diff --git a/matlab/check.m b/matlab/check.m
index deb569d0b..328867803 100644
--- a/matlab/check.m
+++ b/matlab/check.m
@@ -59,7 +59,8 @@ global it_
oo_.exo_simul = tempex;
eigenvalues_ = dr.eigval;
- nyf = nnz(dr.kstate(:,2)>M_.maximum_lag+1);
+ %nyf = nnz(dr.kstate(:,2)>M_.maximum_lag+1);
+ nyf = dr.nyf;
[m_lambda,i]=sort(abs(eigenvalues_));
n_explod = nnz(abs(eigenvalues_) > options_.qz_criterium);
diff --git a/matlab/dr11_sparse.m b/matlab/dr11_sparse.m
new file mode 100644
index 000000000..424b88fb4
--- /dev/null
+++ b/matlab/dr11_sparse.m
@@ -0,0 +1,492 @@
+function [dr,info,M_,options_,oo_] = dr11_sparse(dr,task,M_,options_,oo_, jacobia_, hessian)
+ info = 0;
+ klen = M_.maximum_endo_lag + M_.maximum_endo_lead + 1;
+ kstate = dr.kstate;
+ kad = dr.kad;
+ kae = dr.kae;
+ %kstate
+ %kad
+ %kae
+ nstatic = dr.nstatic;
+ nfwrd = dr.nfwrd;
+ npred = dr.npred;
+ nboth = dr.nboth;
+ %nstatic
+ %nfwrd
+ %npred
+ %nboth
+ order_var = dr.order_var;
+ %order_var
+ nd = size(kstate,1);
+ %nd
+ nz = nnz(M_.lead_lag_incidence);
+ %nz
+
+ sdyn = M_.endo_nbr - nstatic;
+ %sdyn
+% M_.lead_lag_incidence
+ k0 = M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var);
+ k1 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_endo_lag+1),:);
+% size(jacobia_)
+% k0
+ %k1
+ b = jacobia_(:,k0);
+ %full(b)
+
+ if M_.maximum_endo_lead == 0; % backward models
+ a = jacobia_(:,nonzeros(k1'));
+ dr.ghx = zeros(size(a));
+ m = 0;
+ for i=M_.maximum_endo_lag:-1:1
+ k = nonzeros(M_.lead_lag_incidence(i,order_var));
+ dr.ghx(:,m+[1:length(k)]) = -b\a(:,k);
+ m = m+length(k);
+ end
+ if M_.exo_nbr & task~=1
+ dr.ghu = -b\jacobia_(:,nz+1:end);
+ end
+ dr.eigval = eig(transition_matrix(dr,M_));
+ dr.rank = 0;
+ if any(abs(dr.eigval) > options_.qz_criterium)
+ temp = sort(abs(dr.eigval));
+ nba = nnz(abs(dr.eigval) > options_.qz_criterium);
+ temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
+ info(1) = 3;
+ info(2) = temp'*temp;
+ end
+ return;
+ end
+
+ %forward--looking models
+ if nstatic > 0
+ [Q,R] = qr(b(:,1:nstatic));
+ aa = Q'*jacobia_;
+ else
+ aa = jacobia_;
+ end
+% full(aa)
+ a = aa(:,nonzeros(k1'));
+ b = aa(:,k0);
+ %M_.lead_lag_incidence
+ %k0
+ %k1
+ %a
+ %b
+ b10 = b(1:nstatic,1:nstatic);
+ b11 = b(1:nstatic,nstatic+1:end);
+ b2 = b(nstatic+1:end,nstatic+1:end);
+ if any(isinf(a(:)))
+ info = 1;
+ return
+ end
+
+ % buildind D and E
+ d = zeros(nd,nd) ;
+ e = d ;
+
+ k = find(kstate(:,2) >= M_.maximum_endo_lag+2 & kstate(:,3));
+ d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
+ k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
+ e(1:sdyn,k1) = -b2(:,kstate(k1,1)-nstatic);
+ k = find(kstate(:,2) <= M_.maximum_endo_lag+1 & kstate(:,4));
+ e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
+ k2 = find(kstate(:,2) == M_.maximum_endo_lag+1);
+ k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
+ d(1:sdyn,k2) = b2(:,kstate(k2,1)-nstatic);
+
+ if ~isempty(kad)
+ for j = 1:size(kad,1)
+ d(sdyn+j,kad(j)) = 1 ;
+ e(sdyn+j,kae(j)) = 1 ;
+ end
+ end
+ %e
+ %d
+
+ [ss,tt,w,sdim,dr.eigval,info1] = mjdgges(e,d,options_.qz_criterium);
