function varargout = cos(varargin)
%COS (overloaded)

switch class(varargin{1})

 case 'sdpvar'
 varargout{1} = InstantiateElementWiseUnitary(mfilename,varargin{:});
 
 case 'char'
 
 operator = CreateBasicOperator('callback');
 operator.convexity = @convexity;
 operator.bounds = @bounds;
 operator.monotonicity = @monotonicity;
 operator.stationary = @stationary; 
 operator.inflection = @inflection;
 operator.periodic = pi; 
 operator.derivative = @(x)(-sin(x));
 operator.range = [-1 1]; 
 
 varargout{1} = [];
 varargout{2} = operator;
 varargout{3} = varargin{3};

 otherwise
 error(['SDPVAR/' upper(mfilename) ' called with weird argument']);
end

function [L,U] = bounds(xL,xU)
if xU-xL >= 2*pi
 L = -1;
 U = 1;
else
 xL = xL + pi/2;
 xU = xU + pi/2;
 n = floor(( (xL + xU)/2/(2*pi)));
 xL = xL - n*2*pi;
 xU = xU - n*2*pi;
 yL = sin(xL);
 yU = sin(xU);
 L = min([yL yU]);
 U = max([yL yU]);
 if (xL<pi/2 & xU>pi/2) | (xL<-3*pi/2 & xU>-3*pi/2)
 U = 1;
 end
 if (xL < 3*pi/2 & xU > 3*pi/2) | (xL < -pi/2 & xU > -pi/2)
 L = -1;
 end
end

function vexity = convexity(xL,xU)
% Convert to sin
xL = xL + pi/2;
xU = xU + pi/2;
if xU-xL > pi
 vexity = 'none';
else
 n = floor(xU/(2*pi));
 xL = xL - n*2*pi;
 xU = xU - n*2*pi;
	if (xL >= 0 && xU <=pi) || (xL >= -2*pi && xU <=-pi)
 vexity = 'concave';
 elseif (xL >= -pi && xU <= 0) || (xL >= pi && xU <= 2*pi)
 vexity = 'convex';
 else
 vexity = 'none';
 end
end

function mono = monotonicity(xL,xU)
% Convert to sin
xL = xL + pi/2;
xU = xU + pi/2;
if xU-xL > pi
 mono = 'none';
else
 n = floor(xU/(2*pi));
 xL = xL - n*2*pi;
 xU = xU - n*2*pi;
	if (xL >= -pi/2 && xU <=pi/2) || (xL >= 1.5*pi && xU <=2*pi)
 mono = 'increasing';
 elseif (xL >= -1.5*pi && xU <= -pi/2) || (xL >= pi/2 && xU <= 1.5*pi)
 mono = 'decreasing';
 else
 mono = 'none';
 end
end

function inflections = inflection(xL,xU)
r = floor(xU/(pi/2));
t = ceil(xL/(pi/2));
spots = [t:r];
spots = spots(rem(spots,2)~=0);
dir = -double(abs(rem((spots-1)/2,2))==1);
dir(dir==0)=1;
xS = spots*pi/2;
if isempty(xS)
 inflections = [];
else
 xS = [-inf xS];
 dir = [-dir(1) dir];
 inflections = reshape([xS;dir],1,[]);
end

function [xS,fS] = stationary(xL,xU)
r = floor(xU/(pi/2));
t = ceil(xL/(pi/2));
spots = [t:r];
spots = spots(rem(spots,2)==0);
xS = spots*pi/2;
fS = sign(cos(xS));