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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