1 | function varargout = geomean(varargin) |
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2 | %GEOMEAN (overloaded) |
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3 | % |
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4 | % t = GEOMEAN(X) |
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5 | % |
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6 | % For Hermitian matrix X, returns det(X)^(1/length(X)) |
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7 | % |
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8 | % For real vector X, returns prod(X)^(1/length(X)) |
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9 | % |
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10 | % This concave function is monotonically growing in det(P) |
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11 | % for P>0, so it can be used for maximizing det(P), |
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12 | % or to add lower bound constraints on the determinant. |
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13 | % |
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14 | % When GEOMEAN is used in a problem, the domain constraint |
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15 | % set(X>0) is automatically added to the problem. |
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16 | % |
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17 | % If you only use GEOMEAN as the objective function, you |
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18 | % may want to consider GEOMEAN2 which may results in a |
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19 | % slightly smaller SDP model. |
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20 | % |
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21 | % See also SDPVAR, GEOMEAN2, SUMK, SUMABSK |
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22 | |
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23 | % Author Johan Löfberg |
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24 | % $Id: geomean.m,v 1.1 2006/08/10 18:00:20 joloef Exp $ |
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25 | |
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26 | switch class(varargin{1}) |
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27 | |
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28 | case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them. |
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29 | X = varargin{1}; |
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30 | [n,m] = size(X); |
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31 | if is(varargin{1},'hermitian') | min(n,m)==1 |
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32 | varargout{1} = yalmip('addextendedvariable',mfilename,varargin{:}); |
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33 | else |
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34 | % Create one variable for each column |
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35 | y = []; |
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36 | for i = 1:m |
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37 | index = (1+n*(i-1)):i*n; |
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38 | x = extsubsref(X,index); |
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39 | y = [y yalmip('addextendedvariable',mfilename,x)]; |
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40 | end |
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41 | varargout{1} = y; |
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42 | end |
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43 | |
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44 | case 'char' % YALMIP send 'model' when it wants the epigraph or hypograph |
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45 | if isequal(varargin{1},'graph') |
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46 | t = varargin{2}; % Second arg is the extended operator variable |
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47 | X = varargin{3}; % Third arg and above are the args user used when defining t. |
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48 | |
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49 | % Extend if not power of 2 |
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50 | n = length(X); |
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51 | m=2^ceil(log2(n)); |
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52 | X0=X; |
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53 | F = set([]); |
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54 | if n ~= m |
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55 | d=m-n; |
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56 | if size(X,1)==size(X,2) |
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57 | % model determinant |
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58 | % Convert to a real problem |
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59 | if is(X,'complex') |
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60 | X = [real(X) imag(X);-imag(X) real(X)]; |
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61 | n = length(X); |
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62 | % We will now get (detX)^2, so we need to pad |
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63 | % differently to get (detX)^(1/n) |
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64 | d=2*m-n; |
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65 | end |
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66 | |
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67 | D = tril(sdpvar(n,n)); |
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68 | delta = diag(D); |
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69 | F = set([X D;D' diag(delta)] > 0); |
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70 | p = 2^ceil(log2(n)); |
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71 | if 1 |
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72 | x = [delta;ones(d,1)*t]; |
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73 | else |
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74 | % More efficient in detset, but not tested |
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75 | % sufficiently yet |
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76 | x = delta; |
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77 | end |
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78 | |
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79 | elseif size(X,1)>size(X,2) |
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80 | x = [X;ones(d,1)*t]; |
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81 | |
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82 | else |
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83 | x = [X ones(1,d)*t]; |
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84 | end |
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85 | else |
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86 | if size(X,1)==size(X,2) |
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87 | % model determinant |
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88 | % Convert to a real problem |
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89 | if is(X,'complex') |
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90 | X = [real(X) imag(X);-imag(X) real(X)]; |
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91 | n = length(X); |
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92 | % We will now get (detX)^2, so we need to pad |
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93 | % differently to get (detX)^(1/n) |
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94 | d=2*m-n; |
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95 | end |
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96 | |
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97 | D = tril(sdpvar(n,n)); |
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98 | delta = diag(D); |
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99 | F = set([X D;D' diag(delta)] > 0); |
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100 | p = 2^ceil(log2(n)); |
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101 | x = delta; |
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102 | |
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103 | elseif size(X,1)>size(X,2) |
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104 | x = X; |
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105 | |
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106 | elseif size(X,1)<size(X,2) |
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107 | x = X; |
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108 | end |
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109 | end |
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110 | |
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111 | varargout{1} = F + detset(t,x); |
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112 | |
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113 | if (min(size(X))>1) & ishermitian(X0) |
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114 | varargout{2} = struct('convexity','concave','monotonicity','none','definiteness','positive'); |
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115 | else |
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116 | varargout{2} = struct('convexity','concave','monotonicity','increasing','definiteness','positive'); |
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117 | end |
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118 | varargout{3} = X0; %We have altered the original input, lucky we saved it! |
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119 | elseif isequal(varargin{1},'milp') |
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120 | |
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121 | varargout{1} = []; |
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122 | varargout{2} = []; |
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123 | varargout{3} = []; |
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124 | |
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125 | else |
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126 | end |
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127 | otherwise |
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128 | end |
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