Example of Fig 7.7 - 7.8
Barnett-Preisendorfer CCA with with different variance retained
function [u,lam,v,ss]=example550 % %Compute CCA of matrices s z and expand them to file for nmode modes % Uses EOF projection method % For different number of retained modes % sflat = [-30 30]; sflon = [120 300]; zflat = [0 90]; zflon = [120 360]; lnorm = 'full'; [st,inds,fcos]=readsst(sflat,sflon,'season','jfm','scaling','yes'); [zt,indz,fcos]=readz500(zflat,zflon,'season','jfm','scaling','yes'); [z,sdz]=anomaly(zt,lnorm); [s,sdz]=anomaly(st,lnorm); xcross=norm(z*s','fro'); disp(['Total Crosscovariance ' num2str(xcross)]); scut=0.5; zcut=0.5; [u6,v,corr6,varz6,vars,projz,projs]=cccca(z,s,indz,inds,zcut,scut); scut=0.8; zcut=0.8; [u8,v,corr8,varz8,vars,projz,projs]=cccca(z,s,indz,inds,zcut,scut); scut=0.90; zcut=0.90; [u9,v,corr9,varz9,vars,projz,projs]=cccca(z,s,indz,inds,zcut,scut); % PLot EOF ----- titstr=cell(size(1:3)); cont=[]; figure(1) clf; i=1; ii=1; titstr{1} = [' Z Component 50% Expl TC ' num2str(varz6(i)*100,'%-2.0f') '%' ... ' Correlation ' num2str(corr6(ii)*100,'%-2.0f') '%']; titstr{2} = [' Z Component 80% Expl TC ' num2str(varz8(i)*100,'%-2.0f') '%' ... ' Correlation ' num2str(corr8(ii)*100,'%-2.0f') '%']; titstr{3} = [' Z Component 90% Expl TC ' num2str(varz9(i)*100,'%-2.0f') '%' ... ' Correlation ' num2str(corr9(ii)*100,'%-2.0f') '%']; bigtit{1}= ['First Mode ' ]; bigtit{2}= ['CCA-BP']; pict3(bigtit,u6(:,1),u8(:,1), u9(:,1), ... zflat,zflon,cont,titstr,'shading','off'); print('-dpdf','-painters',[mfilename '1Z.pdf']); itstr=cell(size(1:3)); cont=[]; figure(2) clf; i=2; ii=2; titstr{1} = [' Z Component 50% Expl TC ' num2str(varz6(i)*100,'%-2.0f') '%' ... ' Correlation ' num2str(corr6(ii)*100,'%-2.0f') '%']; titstr{2} = [' Z Component 80% Expl TC ' num2str(varz8(i)*100,'%-2.0f') '%' ... ' Correlation ' num2str(corr8(ii)*100,'%-2.0f') '%']; titstr{3} = [' Z Component 90% Expl TC ' num2str(varz9(i)*100,'%-2.0f') '%' ... ' Correlation ' num2str(corr9(ii)*100,'%-2.0f') '%']; bigtit{1}= ['Second Mode ' ]; bigtit{2}= ['CCA-BP']; pict3(bigtit,u6(:,i),u8(:,i), u9(:,i), ... zflat,zflon,cont,titstr,'shading','off'); print('-dpdf','-painters',[mfilename '2Z.pdf']); return
Normalization full Normalization full Total Crosscovariance 10984.0561 Modes for SST 3 --- Variance Retained 0.56744 Modes for Z 2 --- Variance Retained 0.54336 Normalization full Normalization full SVD computed Number of modes computed -- min(iz,is) 2 Correlations 0.92278 0.092036 Expanded Field1 Expanded Field2 Crosscovariance between coefficient of the time series 9.227809e-01 2.359224e-16 -1.249001e-16 Crosscovariance between coefficient of the time series 9.203649e-02 Covariance of Z time series 1.000000e+00 6.487866e-16 6.487866e-16 Covariance of Z time series 1 Covariance of S time series 1.000000e+00 -1.002670e-15 -1.002670e-15 Covariance of S time series 1.000000e+00 Modes for SST 8 --- Variance Retained 0.8169 Modes for Z 7 --- Variance Retained 0.81782 Normalization full Normalization full SVD computed Number of modes computed -- min(iz,is) 7 Correlations 0.96649 0.84036 0.71816 0.61249 0.46162 0.35649 0.16534 Expanded Field1 Expanded Field2 Expanded Field3 Expanded Field4 Expanded Field5 Expanded Field6 Expanded Field7 Crosscovariance between coefficient of the time series 9.664877e-01 5.551115e-17 -2.532696e-16 Crosscovariance between coefficient of the time series -1.387779e-17 -2.046974e-16 6.765422e-17 Crosscovariance between coefficient of the time series -5.204170e-18 -3.677614e-16 8.403573e-01 Crosscovariance between coefficient of the time series -5.342948e-16 9.714451e-17 -1.370432e-16 Crosscovariance between coefficient of the time series -6.036838e-16 -6.557255e-16 -2.081668e-16 