function [alphap, alphaq] = levinson_anti(cor);
% Syntax: [alphap, alphaq] = levinson_anti(cor);
% 
% calculates the alphap and alphaq coefficients of Split Levinson Algortihm
% from speech autocorrelation coefficients. Called by lsf_saoudi.
%
% Function based on article Saoudi, Boucher, Guyader:
% "A new efficient algorithm to compute the LSP parameters for speech coding" 
% Signal Processing, no. 28, 1992, pp. 201-212.
% 
% cor is the vector of correlation coefficients c0...cP, where P is the
%   order of the prediction filter
% alphap is vector of reccurence coefficients of the symetric polynomial,
%   size P+1, value of alpha(1) without importance (alpha0 does not exist)
% alphaq is vector of reccurence coefficients of the antisymetric polynomial,
%   size P+1, value of alpha(1) without importance (alpha0 does not exist)
% - all vectors are COLUMN
% - The function works only for P even
%
% The algorithm uses only one form of split lev. algorithm (antisym) to
% compute both the alphaq and alphaq.
%
% The implementation in Matlab is not "vectorized", so it may be very slow

P=length(cor)-1;
if(P/2 ~= floor(P/2) )
 error ('P is not even');
end
 
%%%% init %%%
alphap=zeros(P+1,1); alphaq=zeros(P+1,1);  % 1st element for nothing
taup=zeros(P+1,1); lambda=zeros(P+1,1);
p=zeros(P+1, P/2);

p(1,1)=0; p(2,2)=-1;
for i=1:P,
  p(i+1, 1)=1;
end
taup(1)=cor(1); lambda(1)=1;

%%%% cycle %%%
for i=1:P,
  t=floor(i/2); l=2*t;		% so for i even, i=l
  taup(i+1)=0;
  
  if (i==l),			% for i even
    for j=0:t-1,
      taup(i+1)=taup(i+1) + ( cor(j+1) - cor(i-j+1) ) * p(i+1,j+1);
    end
  else
    for j=0:t,
      taup(i+1)=taup(i+1) + ( cor(j+1) - cor(i-j+1) ) * p(i+1,j+1);
    end
  end	% de if
  
  alphaq(i+1)=taup(i+1) / taup(i);
  lambda(i+1)=2-alphaq(i+1) / lambda(i);
  alphap(i+1)=lambda(i+1) * (2-lambda(i));
  
  for j=1:t,
    p(i+2,j+1)=p(i+1,j+1) + p(i+1,j) - alphaq(i+1) * p(i,j);  % reccurence
  end  							       % formula
  
  p(i+2,t+2) = 0;

end  % de for i