5.2.3. The for...end loop

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

The 'for...end' loop is a control structure used in MATLAB to execute a block of commands multiple times. The loop continues to run until all values in the specified expression have been processed.

1. The syntax consists of 'for', a variable to take on values, followed by an 'expression' that generates those values.
2. The commands you want to repeat are placed between 'for' and 'end'.
3. Upon reaching 'end', MATLAB exits the loop and continues with any subsequent commands.

Think of the 'for...end' loop as a chef following a recipe that needs to be performed multiple times. For example, if the chef needs to bake 5 batches of cookies, they will refer to the instruction 5 times, where each time they follow the same process until all batches are completed.

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

In this example, 'for ii=1:5' means that the loop will run with 'ii' starting at 1 and increasing by 1 until it reaches 5.

• The command 'x=ii*ii' calculates the square of 'ii' each time the loop runs.
• So, it computes the squares of 1, 2, 3, 4, and 5 during the loop's executions.

Imagine a student who needs to calculate the squares of numbers from 1 to 5 as part of their homework. Each time they get an answer (e.g., 1, 4, 9, 16, 25), they write it down, repeating the process until they finish all calculations.

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

Indentation in programming is used to visually separate blocks of code, making it clearer which commands belong to which loops.

• When working with nested loops (a loop inside another loop), proper indentation becomes crucial to ensuring others (and yourself) can easily read and understand your code.
• MATLAB's built-in editor helps by indenting automatically, enhancing code clarity.

Consider a librarian organizing books on shelves. If they arrange all books in an orderly fashion (indented), it's easy for anyone to find the books they need. However, if the books are all randomly placed (no indentation), one might take much longer to locate a specific book.

Multiple for loops can be nested, in which case indentation helps to improve the readability. The following statements form the 5-by-5 symmetric matrix A with (i,j) element i/j for j >= i:

n = 5; A = eye(n);
for j=2:n
    for i=1:j-1
        A(i,j)=i/j;
        A(j,i)=i/j;
    end
end

In this example, nested loops are used to fill a 5-by-5 symmetric matrix 'A'.

1. The outer loop (with variable 'j') runs from 2 to 'n' (which is 5).
2. The inner loop (with variable 'i') runs from 1 to one less than j, effectively ensuring that each upper triangle element is calculated and filled.
3. 'A(i,j) = i/j' stores the ratio of 'i' to 'j' in the matrix, making 'A' symmetric due to 'A(j,i) = i/j'.

Imagine filling out a grid where you need to input values based on the relationships between rows and columns (like a seating arrangement at a party), ensuring that every pair of guests can sit together in symmetry. This is akin to the way the nested loops construct relationships (fill values) in the matrix.

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