function [F,delta]=aci1(Y)
% Comon, version 6 January 99
% Same program as aci.m of March 92, excepted that
% the call of tfuni1 replaces that of tfuni4.
% [F,delta]=aci1(Y)
% Y is the observations matrix
% This routine outputs a matrix F such that Y=F*Z, Z=pinv(F)*Y,
% and components of Z are uncorrelated and approximately independent
% F is Nxr, where r is the dimension Z;
% Entries of delta are sorted in decreasing order;
% Columns of F are of unit norm;
% The entry of largest modulus in each column of F is positive real.
% Initial and final values of contrast can be fprinted for checking.
% REFERENCE: P.Comon, "Independent Component Analysis, a new concept?",
% Signal Processing, Elsevier, vol.36, no 3, April 1994, 287-314.
%
w=input('Sign of source kurtoses:\n');if length(w)==0,w=-1;end;
[N,TT]=size(Y);T=max(N,TT);N=min(N,TT);
if TT==N, Y=Y';[N,T]=size(Y);end; % Y est maintenant NxT avec N<T.
%%%% STEPS 1 & 2: whitening and projection (PCA)
[U,S,V]=svd(Y',0);tol=max(size(S))*norm(S)*eps;
s=diag(S);I=find(s<tol);r=N;
if length(I)~=0, r=I(1)-1;U=U(:,1:r);S=S(1:r,1:r);V=V(:,1:r);end;
Z=U'*sqrt(T);L=V*S'/sqrt(T);F=L; %%%%%% on a Y=L*Z;
%%%%%% INITIAL CONTRAST
T=length(Z);contraste=0;
for i=1:r,
 gii=Z(i,:)*Z(i,:)'/T;Z2i=Z(i,:).^2;;giiii=Z2i*Z2i'/T;
 qiiii=giiii/gii/gii-3;contraste=contraste+qiiii*qiiii;
end;
%%%% STEPS 3 & 4 & 5: Unitary transform
S=Z;
if N==2,K=1;else,K=1+round(sqrt(N));end;  % K= max number of sweeps
Rot=eye(r);
for k=1:K,                           %%%%%% strating sweeps
Q=eye(r);
  for i=1:r-1,
  for j= i+1:r,
    S1ij=[S(i,:);S(j,:)];
    [qij,theta]=tfuni1(S1ij,w);Sij=qij*S1ij;    %%%%%% processing a pair
    S(i,:)=Sij(1,:);S(j,:)=Sij(2,:);
    Qij=eye(r);Qij(i,i)=qij(1,1);Qij(i,j)=qij(1,2);
    Qij(j,i)=qij(2,1);Qij(j,j)=qij(2,2);
    Q=Qij*Q;
  end;
  end;
Rot=Rot*Q';
end;                                    %%%%%% end sweeps
F=F*Rot;
%%%%%% FINAL CONTRAST
S=Rot'*Z;
T=length(S);contraste=0;
for i=1:r,
 gii=S(i,:)*S(i,:)'/T;S2i=S(i,:).^2;;giiii=S2i*S2i'/T;
 qiiii=giiii/gii/gii-3;contraste=contraste+qiiii*qiiii;
end;
%%%% STEP 6: Norming columns
delta=diag(sqrt(sum(F.*conj(F))));
%%%% STEP 7: Sorting
[d,I]=sort(-diag(delta));E=eye(r);P=E(:,I)';delta=P*delta*P';F=F*P';
%%%% STEP 8: Norming
F=F*inv(delta);
%%%% STEP 9: Phase of columns
[y,I]=max(abs(F));
for i=1:r,Lambda(i)=conj(F(I(i),i));end;Lambda=Lambda./abs(Lambda);
F=F*diag(Lambda);
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