[37] | 1 | function test_pennon_vibration%(file, upper, rank, lambda_bar, resx, resy) |
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| 2 | |
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| 3 | draw = 1; |
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| 4 | |
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| 5 | if nargin < 6 |
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| 6 | draw = 0; |
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| 7 | end |
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| 8 | |
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| 9 | if nargin < 4 |
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| 10 | lambda_bar = 0.0001; |
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| 11 | end |
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| 12 | |
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| 13 | if nargin < 2 |
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| 14 | upper = 10; |
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| 15 | end |
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| 16 | |
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| 17 | if nargin < 3 |
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| 18 | rank = 0; |
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| 19 | end |
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| 20 | |
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| 21 | file = 'shape1'; |
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| 22 | |
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| 23 | load (file); |
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| 24 | |
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| 25 | |
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| 26 | if upper > 0 |
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| 27 | bounds = 1; |
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| 28 | else |
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| 29 | bounds = 0; |
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| 30 | end |
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| 31 | |
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| 32 | tic; |
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| 33 | |
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| 34 | compl = 5.0e-0; |
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| 35 | vol = nelem/3; |
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| 36 | |
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| 37 | % the variables |
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| 38 | u = sdpvar(nnod,1); |
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| 39 | if rank > 0 |
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| 40 | w = sdpvar(nnod,rank); |
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| 41 | end |
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| 42 | |
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| 43 | if bounds > 0 |
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| 44 | r = sdpvar(nelem,1); |
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| 45 | end |
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| 46 | |
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| 47 | alpha = sdpvar(1,1); |
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| 48 | |
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| 49 | lb = 1; |
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| 50 | BIUALL = []; |
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| 51 | NN = zeros(length(u)); |
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| 52 | for ie=1:nelem %for all elements |
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| 53 | len = Bdim(ie); %number of nonzeros in (Bi_1,...,Bi_nig) |
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| 54 | nb = len/nig; %number of nonzeros in Bi ... |
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| 55 | SumBiuuBi = zeros(3,3); |
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| 56 | |
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| 57 | BIU = []; |
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| 58 | for ig=1:nig |
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| 59 | Bi = sparse(Brow(lb:lb+nb-1),Bcol(lb:lb+nb-1),Bval(lb:lb+nb-1),3,nnod); |
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| 60 | Biu = Bi*u; |
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| 61 | SumBiuuBi = SumBiuuBi + Biu*Biu'; |
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| 62 | |
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| 63 | if rank > 0 |
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| 64 | Biw = Bi*w; |
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| 65 | SumBiuuBi = SumBiuuBi + Biw*Biw'; |
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| 66 | %for ir=1:rank |
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| 67 | % ss = Bi*w(:,ir); |
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| 68 | % SumBiuuBi = SumBiuuBi + ss*ss'; |
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| 69 | %end |
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| 70 | end |
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| 71 | lb = lb + nb; |
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| 72 | % BIU = [ BIU Biu]; |
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| 73 | end |
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| 74 | |
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| 75 | NN = NN | full(Bi)'*full(Bi); |
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| 76 | %SumBiuuBi = BIU*BIU'; |
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| 77 | BuuB{ie} = 0.5*SumBiuuBi; |
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| 78 | end |
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| 79 | |
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| 80 | if rank > 0 |
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| 81 | %Compue global mass matrix |
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| 82 | Mass = sparse(nnod,nnod); |
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| 83 | lb = 1; |
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| 84 | for ie = 1:nelem |
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| 85 | len = Bdim(ie); %number of nonzeros in (Bi_1,...,Bi_nig) |
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| 86 | nb = len/nig; %number of nonzeros in Bi ... |
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| 87 | elm=sparse(nnod,nnod); |
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| 88 | for ig=1:nig |
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| 89 | Bi = sparse(Brow(lb:lb+nb-1),Bcol(lb:lb+nb-1),Bval(lb:lb+nb-1),3,nnod); |
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| 90 | elm = elm + Bi'*Bi; |
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| 91 | lb = lb + nb; |
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| 92 | end |
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| 93 | ss = spones(diag(diag(elm))); |
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| 94 | MM{ie} = .5*ss; |
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| 95 | end |
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| 96 | end |
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| 97 | |
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| 98 | if rank > 0 |
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| 99 | % This is to prevent rank-deficient solutions |
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| 100 | G = set(w(1,1)>=0); |
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| 101 | for ir=2:rank |
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| 102 | % G = G+set(w(1,ir)<0); |
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| 103 | G = G+set(w(1,ir)>=0); |
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| 104 | end |
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| 105 | |
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| 106 | % Add matrix constraints |
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| 107 | for ie=1:nelem |
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| 108 | if bounds > 0 |
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| 109 | G = G + set(BuuB{ie}-(lambda_bar*(trace(w'*MM{ie}*w))+alpha+r(ie))*eye(3)<=0); |
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| 110 | else |
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| 111 | G = G + set(BuuB{ie}-(lambda_bar*(trace(w'*MM{ie}*w))+alpha)*eye(3)<=0); |
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| 112 | end |
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| 113 | end |
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| 114 | |
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| 115 | %if rank > 1 |
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| 116 | % G = G + set(w'*w-0.01*eye(rank)>=0); |
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| 117 | %end |
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| 118 | |
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| 119 | if bounds > 0 |
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| 120 | for ie=1:nelem |
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| 121 | G = G + set(r(ie)>=0); |
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| 122 | end |
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| 123 | end |
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| 124 | else |
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| 125 | % Create 1-st constraint |
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| 126 | if bounds > 0 |
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| 127 | G = set(BuuB{1}-(alpha+r(1))*eye(3)<=0); |
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| 128 | % Add constraint 2 to #elements |
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| 129 | for ie=2:nelem |
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| 130 | G = G + set(BuuB{ie}-(alpha+r(ie))*eye(3)<=0); |
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| 131 | end |
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| 132 | for ie=1:nelem |
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| 133 | G = G + set(r(ie)>=0); |
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| 134 | end |
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| 135 | else |
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| 136 | G = set(BuuB{1}-alpha*eye(3)<=0); |
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| 137 | % Add constraint 2 to #elements |
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| 138 | for ie=2:nelem |
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| 139 | G = G + set(BuuB{ie}-alpha*eye(3)<=0); |
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| 140 | end |
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| 141 | end |
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| 142 | |
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| 143 | end |
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| 144 | |
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| 145 | % Create objective |
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| 146 | if bounds > 0 |
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| 147 | Obj = alpha*vol-F'*u+upper*r'*ones(nelem,1); |
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| 148 | else |
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| 149 | Obj = alpha*vol-F'*u; |
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| 150 | end |
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| 151 | |
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| 152 | % Solve the problem |
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| 153 | options = sdpsettings('solver','penbmi','usex0',1,'savedebug',0,... |
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| 154 | 'penbmi.U0',1000,... |
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| 155 | 'penbmi.P0',1000,... |
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| 156 | 'penbmi.PEN_UP',.5,... |
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| 157 | 'penbmi.ALPHA',1e-5,... |
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| 158 | 'penbmi.P_EPS',1e-3,...% 'penbmi.PBM_EPS',1e-3,... |
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| 159 | 'penbmi.PRECISION_2', 1e-4); %1e-7 |
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| 160 | |
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| 161 | toc; |
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| 162 | tic; |
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| 163 | |
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| 164 | sol = solvesdp(G, Obj, options); |
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| 165 | mbg_asserttrue(sol.problem == 0); |
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| 166 | |
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| 167 | |
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| 168 | |
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| 169 | |
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| 170 | toc; |
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