Today's main topic is loop constructions. Loops perform a given action repeatedly. There are two main flavors of loops: the for loop and the while loop.

A for loop repeats a given action a fixed number of times. The general form of a for loop is

for value = vector
  action
end

The action will be performed length(vector) times, with value set to each element of vector successively. It's probably clearer to see this by example.

example 1: Print the numbers from 1 to 10.

for n = 1:10
  fprintf('The value of n is %i\n', n);
end

example 2: Print the numbers from 10 to 0.

for n = 10:-1:0
  fprintf('%i ');
end
fprintf('blast off!\n');

example 3: Write a mysum function that computes the sum of the elements of a vector.

function s = mysum(x)
% return the sum of the components of vector x
 
  s = 0;               % start with partial sum s = 0
  for i = 1:length(x)  % loop over all elements in x
    s = s + x(i);      % add x(i) to the previously computed partial sum
  end
 
end

example 4: Write a function that computes the factorial of n.

function p = factorial(n)
% return the factorial of n (assume n is a positive integer)
 
  p = 1;               % start with partial product p = 1
  for k = 1:n          % loop k over all integers from 1 to n
    p = p*k;           % multiply previous partial product by k
  end
 
end

The for loop is probably the single most important programming construct in numerical mathematics.

A while loop repeats a given action as long as its condition is true. The general form is

while condition
  action
end

In order for the while loop to terminate, the action must modify variables in the condition. For example, the factorial function above could also be written this way…