1 | function varargout = cpower(varargin) |
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2 | %CPOWER Power of SDPVAR variable with convexity knowledge |
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3 | % |
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4 | % CPOWER is recommended if your goal is to obtain |
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5 | % a convex model, since the function CPOWER is implemented |
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6 | % as a so called nonlinear operator. (For p/q ==2 you can |
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7 | % however just as well use the overloaded power) |
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8 | % |
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9 | % t = power(x,p/q) |
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10 | % |
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11 | % For negative p/q, the operator is convex. |
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12 | % For positive p/q with p>q, the operator is convex. |
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13 | % For positive p/q with p<q, the operator is concave. |
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14 | % |
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15 | % A domain constraint x>0 is automatically added if |
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16 | % p/q not is an even integer. |
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17 | % |
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18 | % Note, the complexity of generating the conic representation |
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19 | % of these variables are O(2^L) where L typically is the |
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20 | % smallest integer such that 2^L >= min(p,q) |
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21 | |
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22 | % Author Johan Löfberg |
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23 | % $Id: cpower.m,v 1.1 2006/03/30 13:36:39 joloef Exp $ |
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24 | |
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25 | switch class(varargin{1}) |
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26 | |
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27 | case 'double' |
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28 | varargout{1} = power(varargin{1},varargin{2}); |
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29 | case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them. |
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30 | X = varargin{1}; |
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31 | [n,m] = size(X); |
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32 | if isreal(X) & n*m==1 |
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33 | varargout{1} = yalmip('addextendedvariable',mfilename,varargin{:}); |
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34 | else |
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35 | error('CPOWER can only be applied to real vectors.'); |
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36 | end |
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37 | |
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38 | case 'char' % YALMIP send 'model' when it wants the epigraph or hypograph |
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39 | if isequal(varargin{1},'graph') |
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40 | t = varargin{2}; % Second arg is the extended operator variable |
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41 | X = varargin{3}; % Third arg and above are the args user used when defining t. |
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42 | p = varargin{4}; |
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43 | |
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44 | if p>0 |
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45 | [p,q] = rat(abs(p)); |
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46 | F = pospower(set([]),X,t,p,q); |
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47 | if p>q |
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48 | convexity = 'convex'; |
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49 | monotonicity = 'increasing'; |
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50 | else |
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51 | convexity = 'concave'; |
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52 | monotonicity = 'decreasing'; |
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53 | |
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54 | end |
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55 | else |
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56 | [p,q] = rat(abs(p)); |
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57 | F = negpower(set([]),X,t,p,q); |
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58 | convexity = 'convex'; |
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59 | monotonicity = 'decreasing'; |
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60 | end |
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61 | |
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62 | varargout{1} = F; |
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63 | varargout{2} = struct('convexity',convexity,'monotonicity',monotonicity,'definiteness','positive'); |
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64 | varargout{3} = X; |
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65 | end |
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66 | otherwise |
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67 | end |
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68 | |
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69 | function F = pospower(F,x,t,p,q) |
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70 | if p>q |
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71 | l = ceil(log2(abs(p))); |
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72 | r = 2^l-p; |
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73 | y = [ones(r,1)*x;ones(q,1)*t;ones(2^l-r-q,1)]; |
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74 | F = detset(x,y); |
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75 | else |
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76 | l = ceil(log2(abs(q))); |
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77 | y = [ones(p,1)*x;ones(2^l-q,1)*t;ones(q-p,1)]; |
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78 | F = detset(t,y); |
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79 | end |
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80 | |
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81 | function F = negpower(F,x,t,p,q) |
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82 | l = ceil(log2(abs(p+q))); |
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83 | p = abs(p); |
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84 | q = abs(q); |
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85 | y = [ones(2^l-p-q,1);ones(p,1)*x;ones(q,1)*t]; |
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86 | F = detset(1,y); |
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87 | |
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