109 lines
2.5 KiB
Mathematica
109 lines
2.5 KiB
Mathematica
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function varargout = entropy(varargin)
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%ENTROPY
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%
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% y = ENTROPY(x)
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%
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% Computes/declares concave entropy -sum(x.*log(x))
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%
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% Implemented as evalutation based nonlinear operator. Hence, the concavity
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% of this function is exploited to perform convexity analysis and rigorous
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% modelling.
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%
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% See also CROSSENTROPY, KULLBACKLEIBLER.
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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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% Safe version with defined negative values (helps fmincon when
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% outside feasible region)
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if any(x<=0)
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z = abs(x);z(z==0)=1;
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y = z.*log(z);
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y(x==0) = 0;
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y(x<0) = 3*(x(x<0)-1).^2-3;
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varargout{1} = -sum(y);
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else
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varargout{1} = -sum(x.*log(x));
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end
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case {'sdpvar','ndsdpvar'}
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varargin{1} = reshape(varargin{1},[],1);
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varargout{1} = yalmip('define',mfilename,varargin{1});
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case 'char'
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X = varargin{3};
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F = (X >= 0);
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operator = struct('convexity','concave','monotonicity','none','definiteness','none','model','callback');
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operator.range = [-inf exp(-1)*length(X)];
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operator.domain = [0 inf];
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operator.bounds = @bounds;
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operator.convexhull = @convexhull;
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operator.derivative = @derivative;
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varargout{1} = F;
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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/ENTROPY called with CHAR argument?');
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end
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function df = derivative(x)
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x(x<=0)=eps;
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df = (-1-log(x));
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function [L, U] = bounds(xL,xU)
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t = find(xL==0);
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u = find(xL<0);
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xL(t)=1;
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LU = [-xL.*log(xL) -xU.*log(xU)];
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LU(t,1)=0;
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xL(t) = 0;
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L = min(LU,[],2);
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U = max(LU,[],2);
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U((xL < exp(-1)) & (xU > exp(-1))) = exp(-1);
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L = sum(L);
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U = sum(U);
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function [Ax, Ay, b] = convexhull(xL,xU)
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if length(xL)==1
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xM = (xU+xL)/2;
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f1 = entropy(xL);
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f2 = entropy(xM);
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f3 = entropy(xU);
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df1 = derivative(xL);
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df2 = derivative(xM);
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df3 = derivative(xU);
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[Ax,Ay,b] = convexhullConcave(xL,xM,xU,f1,f2,f3,df1,df2,df3);
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elseif length(xL)==2
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x1 = [xL(1);xL(2)];
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x2 = [xU(1);xL(2)];
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x3 = [xL(1);xU(2)];
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x4 = [xU(1);xU(2)];
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x5 = (xL+xU)/2;
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f1 = entropy(x1);
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f2 = entropy(x2);
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f3 = entropy(x3);
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f4 = entropy(x4);
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f5 = entropy(x5);
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df1 = derivative(x1);
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df2 = derivative(x2);
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df3 = derivative(x3);
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df4 = derivative(x4);
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df5 = derivative(x5);
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[Ax,Ay,b] = convexhullConcave2D(x1,f1,df1,x2,f2,df2,x3,f3,df3,x4,f4,df4,x5,f5,df5);
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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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