Example of Fig 7.4 - 7.5 - 7.6

Barnett-Preisendorfer CCA

function [u,lam,v,ss]=example500
%
% Compute CCA of matrices s z with the
% Barnett-Preisendorfer method
%

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=0.7;
zcut=0.7;
[u,v,corr,varz,vars,projz,projs]=cccca(z,s,indz,inds,zcut,scut);

% PLot EOF  -----
titstr=cell(size(1:3));
cont=[];
figure(1)
clf;
modeindex=[ 1 2 3];

for i=1:3
    ii=modeindex(i);
    titstr{i} = [' Z Component   Expl TC   ' num2str(varz(i)*100,'%-2.0f') '%' ...
        ' Correlation   ' num2str(corr(ii)*100,'%-2.0f') '%'];
end
bigtit{1}= ['   ' ];
bigtit{2}= ['CCA-BP'];

pict3(bigtit,u(:,modeindex(1)),u(:,modeindex(2)), u(:,modeindex(3)), ...
    zflat,zflon,cont,titstr,'shading','off');
print('-dpdf','-painters',[mfilename 'Z.pdf']);

figure(2)
clf;
modeindex=[ 1 2 3];
for i=1:3
    ii=modeindex(i);
    titstr{i} = [' S Component   Expl TC   ' num2str(vars(i)*100,'%-2.0f') '%' ...
        ' Correlation   ' num2str(corr(ii)*100,'%-2.0f') '%'];
end
bigtit{1}= ['   ' ];
bigtit{2}= ['CCA-BP'];


pict3(bigtit,v(:,modeindex(1)),v(:,modeindex(2)), v(:,modeindex(3)), ...
    sflat,sflon,cont,titstr,'shading','off','landcolor',[0.1 0.1 0.1]);
print('-dpdf','-painters',[mfilename 'S.pdf']);

figure(3)
clf;
subplot(211)
sp=size(projz);
tim=max(sp);
plot(1:tim,projz(:,1),'k-',1:tim,projz(:,2),'k--',1:tim,projz(:,3),'k:')
title('Time series of the first three CCA-BP modes -- Z component');
subplot(212)
plot(1:tim,projs(:,1),'k-',1:tim,projs(:,2),'k--',1:tim,projs(:,3),'k:')
title('Time series of the first three CCA-BP modes -- S component');
legend('Mode 1','Mode 2','Mode 3');
print('-dpdf','-painters',[mfilename 'proj.pdf']);


