72 lines
1.8 KiB
Mathematica
72 lines
1.8 KiB
Mathematica
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function varargout = exp(varargin)
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%EXP (overloaded)
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switch class(varargin{1})
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case 'sdpvar'
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x = varargin{1};
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d = size(x);
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x = x(:);
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y = [];
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for i = 1:prod(d)
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xi = extsubsref(x,i);
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if isnumeric(xi)
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y = [y;exp(xi)];
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else
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if isreal(xi)
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if i>1
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y = [y;InstantiateElementWise(mfilename,xi)];
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else
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y = InstantiateElementWise(mfilename,xi);
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end
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else
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re = real(xi);
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im = imag(xi);
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y = [y;exp(re)*(cos(im) + sqrt(-1)*sin(im))];
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end
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end
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end
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varargout{1} = reshape(y,d);
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case 'char'
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varargout{1} = [];
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varargout{2} = createOperator;
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varargout{3} = varargin{3};
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otherwise
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error('SDPVAR/EXP called with CHAR argument?');
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end
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function operator = createOperator
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operator = struct('convexity','convex','monotonicity','increasing','definiteness','positive','model','callback');
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operator.convexhull = @convexhull;
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operator.bounds = @bounds;
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operator.derivative = @(x)exp(x);
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operator.inverse = @(x)log(x);
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operator.range = [0 inf];
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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 = exp(xL);
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U = exp(xU);
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function [Ax, Ay, b, K] = convexhull(xL,xU)
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fL = exp(xL);
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fU = exp(xU);
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if fL == fU
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Ax = [];
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Ay = [];
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b = [];
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else
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dfL = exp(xL);
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dfU = exp(xU);
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% A cut with tangent parallell to upper bound is very efficient
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xM = log((fU-fL)/(xU-xL));
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fM = exp(xM);
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dfM = exp(xM);
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[Ax,Ay,b] = convexhullConvex(xL,xM,xU,fL,fM,fU,dfL,dfM,dfU);
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end
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K = [];
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