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########################################################################
##
## Copyright (C) 1995-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave 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 3 of the License, or
## (at your option) any later version.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {[@var{newphi}, @var{newv}] =} durbinlevinson (@var{c}, @var{oldphi}, @var{oldv})
## Perform one step of the @nospell{Durbin-Levinson} algorithm.
##
## The vector @var{c} specifies the autocovariances
## @code{[gamma_0, @dots{}, gamma_t]} from lag 0 to @var{t}, @var{oldphi}
## specifies the coefficients based on @var{c}(@var{t}-1) and @var{oldv}
## specifies the corresponding error.
##
## If @var{oldphi} and @var{oldv} are omitted, all steps from 1 to @var{t} of
## the algorithm are performed.
## @end deftypefn
function [newphi, newv] = durbinlevinson (c, oldphi, oldv)
if (nargin != 1 && nargin != 3)
print_usage ();
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 ("durbinlevinson: 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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