78 lines
1.8 KiB
Mathematica
78 lines
1.8 KiB
Mathematica
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function varargout = sin(varargin)
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%SIN (overloaded)
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switch class(varargin{1})
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case 'double'
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error('Overloaded SDPVAR/SIN CALLED WITH DOUBLE. Report error')
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case 'sdpvar'
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varargout{1} = InstantiateElementWiseUnitary(mfilename,varargin{:});
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%varargout{1} = InstantiateElementWise(mfilename,varargin{:});
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case 'char'
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% General operator
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operator = struct('convexity','none',...
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'monotonicity','none',...
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'definiteness','none',...
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'model','callback');
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operator.bounds = @bounds;
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operator.convexhull = @convexhull;
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operator.derivative = @(x)(cos(x));
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operator.range = [-1 1];
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operator.domain = [-inf inf];
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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/SIN 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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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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if sin(xL)>=0 & sin(xU)>=0 & xU-xL<pi
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xM = (xL+xU)/2;
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fL = sin(xL);
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fM = sin(xM);
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fU = sin(xU);
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dfL = cos(xL);
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dfM = cos(xM);
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dfU = cos(xU);
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[Ax,Ay,b] = convexhullConcave(xL,xM,xU,fL,fM,fU,dfL,dfM,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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