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