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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.

@c eval libinterp/parse-tree/oct-parse.cc
@anchor{XREFeval}
@deftypefn  {Built-in Function} {} eval (@var{try})
@deftypefnx {Built-in Function} {} eval (@var{try}, @var{catch})
Parse the string @var{try} and evaluate it as if it were an Octave
program.  If that fails, evaluate the optional string @var{catch}.
The string @var{try} is evaluated in the current context,
so any results remain available after @code{eval} returns.

The following example creates the variable @var{A} with the approximate
value of 3.1416 in the current workspace.

@example
eval ("A = acos(-1);");
@end example

If an error occurs during the evaluation of @var{try} then the @var{catch}
string is evaluated, as the following example shows:

@example
@group
eval ('error ("This is a bad example");',
      'printf ("This error occurred:\n%s\n", lasterr ());');
     @print{} This error occurred:
        This is a bad example
@end group
@end example

Programming Note: if you are only using @code{eval} as an error-capturing
mechanism, rather than for the execution of arbitrary code strings,
Consider using try/catch blocks or unwind_protect/unwind_protect_cleanup
blocks instead.  These techniques have higher performance and don't introduce
the security considerations that the evaluation of arbitrary code does.
@seealso{@ref{XREFevalin,,evalin}}
@end deftypefn


@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
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 a list of predicates for numeric objects, and @pxref{Status of
Variables}, for a description of the @code{exist} function.

@c feval libinterp/parse-tree/oct-parse.cc
@anchor{XREFfeval}
@deftypefn {Built-in Function} {} feval (@var{name}, @dots{})
Evaluate the function named @var{name}.  Any arguments after the first
are passed as inputs to the named function.  For example,

@example
@group
feval ("acos", -1)
     @result{} 3.1416
@end group
@end example

@noindent
calls the function @code{acos} with the argument @samp{-1}.

The function @code{feval} can also be used with function handles of
any sort (@pxref{Function Handles}).  Historically, @code{feval} was
the only way to call user-supplied functions in strings, but
function handles are now preferred due to the cleaner syntax they
offer.  For example,

@example
@group
@var{f} = @@exp;
feval (@var{f}, 1)
    @result{} 2.7183
@var{f} (1)
    @result{} 2.7183
@end group
@end example

@noindent
are equivalent ways to call the function referred to by @var{f}.  If it
cannot be predicted beforehand whether @var{f} is a function handle,
function name in a string, or inline function then @code{feval} can be used
instead.
@end deftypefn


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

@c run scripts/miscellaneous/run.m
@anchor{XREFrun}
@deftypefn  {Command} {} run @var{script}
@deftypefnx {Function File} {} run ("@var{script}")
Run @var{script} in the current workspace.

Scripts which reside in directories specified in Octave's load
path, and which end with the extension @file{".m"}, can be run simply by
typing their name.  For scripts not located on the load path, use @code{run}.

The file name @var{script} can be a bare, fully qualified, or relative
filename and with or without a file extension.  If no extension is specified,
Octave will first search for a script with the @file{".m"} extension before
falling back to the script name without an extension.

Implementation Note: If @var{script} includes a path component, then
@code{run} first changes the directory to the directory where @var{script}
is found.  @code{run} then executes the script, and returns to the original
directory. 
@seealso{@ref{XREFpath,,path}, @ref{XREFaddpath,,addpath}, @ref{XREFsource,,source}}
@end deftypefn


@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 @qcode{"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.

@c evalin libinterp/parse-tree/oct-parse.cc
@anchor{XREFevalin}
@deftypefn  {Built-in Function} {} evalin (@var{context}, @var{try})
@deftypefnx {Built-in Function} {} evalin (@var{context}, @var{try}, @var{catch})
Like @code{eval}, except that the expressions are evaluated in the
context @var{context}, which may be either @qcode{"caller"} or
@qcode{"base"}.
@seealso{@ref{XREFeval,,eval}, @ref{XREFassignin,,assignin}}
@end deftypefn


@c assignin libinterp/parse-tree/oct-parse.cc
@anchor{XREFassignin}
@deftypefn {Built-in Function} {} assignin (@var{context}, @var{varname}, @var{value})
Assign @var{value} to @var{varname} in context @var{context}, which
may be either @qcode{"base"} or @qcode{"caller"}.
@seealso{@ref{XREFevalin,,evalin}}
@end deftypefn