1 | function varargout = sumk(varargin) |
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2 | % SUMK Returns sum of k largest (eigen-)values. |
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3 | % |
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4 | % s = SUMK(X,k) |
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5 | % |
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6 | % For a vector X, SUMK returns the sum of the k largest elements. |
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7 | % |
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8 | % For a symmetric matrix X, SUMK returns the sum of the k largest eigen-values. |
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9 | % |
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10 | % See also SUMABSK |
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11 | |
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12 | % Author Johan Löfberg |
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13 | % $Id: sumk.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 | % and a structure descring properties of the operator |
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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('sumk 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('sumk 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('sumk 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('sumk 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 send '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-X+s > 0); |
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68 | varargout{2} = struct('convexity','convex','monotonicity','increasing','definiteness','none'); |
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69 | else |
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70 | varargout{1} = set(t-k*s-trace(Z) > 0) + set(Z > 0) + set(Z-X+s*eye(n) > 0); |
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71 | varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','none'); |
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72 | end |
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73 | varargout{3} = X; |
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74 | else |
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75 | end |
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76 | otherwise |
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77 | end |
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