130 lines
4.1 KiB
Mathematica
130 lines
4.1 KiB
Mathematica
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function [F,obj,BlockedQ,sol] = create_imagemodel(BlockedA,Blockedb,F_parametric,parobj,options);
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% *********************************
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% IMAGE REPRESENTATION
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% Needed for nonlinearly parameterized problems
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% More efficient in some cases
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% *********************************
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g = [];
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vecQ = [];
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sol.problem = 0;
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for i = 1:length(BlockedA)
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q = [];
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A = [];
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for j = 1:length(BlockedA{i})
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n = sqrt(size(BlockedA{i}{j},2));
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BlockedQ{i}{j} = sdpvar(n,n);
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q = [q;reshape(BlockedQ{i}{j},n^2,1)];
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A = [A BlockedA{i}{j}];
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end
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vecQ = [vecQ;q];
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g = [g;Blockedb{i}-A*q];
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end
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g_vars = getvariables(g);
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q_vars = getvariables(vecQ);
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x_vars = setdiff(g_vars,q_vars);
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base = getbase(g);
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if isempty(x_vars)
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A = base(:,1);base = base(:,2:end);
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B = (base(:,ismember(g_vars,q_vars)));
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Bnull = sparsenull(B);
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t = sdpvar(size(Bnull,2),1);
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imQ = -B\A+Bnull*t;
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else
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A = base(:,1);base = base(:,2:end);
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C = base(:,ismember(g_vars,x_vars));
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B = (base(:,ismember(g_vars,q_vars)));
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[Bnull,Q1,R1] = sparsenull(B);
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[ii,jj,kk] = find(Bnull);
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%Bnull(abs(Bnull) < 1e-12) = 0;
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small = find(abs(kk)<1e-12);
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ii(small)=[];
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jj(small)=[];
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kk(small)=[];
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Bnull = sparse(ii,jj,kk,size(Bnull,1),size(Bnull,2));
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t = sdpvar(size(Bnull,2),1);
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if options.sos.model == 2
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imQ = -Q1*(R1'\(A+C*recover(x_vars)))+Bnull*t;
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else
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H = deriveBasis(B);
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imQ = -B\(A+C*recover(x_vars))+H*t;
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end
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end
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notUsed = find(sum(abs(B),2)==0);
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if ~isempty(notUsed)
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ff=g(notUsed);
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if isa(ff,'double')
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if nnz(ff)>0
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sol.yalmiptime = 0; % FIX
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sol.solvertime = 0;
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sol.problem = 2;
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sol.info = yalmiperror(1,'YALMIP');
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F = [];
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obj = [];
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if options.verbose > 0
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disp(' ');
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disp('-> During construction of data, I encountered a situation')
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disp('-> situation that tells me that the problem is trivially infeasible!')
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disp('-> Have you forgotten to define some parametric variables?,')
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disp('-> or perhaps you have a parametric problem where the highest')
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disp('-> power in some of the independent variables is odd for any choice')
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disp('-> of parametric variables, such as x^8+x^7+t*y^3')
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disp('-> Anyway, take a good look at your model again...');
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end
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return
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% error('You seem to have a strange model. Have you forgotten to define some parametric variable?');
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end
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else
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F_parametric = F_parametric + (g(notUsed)==0);
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end
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end
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F_sos = ([]);
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obj = 0;
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for i = 1:length(BlockedQ)
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for j = 1:size(BlockedQ{i},2)
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Q_old = BlockedQ{i}{j};
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Q_old_vars = getvariables(Q_old);
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Q_old_base = getbase(Q_old);
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in_this = [];
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for k = 1:length(Q_old_vars)
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in_this = [in_this;find(Q_old_vars(k)==q_vars)];
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end
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Q_new = Q_old_base(:,1) + Q_old_base(:,2:end)*imQ(in_this);
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Q_new = reshape(Q_new,length(BlockedQ{i}{j}),length(BlockedQ{i}{j}));
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obj = obj+trace(Q_new);
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if ~isa(Q_new,'double')
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switch options.sos.model
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case {2,4}
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F_sos = F_sos + [Q_new>=0];
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case 5
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F_sos = F_sos + [dd(Q_new)];
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case 6
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F_sos = F_sos + [sdd(Q_new)];
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otherwise
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end
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elseif min(eig(Q_new))<-1e-8
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sol.yalmiptime = 0; % FIX
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sol.solvertime = 0;
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sol.problem = 2;
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sol.info = yalmiperror(1,'YALMIP');
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F = [];
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obj = [];
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error('Problem is trivially infeasible. After block-diagonalizing, I found constant negative definite blocks!');
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return
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end
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BlockedQ{i}{j} = Q_new;
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end
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end
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F = F_parametric + F_sos;
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if isa(obj,'double') | (options.sos.traceobj == 0)
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obj = [];
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end
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if ~isempty(parobj)
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obj = parobj;
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end
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