> mssa.rar > EEOF.M
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);
% This function performs an extended empirical orthogonal
% function (EEOF) analysis of matrix 'X', for embedding dimension 'M'. % Each of the L columns of X is a time series of length N.
%
% Returns: E - eigenfunction matrix. (LM by LM)
% V - vector containing variances (unnormalized eigenvalues). % A - matrix of principal components.
% C - lag-covariance matrix.
%
% V is ordered from large to small: E and A are sorted accordingly. %
% Note that X is assumed to be centered. To center the data, use
% the commands:
% [r,c]=size(X); X=X-ones(r,1)*mean(X); before running EEOF. % If you also want to standardize the data, use:
% X=X./(ones(r,1)*std(X));.
%
% If a third argument is supplied, the eigenfunctions/values will
% be reordered into the same format as MSSA output - i. e. L blocks % of size M rather than M blocks of size L.
%
% This function provides the same output, within numerically determined % limits, as MSSA methods using Broomhead-King type covariance estimation:
% it is intended as a check on those functions.
%
% Note that this function is *extremely* computationally intensive
% for large matrices and lags. For example, if X is 1000 by 1000,
% and M = 5, EEOF will take about 10 hours on a Cray YMP! Inputting % a subset of the PCs of X rather than the full data matrix can
% substantially reduce the computational load.
%
% Written by Eric Breitenberger. Version date 1/11/96
%************************************************.edu
%
[N,L]=size(X);
if M*L>=N-M+1, disp('Warning: Covariance matrix may be
ill-conditioned.'), end
% Create the extended matrix:
T=zeros(N-M+1,M*L);
for i=1:M
T(:,L*(i-1)+1:L*i)=X(i:N-M+i,:);
end
% Compute the eigenvectors/values of the covariance matrix:
C=(T'*T)/(N-M+1);
clear X
[E,V]=eig(C);
V=diag(V);
A=T*E; % compute principal components
if nargin==3 % Prepare MSSA-style output:
% sort E,V,C, and A from M blocks of L to L blocks of M.
ind=1:L:(M-1)*L+1;
for i=1:L, index=[index ind+i-1]; end
E=E(index,index);
V=V(index);
% sort the covariance matrix and PCs:
C=C(index,index);
A=A(:,index);
end
% Sort eigenvalues/vectors/PCs in descending order:
[V,ind]=sort(-V);
V=-V';
E=E(:,ind);
A=A(:,ind);
> mssa.rar > EOF.M
function [F,L,B]=eof(X,n,s);
% EOF calculates the empirical orthogonal functions
% and amplitudes (principal components) of the data matrix 'X'. % Syntax: [F,L,B]=eof(X); [F,L,B]=eof(X,.9,'norm');
