[37] | 1 | function Z = mtimes(X,Y) |
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| 2 | %MTIMES (overloaded) |
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| 3 | |
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| 4 | % Author Johan Löfberg |
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| 5 | % $Id: mtimes.m,v 1.57 2006/10/19 12:42:36 joloef Exp $ |
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| 6 | |
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| 7 | % Check classes |
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| 8 | X_is_spdvar = isa(X,'sdpvar'); |
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| 9 | Y_is_spdvar = isa(Y,'sdpvar'); |
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| 10 | |
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| 11 | % Convert block objects |
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| 12 | if ~X_is_spdvar |
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| 13 | if isa(X,'blkvar') |
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| 14 | X = sdpvar(X); |
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| 15 | X_is_spdvar = isa(X,'sdpvar'); |
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| 16 | end |
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| 17 | end |
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| 18 | |
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| 19 | if ~Y_is_spdvar |
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| 20 | if isa(Y,'blkvar') |
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| 21 | Y = sdpvar(Y); |
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| 22 | Y_is_spdvar = isa(Y,'sdpvar'); |
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| 23 | end |
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| 24 | end |
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| 25 | |
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| 26 | % Lame special cases, make sure to reurn |
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| 27 | % empty matrices in the sense that the |
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| 28 | % used MATLAB version |
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| 29 | if isempty(X) |
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| 30 | YY = full(reshape(Y.basis(:,1),Y.dim(1),Y.dim(2))); |
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| 31 | Z = X*YY; |
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| 32 | return |
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| 33 | elseif isempty(Y) |
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| 34 | XX = full(reshape(X.basis(:,1),X.dim(1),X.dim(2))); |
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| 35 | Z = XX*Y; |
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| 36 | return |
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| 37 | end |
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| 38 | |
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| 39 | |
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| 40 | % Optimized calls in different order? |
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| 41 | if X_is_spdvar & Y_is_spdvar |
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| 42 | manytimesfew = length(X.lmi_variables) > 5*length(Y.lmi_variables); |
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| 43 | if manytimesfew |
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| 44 | Z = (Y'*X')'; % Optimized for this order (few variables * many variables) |
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| 45 | return |
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| 46 | end |
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| 47 | end |
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| 48 | |
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| 49 | % Different code for |
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| 50 | % 1 : SDPVAR * DOUBLE |
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| 51 | % 2 : DOUBLE * SDPVAR |
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| 52 | % 3 : SDPVAR * SDPVAR |
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| 53 | switch 2*X_is_spdvar+Y_is_spdvar |
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| 54 | case 3 |
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| 55 | try |
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| 56 | x_isscalar = (X.dim(1)*X.dim(2)==1); |
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| 57 | y_isscalar = (Y.dim(1)*Y.dim(2)==1); |
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| 58 | |
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| 59 | % Optimized unique |
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| 60 | all_lmi_variables = uniquestripped([X.lmi_variables Y.lmi_variables]); |
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| 61 | |
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| 62 | % Create clean SDPVAR object |
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| 63 | Z = X;Z.dim(1) = 1;Z.dim(2) = 1;Z.lmi_variables = all_lmi_variables;Z.basis = []; |
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| 64 | |
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| 65 | % Awkward code due to bug in ML6.5 |
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| 66 | Xbase = reshape(X.basis(:,1),X.dim(1),X.dim(2)); |
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| 67 | Ybase = reshape(Y.basis(:,1),Y.dim(1),Y.dim(2)); |
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| 68 | if x_isscalar |
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| 69 | Xbase = sparse(full(Xbase)); |
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| 70 | end |
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| 71 | if y_isscalar |
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| 72 | Ybase = sparse(full(Ybase)); |
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| 73 | end |
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| 74 | |
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| 75 | index_X = double(ismembc(all_lmi_variables,X.lmi_variables)); |
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| 76 | index_Y = double(ismembc(all_lmi_variables,Y.lmi_variables)); |
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| 77 | iX=find(index_X); |
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| 78 | iY=find(index_Y); |
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| 79 | index_X(iX)=1:length(iX);index_X=index_X(:); |
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| 80 | index_Y(iY)=1:length(iY);index_Y=index_Y(:); |
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| 81 | |
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| 82 | ny = Y.dim(1); |
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| 83 | my = Y.dim(2); |
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| 84 | nx = X.dim(1); |
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| 85 | mx = X.dim(2); |
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| 86 | |
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| 87 | % Pre-allocate sufficiently long |
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| 88 | Z.lmi_variables = [Z.lmi_variables zeros(1,length(X.lmi_variables)*length(Y.lmi_variables))]; |
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| 89 | |
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| 90 | % Pre-calc identity (used a lot |