+
+ %ss
+ %tt
+ %sdim
+ %fprintf('%20.16f\n',dr.eigval)
+
+ if info1
+ info(1) = 2;
+ info(2) = info1;
+ return
+ end
+
+ nba = nd-sdim;
+
+ nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
+ %disp(['task' num2str(task)]);
+ if task == 1
+ dr.rank = rank(w(1:nyf,nd-nyf+1:end));
+ % Under Octave, eig(A,B) doesn't exist, and
+ % lambda = qz(A,B) won't return infinite eigenvalues
+ if ~exist('OCTAVE_VERSION')
+ dr.eigval = eig(e,d);
+% dr.eigval
+ end
+ return
+ end
+
+ if nba ~= nyf
+ temp = sort(abs(dr.eigval));
+ if nba > nyf
+ temp = temp(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
+ info(1) = 3;
+ elseif nba < nyf;
+ temp = temp(nd-nyf+1:nd-nba)-1-options_.qz_criterium;
+ info(1) = 4;
+ end
+ info(2) = temp'*temp;
+ return
+ end
+
+ np = nd - nyf;
+ n2 = np + 1;
+ n3 = nyf;
+ n4 = n3 + 1;
+ % derivatives with respect to dynamic state variables
+ % forward variables
+ w1 =w(1:n3,n2:nd);
+ if condest(w1) > 1e9;
+ info(1) = 5;
+ info(2) = condest(w1);
+ return;
+ else
+ gx = -w1'\w(n4:nd,n2:nd)';
+ end
+
+ % predetermined variables
+ hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
+ hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);
+
+ k1 = find(kstate(n4:nd,2) == M_.maximum_endo_lag+1);
+ k2 = find(kstate(1:n3,2) == M_.maximum_endo_lag+2);
+ dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
+
+ %lead variables actually present in the model
+ j3 = nonzeros(kstate(:,3));
+ j4 = find(kstate(:,3));
+ % derivatives with respect to exogenous variables
+ if M_.exo_nbr
+ fu = aa(:,nz+(1:M_.exo_nbr));
+ a1 = b;
+ aa1 = [];
+ if nstatic > 0
+ aa1 = a1(:,1:nstatic);
+ end
+ dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
+ npred) a1(:,nstatic+npred+1:end)]\fu;
+ else
+ dr.ghu = [];
+ end
+
+ % static variables
+ if nstatic > 0
+ temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
+ j5 = find(kstate(n4:nd,4));
+ temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
+ temp = b10\(temp-b11*dr.ghx);
+ dr.ghx = [temp; dr.ghx];
+ temp = [];
+ end
+
+ if options_.loglinear == 1
+ k = find(dr.kstate(:,2) <= M_.maximum_endo_lag+1);
+ klag = dr.kstate(k,[1 2]);
+ k1 = dr.order_var;
+
+ dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
+ repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
+ dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
+ end
+
+ %% Necessary when using Sims' routines for QZ
+ if options_.use_qzdiv
+ gx = real(gx);
+ hx = real(hx);
+ dr.ghx = real(dr.ghx);
+ dr.ghu = real(dr.ghu);
+ end
+
+ %exogenous deterministic variables
+ if M_.exo_det_nbr > 0
+ f1 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+2:end,order_var))));
+ f0 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var))));
+ fudet = sparse(jacobia_(:,nz+M_.exo_nbr+1:end));
+ M1 = inv(f0+[zeros(M_.endo_nbr,nstatic) f1*gx zeros(M_.endo_nbr,nyf-nboth)]);
+ M2 = M1*f1;
+ dr.ghud = cell(M_.exo_det_length,1);
+ dr.ghud{1} = -M1*fudet;
+ for i = 2:M_.exo_det_length
+ dr.ghud{i} = -M2*dr.ghud{i-1}(end-nyf+1:end,:);
+ end
+ end
+ disp('end0');
+ if options_.order == 1
