71 lines
1.7 KiB
Matlab
Executable File
71 lines
1.7 KiB
Matlab
Executable File
function varargout = cos(varargin)
|
|
%COS (overloaded)
|
|
|
|
switch class(varargin{1})
|
|
|
|
case 'double'
|
|
error('Overloaded SDPVAR/COS CALLED WITH DOUBLE. Report error')
|
|
|
|
case 'sdpvar'
|
|
varargout{1} = InstantiateElementWiseUnitary(mfilename,varargin{:});
|
|
|
|
case 'char'
|
|
|
|
operator = struct('convexity','none','monotonicity','none','definiteness','none','model','callback');
|
|
operator.bounds = @bounds;
|
|
operator.derivative = @(x)(-sin(x));
|
|
operator.range = [-1 1];
|
|
operator.convexhull = @convexhull;
|
|
|
|
varargout{1} = [];
|
|
varargout{2} = operator;
|
|
varargout{3} = varargin{3};
|
|
|
|
otherwise
|
|
error('SDPVAR/COS called with CHAR 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 [Ax, Ay, b] = convexhull(xL,xU)
|
|
% Convert to sin
|
|
xL = xL + pi/2;
|
|
xU = xU + pi/2;
|
|
if sin(xL)>=0 & sin(xU)>=0 & xU-xL<pi
|
|
fL = sin(xL);
|
|
fU = sin(xU);
|
|
dfL = cos(xL);
|
|
dfU = cos(xU);
|
|
[Ax,Ay,b] = convexhullConcave(xL,xU,fL,fU,dfL,dfU);
|
|
elseif sin(xL)<=0 & sin(xU)<=0 & xU-xL<pi
|
|
fL = sin(xL);
|
|
fU = sin(xU);
|
|
dfL = cos(xL);
|
|
dfU = cos(xU);
|
|
[Ax,Ay,b] = convexhullConvex(xL,xU,fL,fU,dfL,dfU);
|
|
else
|
|
[Ax,Ay,b] = convexhullGeneral(xL,xU,@sin);
|
|
end
|
|
% Back to cos
|
|
b=b-Ax*pi/2;
|