view scripts/signal/yulewalker.m @ 20165:f1d0f506ee78 stable

doc: Update more docstrings to have one sentence summary as first line. Reviewed optimization, polynomial, signal script directories. * scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m, scripts/optimization/fminunc.m, scripts/optimization/fsolve.m, scripts/optimization/fzero.m, scripts/optimization/glpk.m, scripts/optimization/lsqnonneg.m, scripts/optimization/pqpnonneg.m, scripts/optimization/qp.m, scripts/optimization/sqp.m, scripts/polynomial/compan.m, scripts/polynomial/mkpp.m, scripts/polynomial/mpoles.m, scripts/polynomial/pchip.m, scripts/polynomial/poly.m, scripts/polynomial/polyaffine.m, scripts/polynomial/polyder.m, scripts/polynomial/polyeig.m, scripts/polynomial/polyfit.m, scripts/polynomial/polygcd.m, scripts/polynomial/polyint.m, scripts/polynomial/polyout.m, scripts/polynomial/polyval.m, scripts/polynomial/ppder.m, scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m, scripts/polynomial/ppval.m, scripts/polynomial/residue.m, scripts/polynomial/roots.m, scripts/polynomial/spline.m, scripts/polynomial/splinefit.m, scripts/polynomial/unmkpp.m, scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m, scripts/signal/arma_rnd.m, scripts/signal/autoreg_matrix.m, scripts/signal/bartlett.m, scripts/signal/blackman.m, scripts/signal/detrend.m, scripts/signal/diffpara.m, scripts/signal/durbinlevinson.m, scripts/signal/fftconv.m, scripts/signal/fftfilt.m, scripts/signal/fftshift.m, scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/hamming.m, scripts/signal/hanning.m, scripts/signal/hurst.m, scripts/signal/ifftshift.m, scripts/signal/periodogram.m, scripts/signal/sinc.m, scripts/signal/sinetone.m, scripts/signal/sinewave.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/signal/spencer.m, scripts/signal/stft.m, scripts/signal/synthesis.m, scripts/signal/unwrap.m, scripts/signal/yulewalker.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Mon, 04 May 2015 21:50:57 -0700
parents 4197fc428c7d
children
line wrap: on
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## Copyright (C) 1995-2015 Friedrich Leisch
##
## 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
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{a}, @var{v}] =} yulewalker (@var{c})
## Fit an AR (p)-model with Yule-Walker estimates given a vector @var{c} of
## autocovariances @code{[gamma_0, @dots{}, gamma_p]}.
##
## Returns the AR coefficients, @var{a}, and the variance of white noise,
## @var{v}.
## @end deftypefn

## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Description: Fit AR model by Yule-Walker method

function [a, v] = yulewalker (c)

  if (nargin != 1)
    print_usage ();
  endif

  p = length (c) - 1;

  if (columns (c) > 1)
    c = c';
  endif

  cp = c(2 : p+1);
  CP = zeros (p, p);

  for i = 1:p
    for j = 1:p
      CP (i, j) = c (abs (i-j) + 1);
    endfor
  endfor

  a = inv (CP) * cp;
  v = c(1) - a' * cp;

endfunction