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 * 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 9.9990 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