return
Normalization full
Normalization full
Total Crosscovariance 10984.0561
Modes for SST 5 --- Variance Retained 0.70138
Modes for Z 5 --- Variance Retained 0.72707
Normalization full
Normalization full
SVD computed
  Number of modes computed  -- min(iz,is)  5 Correlations 0.95556     0.63413     0.42416     0.34084     0.12681
Expanded Field1
Expanded Field2
Expanded Field3
Expanded Field4
Expanded Field5
 Crosscovariance between coefficient of the time series 9.555576e-01 1.179612e-16 -4.935288e-16  
 Crosscovariance between coefficient of the time series 9.714451e-17 4.163336e-16 4.093947e-16  
 Crosscovariance between coefficient of the time series 6.341250e-01 5.030698e-16 1.214306e-16  
 Crosscovariance between coefficient of the time series 2.012279e-16 -2.224783e-16 7.350891e-16  
 Crosscovariance between coefficient of the time series 4.241564e-01 2.990230e-16 -8.109832e-17  
 Crosscovariance between coefficient of the time series 3.677614e-16 3.469447e-18 5.494737e-16  
 Crosscovariance between coefficient of the time series 3.408370e-01 -8.673617e-18 -1.804112e-16  
 Crosscovariance between coefficient of the time series 1.082467e-15 -1.318390e-16 1.700029e-16  
 Crosscovariance between coefficient of the time series 1.268088e-01 
 Covariance of Z  time series 1.000000e+00 3.715778e-15 -5.455705e-16  
 Covariance of Z  time series -1.172239e-15 4.570996e-16 3.715778e-15  
 Covariance of Z  time series 1.000000e+00 -5.455705e-16 1.445025e-15  
 Covariance of Z  time series -3.951700e-15 -5.455705e-16 -5.455705e-16  
 Covariance of Z  time series 1.000000e+00 4.423545e-16 -2.064321e-16  
 Covariance of Z  time series -1.172239e-15 1.445025e-15 4.423545e-16  
 Covariance of Z  time series 1.000000e+00 2.410832e-15 4.570996e-16  
 Covariance of Z  time series -3.951700e-15 -2.064321e-16 2.410832e-15  
 Covariance of Z  time series 1.000000e+00 
 Covariance of S  time series  1.000000e+00 5.617902e-15 3.465110e-16  
 Covariance of S  time series  -6.959711e-15 -1.592476e-15 5.617902e-15  
 Covariance of S  time series  1.000000e+00 1.287897e-15 -5.529431e-16  
 Covariance of S  time series  1.504005e-15 3.465110e-16 1.287897e-15  
 Covariance of S  time series  1.000000e+00 2.949030e-15 -1.249651e-15  
 Covariance of S  time series  -6.959711e-15 -5.529431e-16 2.949030e-15  
 Covariance of S  time series  1.000000e+00 1.585104e-16 -1.592476e-15  
 Covariance of S  time series  1.504005e-15 -1.249651e-15 1.585104e-16  
 Covariance of S  time series  1.000000e+00 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -18.0623 
Contouring to a maximum 19.9827 
Contouring interval is  3.8045 
Contour values are: 
-18.0623 -14.2578 -10.4533 -6.6488 -2.8443 0.9602 4.7647 8.5692 12.3737 16.1782 19.9827 
Maximum field value 19.9827 
Minimum field value -18.0623 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -8.2206 
Contouring to a maximum 4.0796 
Contouring interval is  1.2300 
Contour values are: 
-8.2206 -6.9905 -5.7605 -4.5305 -3.3005 -2.0705 -0.8404 0.3896 1.6196 2.8496 4.0796 
Maximum field value 4.0796 
Minimum field value -8.2206 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -6.3423 
Contouring to a maximum 3.3618 
Contouring interval is  0.9704 
Contour values are: 
-6.3423 -5.3719 -4.4015 -3.4311 -2.4607 -1.4903 -0.5199 0.4506 1.4210 2.3914 3.3618 
Maximum field value 3.3618 
Minimum field value -6.3423 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -9.8872 
Contouring to a maximum 13.8019 
Contouring interval is  2.3689 
Contour values are: 
-9.8872 -7.5183 -5.1494 -2.7805 -0.4116 1.9573 4.3262 6.6952 9.0641 11.4330 13.8019 
Maximum field value 13.8019 
Minimum field value -9.8872 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -6.7434 
Contouring to a maximum 4.5617 
Contouring interval is  1.1305 
Contour values are: 
-6.7434 -5.6129 -4.4824 -3.3519 -2.2213 -1.0908 0.0397 1.1702 2.3007 3.4312 4.5617 
Maximum field value 4.5617 
Minimum field value -6.7434 
Shading is  off 
Reshaping for T30 Gaussian grid
Contouring from a minimum -5.2252 
Contouring to a maximum 4.4103 
Contouring interval is  0.9635 
Contour values are: 
-5.2252 -4.2617 -3.2981 -2.3346 -1.3710 -0.4075 0.5561 1.5196 2.4832 3.4467 4.4103 
Maximum field value 4.4103 
Minimum field value -5.2252 