+ return
+ end
+
+ % Second order
+ %tempex = oo_.exo_simul ;
+
+ %hessian = real(hessext('ff1_',[z; oo_.exo_steady_state]))' ;
+ kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
+ if M_.maximum_endo_lag > 0
+ kk = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); kk];
+ end
+ kk = kk';
+ kk = find(kk(:));
+ nk = size(kk,1) + M_.exo_nbr + M_.exo_det_nbr;
+ k1 = M_.lead_lag_incidence(:,order_var);
+ k1 = k1';
+ k1 = k1(:);
+ k1 = k1(kk);
+ k2 = find(k1);
+ kk1(k1(k2)) = k2;
+ kk1 = [kk1 length(k1)+1:length(k1)+M_.exo_nbr+M_.exo_det_nbr];
+ kk = reshape([1:nk^2],nk,nk);
+ kk1 = kk(kk1,kk1);
+ %[junk,junk,hessian] = feval([M_.fname '_dynamic'],z, oo_.exo_steady_state);
+ hessian(:,kk1(:)) = hessian;
+
+ %oo_.exo_simul = tempex ;
+ %clear tempex
+
+ n1 = 0;
+ n2 = np;
+ zx = zeros(np,np);
+ zu=zeros(np,M_.exo_nbr);
+ for i=2:M_.maximum_endo_lag+1
+ k1 = sum(kstate(:,2) == i);
+ zx(n1+1:n1+k1,n2-k1+1:n2)=eye(k1);
+ n1 = n1+k1;
+ n2 = n2-k1;
+ end
+ kk = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
+ k0 = [1:M_.endo_nbr];
+ gx1 = dr.ghx;
+ hu = dr.ghu(nstatic+[1:npred],:);
+ zx = [zx; gx1];
+ zu = [zu; dr.ghu];
+ for i=1:M_.maximum_endo_lead
+ k1 = find(kk(i+1,k0) > 0);
+ zu = [zu; gx1(k1,1:npred)*hu];
+ gx1 = gx1(k1,:)*hx;
+ zx = [zx; gx1];
+ kk = kk(:,k0);
+ k0 = k1;
+ end
+ zx=[zx; zeros(M_.exo_nbr,np);zeros(M_.exo_det_nbr,np)];
+ zu=[zu; eye(M_.exo_nbr);zeros(M_.exo_det_nbr,M_.exo_nbr)];
+ [nrzx,nczx] = size(zx);
+
+ rhs = -sparse_hessian_times_B_kronecker_C(hessian,zx);
+
+ %lhs
+ n = M_.endo_nbr+sum(kstate(:,2) > M_.maximum_endo_lag+1 & kstate(:,2) < M_.maximum_endo_lag+M_.maximum_endo_lead+1);
+ A = zeros(n,n);
+ B = zeros(n,n);
+ A(1:M_.endo_nbr,1:M_.endo_nbr) = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
+ % variables with the highest lead
+ k1 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead+1);
+ if M_.maximum_endo_lead > 1
+ k2 = find(kstate(:,2) == M_.maximum_endo_lag+M_.maximum_endo_lead);
+ [junk,junk,k3] = intersect(kstate(k1,1),kstate(k2,1));
+ else
+ k2 = [1:M_.endo_nbr];
+ k3 = kstate(k1,1);
+ end
+ % Jacobian with respect to the variables with the highest lead
+ B(1:M_.endo_nbr,end-length(k2)+k3) = jacobia_(:,kstate(k1,3)+M_.endo_nbr);
+ offset = M_.endo_nbr;
+ k0 = [1:M_.endo_nbr];
+ gx1 = dr.ghx;
+ for i=1:M_.maximum_endo_lead-1
+ k1 = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
+ [k2,junk,k3] = find(kstate(k1,3));
+ A(1:M_.endo_nbr,offset+k2) = jacobia_(:,k3+M_.endo_nbr);
+ n1 = length(k1);
+ A(offset+[1:n1],nstatic+[1:npred]) = -gx1(kstate(k1,1),1:npred);
+ gx1 = gx1*hx;
+ A(offset+[1:n1],offset+[1:n1]) = eye(n1);
+ n0 = length(k0);
+ E = eye(n0);
+ if i == 1
+ [junk,junk,k4]=intersect(kstate(k1,1),[1:M_.endo_nbr]);
+ else
+ [junk,junk,k4]=intersect(kstate(k1,1),kstate(k0,1));
+ end
+ i1 = offset-n0+n1;
+ B(offset+[1:n1],offset-n0+[1:n0]) = -E(k4,:);
+ k0 = k1;
+ offset = offset + n1;
+ end
+ [junk,k1,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+M_.maximum_endo_lead+1,order_var));
+ A(1:M_.endo_nbr,nstatic+1:nstatic+npred)=...
