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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