Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / tsa-4.2.4 / rmle.m

diff --git a/octave_packages/tsa-4.2.4/rmle.m b/octave_packages/tsa-4.2.4/rmle.m
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+function [a,VAR,S,a_aux,b_aux,e_aux,MLE,pos] = rmle(arg1,arg2); 
+% RMLE estimates AR Parameters using the Recursive Maximum Likelihood 
+% Estimator according to [1]
+% 
+% Use: [a,VAR]=rmle(x,p)
+    % Input: 
+                % x is a column vector of data
+                % p is the model order
+    % Output:
+                % a is a vector with the AR parameters of the recursive MLE
+                % VAR is the excitation white noise variance estimate
+%
+% Reference(s):
+% [1] Kay S.M., Modern Spectral Analysis - Theory and Applications. 
+%       Prentice Hall, p. 232-233, 1988. 
+%
+                
+%       $Id: rmle.m 9609 2012-02-10 10:18:00Z schloegl $
+%      Copyright (C) 2004 by  Jose Luis Gutierrez <jlg@gmx.at>
+%      Grupo GENESIS - UTN - Argentina
+%
+%    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 3 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/>.
+
+
+x=arg1*1e-6;
+p=arg2;
+
+N=length(x);
+S=zeros(p+1,p+1);
+a_aux=zeros(p+1,p);, a_aux(1,:)=1;
+b_aux=ones(p+1,p);
+e_aux=zeros(p,1);, p_aux=zeros(p,1);
+MLE=zeros(3,1);
+pos=1;
+
+for i=0:p
+    for j=0:p      
+        for n=0:N-1-i-j
+            S(i+1,j+1)=S(i+1,j+1)+x(n+1+i)*x(n+1+j);
+        end
+    end
+end
+
+e0=S(1,1);
+c1=S(1,2);
+d1=S(2,2);
+coef3=1;
+coef2=((N-2)*c1)/((N-1)*d1);
+coef1=-(e0+N*d1)/((N-1)*d1);
+ti=-(N*c1)/((N-1)*d1);
+raices=roots([coef3 coef2 coef1 ti]);
+for o=1:3
+    if raices(o)>-1 && raices(o)<1
+        a_aux(2,1)=raices(o);    
+        b_aux(p+1,1)=raices(o);
+    end
+end
+e_aux(1,1)=S(1,1)+2*a_aux(2,1)*S(1,2)+(a_aux(2,1)^2)*S(2,2);
+p_aux(1,1)=e_aux(1,1)/N;
+
+for k=2:p
+    Ck=S(1:k,2:k+1);
+    Dk=S(2:k+1,2:k+1);
+    ck=a_aux(1:k,k-1)'*Ck*b_aux(p+1:-1:p+2-k,k-1);
+    dk=b_aux(p+1:-1:p+2-k,k-1)'*Dk*b_aux(p+1:-1:p+2-k,k-1);
+    coef3re=1;
+    coef2re=((N-2*k)*ck)/((N-k)*dk);
+    coef1re=-(k*e_aux(k-1,1)+N*dk)/((N-k)*dk);
+    tire=-(N*ck)/((N-k)*dk);
+    raices=roots([coef3re coef2re coef1re tire]);
+    for o=1:3
+        if raices(o,1)>-1 && raices(o,1)<1
+            MLE(o,1)=((1-raices(o)^2)^(k/2))/(((e_aux(k-1)+2*ck*raices(o)+dk*(raices(o)^2))/N)^(N/2));
+        end
+    end
+    [C,I]=max(MLE);
+    k_max=raices(I);
+    for i=1:k-1
+        a_aux(i+1,k)=a_aux(i+1,k-1)+k_max*a_aux(k-i+1,k-1);
+    end
+    a_aux(k+1,k)=k_max;
+    b_aux(p+1-k:p+1,k)=a_aux(1:k+1,k);
+    e_aux(k,1)=e_aux(k-1,1)+2*ck*k_max+dk*k_max^2;
+    p_aux(k,1)=e_aux(k,1)/N;
+end
+
+a=a_aux(:,p)';
+VAR=p_aux(p)*1e12;