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1、function[E，V，A，C]=eeof(X,M,convert)%Syntax:[E,V,A,C>eeof(X,M);[E,V,A,C]=eeof(X,M,1);%Thisfunctionperformsanextendedempiricalorthogonal%function(EEOF)analysisofmatrix’X’，forembeddingdimension’•%EachoftheLcolumnsofXisatimeseriesoflengthN.%%Returns:E-eig
2、enfunctionmatrix.(LMbyLM)%V-vectorcontainingvariances(unnormalizedeigenvalues).%A-matrixofprincipalcomponents.%C-lag-covariancematrix.%%Visorderedfromlargetosmall:EandAaresortedaccordingly.%%NotethatXisassumedtobecentered.Tocenterthedata,use%thecomman
3、ds:%[r,c]=size(X);X=X~ones(r,l)*mean(X);beforerunningEEOF.%Tfyoualsowanttostandardizethedata,use:%Ifathirdargumentissupplied,theeigenfunctions/valueswill%bereorderedintothesameformatasMSSAoutput-i.e.Lblocks%ofsizeMratherthanMblocksofsizeL.%Thisfunctio
4、nprovidesthesameoutput,withinnumericallydetermined%limits,asMSSAmethodsusingBroomhead-Kingtypecovarianceestimation:%itisintendedasacheckonthosefunctions.%Notethatthisfunctionis氺extremely氺computationallyintensive%forlargematricesandlags.Forexample,ifXi
5、s1000by1000，%andM=5,EEOFwilltakeabout10hoursonaCrayYMP!Inputting%asubsetofthePCsofXratherthanthefulldatamatrixcan%substantiallyreducethecomputationalload.%WrittenbyEricBreitenberger.Versiondate1/11/96%Pleasesendcommentsandsuggestionstoeric@gi.alaska.e
6、du[N,L]=size(X);ifM氺L〉=N-M+1，dispCWarning:Covariancematrixmaybeill-conditioned/)，end%Createtheextendedmatrix:T=zeros(N-M+l,;fori=l:MT(:,L*(i-l)+l:L*i)=X(i:N-M+i,:);end%Computetheeigenvectors/valuesofthecovariancematrix:C=(T’*T)/(N-M+1);clearX[E,V]=eig
7、(C);V=diag(V);A=T*R;%computeprincipalcomponentsifnargin==3%PrepareMSSA-styleoutput:%sortE，V，C，andAfromMblocksofLtoLblocksofM.ind=l:L:(M-1)*L+1;fori=l:L,index=[indexind+i-1];endE二E(index，index);V=V(index);%sortthecovariancematrixandPCs:C=C(index,index)
8、;八=八(:，index);end%Sorteigenvalues/vectors/PCsindescendingorder:[V，ind]:sort(-V);v=-v,;E=E(:，ind);A=A(:，ind);www.pudn.com>mssa.rar>EOF.Mfunction[F,L,B]=eof(X,n,s);%EOFcalculatestheempiricalorthogonalfunctions%andamplitudes(principalcomponents)o