+ A(1:M_.endo_nbr,nstatic+[1:npred])+jacobia_(:,k2)*gx1(k1,1:npred);
+ C = hx;
+ D = [rhs; zeros(n-M_.endo_nbr,size(rhs,2))];
+
+
+ dr.ghxx = gensylv(2,A,B,C,D);
+
+ %ghxu
+ %rhs
+ hu = dr.ghu(nstatic+1:nstatic+npred,:);
+ %kk = reshape([1:np*np],np,np);
+ %kk = kk(1:npred,1:npred);
+ %rhs = -hessian*kron(zx,zu)-f1*dr.ghxx(end-nyf+1:end,kk(:))*kron(hx(1:npred,:),hu(1:npred,:));
+
+ rhs = sparse_hessian_times_B_kronecker_C(hessian,zx,zu);
+
+ nyf1 = sum(kstate(:,2) == M_.maximum_endo_lag+2);
+ hu1 = [hu;zeros(np-npred,M_.exo_nbr)];
+ %B1 = [B(1:M_.endo_nbr,:);zeros(size(A,1)-M_.endo_nbr,size(B,2))];
+ [nrhx,nchx] = size(hx);
+ [nrhu1,nchu1] = size(hu1);
+
+ B1 = B*A_times_B_kronecker_C(dr.ghxx,hx,hu1);
+ rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
+
+
+ %lhs
+ dr.ghxu = A\rhs;
+
+ %ghuu
+ %rhs
+ kk = reshape([1:np*np],np,np);
+ kk = kk(1:npred,1:npred);
+
+ rhs = sparse_hessian_times_B_kronecker_C(hessian,zu);
+
+
+ B1 = A_times_B_kronecker_C(B*dr.ghxx,hu1);
+ rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
+
+ %lhs
+ dr.ghuu = A\rhs;
+
+ dr.ghxx = dr.ghxx(1:M_.endo_nbr,:);
+ dr.ghxu = dr.ghxu(1:M_.endo_nbr,:);
+ dr.ghuu = dr.ghuu(1:M_.endo_nbr,:);
+
+
+ % dr.ghs2
+ % derivatives of F with respect to forward variables
+ % reordering predetermined variables in diminishing lag order
+ O1 = zeros(M_.endo_nbr,nstatic);
+ O2 = zeros(M_.endo_nbr,M_.endo_nbr-nstatic-npred);
+ LHS = jacobia_(:,M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var));
+ RHS = zeros(M_.endo_nbr,M_.exo_nbr^2);
+ kk = find(kstate(:,2) == M_.maximum_endo_lag+2);
+ gu = dr.ghu;
+ guu = dr.ghuu;
+ Gu = [dr.ghu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr)];
+ Guu = [dr.ghuu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr*M_.exo_nbr)];
+ E = eye(M_.endo_nbr);
+ M_.lead_lag_incidenceordered = flipud(cumsum(flipud(M_.lead_lag_incidence(M_.maximum_endo_lag+1:end,order_var)),1));
+ if M_.maximum_endo_lag > 0
+ M_.lead_lag_incidenceordered = [cumsum(M_.lead_lag_incidence(1:M_.maximum_endo_lag,order_var),1); M_.lead_lag_incidenceordered];
+ end
+ M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered';
+ M_.lead_lag_incidenceordered = M_.lead_lag_incidenceordered(:);
+ k1 = find(M_.lead_lag_incidenceordered);
+ M_.lead_lag_incidenceordered(k1) = [1:length(k1)]';
+ M_.lead_lag_incidenceordered =reshape(M_.lead_lag_incidenceordered,M_.endo_nbr,M_.maximum_endo_lag+M_.maximum_endo_lead+1)';
+ kh = reshape([1:nk^2],nk,nk);
+ kp = sum(kstate(:,2) <= M_.maximum_endo_lag+1);
+ E1 = [eye(npred); zeros(kp-npred,npred)];
+ H = E1;
+ hxx = dr.ghxx(nstatic+[1:npred],:);
+ for i=1:M_.maximum_endo_lead
+ for j=i:M_.maximum_endo_lead
+ [junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+j+1,order_var));
+ [junk,k3a,k3] = ...
