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/*
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA - Arnaud TORSET
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
*/
/*Resolve the Yule-Walker equations:
|r(0) r(1) ... r(N-1)|| a(1) | |sigma2|
|r(1) r(0) ... r(n-1)|| a(2) | | 0 |
| : : ... : || : |=| 0 |
| : : ... : || : | | 0 |
|r(N-1) r(N-2) ... r(0) ||a(N-1)| | 0 |
using Levinson's algorithm.
r :Correlation coefficients
ar :Auto-Regressive model parameters
sigma2 :Scale constant
rc :Reflection coefficients
*/
#include <stdlib.h>
#include "lev.h"
#include "conj.h"
#include "multiplication.h"
#include "addition.h"
#include "division.h"
#include "subtraction.h"
doubleComplex zleva(doubleComplex* in,int size, doubleComplex* ar, doubleComplex* rc){
int i=0, j=0;
doubleComplex accu=DoubleComplex(0,0);
doubleComplex* ak1;
doubleComplex temp;
doubleComplex sigma2;
/* FIXME : malloc here */
ak1=(doubleComplex*)malloc((unsigned int)size*sizeof(doubleComplex));
/* initialize levinson's algorithm */
temp=zrdivs(in[1],in[0]);
ar[0]=DoubleComplex(-zreals(temp),-zimags(temp));
rc[0]=ar[0];
temp = zmuls(ar[0],zconjs(ar[0]));
sigma2=zmuls(zdiffs(DoubleComplex(1,0), temp), in[0]);
ak1[0]=DoubleComplex(0,0);
/* iterative solution to yule-walker equations */
for (i=1;i<size-1;i++){
accu=DoubleComplex(0,0);
for (j=0;j<i;j++){
temp = zmuls(zconjs(ar[j]),zconjs(in[i-j]));
accu=zadds(accu, temp);
}
temp = zadds(in[i+1],accu);
temp = zrdivs(temp,sigma2);
ak1[i]=DoubleComplex(-zreals(temp),-zimags(temp));
rc[i]=DoubleComplex(zreals(ak1[i]),zimags(ak1[i]));
for (j=0;j<i;j++){
temp = zmuls(ak1[i], zconjs(ar[i-1-j]));
ak1[j] = zadds(ar[j],temp);
}
temp = zmuls(ak1[i], zconjs(ak1[i]));
temp = zdiffs(DoubleComplex(1,0),temp);
sigma2 = zmuls(temp,sigma2);
for (j=0;j<=i;j++){
ar[j]=DoubleComplex(zreals(ak1[j]),zimags(ak1[j]));
}
}
free(ak1);
return sigma2;
}
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