Evaluation
**********

Normally, you evaluate expressions simply by typing them at the Octave prompt, or by asking Octave to interpret commands that you have saved in a file.

Sometimes, you may find it necessary to evaluate an expression that has been computed and stored in a string, or use a string as the name of a function to call.  The eval and feval functions allow you to do just that, and are necessary in order to evaluate commands that are not known until run time, or to write functions that will need to call user-supplied functions.

 -- Built-in Function: eval (TRY, CATCH)
     Parse the string TRY and evaluate it as if it were an Octave program.  If that fails, evaluate the string CATCH. The string TRY is evaluated in the current context, so any results remain available after eval returns.

 -- Built-in Function: feval (NAME, ...)
     Evaluate the function named NAME.  Any arguments after the first are passed on to the named function.  For example,

          feval ("acos", -1)
               => 3.1416

     calls the function acos with the argument -1.

     The function feval is necessary in order to be able to write functions that call user-supplied functions, because Octave does not have a way to declare a pointer to a function (like C) or to declare a special kind of variable that can be used to hold the name of a function (like EXTERNAL in Fortran).  Instead, you must refer to functions by name, and use feval to call them.

Here is a simple-minded function using feval that finds the root of a user-supplied function of one variable using Newton's method.

     function result = newtroot (fname, x)

     # usage: newtroot (fname, x)
     #
     #   fname : a string naming a function f(x).
     #   x     : initial guess

       delta = tol = sqrt (eps);
       maxit = 200;
       fx = feval (fname, x);
       for i = 1:maxit
         if (abs (fx) < tol)
           result = x;
           return;
         else
           fx_new = feval (fname, x + delta);
           deriv = (fx_new - fx) / delta;
           x = x - fx / deriv;
           fx = fx_new;
         endif
       endfor

       result = x;

     endfunction

Note that this is only meant to be an example of calling user-supplied functions and should not be taken too seriously.  In addition to using a more robust algorithm, any serious code would check the number and type of all the arguments, ensure that the supplied function really was a function, etc.  See Predicates for Numeric Objects, for example, for a list of predicates for numeric objects, and see Status of Variables, for a description of the exist function.