function Y = sign(X)
% SIGN   Signum function
% (Quaternion overloading of standard Matlab function.)

% Copyright © 2006 Stephen J. Sangwine and Nicolas Le Bihan.
% See the file : Copyright.m for further details.

% This function is equivalent to unit(X), but we implement it by calling the Matlab function
% using an isomorphic complex number. In the case where X is a complex quaternion we have to
% resort to direct coding, and we call the quaternion unit function. We could choose to use
% unit(X) in both cases, in which case sign(X) would simply be an alias for unit(X).
error(nargchk(1, 1, nargin)), error(nargoutchk(0, 1, nargout))

if isreal(X)
    
    % X is a real quaternion, and we compute the signum of an isomorphic complex number using
    % the standard Matlab sign function, then construct a quaternion with the same axis as the
    % original quaternion.
    
    Y = isoquaternion(sign(isocomplex(X)), X);
else
    
    % X is a complex quaternion, and therefore we cannot use the method
    % above for real quaternions, because it is not possible to construct an
    % isomorphic complex number. We use instead the quaternion unit function.
    
    Y = unit(X);
end;

% Note that a fundamental design feature of the QTFM toolbox is that it should implement all the
% standard Matlab functions and operators that have meaning in both the complex and quaternion
% cases, so that complex code can be easily adapted to work with quaternion matrices. This is why
% we provide the sign function, even though it has a synonym in the unit function. (Why we provide
% the unit function is another issue.)