% first load the results of knitro to be able to plot the diference % path(path,'/home/anitescu/WORKING/STOCHFEM/MATLAB/INTEGRATION'); N=1000; % size of the matrix xsfem0=[ 1 3.95961e-12 1.90326e-12 -2.38447e-12 -2.11497e-12 2.57388e-13 2 3.93092e-12 1.88413e-12 -2.37396e-12 -2.09837e-12 2.61221e-13 3 3.87607e-12 1.84817e-12 -2.35323e-12 -2.06726e-12 2.67245e-13 4 3.79783e-12 1.79777e-12 -2.32269e-12 -2.02362e-12 2.74206e-13 5 3.69914e-12 1.73535e-12 -2.28283e-12 -1.96932e-12 2.8117e-13 6 3.58296e-12 1.66325e-12 -2.23426e-12 -1.90609e-12 2.87453e-13 7 3.45225e-12 1.58372e-12 -2.17767e-12 -1.83554e-12 2.92583e-13 8 3.30988e-12 1.49883e-12 -2.11383e-12 -1.75915e-12 2.96252e-13 9 3.15858e-12 1.41048e-12 -2.04357e-12 -1.67828e-12 2.98283e-13 10 3.00089e-12 1.32034e-12 -1.96777e-12 -1.59419e-12 2.98604e-13 11 2.83915e-12 1.22989e-12 -1.88734e-12 -1.50801e-12 2.97221e-13 12 2.67547e-12 1.14039e-12 -1.80318e-12 -1.42076e-12 2.94198e-13 13 2.51172e-12 1.05286e-12 -1.71622e-12 -1.33336e-12 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0.116614 0.0595398 -0.102666 -0.156397 -0.0756854 994 0.120514 0.0613342 -0.106861 -0.162895 -0.0791668 995 0.124032 0.0629402 -0.1107 -0.168855 -0.0823897 996 0.127109 0.0643336 -0.114104 -0.174153 -0.0852828 997 0.129682 0.0654907 -0.116988 -0.178658 -0.0877695 998 0.131693 0.0663889 -0.119271 -0.182237 -0.0897682 999 0.133085 0.067007 -0.120869 -0.184753 -0.091193 1000 0.133805 0.0673249 -0.121705 -0.186075 -0.0919531]; xsfem=xsfem0(:, 2:6); % discard the index column lambdasfem=[ -0.156353 0.186269 -0.0914538 -0.000360416 0.0195649]; % lambda coefficient from knitro % construct the Q and DQ from the paper Q=2*diag(ones(N,1))-diag(ones(N-1,1),-1)-diag(ones(N-1,1),1); Q(1,1)=1; Q(N,N)=1; DQ=diag(2.*((1:N)/N).*(1-(1:N)/N).*cos((1:N)/N)); yMin=-1; yMax=1; nrSamples=1; % only one sample to do then sparse eigenvalue by hand % to check for the [xvalue,lambda,slambda,xx,sxx,cosangle,residual,cputimes] = ... sampleMinEig(Q,DQ,yMin,yMax,nrSamples,lambdasfem,xsfem); % xvalue: the ordinates (between -1,1) % lambda, slambda: simulated and, respectively, stochastic FEM eigenvalue % cosangle: cosine of angle between the knitro solution and direct % -------- simulation reported in paper % xx: direct simulation eigenvector, N by nrSamples. % sxx: stochastic FEM eigenvector, N by nrSamples. % residual: residual plotted in paper % cputimes: cpu times reported in the paper