Crosscovariance between coefficient of the time series 4.510281e-17 7.181555e-01 3.295975e-16 Crosscovariance between coefficient of the time series 5.377643e-17 4.683753e-17 -2.558717e-16 Crosscovariance between coefficient of the time series 6.938894e-18 1.006140e-16 3.469447e-16 Crosscovariance between coefficient of the time series 6.124852e-01 -2.046974e-16 4.111295e-16 Crosscovariance between coefficient of the time series -5.915407e-16 -1.795439e-16 -3.152860e-16 Crosscovariance between coefficient of the time series 2.200930e-16 -1.457168e-16 4.616181e-01 Crosscovariance between coefficient of the time series -4.466913e-17 -6.505213e-18 -2.298509e-16 Crosscovariance between coefficient of the time series -3.773024e-16 -2.125036e-16 -2.688821e-16 Crosscovariance between coefficient of the time series -7.155734e-17 3.564869e-01 -2.797242e-16 Crosscovariance between coefficient of the time series 2.359224e-16 9.020562e-17 -1.942890e-16 Crosscovariance between coefficient of the time series -7.910339e-16 1.075529e-16 2.810252e-16 Crosscovariance between coefficient of the time series 1.653395e-01 Covariance of Z time series 1.000000e+00 -1.327063e-15 -3.686287e-16 Covariance of Z time series 5.787471e-16 1.098514e-15 -2.536166e-15 Covariance of Z time series -1.813653e-15 -1.327063e-15 1.000000e+00 Covariance of Z time series -2.934285e-15 1.784163e-15 -1.105886e-16 Covariance of Z time series -9.879250e-16 -1.113259e-15 -3.686287e-16 Covariance of Z time series -2.934285e-15 1.000000e+00 2.654127e-16 Covariance of Z time series 1.710437e-15 -1.680947e-15 -1.489260e-15 Covariance of Z time series 5.787471e-16 1.784163e-15 2.654127e-16 Covariance of Z time series 1.000000e+00 -1.382358e-15 2.786833e-15 Covariance of Z time series -1.489260e-15 1.098514e-15 -1.105886e-16 Covariance of Z time series 1.710437e-15 -1.382358e-15 1.000000e+00 Covariance of Z time series 8.082185e-16 -1.946360e-15 -2.536166e-15 Covariance of Z time series -9.879250e-16 -1.680947e-15 2.786833e-15 Covariance of Z time series 8.082185e-16 1.000000e+00 -8.257284e-16 Covariance of Z time series -1.813653e-15 -1.113259e-15 -1.489260e-15 Covariance of Z time series -1.489260e-15 -1.946360e-15 -8.257284e-16 Covariance of Z time series 1 Covariance of S time series 1.000000e+00 -7.284104e-15 -2.064321e-16 Covariance of S time series 1.913183e-15 3.295080e-15 2.447695e-15 Covariance of S time series 4.158132e-15 -7.284104e-15 1.000000e+00 Covariance of S time series -4.054916e-16 -4.939625e-16 -6.469434e-16 Covariance of S time series 7.667478e-16 1.120631e-15 -2.064321e-16 Covariance of S time series -4.054916e-16 1.000000e+00 7.962381e-16 Covariance of S time series 8.165127e-16 -8.238852e-16 -6.192963e-16 Covariance of S time series 1.913183e-15 -4.939625e-16 7.962381e-16 Covariance of S time series 1.000000e+00 5.234528e-16 -2.727853e-15 Covariance of S time series -1.647770e-15 3.295080e-15 -6.469434e-16 Covariance of S time series 8.165127e-16 5.234528e-16 1 Covariance of S time series -1.489260e-15 5.160802e-16 2.447695e-15 Covariance of S time series 7.667478e-16 -8.238852e-16 -2.727853e-15 Covariance of S time series -1.489260e-15 1 3.243933e-16 Covariance of S time series 4.158132e-15 1.120631e-15 -6.192963e-16 Covariance of S time series -1.647770e-15 5.160802e-16 3.243933e-16 Covariance of S time series 1.000000e+00 Modes for SST 13 --- Variance Retained 0.90956 Modes for Z 11 --- Variance Retained 0.91292 Normalization full Normalization full SVD computed Number of modes computed -- min(iz,is) 11 Correlations 0.985 0.95406 0.87046 0.83025 0.79955 0.73534 0.49953 0.4628 0.35591 0.20144 0.11054 Expanded Field1 Expanded Field2 Expanded Field3 Expanded Field4 Expanded Field5 Expanded