[37] | 1 | function y = times(X,Y) |
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| 2 | %TIMES (overloaded) |
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| 3 | |
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| 4 | % Author Johan Löfberg |
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| 5 | % $Id: times.m,v 1.1 2006/08/10 18:00:22 joloef Exp $ |
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| 6 | |
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| 7 | % Check dimensions |
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| 8 | [n,m]=size(X); |
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| 9 | if ~((prod(size(X))==1) | (prod(size(Y))==1)) |
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| 10 | if ~((n==size(Y,1) & (m ==size(Y,2)))) |
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| 11 | error('Matrix dimensions must agree.') |
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| 12 | end |
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| 13 | end; |
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| 14 | |
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| 15 | % Convert block objects |
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| 16 | if isa(X,'blkvar') |
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| 17 | X = sdpvar(X); |
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| 18 | end |
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| 19 | |
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| 20 | if isa(Y,'blkvar') |
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| 21 | Y = sdpvar(Y); |
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| 22 | end |
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| 23 | |
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| 24 | |
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| 25 | if isempty(X) |
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| 26 | YY = full(reshape(Y.basis(:,1),Y.dim(1),Y.dim(2))); |
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| 27 | y = X.*YY; |
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| 28 | return |
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| 29 | elseif isempty(Y) |
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| 30 | XX = full(reshape(X.basis(:,1),X.dim(1),X.dim(2))); |
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| 31 | y = XX.*Y; |
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| 32 | return |
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| 33 | end |
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| 34 | |
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| 35 | if (isa(X,'sdpvar') & isa(Y,'sdpvar')) |
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| 36 | |
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| 37 | if (X.typeflag==5) & (Y.typeflag==5) |
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| 38 | error('Product of norms not allowed'); |
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| 39 | end |
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| 40 | |
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| 41 | try |
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| 42 | |
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| 43 | |
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| 44 | x_isscalar = (X.dim(1)*X.dim(2)==1); |
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| 45 | y_isscalar = (Y.dim(1)*Y.dim(2)==1); |
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| 46 | |
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| 47 | all_lmi_variables = uniquestripped([X.lmi_variables Y.lmi_variables]); |
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| 48 | Z = X;Z.dim(1) = 1;Z.dim(2) = 1;Z.lmi_variables = all_lmi_variables;Z.basis = []; |
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| 49 | |
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| 50 | % Awkward code due to bug in ML6.5 |
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| 51 | Xbase = reshape(X.basis(:,1),X.dim(1),X.dim(2)); |
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| 52 | Ybase = reshape(Y.basis(:,1),Y.dim(1),Y.dim(2)); |
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| 53 | if x_isscalar |
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| 54 | Xbase = sparse(full(Xbase)); |
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| 55 | end |
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| 56 | if y_isscalar |
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| 57 | Ybase = sparse(full(Ybase)); |
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| 58 | end |
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| 59 | |
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| 60 | |
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| 61 | index_Y = zeros(length(all_lmi_variables),1); |
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| 62 | index_X = zeros(length(all_lmi_variables),1); |
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| 63 | for j = 1:length(all_lmi_variables) |
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| 64 | indexy = find(all_lmi_variables(j)==Y.lmi_variables); |
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| 65 | indexx = find(all_lmi_variables(j)==X.lmi_variables); |
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| 66 | if ~isempty(indexy) |
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| 67 | index_Y(j) = indexy; |
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| 68 | end |
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| 69 | if ~isempty(indexx) |
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| 70 | index_X(j) = indexx; |
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| 71 | end |
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| 72 | end |
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| 73 | |
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| 74 | ny = Y.dim(1); |
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| 75 | my = Y.dim(2); |
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| 76 | nx = X.dim(1); |
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| 77 | mx = X.dim(2); |
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| 78 | |
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| 79 | % Linear terms |
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| 80 | base = Xbase.*Ybase; |
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| 81 | Z.basis = base(:); |
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| 82 | x_base_not_zero = nnz(Xbase)>0; |
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| 83 | y_base_not_zero = nnz(Ybase)>0; |
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| 84 | for i = 1:length(all_lmi_variables) |
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| 85 | base = 0; |
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| 86 | if index_Y(i) & x_base_not_zero |
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| 87 | base = Xbase.*getbasematrixwithoutcheck(Y,index_Y(i)); |
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| 88 | end |
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| 89 | if index_X(i) & y_base_not_zero |
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| 90 | base = base + getbasematrixwithoutcheck(X,index_X(i)).*Ybase; |
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| 91 | end |
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| 92 | Z.basis(:,i+1) = base(:); |
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| 93 | end |
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| 94 | |
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| 95 | % Nonlinear terms |
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| 96 | i = i+1; |
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| 97 | ix=1; |
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| 98 | |
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| 99 | new_mt = []; |
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| 100 | mt = yalmip('monomtable'); |
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| 101 | nvar = length(all_lmi_variables); |
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| 102 | local_mt = mt(all_lmi_variables,:); |
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| 103 | theyvars = find(index_Y); |
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| 104 | thexvars = find(index_X); |
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| 105 | |
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| 106 | hash = randn(size(mt,2),1); |
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| 107 | mt_hash = mt*hash; |
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| 108 | |
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| 109 | for ix = thexvars(:)' |
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| 110 | |
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| 111 | if mx==1 |
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| 112 | Xibase = X.basis(:,1+index_X(ix)); |
