[37] | 1 | function varargout = sumabsk(varargin) |
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| 2 | % SUMABSK Returns sum of k largest (by magnitude) (eigen-)values. |
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| 3 | % |
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| 4 | % s = SUMABSK(X,k) |
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| 5 | % |
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| 6 | % For a vector X, SUMABSK returns the sum of the k largest (by magnitude) elements. |
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| 7 | % |
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| 8 | % For a symmetric matrix X, SUMABSK returns the sum of the k largest (by magnitude) eigen-values. |
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| 9 | % |
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| 10 | % See also SUMK |
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| 11 | |
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| 12 | % Author Johan Löfberg |
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| 13 | % $Id: sumabsk.m,v 1.1 2006/03/30 13:36:39 joloef Exp $ |
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| 14 | |
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| 15 | % *************************************************** |
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| 16 | % This file defines a nonlinear operator for YALMIP |
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| 17 | % |
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| 18 | % It can take three different inputs |
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| 19 | % For double inputs, it returns standard double values |
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| 20 | % For sdpvar inputs, it genreates a an internal variable |
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| 21 | % When first input is 'model' it generates the epigraph |
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| 22 | % |
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| 23 | % *************************************************** |
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| 24 | switch class(varargin{1}) |
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| 25 | |
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| 26 | case 'double' % What is the numerical value of this argument (needed for displays etc) |
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| 27 | if nargin == 1 |
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| 28 | error('sumabsk needs two arguments'); |
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| 29 | else |
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| 30 | X = varargin{1}; |
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| 31 | [n,m] = size(X); |
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| 32 | if (min(n,m) > 1 & ~issymmetric(X)) |
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| 33 | error('sumabsk can only be applied on vectors and symmetric matrices'); |
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| 34 | else |
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| 35 | k = min(length(X),varargin{2}); |
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| 36 | if min(n,m)==1 |
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| 37 | sorted = sort(X); |
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| 38 | else |
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| 39 | sorted = sort(eig(X)); |
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| 40 | end |
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| 41 | varargout{1} = sum(sorted(max(1,end-k+1):end)); |
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| 42 | end |
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| 43 | end |
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| 44 | |
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| 45 | case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them. |
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| 46 | X = varargin{1}; |
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| 47 | [n,m] = size(X); |
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| 48 | if (min(n,m) > 1 & ~issymmetric(X)) |
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| 49 | error('sumabsk can only be applied on vectors and symmetric matrices'); |
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| 50 | else |
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| 51 | if nargin < 2 |
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| 52 | error('sumabsk needs two arguments'); |
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| 53 | else |
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| 54 | varargout{1} = yalmip('addextendedvariable',mfilename,varargin{:}); |
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| 55 | end |
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| 56 | end |
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| 57 | |
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| 58 | case 'char' % YALMIP sends 'model' when it wants the epigraph or hypograph |
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| 59 | if isequal(varargin{1},'graph') |
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| 60 | t = varargin{2}; % Second arg is the extended operator variable |
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| 61 | X = varargin{3}; % Third arg and above are the args user used when defining t. |
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| 62 | k = min(varargin{4},length(X)); |
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| 63 | [n,m] = size(X); |
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| 64 | Z = sdpvar(n,m); |
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| 65 | s = sdpvar(1,1); |
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| 66 | if min(n,m)==1 |
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| 67 | varargout{1} = set(t-k*s-sum(Z) > 0) + set(Z > 0) + set(Z+s > X > -Z-s); |
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| 68 | else |
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| 69 | varargout{1} = set(t-k*s-trace(Z) > 0) + set(Z > 0) + set(Z+s*eye(n) > X > -Z-s*eye(n)); |
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| 70 | end |
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| 71 | varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','none'); |
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| 72 | varargout{3} = X; |
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| 73 | else |
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| 74 | end |
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| 75 | otherwise |
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| 76 | end |
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