Field6 Expanded Field7 Expanded Field8 Expanded Field9 Expanded Field10 Expanded Field11 Crosscovariance between coefficient of the time series 9.849972e-01 -4.163336e-16 1.249001e-16 Crosscovariance between coefficient of the time series -2.775558e-17 2.168404e-16 -4.440892e-16 Crosscovariance between coefficient of the time series 1.249001e-16 -3.885781e-16 3.469447e-17 Crosscovariance between coefficient of the time series 3.191891e-16 -7.719519e-17 -4.996004e-16 Crosscovariance between coefficient of the time series 9.540584e-01 2.775558e-16 4.510281e-17 Crosscovariance between coefficient of the time series -4.857226e-17 -1.804112e-16 -3.608225e-16 Crosscovariance between coefficient of the time series -1.804112e-16 4.163336e-16 1.110223e-16 Crosscovariance between coefficient of the time series 4.224052e-16 2.914335e-16 4.718448e-16 Crosscovariance between coefficient of the time series 8.704553e-01 3.816392e-16 4.093947e-16 Crosscovariance between coefficient of the time series 1.110223e-16 -5.828671e-16 5.689893e-16 Crosscovariance between coefficient of the time series 4.510281e-17 1.110223e-16 4.250073e-16 Crosscovariance between coefficient of the time series 1.249001e-16 7.285839e-17 -6.938894e-17 Crosscovariance between coefficient of the time series 8.302467e-01 1.110223e-16 7.494005e-16 Crosscovariance between coefficient of the time series -5.828671e-16 3.469447e-17 2.498002e-16 Crosscovariance between coefficient of the time series 2.324529e-16 -3.642919e-17 -9.020562e-17 Crosscovariance between coefficient of the time series -1.665335e-16 4.523291e-16 2.081668e-16 Crosscovariance between coefficient of the time series 7.995509e-01 4.961309e-16 1.838807e-16 Crosscovariance between coefficient of the time series -5.551115e-17 6.938894e-17 1.457168e-16 Crosscovariance between coefficient of the time series 9.194034e-17 -4.163336e-16 -1.318390e-16 Crosscovariance between coefficient of the time series 8.326673e-17 6.106227e-16 5.863365e-16 Crosscovariance between coefficient of the time series 7.353430e-01 -2.636780e-16 -2.081668e-16 Crosscovariance between coefficient of the time series -2.914335e-16 1.561251e-16 -5.204170e-18 Crosscovariance between coefficient of the time series 1.387779e-16 -5.828671e-16 -3.608225e-16 Crosscovariance between coefficient of the time series -7.216450e-16 -2.636780e-16 0 Crosscovariance between coefficient of the time series 4.995257e-01 8.326673e-17 1.179612e-16 Crosscovariance between coefficient of the time series -8.326673e-17 -7.285839e-17 -2.081668e-16 Crosscovariance between coefficient of the time series -5.481726e-16 3.330669e-16 1.942890e-16 Crosscovariance between coefficient of the time series 2.914335e-16 1.942890e-16 -3.053113e-16 Crosscovariance between coefficient of the time series 4.628004e-01 0 1.769418e-16 Crosscovariance between coefficient of the time series 2.602085e-18 -4.857226e-17 -1.804112e-16 Crosscovariance between coefficient of the time series 5.551115e-17 5.898060e-17 1.665335e-16 Crosscovariance between coefficient of the time series -4.163336e-17 4.024558e-16 1.387779e-16 Crosscovariance between coefficient of the time series 3.559078e-01 -1.665335e-16 1.700029e-16 Crosscovariance between coefficient of the time series 2.081668e-16 4.718448e-16 3.608225e-16 Crosscovariance between coefficient of the time series 3.885781e-16 -1.110223e-16 8.222589e-16 Crosscovariance between coefficient of the time series -1.179612e-16 3.504141e-16 -2.775558e-16 Crosscovariance between coefficient of the time series 2.014433e-01 8.174884e-17 -1.179612e-16 Crosscovariance between coefficient of the time series -4.163336e-17 1.526557e-16 -7.979728e-17 Crosscovariance between coefficient of the time series 