[37] | 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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