1 | function varargout=abs(varargin) |
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2 | %ABS (overloaded) |
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3 | % |
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4 | % t = abs(x) |
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5 | % |
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6 | % The variable t can only be used in convexity preserving |
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7 | % operations such as t<0, min t etc. |
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8 | |
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9 | % Author Johan Löfberg |
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10 | % $Id: abs.m,v 1.17 2005/11/24 10:05:33 joloef Exp $ |
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11 | |
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12 | %% *************************************************** |
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13 | % This file defines a nonlinear operator for YALMIP |
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14 | % |
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15 | % It can take three different inputs |
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16 | % For double inputs, it returns standard double values |
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17 | % For sdpvar inputs, it genreates a an internal variable |
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18 | % When first input is 'model' it generates the epigraph |
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19 | |
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20 | %% *************************************************** |
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21 | switch class(varargin{1}) |
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22 | |
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23 | case 'double' |
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24 | error('Overloaded SDPVAR/ABS CALLED WITH DOUBLE. Report error') |
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25 | |
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26 | case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them. |
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27 | if isreal(varargin{1}) |
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28 | varargout{1} = yalmip('addextendedvariable',mfilename,varargin{1}); |
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29 | else |
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30 | % For complex args, abs(X) is defined [norm(X(i,j),2)] in MATLAB |
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31 | y = []; |
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32 | x = varargin{1}; |
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33 | for i = 1:size(x,1) |
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34 | temp = []; |
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35 | for j = 1:size(x,2) |
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36 | temp = [temp norm(extsubsref(x,i,j))]; |
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37 | end |
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38 | y = [y;temp]; |
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39 | end |
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40 | varargout{1} = y; |
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41 | end |
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42 | |
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43 | case 'char' % YALMIP send 'graph' when it wants the epigraph or hypograph |
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44 | switch varargin{1} |
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45 | case 'graph' |
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46 | % Description using epigraphs |
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47 | t = varargin{2}; |
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48 | X = varargin{3}; |
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49 | varargout{1} = set(-t <= X <= t); |
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50 | varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','positive'); |
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51 | varargout{3} = X; |
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52 | |
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53 | case 'milp' |
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54 | % Exact description using binary variables |
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55 | t = varargin{2}; |
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56 | X = varargin{3}; |
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57 | F = set([]); |
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58 | [M,m]=derivebounds(X); |
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59 | if m>=0 |
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60 | F = F + set(t == X); |
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61 | elseif M<0 |
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62 | F = F + set(t == -X); |
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63 | else |
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64 | d = binvar(1,1); |
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65 | F = F + set(X <= M*d) + set(-2*(M-m)*d <= t+X <= 2*(M-m)*d); |
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66 | F = F + set(X >= m*(1-d)) + set(-2*(M-m)*(1-d) <= t-X <= 2*(M-m)*(1-d)); |
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67 | end |
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68 | varargout{1} = F; |
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69 | varargout{2} = struct('convexity','milp','monotonicity','milp','definiteness','positive'); |
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70 | varargout{3} = X; |
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71 | otherwise |
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72 | error('SDPVAR/ABS called with CHAR argument?'); |
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73 | end |
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74 | otherwise |
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75 | error('Strange type on first argument in SDPVAR/ABS'); |
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76 | end |
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