R/levinson.R

In signal: Signal Processing

## Copyright (C) 1999 Paul Kienzle
##
## 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 of the License, 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 program; If not, see <http://www.gnu.org/licenses/>.
##
## Based on:
##    yulewalker.m
##    Copyright (C) 1995 Friedrich Leisch <Friedrich.Leisch@ci.tuwien.ac.at>
##    GPL license

levinson <- function(x, p=NULL){
    ## Levinson Durbin recursion
    fit <- function(acf, p){
        ref <- numeric(p)
        g <- -acf[2]/acf[1]
        a <- g
        v <- Re( ( 1 - g * Conj(g)) * acf[1] )
        ref[1] <- g
        for(t in 2:p){
            g <- - (acf[t+1] + c(t(a) %*% acf[seq(t, 2, by=-1)])) / v
            a <- c( (a + g * Conj(a[seq(t-1, 1, -1)])), g)
            v <- v * ( 1 - Re(g * Conj(g)) )
            ref[t] <- g
        }
        a <- c(1, a)
        return(list(a=a, v=v, ref=ref))
    }
    if((!is.null(p) && (p!=as.integer(p))) || (p < 2)) 
        stop("p must be integer >= 2.")
    if(is.numeric(x) && is.null(dim(x))){
        lx <- length(x)
        if(is.null(p) || p >= lx) p <- lx - 1
        r <- fit(x, p)
    } else {
        if(is.numeric(x) && !(is.null(dim(x)))){
            lx <- dim(x)
            if(is.null(p) || p >= lx[1]) p <- lx[1] - 1
            zr <- apply(x, 2, function(y) fit(y, p))
            ## Construct output matrices
            zr <- matrix(unlist(zr), nrow=lx[2], byrow=TRUE)
            a <- zr[,1:(p+1), drop=FALSE]
            v <- zr[,p+2]
            ref <- t(zr[,-(1:(p+2)), drop=FALSE])
            r <- list(a=a, v=v, ref=ref)
        } else {
            stop("x must be a numeric vector or matrix.")
        }
    }
    return(r)
}