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 1.3 2006/08/11 11:48:15 joloef Exp $ |
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6 | |
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7 | % Brute-force implementation of multiplication of noncommuting variables |
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8 | % (with possible commuting variables involved) |
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9 | |
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10 | % Check classes |
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11 | X_is_spdvar = isa(X,'sdpvar'); |
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12 | Y_is_spdvar = isa(Y,'sdpvar'); |
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13 | |
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14 | X_is_ncvar = isa(X,'ncvar'); |
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15 | Y_is_ncvar = isa(Y,'ncvar'); |
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16 | |
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17 | % Get all the tables, and expand them so that they correspond to the same |
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18 | % number of variables globally (nonCommutingTable is not up to date after a |
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19 | % new commuting variables has been defined, to save flops) |
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20 | nonCommutingTable = yalmip('nonCommutingTable'); |
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21 | [monomtable,variabletype] = yalmip('monomtable'); |
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22 | if size(monomtable,1)>size(nonCommutingTable,1) |
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23 | nonCommutingTable((1+size(nonCommutingTable,1)):(size(monomtable,1)),1) = (1+size(nonCommutingTable,1)):(size(monomtable,1)); |
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24 | end |
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25 | |
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26 | % Cast commutative variables as nc temporarily by adding them to the table |
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27 | commuting = find(~any(nonCommutingTable,2)); |
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28 | nonCommutingTable(commuting,1) = commuting; |
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29 | |
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30 | x_variables = getvariables(X);Xbase = getbase(X); |
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31 | y_variables = getvariables(Y);Ybase = getbase(Y); |
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32 | temp_monom_table = []; |
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33 | temp_nc_table = []; |
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34 | temp_c_table = []; |
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35 | new_base = []; |
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36 | |
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37 | for i = 0:length(x_variables) |
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38 | if i>0 |
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39 | x_monom = nonCommutingTable(x_variables(i),:); |
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40 | else |
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41 | x_monom = nan; |
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42 | end |
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43 | x_base = Xbase(:,i+1); |
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44 | for j = 0:length(y_variables) |
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45 | if j>0 |
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46 | y_monom = nonCommutingTable(y_variables(j),:); |
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47 | else |
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48 | y_monom = nan; |
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49 | end |
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50 | y_base = Ybase(:,j+1); |
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51 | xy_base = reshape(x_base,size(X))*reshape(y_base,size(Y)); |
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52 | |
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53 | if (i == 0) & (j== 0) |
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54 | new_base = xy_base(:); |
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55 | elseif nnz(xy_base)>0 |
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56 | xy_monom = [x_monom(2:end) y_monom(2:end)]; |
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57 | xy_monom = xy_monom(find(xy_monom)); |
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58 | temp_nc_table(end+1,1:length(xy_monom)) = xy_monom; |
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59 | temp_c_table(end+1,1:2) = [x_monom(1) y_monom(1)]; |
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60 | new_base = [new_base xy_base(:)]; |
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61 | end |
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62 | end |
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63 | end |
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64 | |
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65 | % It could have happended that new commuting monomials where generated |
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66 | % during the multiplication. Check and create these |
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67 | for i = 1:size(temp_c_table,1) |
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68 | aux = spalloc(1,size(monomtable,2),2); |
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69 | if ~isnan(temp_c_table(i,1)) |
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70 | aux = monomtable(temp_c_table(i,1),:) + aux; |
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71 | end |
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72 | if ~isnan(temp_c_table(i,2)) |
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73 | aux = monomtable(temp_c_table(i,2),:) + aux; |
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74 | end |
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75 | if nnz(aux)>0 |
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76 | candidates = findrows(monomtable,aux); |
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77 | if ~isempty(candidates) |
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78 | temp_c_table(i,1) = candidates; |
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79 | else |
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80 | monomtable = [monomtable;aux]; |
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81 | nonCommutingTable(end+1,1) = nan; |
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82 | temp_c_table(i,1) = size(monomtable,1); |
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83 | switch sum(aux) |
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84 | case 1 |
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85 | variabletype(end+1) = 0; |
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86 | case 2 |
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87 | if nnz(aux) == 1 |
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88 | variabletype(end+1) = 2; |
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89 | else |
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90 | variabletype(end+1) = 1; |
