1 | function varargout = solvemp(F,h,ops,x,y) |
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2 | %SOLVEMP Computes solution to multi-parametric optimization problem |
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3 | % |
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4 | % min_z(x) h(x,z) |
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5 | % subject to |
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6 | % F(x,z) > 0 |
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7 | % |
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8 | % |
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9 | % [SOL, DIAGNOSTIC,Z,HPWF,ZPWF] = SOLVEMP(F,h,options,x,y) |
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10 | % |
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11 | % SOL : Multi-parametric solution (see MPT toolbox) |
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12 | % |
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13 | % DIAGNOSTIC : struct with diagnostic information |
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14 | % |
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15 | % Z : SDPVAR object with the detected decision variable z |
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16 | % |
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17 | % HPWF : The value function as a pwf function |
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18 | % |
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19 | % ZPWF : The optimal decision variable as a pfw function |
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20 | % |
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21 | % Input |
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22 | % F : SET object describing the constraints. |
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23 | % h : SDPVAR object describing the objective function h(x,z). |
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24 | % options : solver options. See SDPSETTINGS. Can be []. |
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25 | % x : Parametric variables |
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26 | % y : Requested decision variables (subset of z) |
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27 | % |
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28 | % NOTE : If you are solving a problem leading to an mpMILP, the |
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29 | % output SOL will be a set-valued map. To obtain the minimal |
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30 | % solution (without so called overlaps), run removeOverlaps(SOL). If you |
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31 | % have requested the 5th output ZPWF, overlaps are automatically removed. |
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32 | % If your problem leads to an mpMIQP, the output SOL will also be a |
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33 | % set-valued map, but there is currently no way in MPT to obtain a |
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34 | % non-overlapping solution. To use the solution in MPT, the command |
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35 | % mpt_mergeCS(SOL) can be useful. Notice that the fifth output argument |
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36 | % not will be available for mpMIQP problems. |
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37 | % |
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38 | % See also PARAMETRIC, SET, SDPSETTINGS, YALMIPERROR |
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39 | |
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40 | % Author Johan Löfberg |
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41 | % $Id: solvemp.m,v 1.9 2006/09/13 09:28:52 joloef Exp $ |
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42 | |
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43 | if nargin <= 3 |
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44 | ops = sdpsettings; |
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45 | end |
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46 | |
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47 | if nargin <=3 |
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48 | x = []; |
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49 | y = []; |
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50 | end |
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51 | |
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52 | par_declarations = is(F,'parametric'); |
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53 | if any(par_declarations) |
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54 | x = [x;recover(getvariables(sdpvar(F(find(par_declarations)))))]; |
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55 | F = F(find(~par_declarations)); |
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56 | end |
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57 | |
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58 | if length(x) == 0 |
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59 | error('solvemp must always have 4 input arguments or a parametric declaration'); |
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60 | end |
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61 | |
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62 | if ~isempty(ops) |
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63 | if isequal(ops.solver,'') |
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64 | ops.solver = 'mpt'; |
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65 | end |
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66 | else |
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67 | ops = sdpsettings('solver','mpt'); |
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68 | end |
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69 | |
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70 | if nargin == 4 |
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71 | y = []; |
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72 | ny = 0; |
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73 | my = 0; |
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74 | else |
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75 | % YALMIP wants a vector as desired decsision variable |
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76 | [ny,my] = size(y); |
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77 | y = reshape(y,ny*my,1); |
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78 | end |
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79 | |
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80 | % Robustify first? |
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81 | if length(F) > 0 |
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82 | unc_declarations = is(F,'uncertain'); |
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83 | if any(unc_declarations) |
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84 | w = recover(getvariables(sdpvar(F(find(unc_declarations))))); |
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85 | F = F(find(~unc_declarations)); |
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86 | [F,h,failure] = robustify(F,h,ops,w); |
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87 | if failure |
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88 | error('Derivation of robust counter-part failed') |
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89 | end |
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90 | end |
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91 | end |
