### 10.3 The while Statement

In programming, a loop means a part of a program that is (or at least can be) executed two or more times in succession.

The `while` statement is the simplest looping statement in Octave. It repeatedly executes a statement as long as a condition is true. As with the condition in an `if` statement, the condition in a `while` statement is considered true if its value is nonzero, and false if its value is zero. If the value of the conditional expression in a `while` statement is a vector or a matrix, it is considered true only if it is non-empty and all of the elements are nonzero.

Octave’s `while` statement looks like this:

    while (condition)
      body
    endwhile

Here body is a statement or list of statements that we call the body of the loop, and condition is an expression that controls how long the loop keeps running.

The first thing the `while` statement does is test condition. If condition is true, it executes the statement body. After body has been executed, condition is tested again, and if it is still true, body is executed again. This process repeats until condition is no longer true. If condition is initially false, the body of the loop is never executed.

This example creates a variable `fib` that contains the first ten elements of the Fibonacci sequence.

    fib = ones (1, 10);
    i = 3;
    while (i <= 10)
      fib (i) = fib (i-1) + fib (i-2);
      i++;
    endwhile

Here the body of the loop contains two statements.

The loop works like this: first, the value of `i` is set to 3. Then, the `while` tests whether `i` is less than or equal to 10. This is the case when `i` equals 3, so the value of the `i`-th element of `fib` is set to the sum of the previous two values in the sequence. Then the `i++` increments the value of `i` and the loop repeats. The loop terminates when `i` reaches 11.

A newline is not required between the condition and the body; but using one makes the program clearer unless the body is very simple.