1 | function varargout = and(varargin) |
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2 | %ANd (overloaded) |
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3 | % |
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4 | % z = and(x,y) |
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5 | % z = x & y |
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6 | % |
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7 | % The AND operator is implemented using the concept of nonlinear operators |
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8 | % in YALMIP. X|Y defines a new so called derived variable that can be |
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9 | % treated as any other variable in YALMIP. When SOLVESDP is issued, |
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10 | % constraints are added to the problem to model the AND operator. The new |
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11 | % constraints add constraints to ensure that z, x and y satisfy the |
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12 | % truth-table for AND. |
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13 | % |
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14 | % The model for ARE is set(z<=x)+set(z<=y)+set(1+z>=x+y)+set(binary(z)) |
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15 | % |
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16 | % It is assumed that x and y are binary variables (either explicitely |
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17 | % declared using BINVAR, or constrained using BINARY.) |
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18 | % |
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19 | % See also SDPVAR/AND, BINVAR, BINARY |
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20 | |
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21 | % Author Johan Löfberg |
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22 | % $Id: and.m,v 1.1 2006/08/10 18:00:19 joloef Exp $ |
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23 | |
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24 | switch class(varargin{1}) |
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25 | case 'char' |
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26 | z = varargin{2}; |
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27 | x = varargin{3}; |
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28 | y = varargin{4}; |
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29 | |
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30 | % ******************************************************* |
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31 | % For *some* efficiency,we merge expressions like A&B&C&D |
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32 | xvars = getvariables(x); |
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33 | yvars = getvariables(y); |
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34 | allextvars = yalmip('extvariables'); |
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35 | |
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36 | if (length(xvars)==1) & ismembc(xvars,allextvars) |
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37 | x = expandand(x,allextvars); |
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38 | end |
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39 | |
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40 | if (length(yvars)==1) & ismembc(yvars,allextvars) |
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41 | y = expandand(y,allextvars); |
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42 | end |
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43 | % ******************************************************* |
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44 | |
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45 | varargout{1} = set(x >= z) + set(y >= z) + set(length(x)+length(y)-1+z >= sum(x)+sum(y)) + set(binary(z)); |
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46 | varargout{2} = struct('convexity','milp','monotoncity','milp','definiteness','milp'); |
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47 | varargout{3} = []; |
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48 | |
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49 | case 'sdpvar' |
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50 | x = varargin{1}; |
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51 | y = varargin{2}; |
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52 | |
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53 | varargout{1} = yalmip('addextendedvariable','and',varargin{:}); |
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54 | |
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55 | otherwise |
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56 | end |
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57 | |
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58 | function x = expandand(x,allextvars) |
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59 | |
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60 | xmodel = yalmip('extstruct',getvariables(x)); |
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61 | |
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62 | if isequal(xmodel.fcn,'and') |
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63 | x1 = xmodel.arg{1}; |
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64 | x2 = xmodel.arg{2}; |
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65 | if ismembc(getvariables(xmodel.arg{1}),allextvars) |
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66 | x1 = expandand(xmodel.arg{1},allextvars); |
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67 | end |
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68 | if ismembc(getvariables(xmodel.arg{2}),allextvars) |
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69 | x2 = expandand(xmodel.arg{2},allextvars); |
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70 | end |
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71 | x = [x1 x2]; |
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72 | end |
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