193 lines
9.7 KiB
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193 lines
9.7 KiB
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<title>Description of DiffuseKalmanSmoother1</title>
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > DiffuseKalmanSmoother1.m</div>
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<!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td>
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<td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="../right.png"></a></td></tr></table>-->
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<h1>DiffuseKalmanSmoother1
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</h1>
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>modified by M. Ratto:</strong></div>
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<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function [alphahat,etahat,a, aK] = DiffuseKalmanSmoother1(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf) </strong></div>
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<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre class="comment"> modified by M. Ratto:
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new output argument aK (1-step to k-step predictions)
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new options_.nk: the max step ahed prediction in aK (default is 4)
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new crit1 value for rank of Pinf
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it is assured that P is symmetric
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stephane.adjemian@cepremap.cnrs.fr [09-16-2004]
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See "Filtering and Smoothing of State Vector for Diffuse State Space
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Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series
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Analysis, vol. 24(1), pp. 85-98).</pre></div>
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<!-- crossreference -->
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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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This function calls:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="steady.html" class="code" title="function steady(linear)">steady</a> Copyright (C) 2001 Michel Juillard</li></ul>
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This function is called by:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="DsgeSmoother.html" class="code" title="function [alphahat,etahat,epsilonhat,ahat,SteadyState,trend_coeff,aK] = DsgeSmoother(xparam1,gend,Y)">DsgeSmoother</a> stephane.adjemian@cepremap.cnrs.fr [09-07-2004]</li></ul>
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<!-- crossreference -->
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<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function [alphahat,etahat,a, aK] = DiffuseKalmanSmoother1(T,R,Q,Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf)</a>
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0002 <span class="comment">% modified by M. Ratto:</span>
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0003 <span class="comment">% new output argument aK (1-step to k-step predictions)</span>
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0004 <span class="comment">% new options_.nk: the max step ahed prediction in aK (default is 4)</span>
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0005 <span class="comment">% new crit1 value for rank of Pinf</span>
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0006 <span class="comment">% it is assured that P is symmetric</span>
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0007 <span class="comment">%</span>
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0008 <span class="comment">% stephane.adjemian@cepremap.cnrs.fr [09-16-2004]</span>
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0009 <span class="comment">%</span>
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0010 <span class="comment">% See "Filtering and Smoothing of State Vector for Diffuse State Space</span>
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0011 <span class="comment">% Models", S.J. Koopman and J. Durbin (2003, in Journal of Time Series</span>
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0012 <span class="comment">% Analysis, vol. 24(1), pp. 85-98).</span>
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0013
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0014 <span class="keyword">global</span> options_
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0015
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0016 nk = options_.nk;
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0017 spinf = size(Pinf1);
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0018 spstar = size(Pstar1);
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0019 v = zeros(pp,smpl);
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0020 a = zeros(mm,smpl+1);
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0021 aK = zeros(nk,mm,smpl+1);
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0022 iF = zeros(pp,pp,smpl);
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0023 Fstar = zeros(pp,pp,smpl);
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0024 iFinf = zeros(pp,pp,smpl);
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0025 K = zeros(mm,pp,smpl);
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0026 L = zeros(mm,mm,smpl);
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0027 Linf = zeros(mm,mm,smpl);
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0028 Kstar = zeros(mm,pp,smpl);
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0029 P = zeros(mm,mm,smpl+1);
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0030 Pstar = zeros(spstar(1),spstar(2),smpl+1); Pstar(:,:,1) = Pstar1;
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0031 Pinf = zeros(spinf(1),spinf(2),smpl+1); Pinf(:,:,1) = Pinf1;
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0032 crit = options_.kalman_tol;
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0033 crit1 = 1.e-8;
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0034 <a href="steady.html" class="code" title="function steady(linear)">steady</a> = smpl;
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0035 rr = size(Q,1);
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0036 QQ = R*Q*transpose(R);
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0037 QRt = Q*transpose(R);
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0038 alphahat = zeros(mm,smpl);
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0039 etahat = zeros(rr,smpl);
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0040 r = zeros(mm,smpl);
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0041
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0042 Z = zeros(pp,mm);
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0043 <span class="keyword">for</span> i=1:pp;
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0044 Z(i,mf(i)) = 1;
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0045 <span class="keyword">end</span>
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0046
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0047 t = 0;
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0048 <span class="keyword">while</span> rank(Pinf(:,:,t+1),crit1) & t<smpl
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0049 t = t+1;
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0050 v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
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0051 <span class="keyword">if</span> rcond(Pinf(mf,mf,t)) < crit
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0052 <span class="keyword">return</span>
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0053 <span class="keyword">end</span>
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0054 iFinf(:,:,t) = inv(Pinf(mf,mf,t));
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0055 Kinf(:,:,t) = T*Pinf(:,mf,t)*iFinf(:,:,t);
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0056 a(:,t+1) = T*a(:,t) + Kinf(:,:,t)*v(:,t);
