence is essential for writing accurate MATLAB expressions. When mathematical operations occur in an expression, MATLAB evaluates them based on a set hierarchy, ensuring that certain operations occur before others (like multiplication before addition). Using parentheses correctly can help alter this order and clarify intent, guaranteeing the right calculations take place.

Consider preparing a complex recipe. You need to follow a specific order of steps: chopping vegetables, sautéing them, and then adding them to the sauce. If you don’t follow this order, the dish might not turn out correctly (like doing addition before multiplication in math). Using parentheses is akin to setting aside the necessary steps to ensure everything cooks to perfection.

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