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trunk: implemented more efficient formulas for smoother 

git-svn-id: https://www.dynare.org/svn/dynare/trunk@3276 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
michel 2009-12-19 22:43:23 +00:00
parent 2b5e551ad2
commit 3885bddd6d
1 changed files with 50 additions and 49 deletions
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99
matlab/DiffuseKalmanSmoother3_Z.m
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@ -83,11 +83,11 @@ end
Fstar = zeros(pp,smpl_diff); Fstar = zeros(pp,smpl_diff);
Finf = zeros(pp,smpl_diff); Finf = zeros(pp,smpl_diff);
Fi = zeros(pp,smpl_diff); Fi = zeros(pp,smpl);
Ki = zeros(mm,pp,smpl); Ki = zeros(mm,pp,smpl);
Li = zeros(mm,mm,pp,smpl); %Li = zeros(mm,mm,pp,smpl);
Linf = zeros(mm,mm,pp,smpl_diff); %Linf = zeros(mm,mm,pp,smpl_diff);
L0 = zeros(mm,mm,pp,smpl_diff); %L0 = zeros(mm,mm,pp,smpl_diff);
Kstar = zeros(mm,pp,smpl_diff); Kstar = zeros(mm,pp,smpl_diff);
P = zeros(mm,mm,smpl+1); P = zeros(mm,mm,smpl+1);
P1 = P; P1 = P;
@ -126,8 +126,8 @@ while newRank & t < smpl
if Finf(i,t) > crit & newRank if Finf(i,t) > crit & newRank
icc=icc+1; icc=icc+1;
Kinf(:,i,t) = Pinf(:,:,t)*Zi'; Kinf(:,i,t) = Pinf(:,:,t)*Zi';
Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t); % Linf(:,:,i,t) = eye(mm) - Kinf(:,i,t)*Z(i,:)/Finf(i,t);
L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Zi/Finf(i,t); % L0(:,:,i,t) = (Kinf(:,i,t)*Fstar(i,t)/Finf(i,t) - Kstar(:,i,t))*Zi/Finf(i,t);
a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t); a(:,t) = a(:,t) + Kinf(:,i,t)*v(i,t)/Finf(i,t);
Pstar(:,:,t) = Pstar(:,:,t) + ... Pstar(:,:,t) = Pstar(:,:,t) + ...
Kinf(:,i,t)*Kinf(:,i,t)'*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ... Kinf(:,i,t)*Kinf(:,i,t)'*Fstar(i,t)/(Finf(i,t)*Finf(i,t)) - ...
@ -156,7 +156,7 @@ while newRank & t < smpl
%% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition %% Note that : (1) rank(Pinf)=0 implies that Finf = 0, (2) outside this loop (when for some i and t the condition
%% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that %% rank(Pinf)=0 is satisfied we have P = Pstar and F = Fstar and (3) Finf = 0 does not imply that
%% rank(Pinf)=0. [stéphane,11-03-2004]. %% rank(Pinf)=0. [stéphane,11-03-2004].
Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); % we need to store Li for DKF smoother % Li(:,:,i,t) = eye(mm)-Kstar(:,i,t)*Z(i,:)/Fstar(i,t); % we need to store Li for DKF smoother
a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t); a(:,t) = a(:,t) + Kstar(:,i,t)*v(i,t)/Fstar(i,t);
Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*Kstar(:,i,t)'/Fstar(i,t); Pstar(:,:,t) = Pstar(:,:,t) - Kstar(:,i,t)*Kstar(:,i,t)'/Fstar(i,t);
Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)'; Pstar(:,:,t)=tril(Pstar(:,:,t))+tril(Pstar(:,:,t),-1)';
@ -177,8 +177,8 @@ end
d = t; d = t;
P(:,:,d+1) = Pstar(:,:,d+1); P(:,:,d+1) = Pstar(:,:,d+1);
Linf = Linf(:,:,:,1:d); %Linf = Linf(:,:,:,1:d);
L0 = L0(:,:,:,1:d); %L0 = L0(:,:,:,1:d);
Fstar = Fstar(:,1:d); Fstar = Fstar(:,1:d);
Finf = Finf(:,1:d); Finf = Finf(:,1:d);
Kstar = Kstar(:,:,1:d); Kstar = Kstar(:,:,1:d);
@ -198,7 +198,7 @@ while notsteady & t<smpl
Fi(i,t) = Zi*P(:,:,t)*Zi'; Fi(i,t) = Zi*P(:,:,t)*Zi';
Ki(:,i,t) = P(:,:,t)*Zi'; Ki(:,i,t) = P(:,:,t)*Zi';
if Fi(i,t) > crit if Fi(i,t) > crit
Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t); % Li(:,:,i,t) = eye(mm)-Ki(:,i,t)*Z(i,:)/Fi(i,t);
a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t); a(:,t) = a(:,t) + Ki(:,i,t)*v(i,t)/Fi(i,t);
P(:,:,t) = P(:,:,t) - Ki(:,i,t)*Ki(:,i,t)'/Fi(i,t); P(:,:,t) = P(:,:,t) - Ki(:,i,t)*Ki(:,i,t)'/Fi(i,t);
P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)'; P(:,:,t)=tril(P(:,:,t))+tril(P(:,:,t),-1)';
@ -212,45 +212,45 @@ while notsteady & t<smpl
PK(jnk,:,:,t+jnk) = Pf; PK(jnk,:,:,t+jnk) = Pf;
end end
P(:,:,t+1) = T*P(:,:,t)*T' + QQ; P(:,:,t+1) = T*P(:,:,t)*T' + QQ;
notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit); % notsteady = ~(max(max(abs(P(:,:,t+1)-P(:,:,t))))<crit);
end
P_s=tril(P(:,:,t))+tril(P(:,:,t),-1)';
P1_s=tril(P1(:,:,t))+tril(P1(:,:,t),-1)';
Fi_s = Fi(:,t);
Ki_s = Ki(:,:,t);
L_s =Li(:,:,:,t);
if t<smpl
P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
P1 = cat(3,P1(:,:,1:t),repmat(P1_s,[1 1 smpl-t]));
Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t]));
Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t]));
Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t]));
end
while t<smpl
t=t+1;
a(:,t) = a1(:,t);
for i=1:pp
Zi = Z(i,:);
v(i,t) = Y(i,t) - Zi*a(:,t);
if Fi_s(i) > crit
a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
end
end
a1(:,t+1) = T*a(:,t);
Pf = P(:,:,t);
for jnk=1:nk,
Pf = T*Pf*T' + QQ;
aK(jnk,:,t+jnk) = T^jnk*a(:,t);
PK(jnk,:,:,t+jnk) = Pf;
end
end end
% $$$ P_s=tril(P(:,:,t))+tril(P(:,:,t),-1)';
% $$$ P1_s=tril(P1(:,:,t))+tril(P1(:,:,t),-1)';
% $$$ Fi_s = Fi(:,t);
% $$$ Ki_s = Ki(:,:,t);
% $$$ L_s =Li(:,:,:,t);
% $$$ if t<smpl
% $$$ P = cat(3,P(:,:,1:t),repmat(P_s,[1 1 smpl-t]));
