58 lines
1.3 KiB
Mathematica
58 lines
1.3 KiB
Mathematica
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function varargout = sqrtm_internal(varargin)
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%SQRTM (overloaded)
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switch class(varargin{1})
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case {'double', 'gem', 'sgem'}
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varargout{1} = sqrt(varargin{1});
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case 'sdpvar'
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varargout{1} = InstantiateElementWise(mfilename,varargin{:});
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case 'char'
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X = varargin{3};
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F = (X >= eps);
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varargout{1} = F;
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varargout{2} = struct('convexity','concave','monotonicity','increasing','definiteness','positive','convexhull',@convexhull,'bounds',@bounds,'model','callback','derivative',@(x) 1./(eps + 2*abs(x).^0.5),'inverse',@(x)x.^2);
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varargout{3} = X;
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otherwise
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error('SDPVAR/SQRTM called with CHAR argument?');
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end
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function [L,U] = bounds(xL,xU)
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if xL < 0
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% The variable is not bounded enough yet
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L = 0;
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else
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L = sqrt(xL);
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end
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if xU < 0
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% This is an infeasible problem
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L = inf;
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U = -inf;
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else
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U = sqrt(xU);
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end
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function [Ax, Ay, b] = convexhull(xL,xU)
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if xL < 0 | xU == 0
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Ax = []
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Ay = [];
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b = [];
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else
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fL = sqrt(xL);
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fU = sqrt(xU);
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dfL = 1/(2*sqrt(xL));
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dfU = 1/(2*sqrt(xU));
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[Ax,Ay,b] = convexhullConcave(xL,xU,fL,fU,dfL,dfU);
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remove = isinf(b) | isinf(Ax) | isnan(b);
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if any(remove)
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remove = find(remove);
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Ax(remove)=[];
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b(remove)=[];
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Ay(remove)=[];
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end
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end
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