It may be necessary for some functions to return more than one value. This may be accomplished by returning a vector of values, but many times it is convenient to use passing a reference to a variable. You pass a reference to a variable to a function, and the function will set the variable for you using a dereference. You do not have to use references only for this purpose, but this is their main use.

When using functions that return values through references in the argument list, just pass the variable name with an ampersand. For example the following code will compute an eigenvalue of a matrix A with initial eigenvector guess x, and store the computed eigenvector into the variable named v:

RayleighQuotientIteration (A,x,0.001,100,&v)

The details of how references work and the syntax is similar to the C language. The operator & references a variable and * dereferences a variable. Both can only be applied to an identifier, so **a is not a legal expression in GEL.

References are best explained by an example:

a=1;
b=&a;
*b=2;

now a contains 2. You can also reference functions:

function f(x) = x+1;
t=&f;
*t(3)

gives us 4.

The first time a variable is referenced, it is created in the current context unless it exists. So if we make a function that sets the variable to 2, such as function f(k) = (*k=2), then the call f(&n) will declare a new variable n then the function f will run and set it to 2. So there is no need to write something like n=0;f(&n). A new variable in the current context is created even if a variable exists in a higher context, such as in the global context. So for example after

n=3;
function f(k) = (*k=2);
function g() = (f(&n);print(n));
g();

the variable n is still 3 and not 2. That is because inside g, when n is referenced, it is a new variable in the context of g. The function f then sets this n to 2, and then 2 is printed, but the n in the global context is not touched. So we can use references to get values out of functions and we do not need to explicitly declare them, nor do we have to worry about messing up global variables that the user might be using for something else.