% $$$ P1 = cat(3,P1(:,:,1:t),repmat(P1_s,[1 1 smpl-t]));
% $$$ Fi = cat(2,Fi(:,1:t),repmat(Fi_s,[1 1 smpl-t]));
% $$$ Li = cat(4,Li(:,:,:,1:t),repmat(L_s,[1 1 smpl-t]));
% $$$ Ki = cat(3,Ki(:,:,1:t),repmat(Ki_s,[1 1 smpl-t]));
% $$$ end
% $$$ while t<smpl
% $$$ t=t+1;
% $$$ a(:,t) = a1(:,t);
% $$$ for i=1:pp
% $$$ Zi = Z(i,:);
% $$$ v(i,t) = Y(i,t) - Zi*a(:,t);
% $$$ if Fi_s(i) > crit
% $$$ a(:,t) = a(:,t) + Ki_s(:,i)*v(i,t)/Fi_s(i);
% $$$ end
% $$$ end
% $$$ a1(:,t+1) = T*a(:,t);
% $$$ Pf = P(:,:,t);
% $$$ for jnk=1:nk,
% $$$ Pf = T*Pf*T' + QQ;
% $$$ aK(jnk,:,t+jnk) = T^jnk*a(:,t);
% $$$ PK(jnk,:,:,t+jnk) = Pf;
% $$$ end
% $$$ end
ri=zeros(mm,1); ri=zeros(mm,1);
t = smpl+1; t = smpl+1;
while t > d+1 while t > d+1
t = t-1; t = t-1;
for i=pp:-1:1 for i=pp:-1:1
if Fi(i,t) > crit if Fi(i,t) > crit
ri = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri; ri = Z(i,:)'/Fi(i,t)*v(i,t)+ri-Ki(:,i,t)'*ri/Fi(i,t)*Z(i,:)';
end end
end end
r(:,t) = ri; r(:,t) = ri;
@ -267,10 +267,11 @@ if d
% if Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d), % use of options_.diffuse_d to be sure of DKF termination % if Finf(i,t) > crit & ~(t==d & i>options_.diffuse_d), % use of options_.diffuse_d to be sure of DKF termination
if Finf(i,t) > crit if Finf(i,t) > crit
r1(:,t) = Z(i,:)'*v(i,t)/Finf(i,t) + ... r1(:,t) = Z(i,:)'*v(i,t)/Finf(i,t) + ...
L0(:,:,i,t)'*r0(:,t) + Linf(:,:,i,t)'*r1(:,t); (Kinf(:,i,t)'*Fstar(i,t)/Finf(i,t)-Kstar(:,i,t)')*r0(:,t)/Finf(i,t)*Z(i,:)' + ...
r0(:,t) = Linf(:,:,i,t)'*r0(:,t); r1(:,t)-Kinf(:,i,t)'*r1(:,t)/Finf(i,t)*Z(i,:)';
r0(:,t) = r0(:,t)-Kinf(:,i,t)'*r0(:,t)/Finf(i,t)*Z(i,:)';
elseif Fstar(i,t) > crit % step needed whe Finf == 0 elseif Fstar(i,t) > crit % step needed whe Finf == 0
r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+Li(:,:,i,t)'*r0(:,t); r0(:,t) = Z(i,:)'/Fstar(i,t)*v(i,t)+r0(:,t)-(Kstar(:,i,t)'*r0(:,t))/Fstar(i,t)*Z(i,:)';
end end
end end
alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t); alphahat(:,t) = a1(:,t) + Pstar1(:,:,t)*r0(:,t) + Pinf1(:,:,t)*r1(:,t);
@ -290,7 +291,7 @@ if nargout > 7
ri_d = zeros(mm,1); ri_d = zeros(mm,1);
for i=pp:-1:1 for i=pp:-1:1
if Fi(i,t) > crit if Fi(i,t) > crit
ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+Li(:,:,i,t)'*ri_d; ri_d = Z(i,:)'/Fi(i,t)*v(i,t)+ri_d-Ki(:,i,t)'*ri_d/Fi(i,t)*Z(i,:)';
end end
end end
@ -298,11 +299,11 @@ if nargout > 7
eta_tm1t = QRt*ri_d; eta_tm1t = QRt*ri_d;
% calculate decomposition % calculate decomposition
Ttok = eye(mm,mm); Ttok = eye(mm,mm);
AAA = P1(:,:,t)*Z'*ZRQinv*Z*R;
for h = 1:nk for h = 1:nk
BBB = Ttok*AAA;
for j=1:rr for j=1:rr
eta=zeros(rr,1); decomp(h,:,j,t+h) = eta_tm1t(j)*BBB(:,j);
eta(j) = eta_tm1t(j);
decomp(h,:,j,t+h) = Ttok*P1(:,:,t)*Z'*ZRQinv*Z*R*eta;
end end
Ttok = T*Ttok; Ttok = T*Ttok;
end end