39 lines
1.3 KiB
Mathematica
39 lines
1.3 KiB
Mathematica
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function varargout = norm_tv(varargin)
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% NORM_TV Returns total variation semi-norm
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switch class(varargin{1})
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case 'double' % What is the numerical value of this argument (needed for displays etc)
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X = varargin{1};
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[n,m] = size(X);
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Dx = [diff(X,1,1);zeros(1,m)];
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Dy = [diff(X,1,2) zeros(n,1)];
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Z = [Dx(:);Dy(:)];
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varargout{1} = sum(sqrt(sum(Z.^2,1)));
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case 'sdpvar'
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varargout{1} = yalmip('define',mfilename,varargin{:});
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case 'char' % YALMIP sends 'model' when it wants the epigraph or hypograph
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if isequal(varargin{1},'graph')
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t = varargin{2};
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X = varargin{3};
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[n,m] = size(X);
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Dx = [diff(X,1,1);zeros(1,m)];
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Dy = [diff(X,1,2) zeros(n,1)];
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T = sdpvar(n,m,'full');
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F = cone([reshape(T,1,[]);reshape(Dx,1,[]);reshape(Dy,1,[])]);
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F = [F, sum(sum(T)) <= t];
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varargout{1} = F;
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varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','positive','model','graph');
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varargout{3} = X;
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else
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varargout{1} = [];
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varargout{2} = [];
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varargout{3} = [];
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end
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otherwise
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end
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