ans =

   1.0e+03 *

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    9.9990    9.9990    9.9990    9.9990    9.9990
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   -0.0093   -0.0007    0.0003   -0.0070   -0.0046
   -0.0116   -0.0010    0.0007   -0.0064   -0.0044
   -0.0135   -0.0013    0.0011   -0.0056   -0.0039
   -0.0150   -0.0016    0.0015   -0.0046   -0.0031
   -0.0158   -0.0018    0.0018   -0.0035   -0.0021
   -0.0161   -0.0021    0.0021   -0.0023   -0.0008
   -0.0157   -0.0023    0.0024   -0.0011    0.0006
   -0.0146   -0.0026    0.0024    0.0001    0.0021
   -0.0130   -0.0029    0.0023    0.0012    0.0036
   -0.0109   -0.0031    0.0019    0.0022    0.0051
   -0.0084   -0.0034    0.0014    0.0032    0.0065
   -0.0054   -0.0036    0.0007    0.0040    0.0078
   -0.0020   -0.0038   -0.0001    0.0045    0.0089
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   -0.0003    0.0032   -0.0012    0.0010   -0.0094
   -0.0008    0.0021   -0.0006    0.0011   -0.0112
    9.9990    9.9990    9.9990    9.9990    9.9990
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    9.9990    9.9990    9.9990    9.9990    9.9990
   -0.0040   -0.0007    0.0011   -0.0037   -0.0092
   -0.0033   -0.0002    0.0009   -0.0044   -0.0077
   -0.0021    0.0003    0.0006   -0.0052   -0.0054
   -0.0005    0.0006    0.0001   -0.0060   -0.0025
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   -0.0009   -0.0000   -0.0008   -0.0081   -0.0004
   -0.0029   -0.0001   -0.0006   -0.0081   -0.0002
   -0.0048   -0.0004   -0.0004   -0.0079    0.0007
   -0.0065   -0.0007   -0.0002   -0.0074    0.0019
   -0.0079   -0.0011    0.0001   -0.0066    0.0035
   -0.0088   -0.0015    0.0003   -0.0054    0.0052
   -0.0090   -0.0018    0.0005   -0.0039    0.0070
   -0.0084   -0.0021    0.0008   -0.0021    0.0087
   -0.0071   -0.0023    0.0009   -0.0004    0.0100
   -0.0052   -0.0025    0.0010    0.0012    0.0109
   -0.0030   -0.0026    0.0008    0.0024    0.0114
   -0.0007   -0.0027    0.0005    0.0034    0.0118
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    0.0084   -0.0026   -0.0012    0.0050    0.0116
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    0.0121   -0.0019   -0.0021    0.0046    0.0101
    0.0136   -0.0013   -0.0026    0.0043    0.0090
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    9.9990    9.9990    9.9990    9.9990    9.9990
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    9.9990    9.9990    9.9990    9.9990    9.9990
   -0.0031   -0.0009    0.0012   -0.0034   -0.0056
   -0.0018   -0.0005    0.0007   -0.0042   -0.0030
   -0.0001   -0.0001    0.0001   -0.0050    0.0002
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    0.0064    0.0009   -0.0017   -0.0062    0.0098
    0.0063    0.0009   -0.0016   -0.0064    0.0090
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    0.0005   -0.0003   -0.0016   -0.0074    0.0076
    0.0005   -0.0006   -0.0016   -0.0066    0.0097
    0.0011   -0.0009   -0.0016   -0.0053    0.0118
    0.0020   -0.0011   -0.0015   -0.0038    0.0137
    0.0031   -0.0013   -0.0014   -0.0021    0.0150
    0.0043   -0.0014   -0.0012   -0.0005    0.0158
    0.0054   -0.0016   -0.0010    0.0009    0.0159
    0.0064   -0.0017   -0.0008    0.0020    0.0156
    0.0073   -0.0018   -0.0007    0.0028    0.0151
    0.0082   -0.0019   -0.0006    0.0034    0.0146
    0.0092   -0.0020   -0.0007    0.0039    0.0140
    0.0103   -0.0020   -0.0009    0.0042    0.0135
    0.0115   -0.0020   -0.0010    0.0044    0.0130
    0.0126   -0.0019   -0.0012    0.0044    0.0124
    0.0138   -0.0017   -0.0015    0.0043    0.0117
    0.0149   -0.0014   -0.0017    0.0041    0.0108
    0.0158   -0.0010   -0.0020    0.0038    0.0098
    0.0166   -0.0004   -0.0023    0.0033    0.0085
    0.0170    0.0004   -0.0026    0.0025    0.0070
    0.0167    0.0012   -0.0028    0.0015    0.0055
    0.0160    0.0018   -0.0029    0.0005    0.0041
    0.0151    0.0023   -0.0029   -0.0006    0.0031
    0.0142    0.0025   -0.0029   -0.0015    0.0025
    0.0135    0.0025   -0.0029   -0.0022    0.0024
    0.0129    0.0023   -0.0029   -0.0028    0.0026
    0.0125    0.0020   -0.0029   -0.0033    0.0032
    0.0123    0.0017   -0.0030   -0.0035    0.0041
    0.0122    0.0015   -0.0030   -0.0037    0.0052
    0.0122    0.0013   -0.0032   -0.0036    0.0065
    0.0123    0.0011   -0.0033   -0.0035    0.0080
    0.0125    0.0010   -0.0034   -0.0033    0.0095
    0.0126    0.0008   -0.0034   -0.0029    0.0109
    0.0126    0.0007   -0.0033   -0.0025    0.0122
    0.0123    0.0005   -0.0031   -0.0021    0.0131
    0.0117    0.0005   -0.0027   -0.0017    0.0135
    0.0110    0.0007   -0.0024   -0.0013    0.0135
    0.0101    0.0009   -0.0020   -0.0011    0.0132
    0.0094    0.0013   -0.0017   -0.0010    0.0127
    0.0087    0.0017   -0.0013   -0.0009    0.0120
    0.0081    0.0020   -0.0011   -0.0008    0.0112
    0.0077    0.0023   -0.0008   -0.0007    0.0104
    0.0073    0.0025   -0.0004   -0.0006    0.0093
    0.0068    0.0026    0.0001   -0.0005    0.0078
    0.0061    0.0026    0.0007   -0.0003    0.0059
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    9.9990    9.9990    9.9990    9.9990    9.9990
   -0.0005   -0.0012    0.0004   -0.0024    0.0003
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    9.9990    9.9990    9.9990    9.9990    9.9990
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    9.9990    9.9990    9.9990    9.9990    9.9990
    0.0039   -0.0010   -0.0012   -0.0006    0.0069
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    9.9990    9.9990    9.9990    9.9990    9.9990
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    9.9990    9.9990    9.9990    9.9990    9.9990
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