59 lines
1.4 KiB
Mathematica
59 lines
1.4 KiB
Mathematica
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function varargout = logsumexp(varargin)
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%LOGSUMEXP
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%
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% y = LOGSUMEXP(x)
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%
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% Computes/declares log of sum of exponentials log(sum(exp(x)))
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%
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% Implemented as evalutation based nonlinear operator. Hence, the convexity
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% of this function is exploited to perform convexity analysis and rigorous
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% modelling.
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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} = log(sum(exp(x)));
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case 'sdpvar'
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if min(size(varargin{1}))>1
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x = varargin{1};
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y = [];
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for i = 1:size(x,2)
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y = [y yalmip('define',mfilename,x(:,i))];
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end
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varargout{1} = y;
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elseif max(size(varargin{1}))==1
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varargout{1} = varargin{1};
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else
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varargout{1} = yalmip('define',mfilename,varargin{1});
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end
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case 'char'
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X = varargin{3};
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operator = struct('convexity','convex','monotonicity','none','definiteness','none','model','callback');
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operator.bounds = @bounds;
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operator.derivative = @(x) exp(x)./(sum(exp(x)));
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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} = X;
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otherwise
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error('SDPVAR/LOG called with CHAR argument?');
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end
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function [L, U] = bounds(xL,xU)
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L = log(sum(exp(xL)));
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U = log(sum(exp(xU)));
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function [Ax, Ay, b] = convexhull(xL,xU)
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Ax = [];
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Ay = [];
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b = [];
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