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| 91 | speyemy = sparse(1:my,1:my,1,my,my); |
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| 92 | |
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| 93 | % Linear terms |
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| 94 | inner_vector_product = (X.dim(1)==1 & Y.dim(2)==1 & (X.dim(2) == Y.dim(1))); |
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| 95 | if inner_vector_product |
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| 96 | base1=Xbase*Y.basis;base1=base1(2:end); |
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| 97 | base2=Ybase.'*X.basis;base2=base2(2:end); |
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| 98 | [i1,j1,k1]=find(base1); |
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| 99 | [i2,j2,k2]=find(base2); |
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| 100 | base1 = sparse(i1,iY(j1),k1,1,length(all_lmi_variables)); |
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| 101 | base2 = sparse(i2,iX(j2),k2,1,length(all_lmi_variables)); |
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| 102 | Z.basis = [Xbase*Ybase base1+base2]; |
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| 103 | else |
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| 104 | base0 = Xbase*Ybase; |
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| 105 | if x_isscalar |
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| 106 | base1 = Xbase*Y.basis(:,2:end); |
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| 107 | base2 = Ybase(:)*X.basis(:,2:end); |
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| 108 | elseif y_isscalar |
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| 109 | base1 = Xbase(:)*Y.basis;base1=base1(:,2:end); |
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| 110 | base2 = X.basis*Ybase;base2=base2(:,2:end); |
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| 111 | else |
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| 112 | base1 = kron(speyemy,Xbase)*Y.basis(:,2:end); |
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| 113 | base2 = kron(Ybase.',speye(nx))*X.basis(:,2:end); |
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| 114 | end |
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| 115 | [i1,j1,k1]=find(base1); |
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| 116 | [i2,j2,k2]=find(base2); |
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| 117 | base1 = sparse(i1,iY(j1),k1,size(base0(:),1),length(all_lmi_variables)); |
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| 118 | base2 = sparse(i2,iX(j2),k2,size(base0(:),1),length(all_lmi_variables)); |
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| 119 | Z.basis = [base0(:) base1+base2]; |
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| 120 | end |
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| 121 | |
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| 122 | % Loop start for nonlinear terms |
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| 123 | i = length(all_lmi_variables)+1; |
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| 124 | |
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| 125 | [mt,oldvariabletype,mt_hash,hash] = yalmip('monomtable'); |
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| 126 | |
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| 127 | % Check if problem is bilinear. We can exploit this later |
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| 128 | % to improve performance significantly... |
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| 129 | bilinearproduct = 0; |
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| 130 | candofastlocation = 0; |
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| 131 | if all(oldvariabletype(X.lmi_variables)==0) & all(oldvariabletype(Y.lmi_variables)==0) |
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| 132 | % if isempty(intersect(X.lmi_variables,Y.lmi_variables)) |
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| 133 | if ~any(ismembc(X.lmi_variables,Y.lmi_variables)) |
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| 134 | bilinearproduct = 1; |
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| 135 | try |
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| 136 | dummy = ismembc2(1,1); % Not available in all versions (needed in ismember) |
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| 137 | candofastlocation = 1; |
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| 138 | catch |
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| 139 | end |
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| 140 | end |
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| 141 | end |
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| 142 | |
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| 143 | oldmt = mt; |
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| 144 | local_mt = mt(all_lmi_variables,:); |
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| 145 | used_variables = any(local_mt,1); |
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| 146 | local_mt = local_mt(:,used_variables); |
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| 147 | |
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| 148 | possibleOld = find(any(mt(:,used_variables),2)); |
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| 149 | if all(oldvariabletype <=3) |
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| 150 | % All monomials have non-negative integer powers |
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| 151 | % no chance of x^2*x^-1, hence all products |
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| 152 | % are nonlinear |
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| 153 | possibleOld = possibleOld(find(oldvariabletype(possibleOld))); |
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| 154 | if size(possibleOld,1)==0 |
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| 155 | possibleOld = []; |
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| 156 | end |
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| 157 | end |
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| 158 | |
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| 159 | if bilinearproduct & ~isempty(possibleOld) |
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| 160 | if length(X.lmi_variables)<=length(Y.lmi_variables) |
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| 161 | temp = mt(:,X.lmi_variables); |
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| 162 | temp = temp(possibleOld,:); |
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| 163 | possibleOld=possibleOld(find(any(temp,2))); |
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| 164 | else |
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| 165 | temp = mt(:,Y.lmi_variables); |
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| 166 | temp = temp(possibleOld,:); |
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| 167 | possibleOld=possibleOld(find(any(temp,2))); |
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| 168 | end |
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| 169 | end |
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| 170 | |
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| 171 | theyvars = find(index_Y); |
