72 lines
1.9 KiB
Mathematica
72 lines
1.9 KiB
Mathematica
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function varargout = kullbackleibler(varargin)
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% KULLBACKLEIBLER
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%
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% y = KULLBACKLEIBLER(x,y)
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%
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% Computes/declares the convex Kullback-Leibler divergence sum(x.*log(x./y))
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% Alternatively -sum(x.*log(y/x)), i.e., negated perspectives of log(y)
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%
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% See also ENTROPY, CROSSENTROPY
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switch class(varargin{1})
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case 'double'
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if nargin == 1
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z = varargin{1};
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z = reshape(z,[],2);
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x = z(:,1);
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y = z(:,2);
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else
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x = varargin{1}(:);
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y = varargin{2}(:);
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end
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l = log(x./y);
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l(x<=0) = 0;
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l = real(l);
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varargout{1} = sum(x.*l);
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case {'sdpvar','ndsdpvar'}
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varargin{1} = reshape(varargin{1},[],1);
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varargin{2} = reshape(varargin{2},[],1);
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if length(varargin{1})~=length(varargin{2})
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if length(varargin{1})==1
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varargin{1} = repmat(varargin{1},length(varargin{2}),1);
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elseif length(varargin{2})==1
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varargin{2} = repmat(varargin{2},length(varargin{1}),1);
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else
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error('Dimension mismatch in kullbackleibler')
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end
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end
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varargout{1} = yalmip('define',mfilename,[varargin{1};varargin{2}]);
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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','convex','monotonicity','none','definiteness','none','model','callback');
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operator.range = [-inf inf];
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operator.domain = [0 inf];
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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/KULLBACKLEIBLER called with CHAR argument?');
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end
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function df = derivative(x)
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z = abs(reshape(x,[],2));
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x = z(:,1);
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y = z(:,2);
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% Use KL = -Entropy + Cross Entropy
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df = [1+log(x);0*y] + [-log(y);-x./y];
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