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