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0057 aK(1,:,t+1) = a(:,t+1);
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0058 <span class="keyword">for</span> jnk=2:nk,
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0059 aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
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0060 <span class="keyword">end</span>
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0061 Linf(:,:,t) = T - Kinf(:,:,t)*Z;
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0062 Fstar(:,:,t) = Pstar(mf,mf,t);
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0063 Kstar(:,:,t) = (T*Pstar(:,mf,t)-Kinf(:,:,t)*Fstar(:,:,t))*iFinf(:,:,t);
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0064 Pstar(:,:,t+1) = T*Pstar(:,:,t)*transpose(T)-T*Pstar(:,mf,t)*transpose(Kinf(:,:,t))-Kinf(:,:,t)*Pinf(mf,mf,t)*transpose(Kstar(:,:,t)) + QQ;
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0065 Pinf(:,:,t+1) = T*Pinf(:,:,t)*transpose(T)-T*Pinf(:,mf,t)*transpose(Kinf(:,:,t));
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0066 <span class="keyword">end</span>
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0067 d = t;
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0068 P(:,:,d+1) = Pstar(:,:,d+1);
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0069 iFinf = iFinf(:,:,1:d);
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0070 Linf = Linf(:,:,1:d);
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0071 Fstar = Fstar(:,:,1:d);
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0072 Kstar = Kstar(:,:,1:d);
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0073 Pstar = Pstar(:,:,1:d);
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0074 Pinf = Pinf(:,:,1:d);
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0075 notsteady = 1;
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0076 <span class="keyword">while</span> notsteady & t<smpl
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0077 t = t+1;
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0078 v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
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0079 P(:,:,t)=tril(P(:,:,t))+transpose(tril(P(:,:,t),-1));
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0080 <span class="keyword">if</span> rcond(P(mf,mf,t)) < crit
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0081 <span class="keyword">return</span>
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0082 <span class="keyword">end</span>
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0083 iF(:,:,t) = inv(P(mf,mf,t));
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0084 K(:,:,t) = T*P(:,mf,t)*iF(:,:,t);
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0085 L(:,:,t) = T-K(:,:,t)*Z;
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0086 a(:,t+1) = T*a(:,t) + K(:,:,t)*v(:,t);
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0087 aK(1,:,t+1) = a(:,t+1);
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0088 <span class="keyword">for</span> jnk=2:nk,
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0089 aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
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0090 <span class="keyword">end</span>
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0091 P(:,:,t+1) = T*P(:,:,t)*transpose(T)-T*P(:,mf,t)*transpose(K(:,:,t)) + QQ;
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0092 notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
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0093 <span class="keyword">end</span>
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0094 K_s = K(:,:,t);
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0095 iF_s = iF(:,:,t);
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0096 P_s = P(:,:,t+1);
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0097 <span class="keyword">if</span> t<smpl
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0098 t_steady = t+1;
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0099 P = cat(3,P(:,:,1:t),repmat(P(:,:,t),[1 1 smpl-t_steady+1]));
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0100 iF = cat(3,iF(:,:,1:t),repmat(inv(P_s(mf,mf)),[1 1 smpl-t_steady+1]));
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0101 L = cat(3,L(:,:,1:t),repmat(T-K_s*Z,[1 1 smpl-t_steady+1]));
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0102 K = cat(3,K(:,:,1:t),repmat(T*P_s(:,mf)*iF_s,[1 1 smpl-t_steady+1]));
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0103 <span class="keyword">end</span>
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0104 <span class="keyword">while</span> t<smpl
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0105 t=t+1;
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0106 v(:,t) = Y(:,t) - a(mf,t) - trend(:,t);
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0107 a(:,t+1) = T*a(:,t) + K_s*v(:,t);
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0108 aK(1,:,t+1) = a(:,t+1);
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0109 <span class="keyword">for</span> jnk=2:nk,
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0110 aK(jnk,:,t+jnk) = T^(jnk-1)*a(:,t+1);
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0111 <span class="keyword">end</span>
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0112 <span class="keyword">end</span>
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0113 t = smpl+1;
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0114 <span class="keyword">while</span> t>d+1 & t>2
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0115 t = t-1;
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0116 r(:,t-1) = transpose(Z)*iF(:,:,t)*v(:,t) + transpose(L(:,:,t))*r(:,t);
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0117 alphahat(:,t) = a(:,t) + P(:,:,t)*r(:,t-1);
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0118 etahat(:,t) = QRt*r(:,t);
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0119 <span class="keyword">end</span>
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0120 <span class="keyword">if</span> d
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0121 r0 = zeros(mm,d); r0(:,d) = r(:,d);
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0122 r1 = zeros(mm,d);
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0123 <span class="keyword">for</span> t = d:-1:2
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0124 r0(:,t-1) = transpose(Linf(:,:,t))*r0(:,t);
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0125 r1(:,t-1) = transpose(Z)*(iFinf(:,:,t)*v(:,t)-transpose(Kstar(:,:,t))*r0(:,t)) + transpose(Linf(:,:,t))*r1(:,t);
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0126 alphahat(:,t) = a(:,t) + Pstar(:,:,t)*r0(:,t-1) + Pinf(:,:,t)*r1(:,t-1);
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0127 etahat(:,t) = QRt*r0(:,t);
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0128 <span class="keyword">end</span>
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0129 r0_0 = transpose(Linf(:,:,1))*r0(:,1);
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0130 r1_0 = transpose(Z)*(iFinf(:,:,1)*v(:,1)-transpose(Kstar(:,:,1))*r0(:,1)) + transpose(Linf(:,:,1))*r1(:,1);
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0131 alphahat(:,1) = a(:,1) + Pstar(:,:,1)*r0_0 + Pinf(:,:,1)*r1_0;
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0132 etahat(:,1) = QRt*r0(:,1);
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0133 <span class="keyword">else</span>
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0134 r0 = transpose(Z)*iF(:,:,1)*v(:,1) + transpose(L(:,:,1))*r(:,1);
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0135 alphahat(:,1) = a(:,1) + P(:,:,1)*r0;
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0136 etahat(:,1) = QRt*r(:,1);
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0137 <span class="keyword">end</span></pre></div>
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<hr><address>Generated on Fri 16-Jun-2006 09:09:06 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address>
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