81 lines
2.6 KiB
Mathematica
81 lines
2.6 KiB
Mathematica
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function [F,obj,BlockedQ,Primal_matrices,Free_variables] = create_kernelmodel(BlockedA,Blockedb,F_parametric,parobj,options,sparsityPattern);
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% To get the primal kernel representation, we simply use
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% the built-in dualization module!
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% First, write the problem in primal kernel format
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traceobj = 0;
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dotraceobj = options.sos.traceobj;
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F = F_parametric;
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for i = 1:length(Blockedb)
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sizematrixSOS = sqrt(size(Blockedb{i},2));
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for k = 1:sizematrixSOS
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for r = k:sizematrixSOS
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res{(k-1)*sizematrixSOS+r} = 0;
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end
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end
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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*sizematrixSOS,n*sizematrixSOS);
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F = F + lmi(BlockedQ{i}{j});
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if sizematrixSOS>0
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% Matrix valued sum of sqaures
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% Loop over all elements
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starttop = 1;
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for k = 1:sizematrixSOS
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startleft = 1;
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for r = 1:sizematrixSOS
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if k<=r
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Qkr = BlockedQ{i}{j}(starttop:starttop+n-1,startleft:startleft+n-1);
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res{(k-1)*sizematrixSOS+r} = res{(k-1)*sizematrixSOS+r} + BlockedA{i}{j}*reshape(Qkr,n^2,1);
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end
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startleft = startleft + n;
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end
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starttop = starttop + n;
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end
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else
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% Standard case
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res{1} = res{1} + BlockedA{i}{j}*reshape(BlockedQ{i}{j},n^2,1);
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end
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if dotraceobj
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traceobj = traceobj + trace(BlockedQ{i}{j});
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end
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end
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for k = 1:sizematrixSOS
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for r = k:sizematrixSOS
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F = F + (res{(k-1)*sizematrixSOS+r} == Blockedb{i}(:,(k-1)*sizematrixSOS+r));
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end
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end
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end
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% % Constrain elements according to a desired sparsity
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if ~isempty(sparsityPattern)
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res = [];
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for i = 1:length(BlockedQ)
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for j = 1:length(BlockedQ{i})
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if ~isempty(sparsityPattern{i}{j})
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H = spalloc(length(BlockedQ{i}{j}),length(BlockedQ{i}{j}),length(sparsityPattern{i}{j}));
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H(sparsityPattern{i}{j}) = 1;
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k = find(triu(H));
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res = [res;BlockedQ{i}{j}(k)];
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end
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end
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end
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F = F + (0 == res);
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end
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% And get the primal model of this
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if isempty(parobj)
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if options.sos.traceobj
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[F,obj,Primal_matrices,Free_variables] = dualize(F,traceobj,1,options.sos.extlp);
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else
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[F,obj,Primal_matrices,Free_variables] = dualize(F,[],1,options.sos.extlp);
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end
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else
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[F,obj,Primal_matrices,Free_variables] = dualize(F,parobj,1,options.sos.extlp);
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end
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% In dual mode, we maximize
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obj = -obj;
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