2.151057e-16 -4.440892e-16 6.938894e-18 Crosscovariance between coefficient of the time series 8.326673e-17 1.908196e-16 -1.942890e-16 Crosscovariance between coefficient of the time series 1.105444e-01 Covariance of Z time series 1.000000e+00 -1.739928e-15 -1.164867e-15 Covariance of Z time series -5.898060e-16 1.290201e-15 -9.436896e-16 Covariance of Z time series 3.391384e-16 -1.990595e-16 1.028474e-15 Covariance of Z time series 2.064321e-15 2.462440e-15 -1.739928e-15 Covariance of Z time series 1.000000e+00 3.538836e-16 -1.931615e-15 Covariance of Z time series 1.341809e-15 -3.649425e-16 7.814929e-16 Covariance of Z time series -1.085612e-15 1.621966e-16 -9.141993e-16 Covariance of Z time series 1.445025e-15 -1.164867e-15 3.538836e-16 Covariance of Z time series 1.000000e+00 -1.540868e-15 4.902762e-16 Covariance of Z time series -5.160802e-16 -1.024788e-15 1.113259e-15 Covariance of Z time series -5.898060e-16 -3.538836e-16 -6.340414e-16 Covariance of Z time series -5.898060e-16 -1.931615e-15 -1.540868e-15 Covariance of Z time series 1.000000e+00 8.404735e-16 -1.198043e-15 Covariance of Z time series -1.887379e-15 1.194357e-15 -3.612562e-16 Covariance of Z time series 1.533496e-15 8.404735e-16 1.290201e-15 Covariance of Z time series 1.341809e-15 4.902762e-16 8.404735e-16 Covariance of Z time series 1.000000e+00 1.253338e-15 -5.750608e-16 Covariance of Z time series -4.423545e-16 -1.616437e-15 7.778066e-16 Covariance of Z time series -2.565656e-15 -9.436896e-16 -3.649425e-16 Covariance of Z time series -5.160802e-16 -1.198043e-15 1.253338e-15 Covariance of Z time series 1.000000e+00 7.225123e-16 8.773364e-16 Covariance of Z time series 4.276093e-16 -5.441882e-16 4.128642e-16 Covariance of Z time series 3.391384e-16 7.814929e-16 -1.024788e-15 Covariance of Z time series -1.887379e-15 -5.750608e-16 7.225123e-16 Covariance of Z time series 1.000000e+00 -1.739928e-15 -4.423545e-16 Covariance of Z time series -6.782769e-16 -1.069023e-15 -1.990595e-16 Covariance of Z time series -1.085612e-15 1.113259e-15 1.194357e-15 Covariance of Z time series -4.423545e-16 8.773364e-16 -1.739928e-15 Covariance of Z time series 1.000000e+00 9.307876e-16 0 Covariance of Z time series -1.002670e-15 1.028474e-15 1.621966e-16 Covariance of Z time series -5.898060e-16 -3.612562e-16 -1.616437e-15 Covariance of Z time series 4.276093e-16 -4.423545e-16 9.307876e-16 Covariance of Z time series 1.000000e+00 -1.518750e-15 8.201989e-16 Covariance of Z time series 2.064321e-15 -9.141993e-16 -3.538836e-16 Covariance of Z time series 1.533496e-15 7.778066e-16 -5.441882e-16 Covariance of Z time series -6.782769e-16 0 -1.518750e-15 Covariance of Z time series 1.000000e+00 -4.865899e-16 2.462440e-15 Covariance of Z time series 1.445025e-15 -6.340414e-16 8.404735e-16 Covariance of Z time series -2.565656e-15 4.128642e-16 -1.069023e-15 Covariance of Z time series -1.002670e-15 8.201989e-16 -4.865899e-16 Covariance of Z time series 1.000000e+00 Covariance of S time series 1.000000e+00 -6.163473e-15 -1.194357e-15 Covariance of S time series -2.219145e-15 1.371299e-15 3.008011e-15 Covariance of S time series -1.533496e-15 4.570996e-16 -1.651457e-15 Covariance of S time series 4.497271e-16 7.372575e-17 -6.163473e-15 Covariance of S time series 1.000000e+00 6.635317e-16 4.128642e-16 Covariance of S time series -4.423545e-17 1.205416e-15 5.013351e-16 Covariance of S time series -3.243933e-16 8.109832e-17 7.372575e-17 Covariance of S time series -1.190671e-15 -1.194357e-15 6.635317e-16 Covariance of S time series 1.000000e+00 -9.952976e-17 -5.087077e-16 Covariance of S time series 1.459770e-15 1.990595e-16 -5.160802e-16 Covariance of S time series 3.243933e-16 6.930220e-16 4.423545e-16 Covariance of S