42 lines
1.3 KiB
Mathematica
42 lines
1.3 KiB
Mathematica
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function varargout = norm_nuclear(varargin)
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% NORM_NUCLEAR Returns sum of singular values
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%
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% s = SUMK(X,k)
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%
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% For a vector X, NORM_NUCLEAR returns the sum of singular values
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%
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% For a matrix X, NORM_NUCLEAR returns the sum of absolute values.
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%
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% See also SUMABSK
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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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varargout{1} = sum(svd(varargin{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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if is(X,'real')
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U = sdpvar(m);
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V = sdpvar(n);
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else
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U = sdpvar(m,m,'hermitian','complex');
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V = sdpvar(n,n,'hermitian','complex');
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end
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F = [trace(U)+trace(V) <= 2*t, [U X';X V]>=0];
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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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