+ find(M_.lead_lag_incidenceordered(M_.maximum_endo_lag+j+1,:));
+ nk3a = length(k3a);
+ B1 = sparse_hessian_times_B_kronecker_C(hessian(:,kh(k3,k3)),gu(k3a,:));
+ RHS = RHS + jacobia_(:,k2)*guu(k2a,:)+B1;
+ end
+ % LHS
+ [junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+i+1,order_var));
+ LHS = LHS + jacobia_(:,k2)*(E(k2a,:)+[O1(k2a,:) dr.ghx(k2a,:)*H O2(k2a,:)]);
+
+ if i == M_.maximum_endo_lead
+ break
+ end
+
+ kk = find(kstate(:,2) == M_.maximum_endo_lag+i+1);
+ gu = dr.ghx*Gu;
+ [nrGu,ncGu] = size(Gu);
+ G1 = A_times_B_kronecker_C(dr.ghxx,Gu);
+ G2 = A_times_B_kronecker_C(hxx,Gu);
+ guu = dr.ghx*Guu+G1;
+ Gu = hx*Gu;
+ Guu = hx*Guu;
+ Guu(end-npred+1:end,:) = Guu(end-npred+1:end,:) + G2;
+ H = E1 + hx*H;
+ end
+ RHS = RHS*M_.Sigma_e(:);
+ dr.fuu = RHS;
+ %RHS = -RHS-dr.fbias;
+ RHS = -RHS;
+ dr.ghs2 = LHS\RHS;
+
+ % deterministic exogenous variables
+ if M_.exo_det_nbr > 0
+ hud = dr.ghud{1}(nstatic+1:nstatic+npred,:);
+ zud=[zeros(np,M_.exo_det_nbr);dr.ghud{1};gx(:,1:npred)*hud;zeros(M_.exo_nbr,M_.exo_det_nbr);eye(M_.exo_det_nbr)];
+ R1 = hessian*kron(zx,zud);
+ dr.ghxud = cell(M_.exo_det_length,1);
+ kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
+ kp = nstatic+[1:npred];
+ dr.ghxud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{1}(kp,:)));
+ Eud = eye(M_.exo_det_nbr);
+ for i = 2:M_.exo_det_length
+ hudi = dr.ghud{i}(kp,:);
+ zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zx,zudi);
+ dr.ghxud{i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hx,Eud)+dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{i}(kp,:)))-M1*R2;
+ end
+ R1 = hessian*kron(zu,zud);
+ dr.ghudud = cell(M_.exo_det_length,1);
+ kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
+
+ dr.ghuud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghu(kp,:),dr.ghud{1}(kp,:)));
+ Eud = eye(M_.exo_det_nbr);
+ for i = 2:M_.exo_det_length
+ hudi = dr.ghud{i}(kp,:);
+ zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zu,zudi);
+ dr.ghuud{i} = -M2*dr.ghxud{i-1}(kf,:)*kron(hu,Eud)-M1*R2;
+ end
+ R1 = hessian*kron(zud,zud);
+ dr.ghudud = cell(M_.exo_det_length,M_.exo_det_length);
+ dr.ghudud{1,1} = -M1*R1-M2*dr.ghxx(kf,:)*kron(hud,hud);
+ for i = 2:M_.exo_det_length
+ hudi = dr.ghud{i}(nstatic+1:nstatic+npred,:);
+ zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi+dr.ghud{i-1}(kf,:);zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zudi,zudi);
+ dr.ghudud{i,i} = -M2*(dr.ghudud{i-1,i-1}(kf,:)+...
+ 2*dr.ghxud{i-1}(kf,:)*kron(hudi,Eud) ...
+ +dr.ghxx(kf,:)*kron(hudi,hudi))-M1*R2;
+ R2 = hessian*kron(zud,zudi);
+ dr.ghudud{1,i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hud,Eud)+...
+ dr.ghxx(kf,:)*kron(hud,hudi))...
+ -M1*R2;
+ for j=2:i-1
+ hudj = dr.ghud{j}(kp,:);
+ zudj=[zeros(np,M_.exo_det_nbr);dr.ghud{j};gx(:,1:npred)*hudj;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zudj,zudi);
+ dr.ghudud{j,i} = -M2*(dr.ghudud{j-1,i-1}(kf,:)+dr.ghxud{j-1}(kf,:)* ...
+ kron(hudi,Eud)+dr.ghxud{i-1}(kf,:)* ...
+ kron(hudj,Eud)+dr.ghxx(kf,:)*kron(hudj,hudi))-M1*R2;
+ end
+
+ end
+ disp('end');
+ end
\ No newline at end of file
diff --git a/matlab/dr1_sparse.m b/matlab/dr1_sparse.m
new file mode 100644
index 000000000..064d307ce
--- /dev/null
+++ b/matlab/dr1_sparse.m
@@ -0,0 +1,234 @@
+function [dr,info,M_,options_,oo_] = dr1_sparse(dr,task,M_,options_,oo_)
+% Computes the reduced form solution of a rational expectation model (first or second order
+% approximation of the stochastic model around the deterministic steady state).
+%
+% INPUTS
+% dr [matlab structure] Decision rules for stochastic simulations.
+% task [integer] if task = 0 then dr1 computes decision rules.
+% if task = 1 then dr1 computes eigenvalues.
+% M_ [matlab structure] Definition of the model.
+% options_ [matlab structure] Global options.
+% oo_ [matlab structure] Results
+%
+% OUTPUTS
+% dr [matlab structure] Decision rules for stochastic simulations.
+% info [integer] info=1: the model doesn't define current variables uniquely
+% info=2: problem in mjdgges.dll info(2) contains error code.
+% info=3: BK order condition not satisfied info(2) contains "distance"
+% absence of stable trajectory.
+% info=4: BK order condition not satisfied info(2) contains "distance"
+% indeterminacy.
