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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