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Page Revision: 2010/08/19 02:06

User Functions are functions that you write yourself. They can only return a single value or a matrix.

Examples

Here's a function to round a floating point number down to the next integer smaller than or equal to the argument.

floor function

Here's a function that returns a matrix. I didn't say it was a useful function.

funny matrix function

As one could see function is defined by its name and arguments given in parenthesis like:

f(x,y):=x+y+a+2.5-f(x)+f(y)-f

On the LHS of the assignment operator there is f as the function name, x,y are function fictive (dummy) arguments. On the RHS is the function definition by an expression. As one can note, functions can have the same name, and are distinguished by different number of arguments like f(x,y)-two arguments, f(x)-one argument. Even f as a variable can exist. Function is called by its name and real arguments. Real arguments can be constants, variables and expression. Function is returning a value and, therefore, may be as a part of an expression.

Besides variables, function can have another function as an argument. Here is an example:

function as function argument

Hints

Redefining the Inputs to a Function

Shown below is a common mistake:

common mistake

Explanation: The common mistake shown above is avoided if the function is defined first. The variables should be assigned to their desired values only after the function is defined. Smath (like Mathcad) calculates from the top-left corner towards the bottom-right corner of the worksheet; therefore, if a variable is defined and then a function is defined using that variable, Smath defines the new function using the previously assigned VALUE of the variable. Changing the variable lower on the worksheet cannot redefine the function because the function was defined higher up on the worksheet. Therefore, if the user wants to be able to edit variable values used within a function, the function must be defined first using previously UNDEFINED variables and then the variables can be defined (and redefined as many times as desired) lower down on the worksheet. See graphic below for correct usage:

correct usage

Function Overloading

Functions can have the same name

Reserved Words

Reserved words?

Redefining SMath function - take care!

Arguments as Scalars or Matrices

Scalar? Matrix? arguments

Defining Functions with 'for' Loop

Using for loop