+% info=5: BK rank condition not satisfied.
+% M_ [matlab structure]
+% options_ [matlab structure]
+% oo_ [matlab structure]
+%
+% ALGORITHM
+% ...
+%
+% SPECIAL REQUIREMENTS
+% none.
+%
+
+% Copyright (C) 1996-2008 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare 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.
+%
+% Dynare 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 Dynare. If not, see .
+
+ info = 0;
+
+ options_ = set_default_option(options_,'loglinear',0);
+ options_ = set_default_option(options_,'noprint',0);
+ options_ = set_default_option(options_,'olr',0);
+ options_ = set_default_option(options_,'olr_beta',1);
+ options_ = set_default_option(options_,'qz_criterium',1.000001);
+
+ xlen = M_.maximum_endo_lead + M_.maximum_endo_lag + 1;
+ klen = M_.maximum_endo_lag + M_.maximum_endo_lead + 1;
+ iyv = M_.lead_lag_incidence';
+ iyv = iyv(:);
+ iyr0 = find(iyv) ;
+ it_ = M_.maximum_lag + 1 ;
+
+ if M_.exo_nbr == 0
+ oo_.exo_steady_state = [] ;
+ end
+
+ % expanding system for Optimal Linear Regulator
+ if options_.ramsey_policy
+ if isfield(M_,'orig_model')
+ orig_model = M_.orig_model;
+ M_.endo_nbr = orig_model.endo_nbr;
+ M_.endo_names = orig_model.endo_names;
+ M_.lead_lag_incidence = orig_model.lead_lag_incidence;
+ M_.maximum_lead = orig_model.maximum_lead;
+ M_.maximum_endo_lead = orig_model.maximum_endo_lead;
+ M_.maximum_lag = orig_model.maximum_lag;
+ M_.maximum_endo_lag = orig_model.maximum_endo_lag;
+ end
+ old_solve_algo = options_.solve_algo;
+ % options_.solve_algo = 1;
+ oo_.steady_state = dynare_solve('ramsey_static',oo_.steady_state,0,M_,options_,oo_,it_);
+ options_.solve_algo = old_solve_algo;
+ [junk,junk,multbar] = ramsey_static(oo_.steady_state,M_,options_,oo_,it_);
+ [jacobia_,M_] = ramsey_dynamic(oo_.steady_state,multbar,M_,options_,oo_,it_);
+ klen = M_.maximum_lag + M_.maximum_lead + 1;
+ dr.ys = [oo_.steady_state;zeros(M_.exo_nbr,1);multbar];
+% $$$ if options_.ramsey_policy == 2
+% $$$ mask = M_.orig_model.lead_lag_incidence ~= 0;
+% $$$ incidence_submatrix = M_.lead_lag_incidence(M_.orig_model.maximum_lead+(1:size(mask,1)),1:M_.orig_model.endo_nbr);
+% $$$ k = nonzeros((incidence_submatrix.*mask)');
+% $$$ nl = nnz(M_.lead_lag_incidence);
+% $$$ k = [k; nl+(1:M_.exo_nbr)'];
+% $$$ kk = reshape(1:(nl+M_.exo_nbr)^2,nl+M_.exo_nbr,nl+M_.exo_nbr);
+% $$$ kk2 = kk(k,k);
+% $$$
+% $$$ k1 = find(M_.orig_model.lead_lag_incidence');
+% $$$ y = repmat(oo_.dr.ys(1:M_.orig_model.endo_nbr),1,M_.orig_model.maximum_lag+M_.orig_model.maximum_lead+1);
+% $$$ [f,fJ,fh] = feval([M_.fname '_dynamic'],y(k1),zeros(1,M_.exo_nbr), M_.params, it_);
+% $$$
+% $$$ % looking for dynamic variables that are both in the original model
+% $$$ % and in the optimal policy model
+% $$$ k1 = k1+nnz(M_.lead_lag_incidence(1:M_.orig_model.maximum_lead,1:M_.orig_model.endo_nbr));
+% $$$ hessian = sparse([],[],[],size(jacobia_,1),(nl+M_.exo_nbr)^2,nnz(fh));
+% $$$ hessian(M_.orig_model.endo_nbr+(1:size(fh,1)),kk2) = fh;
+% $$$ options_.order = 2;
+% $$$ elseif options_.ramsey_policy == 3
+% $$$ maxlag1 = M_.orig_model.maximum_lag;
+% $$$ maxlead1 = M_.orig_model.maximum_lead;
+% $$$ endo_nbr1 = M_.orig_model.endo_nbr;