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| 172 | thexvars = find(index_X); |
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| 173 | |
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| 174 | possibleOldHash = mt_hash(possibleOld); |
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| 175 | oldhash = hash; |
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| 176 | hash = hash(used_variables); |
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| 177 | new_mt_hash = []; |
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| 178 | new_mt_hash_transpose = []; |
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| 179 | new_mt = []; |
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| 180 | changed_mt = 0; |
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| 181 | local_mt = local_mt'; |
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| 182 | nvar = size(mt,1); |
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| 183 | |
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| 184 | for ix = thexvars(:)' |
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| 185 | |
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| 186 | mt_x = local_mt(:,ix); |
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| 187 | |
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| 188 | testthese = theyvars(:)'; |
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| 189 | |
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| 190 | % Compute [vec(Xbasis*Ybasis1) vec(Xbasis*Ybasis2) ...] |
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| 191 | % in one shot using vectorization and Kronecker tricks |
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| 192 | % Optimized and treat special case scalar*matrix etc |
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| 193 | if x_isscalar |
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| 194 | Xibase = X.basis(:,1+index_X(ix)); |
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| 195 | allprodbase = Xibase * Y.basis(:,1+index_Y(testthese)); |
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| 196 | elseif y_isscalar |
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| 197 | Xibase = X.basis(:,1+index_X(ix)); |
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| 198 | allprodbase = Xibase * Y.basis(:,1+index_Y(testthese)); |
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| 199 | elseif inner_vector_product |
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| 200 | Xibase = X.basis(:,1+index_X(ix)).'; |
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| 201 | allprodbase = Xibase*Y.basis(:,1+index_Y(testthese)); |
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| 202 | else |
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| 203 | Xibase = reshape(X.basis(:,1+index_X(ix)),nx,mx); |
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| 204 | temp = kron(speyemy,Xibase); |
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| 205 | allprodbase = temp * Y.basis(:,1+index_Y(testthese)); |
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| 206 | end |
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| 207 | |
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| 208 | % Keep non-zero matrices |
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| 209 | nonzeromatrices = find(sum(abs(allprodbase),1)>1e-12); |
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| 210 | testthese = testthese(nonzeromatrices); |
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| 211 | allprodbase = allprodbase(:,nonzeromatrices); |
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| 212 | |
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| 213 | % Some data for vectorization |
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| 214 | nyvars = length(testthese); |
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| 215 | if prod(size(mt_x))==1 % Bug in Solaris and Linux, ML 6.X |
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| 216 | allmt_xplusy = local_mt(:,testthese) + sparse(repmat(full(mt_x),1,nyvars)); |
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| 217 | else |
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| 218 | allmt_xplusy = local_mt(:,testthese) + repmat(mt_x,1,nyvars); |
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| 219 | end |
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| 220 | allhash = allmt_xplusy'*hash; |
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| 221 | thesewhereactuallyused = zeros(1,nyvars); |
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| 222 | copytofrom = ones(1,nyvars); |
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| 223 | acounter = 0; |
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| 224 | |
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| 225 | |
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| 226 | % Special case : x*inv(x) and similiar... |
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| 227 | sum_to_constant = abs(allhash)<eps; |
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| 228 | add_these = find(sum_to_constant); |
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| 229 | if ~isempty(add_these) |
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| 230 | prodbase = allprodbase(:,add_these); |
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| 231 | Z.basis(:,1) = Z.basis(:,1) + sum(prodbase,2); |
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| 232 | copytofrom(add_these) = 0; |
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| 233 | end |
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| 234 | indicies = find(~sum_to_constant); |
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| 235 | indicies = indicies(:)'; |
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| 236 | |
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| 237 | allbefore_in_old = 1; |
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| 238 | if bilinearproduct & candofastlocation |
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| 239 | [dummy,allbefore_in_old] = ismember(allhash,possibleOldHash); |
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| 240 | end |
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| 241 | |
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| 242 | |
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| 243 | if bilinearproduct & candofastlocation & (nnz(allbefore_in_old)==0) |
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| 244 | % All nonlinear variables are new, so we can create them at once |
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| 245 | changed_mt=1; |
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| 246 | thesewhereactuallyused = thesewhereactuallyused+1; |
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| 247 | Z.lmi_variables(i:(i+length(indicies)-1)) = (nvar+1):(nvar+length(indicies)); |
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| 248 | nvar = nvar + length(indicies); |
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| 249 | i = i + length(indicies); |
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| 250 | else |
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| 251 | isemptynew_mt_hash = isempty(new_mt_hash); |
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| 252 | |
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| 253 | for acounter = indicies |
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| 254 | |
