trunk: implemented more efficient formulas for smoother
git-svn-id: https://www.dynare.org/svn/dynare/trunk@3276 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
parent
2b5e551ad2
commit
3885bddd6d
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@ -83,11 +83,11 @@ end
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Fstar = zeros(pp,smpl_diff);
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Fstar = zeros(pp,smpl_diff);
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Finf = zeros(pp,smpl_diff);
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Finf = zeros(pp,smpl_diff);
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Fi = zeros(pp,smpl_diff);
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Fi = zeros(pp,smpl);
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Ki = zeros(mm,pp,smpl);
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Ki = zeros(mm,pp,smpl);
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Li = zeros(mm,mm,pp,smpl);
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%Li = zeros(mm,mm,pp,smpl);
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Linf = zeros(mm,mm,pp,smpl_diff);
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%Linf = zeros(mm,mm,pp,smpl_diff);
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L0 = zeros(mm,mm,pp,smpl_diff);
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%L0 = zeros(mm,mm,pp,smpl_diff);
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Kstar = zeros(mm,pp,smpl_diff);
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Kstar = zeros(mm,pp,smpl_diff);
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P = zeros(mm,mm,smpl+1);
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P = zeros(mm,mm,smpl+1);
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P1 = P;
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P1 = P;
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@ -126,8 +126,8 @@ while newRank & t < smpl
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if Finf(i,t) > crit & newRank
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if Finf(i,t) > crit & newRank
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icc=icc+1;
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icc=icc+1;
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Kinf(:,i,t) = Pinf(:,:,t)*Zi';
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Kinf(:,i,t) = Pinf(:,:,t)*Zi';
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Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t);
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% Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t);
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L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Zi/Finf(i,t);
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% L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Zi/Finf(i,t);
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a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t);
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a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t);
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Pstar(:,:,t) = Pstar(:,:,t) + ...
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Pstar(:,:,t) = Pstar(:,:,t) + ...
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Kinf(:,i,t)*Kinf(:,i,t)'*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ...
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Kinf(:,i,t)*Kinf(:,i,t)'*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ...
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@ -156,7 +156,7 @@ while newRank & t < smpl
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%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition
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%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition
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%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that
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%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that
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%% rank(Pinf)=0. [stéphane,11-03-2004].
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%% rank(Pinf)=0. [stéphane,11-03-2004].
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Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); % we need to store Li for DKF smoother
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% Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); % we need to store Li for DKF smoother
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a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
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a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
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Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*Kstar(:,i,t)'/Fstar(i,t);
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Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*Kstar(:,i,t)'/Fstar(i,t);
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Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
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Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
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@ -177,8 +177,8 @@ end
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d = t;
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d = t;
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P(:,:,d+1) = Pstar(:,:,d+1);
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P(:,:,d+1) = Pstar(:,:,d+1);
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Linf = Linf(:,:,:,1:d);
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%Linf = Linf(:,:,:,1:d);
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L0 = L0(:,:,:,1:d);
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%L0 = L0(:,:,:,1:d);
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Fstar = Fstar(:,1:d);
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Fstar = Fstar(:,1:d);
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Finf = Finf(:,1:d);
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Finf = Finf(:,1:d);
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Kstar = Kstar(:,:,1:d);
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Kstar = Kstar(:,:,1:d);
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@ -198,7 +198,7 @@ while notsteady & t<smpl
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Fi(i,t) = Zi*P(:,:,t)*Zi';
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Fi(i,t) = Zi*P(:,:,t)*Zi';
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Ki(:,i,t) = P(:,:,t)*Zi';
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Ki(:,i,t) = P(:,:,t)*Zi';
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if Fi(i,t) > crit
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if Fi(i,t) > crit
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Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t);
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% Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t);
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a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
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a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
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P(:,:,t) = P(:,:,t) - Ki(:,i,t)*Ki(:,i,t)'/Fi(i,t);
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P(:,:,t) = P(:,:,t) - Ki(:,i,t)*Ki(:,i,t)'/Fi(i,t);
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P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)';
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P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)';
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@ -212,45 +212,45 @@ while notsteady & t<smpl
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PK(jnk,:,:,t+jnk) = Pf;
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PK(jnk,:,:,t+jnk) = Pf;
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end
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end
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P(:,:,t+1) = T*P(:,:,t)*T' + QQ;
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P(:,:,t+1) = T*P(:,:,t)*T' + QQ;
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notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
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% notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
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end
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P_s=tril(P(:,:,t))+tril(P(:,:,t),-1)';
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P1_s=tril(P1(:,:,t))+tril(P1(:,:,t),-1)';
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Fi_s = Fi(:,t);
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Ki_s = Ki(:,:,t);
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L_s =Li(:,:,:,t);
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if t<smpl
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P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
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P1 = cat(3,P1(:,:,1:t),repmat(P1_s,[1 1 smpl-t]));
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Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t]));
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Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t]));
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Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t]));
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end
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while t<smpl
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t=t+1;
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a(:,t) = a1(:,t);