time series -2.219145e-15 4.128642e-16 -9.952976e-17 Covariance of S time series 1.000000e+00 8.847090e-17 3.066991e-15 Covariance of S time series -2.727853e-16 6.856495e-16 7.704341e-16 Covariance of S time series 4.239230e-16 1.769418e-16 1.371299e-15 Covariance of S time series -4.423545e-17 -5.087077e-16 8.847090e-17 Covariance of S time series 1.000000e+00 4.644722e-16 -2.580401e-16 Covariance of S time series 7.372575e-16 5.898060e-16 -1.194357e-15 Covariance of S time series 1.017415e-15 3.008011e-15 1.205416e-15 Covariance of S time series 1.459770e-15 3.066991e-15 4.644722e-16 Covariance of S time series 1.000000e+00 4.202368e-16 -5.317470e-16 Covariance of S time series 6.192963e-16 1.621966e-15 -4.276093e-16 Covariance of S time series -1.533496e-15 5.013351e-16 1.990595e-16 Covariance of S time series -2.727853e-16 -2.580401e-16 4.202368e-16 Covariance of S time series 1.000000e+00 8.478461e-16 1.059808e-15 Covariance of S time series -2.064321e-16 5.455705e-16 4.570996e-16 Covariance of S time series -3.243933e-16 -5.160802e-16 6.856495e-16 Covariance of S time series 7.372575e-16 -5.317470e-16 8.478461e-16 Covariance of S time series 1.000000e+00 2.949030e-17 3.022756e-16 Covariance of S time series 1.474515e-16 -1.651457e-15 8.109832e-17 Covariance of S time series 3.243933e-16 7.704341e-16 5.898060e-16 Covariance of S time series 6.192963e-16 1.059808e-15 2.949030e-17 Covariance of S time series 1.000000e+00 -6.782769e-16 2.322361e-16 Covariance of S time series 4.497271e-16 7.372575e-17 6.930220e-16 Covariance of S time series 4.239230e-16 -1.194357e-15 1.621966e-15 Covariance of S time series -2.064321e-16 3.022756e-16 -6.782769e-16 Covariance of S time series 1.000000e+00 -1.194357e-15 7.372575e-17 Covariance of S time series -1.190671e-15 4.423545e-16 1.769418e-16 Covariance of S time series 1.017415e-15 -4.276093e-16 5.455705e-16 Covariance of S time series 1.474515e-16 2.322361e-16 -1.194357e-15 Covariance of S time series 1.000000e+00 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -18.1029 Contouring to a maximum 20.0421 Contouring interval is 3.8145 Contour values are: -18.1029 -14.2884 -10.4739 -6.6594 -2.8449 0.9696 4.7841 8.5986 12.4131 16.2276 20.0421 Maximum field value 20.0421 Minimum field value -18.1029 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -19.9468 Contouring to a maximum 18.1873 Contouring interval is 3.8134 Contour values are: -19.9468 -16.1334 -12.3200 -8.5065 -4.6931 -0.8797 2.9337 6.7471 10.5605 14.3739 18.1873 Maximum field value 18.1873 Minimum field value -19.9468 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -20.2550 Contouring to a maximum 18.3057 Contouring interval is 3.8561 Contour values are: -20.2550 -16.3989 -12.5429 -8.6868 -4.8307 -0.9747 2.8814 6.7375 10.5935 14.4496 18.3057 Maximum field value 18.3057 Minimum field value -20.2550 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -14.1738 Contouring to a maximum 17.5266 Contouring interval is 3.1700 Contour values are: -14.1738 -11.0038 -7.8337 -4.6637 -1.4936 1.6764 4.8464 8.0165 11.1865 14.3566 17.5266 Maximum field value 17.5266 Minimum field value -14.1738 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -7.7212 Contouring to a maximum 4.2150 Contouring interval is 1.1936 Contour values are: -7.7212 -6.5276 -5.3340 -4.1403 -2.9467 -1.7531 -0.5595 0.6341 1.8277 3.0214 4.2150 Maximum field value 4.2150 Minimum field value -7.7212 Shading is off Reshaping for T30 Gaussian grid Contouring from a minimum -6.8547 Contouring to a maximum 3.7473 Contouring interval is 1.0602 Contour values are: -6.8547 -5.7945 -4.7343 -3.6741 -2.6139 -1.5537 -0.4935 0.5667 1.6269 2.6871 3.7473 Maximum field value 3.7473 Minimum field value -6.8547

