[37] | 1 | function [BlockedQ,residuals] = postprocesssos(BlockedA,Blockedb,BlockedQ,sparsityPattern,options); |
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| 2 | |
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| 3 | BlockedQ=applysparsity(BlockedQ,sparsityPattern); |
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| 4 | |
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| 5 | for passes = 1:1:options.sos.postprocess |
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| 6 | for constraint = 1:length(BlockedQ) |
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| 7 | mismatch = computeresiduals(BlockedA,Blockedb,BlockedQ,constraint); |
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| 8 | [ii,jj ]= sort(abs(mismatch)); |
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| 9 | jj = flipud(jj); |
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| 10 | for j = jj(:)'%1:size(BlockedA{constraint}{1},1) |
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| 11 | if abs(mismatch(j))>0 |
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| 12 | for i = 1:length(BlockedA{constraint}) |
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| 13 | n=sqrt(size(BlockedA{constraint}{i},2)); |
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| 14 | Ai=reshape(BlockedA{constraint}{i}(j,:),n,n); |
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| 15 | nnzAi = nnz(Ai); |
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| 16 | if nnzAi>0 |
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| 17 | dAi = Ai*mismatch(j)/nnzAi; |
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| 18 | Qi = BlockedQ{constraint}{i}; |
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| 19 | % [R,p] = chol(BlockedQ{constraint}{i}-Ai*mismatch(j)/nnzAi); |
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| 20 | [R,p] = chol(Qi-dAi); |
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| 21 | if p |
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| 22 | % gevps=eig(BlockedQ{constraint}{i},full(Ai)*mismatch(j)/nnzAi); |
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| 23 | gevps=eig(Qi,full(dAi)); |
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| 24 | gevps=gevps(gevps>=0); |
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| 25 | gevps=gevps(~isinf(gevps)); |
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| 26 | if isempty(gevps) |
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| 27 | gevps=1; |
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| 28 | end |
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| 29 | lambda=max(0,min(1,min(gevps))); |
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| 30 | % [R,p] = chol(BlockedQ{constraint}{i}-Ai*lambda*mismatch(j)/nnzAi); |
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| 31 | [R,p] = chol(Qi-dAi*lambda); |
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| 32 | else |
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| 33 | lambda = 1; |
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| 34 | end |
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| 35 | % dAi = Ai*mismatch(j)/nnzAi; |
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| 36 | if ~p |
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| 37 | % BlockedQ{constraint}{i}=BlockedQ{constraint}{i}-Ai*lambda*mismatch(j)/nnzAi; |
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| 38 | BlockedQ{constraint}{i}=Qi-dAi*lambda; |
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| 39 | mismatch(j)=mismatch(j)*(1-lambda); |
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| 40 | else |
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| 41 | %lambda=1; |
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| 42 | while lambda>1e-4 & (p~=0) |
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| 43 | lambda=lambda/sqrt(2); |
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| 44 | % [R,p]= chol(BlockedQ{constraint}{i}-Ai*lambda*mismatch(j)/nnzAi); |
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| 45 | [R,p]= chol(Qi-dAi*lambda); |
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| 46 | end |
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| 47 | % if min(eig(BlockedQ{constraint}{i}-Ai*lambda*mismatch(j)/nnzAi))>=0 |
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| 48 | if min(eig(Qi-dAi*lambda))>=0 |
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| 49 | % BlockedQ{constraint}{i}=BlockedQ{constraint}{i}-Ai*lambda*mismatch(j)/nnzAi; |
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| 50 | BlockedQ{constraint}{i}=Qi-dAi*lambda; |
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| 51 | mismatch(j)=mismatch(j)*(1-lambda); |
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| 52 | end |
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| 53 | end |
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| 54 | end |
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| 55 | end |
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| 56 | end |
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| 57 | end |
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| 58 | end |
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| 59 | end |
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| 60 | |
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| 61 | for constraint = 1:length(BlockedQ) |
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| 62 | residuals(constraint,1) = norm(computeresiduals(BlockedA,Blockedb,BlockedQ,constraint),'inf'); |
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| 63 | end |
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| 64 | |
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| 65 | function mismatch = computeresiduals(BlockedA,Blockedb,BlockedQ,constraint); |
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| 66 | lhs=0; |
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| 67 | for k=1:length(BlockedA{constraint}) |
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| 68 | lhs=lhs+BlockedA{constraint}{k}*BlockedQ{constraint}{k}(:); |
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| 69 | end |
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| 70 | mismatch = lhs-Blockedb{constraint}; |
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| 71 | |
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| 72 | function BlockedQ=applysparsity(BlockedQ,sparsityPattern); |
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| 73 | if ~isempty(sparsityPattern) |
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| 74 | |
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| 75 | for i = 1:length(BlockedQ) |
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| 76 | for j = 1:length(BlockedQ{i}) |
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| 77 | BlockedQ{i}{j}(sparsityPattern{i}{j}) = 0; |
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| 78 | end |
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| 79 | end |
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| 80 | end |
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| 81 | |
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