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92 | |
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93 | sol = solvesdp(F,h,ops,x,y); |
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94 | |
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95 | if isfield(sol,'mpsol') |
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96 | if ~isfield(sol.mpsol,'model') |
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97 | varargout{1} = []; |
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98 | varargout{2} = sol; |
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99 | varargout{3} = []; |
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100 | varargout{4} = []; |
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101 | varargout{5} = []; |
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102 | elseif isempty(sol.mpsol.model{1}) |
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103 | varargout{1} = sol.mpsol.model; |
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104 | varargout{2} = sol; |
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105 | varargout{3} = []; |
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106 | varargout{4} = []; |
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107 | varargout{5} = []; |
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108 | else |
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109 | |
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110 | mpsolution = sol.mpsol.model; |
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111 | varargout{1} = sol.mpsol.model; |
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112 | |
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113 | if nargout > 2 |
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114 | z = recover(sol.solveroutput.U); |
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115 | x = recover(sol.solveroutput.x); |
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116 | varargout{3}= z; |
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117 | end |
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118 | |
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119 | if nargout > 3 |
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120 | % User wants the value function |
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121 | if length(mpsolution) == 1 |
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122 | if isequal(mpsolution{1}.convex,1) |
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123 | % Simple mpLP value function |
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124 | if ops.mp.simplify |
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125 | s = mpsolution{1}; |
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126 | s.Fi = s.Bi; |
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127 | s.Gi = s.Ci; |
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128 | s = mpt_simplify(s); |
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129 | s.Bi = s.Fi; |
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130 | s.Ci = s.Gi; |
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131 | varargout{4} = pwf(s,x,'convex'); |
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132 | else |
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133 | varargout{4} = pwf(mpsolution{1},x,'convex'); |
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134 | end |
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135 | else |
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136 | % Probably generated from removing overlaps |
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137 | varargout{4} = pwf(mpsolution,x,'general'); |
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138 | end |
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139 | else |
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140 | % No overlap removal done |
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141 | varargout{4} = pwf(mpsolution,x,'convexoverlapping'); |
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142 | end |
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143 | end |
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144 | |
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145 | if nargout > 4 |
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146 | % User wants optimizer in YALMIP format |
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147 | % Any overlaps? |
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148 | anyQP = 0; |
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149 | if length(varargout{1}) > 1 |
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150 | for i = 1:length(sol.mpsol.model) |
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151 | if nnz([sol.mpsol.model{i}.Ai{:}])>0 |
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152 | anyQP = 1; |
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153 | break |
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154 | end |
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155 | end |
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156 | if ~anyQP |
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157 | minimalmodel{1} = mpt_removeOverlaps(sol.mpsol.model); |
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158 | varargout{1} = minimalmodel; |
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159 | end |
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160 | else |
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161 | minimalmodel = varargout{1}; |
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162 | end |
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163 | % PWA assumes we want Bi and Ci |
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164 | if ~anyQP |
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165 | minimalmodel{1}.Ai = cell(1,length(minimalmodel{1}.Fi)); |
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166 | minimalmodel{1}.Bi = minimalmodel{1}.Fi; |
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167 | minimalmodel{1}.Ci = minimalmodel{1}.Gi; |
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168 | varargout{5} = pwf(minimalmodel,x,'general'); |
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169 | if min([ny my])>0 |
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170 | varargout{5} = reshape(varargout{5},ny,my); |
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171 | end |
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172 | else |
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173 | disp('Optimizer (5th output) not available for overlapping quadratic problems.'); |
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174 | varargout{5} = []; |
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175 | end |
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176 | end |
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177 | end |
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178 | else |
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179 | varargout{1} = []; |
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180 | varargout{2} = sol; |
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181 | varargout{3} = []; |
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182 | varargout{4} = []; |
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183 | varargout{5} = []; |
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184 | end |
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185 | varargout{2} = sol; |
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186 | |
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