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for i=1:pp
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Zi = Z(i,:);
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v(i,t) = Y(i,t) - Zi*a(:,t);
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if Fi_s(i) > crit
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a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
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end
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end
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a1(:,t+1) = T*a(:,t);
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Pf = P(:,:,t);
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for jnk=1:nk,
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Pf = T*Pf*T' + QQ;
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aK(jnk,:,t+jnk) = T^jnk*a(:,t);
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PK(jnk,:,:,t+jnk) = Pf;
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end
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end
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end
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% $$$ P_s=tril(P(:,:,t))+tril(P(:,:,t),-1)';
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% $$$ P1_s=tril(P1(:,:,t))+tril(P1(:,:,t),-1)';
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% $$$ Fi_s = Fi(:,t);
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% $$$ Ki_s = Ki(:,:,t);
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% $$$ L_s =Li(:,:,:,t);
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% $$$ if t<smpl
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% $$$ P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
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% $$$ P1 = cat(3,P1(:,:,1:t),repmat(P1_s,[1 1 smpl-t]));
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% $$$ Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t]));
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% $$$ Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t]));
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% $$$ Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t]));
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% $$$ end
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% $$$ while t<smpl
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% $$$ t=t+1;
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% $$$ a(:,t) = a1(:,t);
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% $$$ for i=1:pp
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% $$$ Zi = Z(i,:);
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% $$$ v(i,t) = Y(i,t) - Zi*a(:,t);
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% $$$ if Fi_s(i) > crit
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% $$$ a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
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% $$$ end
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% $$$ end
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% $$$ a1(:,t+1) = T*a(:,t);
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% $$$ Pf = P(:,:,t);
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% $$$ for jnk=1:nk,
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% $$$ Pf = T*Pf*T' + QQ;
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% $$$ aK(jnk,:,t+jnk) = T^jnk*a(:,t);
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% $$$ PK(jnk,:,:,t+jnk) = Pf;
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% $$$ end
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% $$$ end
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ri=zeros(mm,1);
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ri=zeros(mm,1);
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t = smpl+1;
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t = smpl+1;
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while t > d+1
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while t > d+1
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t = t-1;
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t = t-1;
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for i=pp:-1:1
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for i=pp:-1:1
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if Fi(i,t) > crit
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if Fi(i,t) > crit
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ri = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri;
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ri = Z(i,:)'/Fi(i,t)*v(i,t)+ri-Ki(:,i,t)'*ri/Fi(i,t)*Z(i,:)';
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end
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end
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end
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end
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r(:,t) = ri;
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r(:,t) = ri;
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@ -267,10 +267,11 @@ if d
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% if Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d), % use of options_.diffuse_d to be sure of DKF termination
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% if Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d), % use of options_.diffuse_d to be sure of DKF termination
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if Finf(i,t) > crit
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if Finf(i,t) > crit
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r1(:,t) = Z(i,:)'*v(i,t)/Finf(i,t) + ...
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r1(:,t) = Z(i,:)'*v(i,t)/Finf(i,t) + ...
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L0(:,:,i,t)'*r0(:,t) + Linf(:,:,i,t)'*r1(:,t);
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(Kinf(:,i,t)'*Fstar(i,t)/Finf(i,t)-Kstar(:,i,t)')*r0(:,t)/Finf(i,t)*Z(i,:)' + ...
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r0(:,t) = Linf(:,:,i,t)'*r0(:,t);
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r1(:,t)-Kinf(:,i,t)'*r1(:,t)/Finf(i,t)*Z(i,:)';
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r0(:,t) = r0(:,t)-Kinf(:,i,t)'*r0(:,t)/Finf(i,t)*Z(i,:)';
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elseif Fstar(i,t) > crit % step needed whe Finf == 0
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elseif Fstar(i,t) > crit % step needed whe Finf == 0
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r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+Li(:,:,i,t)'*r0(:,t);
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r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+r0(:,t)-(Kstar(:,i,t)'*r0(:,t))/Fstar(i,t)*Z(i,:)';
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end
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end
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end
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end
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alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
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alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
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@ -290,7 +291,7 @@ if nargout > 7
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ri_d = zeros(mm,1);
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ri_d = zeros(mm,1);
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for i=pp:-1:1
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for i=pp:-1:1
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if Fi(i,t) > crit
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if Fi(i,t) > crit
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ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri_d;
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ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+ri_d-Ki(:,i,t)'*ri_d/Fi(i,t)*Z(i,:)';
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end
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end
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end
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end
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@ -298,11 +299,11 @@ if nargout > 7
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eta_tm1t = QRt*ri_d;
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eta_tm1t = QRt*ri_d;
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% calculate decomposition
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% calculate decomposition
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Ttok = eye(mm,mm);
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Ttok = eye(mm,mm);
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AAA = P1(:,:,t)*Z'*ZRQinv*Z*R;
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for h = 1:nk
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for h = 1:nk
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BBB = Ttok*AAA;
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for j=1:rr
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for j=1:rr
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eta=zeros(rr,1);
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decomp(h,:,j,t+h) = eta_tm1t(j)*BBB(:,j);
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eta(j) = eta_tm1t(j);
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decomp(h,:,j,t+h) = Ttok*P1(:,:,t)*Z'*ZRQinv*Z*R*eta;
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end
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end
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Ttok = T*Ttok;
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Ttok = T*Ttok;
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end
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end
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