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| 255 | current_hash = allhash(acounter); |
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| 256 | |
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| 257 | % Ok, braze your self for some horrible special case |
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| 258 | % treatment etc... |
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| 259 | if isemptynew_mt_hash | bilinearproduct % only search among old monomials |
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| 260 | if bilinearproduct & candofastlocation |
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| 261 | before = allbefore_in_old(acounter); |
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| 262 | if before==0 |
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| 263 | before = []; |
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| 264 | else |
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| 265 | before = possibleOld(before); |
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| 266 | end |
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| 267 | else |
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| 268 | before = possibleOld(findhash(possibleOldHash,current_hash)); |
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| 269 | % before = possibleOld(findhash(possibleOldHash,current_hash,length(possibleOldHash))); |
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| 270 | end |
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| 271 | else |
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| 272 | before = findhash(new_mt_hash,current_hash); % first among new monomials |
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| 273 | % before = findhash(new_mt_hash_transpose,current_hash,topp); % first among new monomials |
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| 274 | if before % Try new if we failed finding any match |
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| 275 | before=before+size(mt_hash,1); |
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| 276 | else |
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| 277 | before = possibleOld(findhash(possibleOldHash,current_hash)); |
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| 278 | % before = possibleOld(findhash(possibleOldHash,current_hash,length(possibleOldHash))); |
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| 279 | end |
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| 280 | end |
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| 281 | if before |
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| 282 | Z.lmi_variables(i) = before; |
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| 283 | else |
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| 284 | changed_mt=1; |
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| 285 | isemptynew_mt_hash=0; |
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| 286 | thesewhereactuallyused(acounter) = 1; |
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| 287 | if ~bilinearproduct % We don't need to update until later since it not is used inside the loop |
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| 288 | new_mt_hash = [new_mt_hash;current_hash]; |
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| 289 | % new_mt_hash_transpose(topp) = current_hash;topp = topp + 1; |
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| 290 | end |
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| 291 | nvar = nvar + 1; |
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| 292 | Z.lmi_variables(i) = nvar; |
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| 293 | end |
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| 294 | i = i+1; |
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| 295 | end |
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| 296 | end |
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| 297 | if all(copytofrom) |
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| 298 | Z.basis = [Z.basis allprodbase]; |
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| 299 | else |
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| 300 | Z.basis = [Z.basis allprodbase(:,find(copytofrom))]; |
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| 301 | end |
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| 302 | if all(thesewhereactuallyused) |
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| 303 | new_mt = [new_mt allmt_xplusy]; |
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| 304 | else |
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| 305 | new_mt = [new_mt allmt_xplusy(:,find(thesewhereactuallyused))]; |
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| 306 | end |
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| 307 | if bilinearproduct |
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| 308 | new_mt_hash = [new_mt_hash;allhash(find(thesewhereactuallyused))]; |
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| 309 | end |
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| 310 | end |
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| 311 | % |
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| 312 | % try |
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| 313 | % new_mt_hash_transpose = new_mt_hash_transpose(1:topp-1); |
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| 314 | % norm(new_mt_hash_transpose-new_mt_hash); |
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| 315 | % catch |
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| 316 | % 1 |
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| 317 | % end |
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| 318 | |
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| 319 | if ~isempty(new_mt) |
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| 320 | [i1,j1,k1] = find(mt); |
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| 321 | [ii1,jj1,kk1] = find(new_mt'); |
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| 322 | uv = find(used_variables);uv=uv(:); |
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| 323 | mt = sparse([i1(:);ii1(:)+size(mt,1)],[j1(:);uv(jj1(:))],[k1(:);kk1(:)],size(mt,1)+size(new_mt,2),size(mt,2)); |
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| 324 | end |
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| 325 | |
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| 326 | % We pre-allocated a sufficiently long, now pick the ones we |
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| 327 | % actually filled with values |
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| 328 | Z.lmi_variables = Z.lmi_variables(1:i-1); |
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| 329 | |
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| 330 | % Fucked up order (lmi_variables should be sorted) |
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| 331 | if any(diff(Z.lmi_variables)<0) |
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| 332 | [i,j]=sort(Z.lmi_variables); |
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| 333 | Z.basis = [Z.basis(:,1) Z.basis(:,j+1)]; |
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| 334 | Z.lmi_variables = Z.lmi_variables(j); |
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| 335 | end |
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| 336 | |