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91 | end |
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92 | otherwise |
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93 | variabletype(end+1) = 3; |
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94 | end |
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95 | end |
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96 | end |
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97 | end |
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98 | |
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99 | temp_nc_table = [temp_c_table(:,1) temp_nc_table]; |
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100 | % Okay, now we have the monomials. Now we have to match them to |
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101 | % possible earlier monomials |
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102 | if size(nonCommutingTable,2) < size(temp_nc_table,2) |
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103 | nonCommutingTable(1,size(temp_nc_table,2)) = 0; |
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104 | elseif size(temp_nc_table,2) < size(nonCommutingTable,2) |
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105 | temp_nc_table(1,size(nonCommutingTable,2)) = 0; |
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106 | end |
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107 | for i = 1:size(temp_nc_table,1) |
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108 | candidates = findrows_nan(nonCommutingTable,temp_nc_table(i,:)); |
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109 | if isempty(candidates) |
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110 | nonCommutingTable = [nonCommutingTable;temp_nc_table(i,:)]; |
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111 | monomtable(end+1,end+1) = 0; |
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112 | involved = temp_nc_table(i,1+find(temp_nc_table(i,2:end))); |
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113 | switch length(involved) |
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114 | case 1 |
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115 | if isnan(temp_nc_table(i,1)) |
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116 | variabletype(end+1) = 0; |
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117 | else |
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118 | if variabletype(temp_nc_table(i,1)) == 0 |
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119 | variabletype(end+1) = 1; |
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120 | else |
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121 | variabletype(end+1) = 3; |
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122 | end |
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123 | end |
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124 | case 2 |
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125 | if isnan(temp_nc_table(i,1)) |
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126 | if involved(1) == involved(2) |
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127 | variabletype(end+1) = 2; |
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128 | else |
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129 | variabletype(end+1) = 1; |
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130 | end |
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131 | else |
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132 | variabletype(end+1) = 3; |
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133 | end |
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134 | otherwise |
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135 | variabletype(end+1) = 3; |
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136 | end |
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137 | lmivariables(i) = size(nonCommutingTable,1); |
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138 | else |
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139 | lmivariables(i) = candidates; |
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140 | |
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141 | end |
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142 | end |
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143 | |
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144 | % Create an output variable quickly |
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145 | if X_is_ncvar |
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146 | Z = X; |
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147 | else |
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148 | Z = Y; |
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149 | end |
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150 | Z.basis = new_base; |
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151 | Z.lmi_variables = lmivariables; |
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152 | |
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153 | % Fucked up order (lmi_variables should be sorted and unique) |
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154 | if any(diff(Z.lmi_variables)<0) |
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155 | [i,j]=sort(Z.lmi_variables); |
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156 | Z.basis = [Z.basis(:,1) Z.basis(:,j+1)]; |
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157 | Z.lmi_variables = Z.lmi_variables(j); |
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158 | end |
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159 | [un_Z_vars2] = uniquestripped(Z.lmi_variables); |
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160 | if length(un_Z_vars2) < length(Z.lmi_variables) |
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161 | [un_Z_vars,hh,jj] = unique(Z.lmi_variables); |
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162 | if length(Z.lmi_variables) ~=length(un_Z_vars) |
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163 | Z.basis = Z.basis*sparse([1 1+jj],[1 1+(1:length(jj))],ones(1,1+length(jj)))'; |
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164 | Z.lmi_variables = un_Z_vars; |
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165 | end |
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166 | end |
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167 | Z.dim = size(xy_base); |
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168 | Z = clean(Z); |
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169 | if size(monomtable,2) < size(monomtable,1) |
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170 | monomtable(size(monomtable,1),size(monomtable,1)) = 0; |
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171 | end |
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172 | yalmip('nonCommutingTable',nonCommutingTable); |
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173 | yalmip('setmonomtable',monomtable,variabletype); |
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174 | |
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175 | function c = findrows_nan(a,b) |
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176 | a(isnan(a)) = 0; |
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177 | b(isnan(b)) = 0; |
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178 | c=findrows(a,b); |
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