Example of Fig 5.6
Analytical Examples of Complex EOF
function zh=example56 % % Eof of signal and noise % % Generate signal data clf; n=34; m=20; mode=1; xnum=2; ynum=0; omega=4; u=linspace(0,2*pi,m); v=linspace(0,2*pi,n); [x,y]=meshgrid(u); for j = 1:n a(:,:,j) = 10*sin(ynum*y+ xnum*x - omega*v(j)) + 10*randn(length(u)); surf(x,y,a(:,:,j)); colormap(gray);brighten(0.5); end % for j = 1:n z(:,j) = reshape(a(:,:,j),[m*m 1]); end size(z) zh=hilbert(z')'; [uu,ss,v]=svd(zh,0); % % Compute explained variances % lam = diag(ss.^2)/sum(diag(ss.^2)); % u=uu(:,mode);size(u) subplot(4,1,1) contourf(reshape(real(u),[ m m]));colormap(gray); brighten(0.5); title([' Real Part CEOF 1 ' num2str(lam(mode)*100,2) '%'],'fontname','times') subplot(4,1,2) contourf(reshape(imag(u),[ m m]));colormap(gray); brighten(0.5); title([' Imaginary Part CEOF 1 ' num2str(lam(mode)*100,2) '%'],'fontname','times') subplot(4,1,3) contourf(reshape(abs(u),[ m m]));colormap(gray); brighten(0.5);hold quiver(1:m,1:m,reshape(real(u),[ m m]),reshape(imag(u),[ m m])); hold off title([' Phase and Amplitude CEOF 1 ' num2str(lam(mode)*100,2) '%'],'fontname','times') subplot(4,1,4) plot(1:n, real(v(:,1)), 1:n, imag(v(:,1)),'--'); legend('Real Part','Imag Part'); title(' Time coefficients for propagating wave') orient tall; print('-dpdf','-painters','-adobecset',[mfilename 'b.pdf']);
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