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| 337 | [un_Z_vars2] = uniquestripped(Z.lmi_variables); |
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| 338 | if length(un_Z_vars2) < length(Z.lmi_variables) |
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| 339 | [un_Z_vars,hh,jj] = unique(Z.lmi_variables); |
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| 340 | if length(Z.lmi_variables) ~=length(un_Z_vars) |
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| 341 | Z.basis = Z.basis*sparse([1 1+jj],[1 1+(1:length(jj))],ones(1,1+length(jj)))'; |
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| 342 | Z.lmi_variables = un_Z_vars; |
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| 343 | end |
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| 344 | end |
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| 345 | |
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| 346 | if changed_mt%~isequal(mt,oldmt) |
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| 347 | newmt = mt(size(oldmt,1)+1:end,:); |
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| 348 | nonlinear = ~(sum(newmt,2)==1 & sum(newmt~=0,2)==1); |
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| 349 | newvariabletype = spalloc(size(newmt,1),1,nnz(nonlinear))'; |
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| 350 | nonlinearvariables = find(nonlinear); |
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| 351 | newvariabletype = sparse(nonlinearvariables,ones(length(nonlinearvariables),1),3,size(newmt,1),1)'; |
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| 352 | if ~isempty(nonlinear) |
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| 353 | %mt = internal_sdpvarstate.monomtable; |
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| 354 | %newvariabletype(nonlinear) = 3; |
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| 355 | quadratic = sum(newmt,2)==2; |
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| 356 | newvariabletype(quadratic) = 2; |
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| 357 | bilinear = max(newmt,[],2)<=1; |
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| 358 | newvariabletype(bilinear & quadratic) = 1; |
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| 359 | sigmonial = any(0>newmt,2) | any(newmt-fix(newmt),2); |
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| 360 | newvariabletype(sigmonial) = 4; |
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| 361 | end |
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| 362 | yalmip('setmonomtable',mt,[oldvariabletype newvariabletype],[mt_hash;new_mt_hash],oldhash); |
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| 363 | end |
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| 364 | |
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| 365 | if ~(x_isscalar | y_isscalar) |
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| 366 | Z.dim(1) = X.dim(1); |
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| 367 | Z.dim(2) = Y.dim(2); |
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| 368 | else |
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| 369 | Z.dim(1) = max(X.dim(1),Y.dim(1)); |
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| 370 | Z.dim(2) = max(X.dim(2),Y.dim(2)); |
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| 371 | end |
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| 372 | catch |
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| 373 | error(lasterr) |
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| 374 | end |
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| 375 | % Reset info about conic terms |
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| 376 | Z.conicinfo = [0 0]; |
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| 377 | Z = clean(Z); |
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| 378 | |
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| 379 | case 2 |
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| 380 | |
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| 381 | n_X = X.dim(1); |
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| 382 | m_X = X.dim(2); |
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| 383 | [n_Y,m_Y] = size(Y); |
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| 384 | |
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| 385 | x_isscalar = (n_X*m_X==1); |
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| 386 | y_isscalar = (n_Y*m_Y==1); |
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| 387 | |
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| 388 | if ~x_isscalar |
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| 389 | if ((m_X~= n_Y & ~y_isscalar)) |
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| 390 | error('Inner matrix dimensions must agree.') |
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| 391 | end |
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| 392 | end |
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| 393 | |
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| 394 | n = n_X; |
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| 395 | m = m_Y; |
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| 396 | Z = X; |
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| 397 | |
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| 398 | if x_isscalar |
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| 399 | if y_isscalar |
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| 400 | if Y==0 |
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| 401 | Z = 0; |
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| 402 | return |
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| 403 | else |
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| 404 | Z.basis = Z.basis*Y; |
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| 405 | % Reset info about conic terms |
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| 406 | Z.conicinfo = [0 0]; |
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| 407 | return |
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| 408 | end |
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| 409 | else |
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| 410 | Z.dim(1) = n_Y; |
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| 411 | Z.dim(2) = m_Y; |
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| 412 | Z.basis = kron(Z.basis,Y(:)); |
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| 413 | Z.conicinfo = [0 0]; |
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| 414 | Z = clean(Z); |
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| 415 | return |
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| 416 | end |
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| 417 | elseif y_isscalar |
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| 418 | Z.dim(1) = n_X; |
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| 419 | Z.dim(2) = m_X; |
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| 420 | Z.basis = Z.basis*Y; |
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| 421 | Z.conicinfo = [0 0]; |
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| 422 | Z = clean(Z); |
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| 423 | return |
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| 424 | end |
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| 425 | |
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| 426 | Z.dim(1) = n; |