+% $$$ lead_lag_incidence1 = M_.orig_model.lead_lag_incidence;
+% $$$ y = repmat(oo_.dr.ys(1:M_.orig_model.endo_nbr),1,M_.orig_model.maximum_lag+M_.orig_model.maximum_lead+1);
+% $$$ k1 = find(M_.orig_model.lead_lag_incidence');
+% $$$ [f,fj,fh] = feval([M_.fname '_dynamic'],y(k1),zeros(1,M_.exo_nbr), M_.params, it_);
+% $$$ nrj = size(fj,1);
+% $$$
+% $$$ iy = M_.lead_lag_incidence;
+% $$$ kstate = oo_.dr.kstate;
+% $$$ inv_order_var = oo_.dr.inv_order_var;
+% $$$ offset = 0;
+% $$$ i3 = zeros(0,1);
+% $$$ i4 = find(kstate(:,2) <= M_.maximum_lag+1);
+% $$$ kstate1 = kstate(i4,:);
+% $$$ kk2 = zeros(0,1);
+% $$$ % lagged variables
+% $$$ for i=2:M_.maximum_lag + 1
+% $$$ i1 = find(kstate(:,2) == i);
+% $$$ k1 = kstate(i1,:);
+% $$$ i2 = find(oo_.dr.order_var(k1(:,1)) <= M_.orig_model.endo_nbr);
+% $$$ i3 = [i3; i2+offset];
+% $$$ offset = offset + size(k1,1);
+% $$$ i4 = find(kstate1(:,2) == i);
+% $$$ kk2 = [kk2; i4];
+% $$$ end
+% $$$ i2 = find(oo_.dr.order_var(k1(:,1)) > M_.orig_model.endo_nbr);
+% $$$ j2 = k1(i2,1);
+% $$$ nj2 = length(j2);
+% $$$ k2 = offset+(1:nj2)';
+% $$$ offset = offset + length(i2);
+% $$$ i3 = [i3; ...
+% $$$ find(M_.orig_model.lead_lag_incidence(M_.orig_model.maximum_lag+1:end,:)')+offset];
+% $$$ i3 = [i3; (1:M_.exo_nbr)'+length(i3)];
+% $$$ ni3 = length(i3);
+% $$$ nrfj = size(fj,1);
+% $$$ jacobia_ = zeros(nrfj+length(j2),ni3);
+% $$$ jacobia_(1:nrfj,i3) = fj;
+% $$$ jacobia_(nrfj+(1:nj2),1:size(oo_.dr.ghx,2)) = oo_.dr.ghx(j2,:);
+% $$$ jacobia_(nrfj+(1:nj2),k2) = eye(nj2);
+% $$$ kk1 = reshape(1:ni3^2,ni3,ni3);
+% $$$ hessian = zeros(nrfj+length(j2),ni3^2);
+% $$$ hessian(1:nrfj,kk1(i3,i3)) = fh;
+% $$$
+% $$$ k = find(any(M_.lead_lag_incidence(1:M_.maximum_lag, ...
+% $$$ M_.orig_model.endo_nbr+1:end)));
+% $$$ if maxlead1 > maxlag1
+% $$$ M_.lead_lag_incidence = [ [zeros(maxlead1-maxlag1,endo_nbr1); ...
+% $$$ lead_lag_incidence1] ...
+% $$$ [M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
+% $$$ k); zeros(maxlead1,length(k))]];
+% $$$ elseif maxlag1 > maxlead1
+% $$$ M_.lead_lag_incidence = [ [lead_lag_incidence1; zeros(maxlag1- ...
+% $$$ maxlead1,endo_nbr1);] ...
+% $$$ [M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
+% $$$ k); zeros(maxlead1,length(k))]];
+% $$$ else % maxlag1 == maxlead1
+% $$$ M_.lead_lag_incidence = [ lead_lag_incidence1
+% $$$ [M_.lead_lag_incidence(M_.maximum_lag+(1:maxlead1), ...
+% $$$ k); zeros(maxlead1,length(k))]];
+% $$$ end
+% $$$ M_.maximum_lag = max(maxlead1,maxlag1);
+% $$$ M_.maximum_endo_lag = M_.maximum_lag;
+% $$$ M_.maximum_lead = M_.maximum_lag;
+% $$$ M_.maximum_endo_lead = M_.maximum_lag;
+% $$$
+% $$$ M_.endo_names = strvcat(M_.orig_model.endo_names, M_.endo_names(endo_nbr1+k,:));
+% $$$ M_.endo_nbr = endo_nbr1+length(k);
+% $$$ end
+ else
+ klen = M_.maximum_lag + M_.maximum_lead + 1;
+ iyv = M_.lead_lag_incidence';
+ iyv = iyv(:);
+ iyr0 = find(iyv) ;
+ it_ = M_.maximum_lag + 1 ;
+
+ if M_.exo_nbr == 0
+ oo_.exo_steady_state = [] ;
+ end
+
+ it_ = M_.maximum_lag + 1;
+ z = repmat(dr.ys,1,klen);
+ z = z(iyr0) ;
+ if options_.model_mode==0
+ if options_.order == 1
+ [junk,jacobia_] = feval([M_.fname '_dynamic'],z,[oo_.exo_simul ...
