As we have seen informally along the way, the S-PLUS language allows the user to create objects of mode function. These are true S-PLUS functions that are stored in a special internal form and may be used in further expressions and so on. In the process the language gains enormously in power, convenience and elegance, and learning to write useful functions is one of the main ways to make your use of S-PLUS comfortable and productive.
It should be emphasized that most of the functions supplied as part of the S-PLUS system, such as mean(), var(), postscript() and so on, are themselves written in S-PLUS and thus do not differ materially from user written functions.
A function is defined by an assignment of the form
name <- function(arg
, arg
, ... ) expression
The expression is an S-PLUS expression, (usually a
grouped expression), that uses the arguments, arg
, to calculate a
value. The value of the expression is the value returned for the function.
A call to the function then usually takes the form name(expr, expr, ...) and may occur anywhere a function call is legitimate.
For example, consider a function to emulate directly the MATLAB
backslash command, which returns the coefficients of the orthogonal
projection of the vector 
onto the column space of the matrix, 
.
Thus given a vector 
and a matrix 
then
where 
is a generalized inverse of 
.
> bslash <- function(X, y)
{
X <- qr(X)
qr.coef(X, y)
}
After this object is created it is permanent, like all objects, and may be used in statements such as
regcoeff <- bslash(Design, yvar)
and so on.
The classical S-PLUS function lsfit() does this job quite well, and more. It in turn uses the functions qr() and qr.coef() in the slightly counterintuitive way above to do this part of the calculation. Hence there is probably some value in having just this part isolated in a simple to use function if it is going to be in frequent use. If so, we may wish to make it a matrix binary operator for even more convenient use.