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| 427 | Z.dim(2) = m; |
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| 428 | Z.basis = kron(Y.',speye(n_X))*X.basis; |
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| 429 | Z.conicinfo = [0 0]; |
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| 430 | Z = clean(Z); |
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| 431 | |
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| 432 | case 1 |
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| 433 | |
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| 434 | n_Y = Y.dim(1); |
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| 435 | m_Y = Y.dim(2); |
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| 436 | [n_X,m_X] = size(X); |
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| 437 | |
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| 438 | x_isscalar = (n_X*m_X==1); |
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| 439 | y_isscalar = (n_Y*m_Y==1); |
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| 440 | |
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| 441 | if ~x_isscalar |
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| 442 | if ((m_X~= n_Y & ~y_isscalar)) |
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| 443 | error('Inner matrix dimensions must agree.') |
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| 444 | end |
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| 445 | end |
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| 446 | |
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| 447 | n = n_X; |
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| 448 | m = m_Y; |
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| 449 | Z = Y; |
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| 450 | |
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| 451 | % Special cases |
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| 452 | if x_isscalar |
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| 453 | if y_isscalar |
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| 454 | if X==0 |
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| 455 | Z = 0; |
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| 456 | return |
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| 457 | else |
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| 458 | Z.basis = Z.basis*X; |
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| 459 | Z.conicinfo = [0 0]; |
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| 460 | return |
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| 461 | end |
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| 462 | else |
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| 463 | Z.dim(1) = n_Y; |
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| 464 | Z.dim(2) = m_Y; |
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| 465 | try |
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| 466 | Z.basis = sparse(X)*Y.basis; |
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| 467 | catch |
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| 468 | % This works better when low on memory in some cases |
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| 469 | [i,j,k] = find(Y.basis); |
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| 470 | Z.basis = sparse(i,j,X*k,size(Y.basis,1),size(Y.basis,2)); |
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| 471 | end |
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| 472 | Z.conicinfo = [0 0]; |
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| 473 | Z = clean(Z); |
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| 474 | return |
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| 475 | end |
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| 476 | elseif y_isscalar |
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| 477 | Z.dim(1) = n_X; |
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| 478 | Z.dim(2) = m_X; |
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| 479 | Z.basis = X(:)*Y.basis; |
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| 480 | Z = clean(Z); |
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| 481 | return |
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| 482 | end |
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| 483 | |
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| 484 | if m_Y==1 |
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| 485 | Z.basis = X*Y.basis; |
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| 486 | else |
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| 487 | try |
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| 488 | speyemy = speye(m_Y); |
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| 489 | kronX = kron(speyemy,X); |
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| 490 | Z.basis = kronX*Y.basis; |
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| 491 | catch |
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| 492 | for i = 1:size(Y.basis,2); |
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| 493 | dummy = X*reshape(Y.basis(:,i),Y.dim(1),Y.dim(2)); |
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| 494 | Z.basis(:,i) = dummy(:); |
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| 495 | end |
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| 496 | end |
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| 497 | end |
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| 498 | Z.dim(1) = n; |
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| 499 | Z.dim(2) = m; |
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| 500 | Z.conicinfo = [0 0]; |
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| 501 | Z = clean(Z); |
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| 502 | |
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| 503 | otherwise |
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| 504 | error('Logical error in mtimes. Report bug') |
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| 505 | end |
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| 506 | |
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| 507 | |
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| 508 | |
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| 509 | function Z=clean(X) |
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| 510 | temp = any(X.basis,1); |
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| 511 | temp = temp(2:end); |
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| 512 | index = find(temp); |
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| 513 | if ~isempty(index) |
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| 514 | Z = X; |
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| 515 | if length(index)~=length(Z.lmi_variables) |
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| 516 | Z.basis = Z.basis(:,[1 1+index]); |
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| 517 | Z.lmi_variables = Z.lmi_variables(index); |
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| 518 | end |
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| 519 | else |
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| 520 | Z = full(reshape(X.basis(:,1),X.dim(1),X.dim(2))); |
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| 521 | end |
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