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## Copyright (C) 1995 Friedrich Leisch
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: durbinlevinson (c, [oldphi, oldv])
##
## Performs one step of the Durbin-Levinson algorithm.
##
## The vector c_t = [gamma_0, ..., gamma_t] contains the autocovariances
## from lag 0 to t, oldphi the coefficients based on c_(t-1) and oldv
## the corresponding error.
##
## If oldphi is omitted, all steps from 1 to t of the algorithm are
## performed.
## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Description: Perform one step of the Durbin-Levinson algorithm
function [newphi, newv] = durbinlevinson (c, oldphi, oldv)
if( !((nargin == 1) || (nargin == 3)) )
usage ("durbinlevinson (c, [oldphi, oldv])");
endif
if( columns (c) > 1 )
c=c';
endif
newphi = 0;
newv = 0;
if (nargin == 3)
t = length (oldphi) + 1;
if (length (c) < t+1)
error ("durbilevinson: c too small");
endif
if (oldv == 0)
error ("durbinlevinson: oldv = 0");
endif
if (rows (oldphi) > 1 )
oldphi = oldphi';
endif
newphi = zeros (1, t);
newphi(1) = ( c(t+1) - oldphi * c(2:t) ) / oldv;
for i = 2 : t
newphi(i) = oldphi(i-1) - newphi(1) * oldphi(t-i+1);
endfor
newv = ( 1 - newphi(1)^2 ) * oldv;
elseif(nargin == 1)
tt = length (c)-1;
oldphi = c(2) / c(1);
oldv = ( 1 - oldphi^2 ) * c(1);
for t = 2 : tt
newphi = zeros (1, t);
newphi(1) = ( c(t+1) - oldphi * c(2:t) ) / oldv;
for i = 2 : t
newphi(i) = oldphi(i-1) - newphi(1) * oldphi(t-i+1);
endfor
newv = ( 1 - newphi(1)^2 ) * oldv;
oldv = newv;
oldphi = newphi;
endfor
endif
endfunction
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