64 lines
1.8 KiB
Mathematica
64 lines
1.8 KiB
Mathematica
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function varargout = logistic(varargin)
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% LOGISTIC Returns logistic function 1./(1+exp(-x))
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%
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% y = LOGISTIC(x)
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%
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% For a real vector x, LOGISTIC returns (1+exp(-x)).^-1
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switch class(varargin{1})
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case 'double'
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x = varargin{1};
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varargout{1} = 1./(1+exp(-x));
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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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[M,m] = derivebounds(varargin{3});
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if m >= 0
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operator = struct('convexity','concave','monotonicity','increasing','definiteness','positive','model','callback');
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elseif M <= 0
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operator = struct('convexity','convex','monotonicity','increasing','definiteness','positive','model','callback');
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else
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operator = struct('convexity','none','monotonicity','increasing','definiteness','positive','model','callback');
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end
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operator.convexhull = @convexhull;
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operator.bounds = @bounds;
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operator.derivative = @(x)logistic(x).*(1-logistic(x));
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operator.inverse = @(x)(log(x)-log(1-x));
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operator.range = [0 1];
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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/LOGISTIC called with CHAR argument?');
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end
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% Bounding functions for the branch&bound solver
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function [L,U] = bounds(xL,xU)
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L = 1./(1+exp(-xL));
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U = 1./(1+exp(-xU));
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function [Ax, Ay, b, K] = convexhull(xL,xU)
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if xU <=0
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fL = logistic(xL);
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fU = logistic(xU);
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dfL = fL*(1-fL);
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dfU = fU*(1-fU);
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[Ax,Ay,b] = convexhullConvex(xL,xU,fL,fU,dfL,dfU);
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elseif xL>=0
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fL = logistic(xL);
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fU = logistic(xU);
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dfL = fL*(1-fL);
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dfU = fU*(1-fU);
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[Ax,Ay,b] = convexhullConcave(xL,xU,fL,fU,dfL,dfU);
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else
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Ax = [];
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Ay = [];
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b = [];
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end
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K = [];
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