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@node Evaluation
@chapter 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, which is exactly what the
@code{eval} function lets you do.

@DOCSTRING(eval)

@menu
* Calling a Function by its Name::
* Evaluation in a Different Context::
@end menu

@node Calling a Function by its Name
@section Calling a Function by its Name

The @code{feval} function allows you to call a function from a string
containing its name.  This is useful when writing a function that needs to
call user-supplied functions.  The @code{feval} function takes the name
of the function to call as its first argument, and the remaining 
arguments are given to the function.

The following example is a simple-minded function using @code{feval}
that finds the root of a user-supplied function of one variable using
Newton's method.

@example
@cindex Fordyce, A. P.
@findex newtroot
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
@end example

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.  @xref{Predicates for Numeric Objects}, for example,
for a list of predicates for numeric objects, and see @ref{Status of
Variables}, for a description of the @code{exist} function.

@DOCSTRING(feval)

A similar function @code{run} exists for calling user script files, that
are not necessarily on the user path

@DOCSTRING(run)

@node Evaluation in a Different Context
@section Evaluation in a Different Context

Before you evaluate an expression you need to substitute
the values of the variables used in the expression.  These
are stored in the symbol table.  Whenever the interpreter
starts a new function it saves the current symbol table
and creates a new one, initializing it with the list of
function parameters and a couple of predefined variables
such as @code{nargin}.  Expressions inside the function use the
new symbol table.

Sometimes you want to write a function so that when you
call it, it modifies variables in your own context.  This
allows you to use a pass-by-name style of function,
which is similar to using a pointer in programming languages such
as C.

Consider how you might write @code{save} and @code{load} as
m-files.  For example:

@example
@group
function create_data
  x = linspace (0, 10, 10);
  y = sin (x);
  save mydata x y
endfunction
@end group
@end example

With @code{evalin}, you could write @code{save} as follows:

@example
@group
function save (file, name1, name2)
  f = open_save_file (file);
  save_var(f, name1, evalin ("caller", name1));
  save_var(f, name2, evalin ("caller", name2));
endfunction
@end group
@end example

@noindent
Here, @samp{caller} is the @code{create_data} function and @code{name1}
is the string @code{"x"}, which evaluates simply as the value of @code{x}.

You later want to load the values back from @code{mydata}
in a different context:

@example
@group
function process_data
  load mydata
  @dots{} do work @dots{}
endfunction
@end group
@end example

@noindent
With @code{assignin}, you could write @code{load} as follows:

@example
@group
function load (file)
  f = open_load_file (file);
  [name, val] = load_var (f);
  assignin ("caller", name, val);
  [name, val] = load_var (f);
  assignin ("caller", name, val);
endfunction
@end group
@end example

@noindent
Here, @samp{caller} is the @code{process_data} function.

You can set and use variables at the command prompt
using the context @samp{base} rather than @samp{caller}.

These functions are rarely used in practice.  One
example is the @code{fail (@samp{code}, @samp{pattern})} function
which evaluates @samp{code} in the caller's context and
checks that the error message it produces matches
the given pattern.  Other examples such as @code{save} and @code{load}
are written in C++ where all Octave variables
are in the @samp{caller} context and @code{evalin} is not needed.

@DOCSTRING(evalin)

@DOCSTRING(assignin)
