You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: adiff.m
    path of file: ./repos/OPTI/Utilities/@adiff
    
    the code of the file until where you have to start completion: function ad = adiff(a,b,c)
% adiff(x) creates an autodiff object from a column vector x.
% adiff(x,'sparse') makes the adiff jacobian sparse
% adiff(x,dx,firstx) creates an adiff object from parts (internal use only)
%

    
function ad = adiff(a,b,c)
% adiff(x) creates an autodiff object from a column vector x.
% adiff(x,'sparse') makes the adiff jacobian sparse
% adiff(x,dx,firstx) creates an adiff object from parts (internal use only)
%
% The adiff object that results has two parts, a value and a jacobian
% derivative. For example,
% a = adiff(1:10) yields a 10 dimensional adiff object. The value of
% a is 1:10, which are taken to be the values of 10 variables x(1)..x(10).
% The jacobian of a is the matrix dx(i)/dx(j), which is of course I.
%
% Following some calculations, we may have an adiff object b. The value of
% b is the result of the calculation, say some number 'y'. The jacobian of
% b is the row vector dy/dx(i), where x(i) are the original assumed variables. For
% example, if b=sum(a), then the value of b is 55, and the jacobian is ones(1,10).
%
% The value and jacobian can be retrieved using autoget.
%
% One very important restriction is that all the 
% calculations must be done starting with a single adiff object, otherwise
% the jacobian will not be computed correctly. For example, 
% a = adiff(1:10) yields a 10 dimensional adiff object
% b = adiff(1:3) yields a 3 dimensional adiff object; the three values
% of b are in no way related to the 10 values of a.


switch nargin
case 0
   z = struct('x',[],'dx',[],'root',[]);
case 1
   z = struct('x',a(:),'dx',eye(length(a)),'root',a(:));
case 2
   if ischar(b)&strcmp(b,'sparse')
      z = struct('x',a(:),'dx',speye(length(a)),'root',a(:));
   else
      error('Second argument must be ''sparse'' ');
   end