modschaffer4(X)

function varargout = modschaffer4(X)
% modified Schaffer function, #4
%
%   MODSCHAFFER4([x1, x2]) returns the value of the 4th Schaffer
%   function at the specified points. [x1] and [x2] may be vectors.
%   The search domain is
%
%               -100 < x_i < 100
%
%   The global minimum is 
%
%               f(x1, x2) = f(0, 1.25313) = 0.292579.

% Author: Rody P.S. Oldenhuis
% Delft University of Technology
% E-mail: [e-mail]
% Last edited 20/Jul/2009

    % if no input is given, return dimensions, bounds and minimum
    if (nargin == 0)
        varargout{1} = 2;  % # dims
        varargout{2} = [-100, -100]; % LB
        varargout{3} = [+100, +100]; % UB
        varargout{4} = [0, 1.253131828927371e+000]; % solution
        varargout{5} = 2.925786320359805e-001; % function value at solution
        
    % otherwise, output function value
    else 

        % keep values within the search interval
        X(X < -100) = inf;      X(X > 100) = inf;
        
        % split input vector X into x1, x2
        if size(X, 1) == 2
            x1 = X(1, :);        x2 = X(2, :);
        else
            x1 = X(:, 1);        x2 = X(:, 2);
        end
        
        % output function value
        varargout{1} = 0.5  + (cos(sin(abs(x1.^2 - x2.^2))).^2 - 0.5) ./ (1+0.001*(x1.^2 + x2.^2)).^2;
    
    end
     
end