# Control Flow¶

In some cases, a function is simply a fixed set of step by step calculations. But in other cases, some kind of looping or iteration is required. In this section, we’ll cover the different control structures that are allowed within a function definition.

## Branching¶

We’ve already seen use cases involving if statements and expressions. These are, of course, allowed inside functions as well. In fact, in an equation section there is a restriction on if statements that each branch of the if statement (i.e., under all conditions) generate the same number of equations. But that restriction does not apply in an algorithm section (e.g., in a function definition).

## Looping¶

In an equation section, looping is (just like with branching) restricted to ensure that the number of equations generated is the same regardless of the state of the system. For this reason, the only looping construct allowed in an equation section (and, therefore, the only one we have discussed up until now) is the for loop.

The syntax of a for loop is the same in a function as it is in any other context. It identifies an iteration variable and then assigns that iteration variable a set of values contained in a vector, e.g.,

algorithm
for i in 1:10 loop
// Statements
end for;


There two main differences between an equation section and an algorithm section is that an algorithm section uses explicit assignment statements instead of equations and, since there are no equations, there are no concerns about generating a specified number of equations when using if or for.

In addition, an algorithm section allows us the opportunity to be more flexible by permitting the use of while loops as well. A while loop is not permitted in an equation section because, by its very nature, the number of iterations (and, therefore, the number of equations created in an equation section) is unpredictable. But this unpredictability is not an issue in an algorithm section.

As we already saw in the InterpolateVector function from our previous discussion of Interpolation, the syntax for a while loop is:

  while x>=ybar[i+1,1] loop
i := i + 1;
end while;


The main elements of the while loop are the condition expression that determines whether to continue looping and the statements within the while loop.

## break and return¶

When iterating, it is sometimes necessary to terminate the iterations prematurely. For example, in a for loop, the number of iterations is normally determined by the vector of values being iterated over. But there are cases where subsequent iterations are unnecessary. Similarly, in a while loop, it may be convenient to have a check within the while loop that indicates when to terminate. In these cases, a break statement can be used to terminate the innermost loop.

Another issue of control flow involves when to terminate and exit from the algorithm section itself. There are many circumstances in which all the output variables have been assigned their final values. While it is always true that if and else statements can be used to prevent any further calculations and assignments, it is often more readable to simply indicate clearly that no further calculations are needed. In such cases, the return statement can be used to terminate any further processing within a function’s algorithm section. When a return statement is encountered, whatever values are currently associated with the output variables are the ones that will be returned.