74 lines
2.8 KiB
Mathematica
74 lines
2.8 KiB
Mathematica
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function varargout = sumabsk(varargin)
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% SUMABSK Returns sum of k largest (by magnitude) (eigen-)values.
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%
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% s = SUMABSK(X,k)
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%
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% For a real vector X, SUMABSK returns the sum of the k largest (by magnitude) elements.
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%
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% For an Hermitian matrix X, SUMABSK returns the sum of the k largest (by magnitude) eigen-values.
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%
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% See also SUMK
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% ***************************************************
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% This file defines a nonlinear operator for YALMIP
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%
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% It can take three different inputs
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% For double inputs, it returns standard double values
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% For sdpvar inputs, it genreates a an internal variable
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% When first input is 'model' it generates the epigraph
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%
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% ***************************************************
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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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if nargin == 1
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error('sumabsk needs two arguments');
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else
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X = varargin{1};
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[n,m] = size(X);
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if (min(n,m) > 1 & ~ishermitian(X)) | (n~=m & ~isreal(X))
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error('sumabsk can only be applied on real vectors and Hermitian matrices');
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else
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k = min(length(X),varargin{2});
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if min(n,m)==1
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sorted = sort(abs(X));
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else
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sorted = sort(abs(eig(X)));
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end
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varargout{1} = sum(sorted(max(1,end-k+1):end));
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end
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end
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case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them.
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X = varargin{1};
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[n,m] = size(X);
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if (min(n,m) > 1 & ~ishermitian(X)) | (n~=m & ~isreal(X))
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error('sumabsk can only be applied on real vectors and Hermitian matrices');
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else
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if nargin < 2
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error('sumabsk needs two arguments');
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else
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varargout{1} = yalmip('define',mfilename,varargin{:});
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end
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end
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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}; % Second arg is the extended operator variable
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X = varargin{3}; % Third arg and above are the args user used when defining t.
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k = min(varargin{4},length(X));
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[n,m] = size(X);
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Z = sdpvar(n,m);
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s = sdpvar(1,1);
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if min(n,m)==1
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varargout{1} = (t-k*s-sum(Z) >= 0) + (Z >= 0) + (Z+s >= X >= -Z-s);
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else
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varargout{1} = (t-k*s-trace(Z) >= 0) + (Z >= 0) + (Z+s*eye(n) >= X >= -Z-s*eye(n));
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end
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varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','none','model','graph');
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varargout{3} = X;
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else
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end
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otherwise
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end
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