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| 113 | else |
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| 114 | Xibase = reshape(X.basis(:,1+index_X(ix)),nx,mx); |
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| 115 | end |
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| 116 | mt_x = local_mt(ix,:); |
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| 117 | |
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| 118 | for iy = theyvars(:)' |
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| 119 | ff=Y.basis(:,1+index_Y(iy)); |
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| 120 | Yibase = reshape(ff,ny,my); |
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| 121 | prodbase = Xibase.*Yibase; |
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| 122 | if (norm(prodbase,inf)>1e-12) |
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| 123 | mt_y = local_mt(iy,:); |
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| 124 | % Idiot-hash the lists |
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| 125 | new_hash = (mt_x+mt_y)*hash; |
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| 126 | if abs(new_hash)<eps%if nnz(mt_x+mt_y)==0 |
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| 127 | Z.basis(:,1) = Z.basis(:,1) + prodbase(:); |
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| 128 | else |
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| 129 | before = find(abs(mt_hash-(mt_x+mt_y)*hash)<eps); |
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| 130 | if isempty(before) |
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| 131 | mt = [mt;mt_x+mt_y]; |
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| 132 | mt_hash = [mt_hash;(mt_x+mt_y)*hash]; |
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| 133 | Z.lmi_variables = [Z.lmi_variables size(mt,1)]; |
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| 134 | else |
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| 135 | Z.lmi_variables = [Z.lmi_variables before]; |
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| 136 | end |
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| 137 | Z.basis(:,i+1) = prodbase(:);i = i+1; |
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| 138 | end |
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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 | % Fucked up order |
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| 144 | if any(diff(Z.lmi_variables)<0) |
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| 145 | [i,j]=sort(Z.lmi_variables); |
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| 146 | Z.lmi_variables = Z.lmi_variables(j); |
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| 147 | Z.basis(:,2:end) = Z.basis(:,j+1); |
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| 148 | end |
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| 149 | |
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| 150 | % FIX : Speed up |
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| 151 | if length(Z.lmi_variables) ~=length(unique(Z.lmi_variables)) |
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| 152 | un_Z_vars = unique(Z.lmi_variables); |
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| 153 | newZbase = Z.basis(:,1); |
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| 154 | for i = 1:length(un_Z_vars) |
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| 155 | newZbase = [newZbase sum(Z.basis(:,find(un_Z_vars(i)==Z.lmi_variables)+1),2)]; |
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| 156 | end |
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| 157 | Z.basis = newZbase; |
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| 158 | Z.lmi_variables = un_Z_vars; |
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| 159 | end |
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| 160 | |
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| 161 | yalmip('setmonomtable',mt); |
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| 162 | |
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| 163 | if ~(x_isscalar | y_isscalar) |
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| 164 | Z.dim(1) = X.dim(1); |
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| 165 | Z.dim(2) = Y.dim(2); |
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| 166 | else |
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| 167 | Z.dim(1) = max(X.dim(1),Y.dim(1)); |
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| 168 | Z.dim(2) = max(X.dim(2),Y.dim(2)); |
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| 169 | end |
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| 170 | catch |
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| 171 | error(lasterr) |
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| 172 | end |
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| 173 | % Reset info about conic terms |
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| 174 | Z.conicinfo = [0 0]; |
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| 175 | y = clean(Z); |
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| 176 | return |
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| 177 | end |
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| 178 | |
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| 179 | if isa(X,'sdpvar') |
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| 180 | lmi_variables = getvariables(X); |
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| 181 | nv = length(lmi_variables); |
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| 182 | y = X; |
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| 183 | n = X.dim(1); |
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| 184 | m = X.dim(2); |
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| 185 | temp = (reshape(X.basis(:,1),n,m)).*Y; |
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| 186 | y.basis = temp(:); |
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| 187 | for i = 1:nv |
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| 188 | temp = (reshape(X.basis(:,i+1),n,m)).*Y; |
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| 189 | % temp = temp(:); |
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| 190 | % [i1,j1,s1] = find(temp); |
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| 191 | y.basis(:,i+1) = temp(:); |
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| 192 | % y.basis(i1,i+1) = temp(i1); |
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| 193 | end; |
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| 194 | y.dim(1) = size(temp,1); |
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| 195 | y.dim(2) = size(temp,2); |
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| 196 | end |
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| 197 | |
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| 198 | if isa(Y,'sdpvar') |
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| 199 | lmi_variables = getvariables(Y); |
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| 200 | nv = length(lmi_variables); |
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| 201 | y = Y; |
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| 202 | n = Y.dim(1); |
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| 203 | m = Y.dim(2); |
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| 204 | temp = X.*(reshape(Y.basis(:,1),n,m)); |
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| 205 | y.basis = temp(:); |
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| 206 | if m==1 |
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| 207 | for i = 1:nv |
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| 208 | y.basis(:,i+1) = X.*Y.basis(:,i+1); |
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| 209 | end |
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| 210 | else |
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| 211 | for i = 1:nv |
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| 212 | temp = X.*(reshape(Y.basis(:,i+1),n,m)); |
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| 213 | y.basis(:,i+1) = temp(:); |
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| 214 | end |
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| 215 | end |
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| 216 | y.dim(1) = size(temp,1); |
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| 217 | y.dim(2) = size(temp,2); |
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| 218 | end |
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| 219 | % Reset info about conic terms |
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| 220 | y.conicinfo = [0 0]; |
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| 221 | y = clean(y); |
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| 222 | |
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| 223 | |
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