+ oo_.exo_det_simul], M_.params, it_);
+ hessian = 0;
+ elseif options_.order == 2
+ [junk,jacobia_,hessian] = feval([M_.fname '_dynamic'],z,...
+ [oo_.exo_simul ...
+ oo_.exo_det_simul], M_.params, it_);
+ end
+ dr=set_state_space(dr,M_);
+ if options_.debug
+ save([M_.fname '_debug.mat'],'jacobia_')
+ end
+ [dr,info,M_,options_,oo_] = dr11_sparse(dr,task,M_,options_,oo_, jacobia_, hessian);
+ dr.nyf = nnz(dr.kstate(:,2)>M_.maximum_lag+1);
+ elseif options_.model_mode==1
+ if options_.order == 1
+ [junk,jacobia_] = feval([M_.fname '_dynamic'],ones(M_.maximum_lag+M_.maximum_lead+1,1)*dr.ys',[oo_.exo_simul ...
+ oo_.exo_det_simul], it_);
+ dr.eigval = [];
+ dr.nyf = 0;
+ dr.rank = 0;
+ for i=1:length(M_.block_structure.block)
+ %disp(['block ' num2str(i)]);
+ M_.block_structure.block(i).dr.Null=0;
+ M_.block_structure.block(i).dr=set_state_space(M_.block_structure.block(i).dr,M_.block_structure.block(i));
+ jcb_=jacobia_(M_.block_structure.block(i).equation,repmat(M_.block_structure.block(i).variable,1,M_.block_structure.block(i).maximum_endo_lag+M_.block_structure.block(i).maximum_endo_lead+1)+kron([M_.maximum_endo_lag-M_.block_structure.block(i).maximum_endo_lag:M_.maximum_endo_lag+M_.block_structure.block(i).maximum_endo_lead],M_.endo_nbr*ones(1,M_.block_structure.block(i).endo_nbr)));
+ jcb_=jcb_(:,find(any(jcb_,1)));
+ hss_=0; %hessian(M_.block_structure.block(i).equation,M_.block_structure.block(i).variable);
+ dra = M_.block_structure.block(i).dr;
+ M_.block_structure.block(i).exo_nbr=M_.exo_nbr;
+ [dra ,info,M_.block_structure.block(i),options_,oo_] = dr11_sparse(dra ,task,M_.block_structure.block(i),options_,oo_, jcb_, hss_);
+ M_.block_structure.block(i).dr = dra;
+ dr.eigval = [dr.eigval; dra.eigval];
+ dr.nyf = dr.nyf + nnz(dra.kstate(:,2)>M_.block_structure.block(i).maximum_endo_lag+1);
+ dr.rank = dr.rank + dra.rank;
+ end;
+ end
+ end
+ end
+
diff --git a/matlab/model_info.m b/matlab/model_info.m
new file mode 100644
index 000000000..897e5b31b
--- /dev/null
+++ b/matlab/model_info.m
@@ -0,0 +1,87 @@
+function model_info;
+ global M_;
+ fprintf(' Informations about %s\n',M_.fname);
+ fprintf(strcat(' ===================',char(ones(1,length(M_.fname))*'='),'\n\n'));
+ if(isfield(M_,'block_structure'))
+ nb_blocks=length(M_.block_structure.block);
+ fprintf('The model has %d equations and is decomposed in %d blocks as follow:\n',M_.endo_nbr,nb_blocks);
+ fprintf('==============================================================================================================\n');
+ fprintf('| %10s | %10s | %30s | %14s | %30s |\n','Block n°','Size','Block Type','Equation','Dependent variable');
+ fprintf('|============|============|================================|================|================================|\n');
+ for i=1:nb_blocks
+ size_block=length(M_.block_structure.block(i).equation);
+ if(i>1)
+ fprintf('|------------|------------|--------------------------------|----------------|--------------------------------|\n');
+ end;
+ for j=1:size_block
+ if(j==1)
+ fprintf('| %3d (%4d) | %10d | %30s | %14d | %30s |\n',i,M_.block_structure.block(i).num,size_block,Sym_type(M_.block_structure.block(i).Simulation_Type),M_.block_structure.block(i).equation(j),M_.endo_names(M_.block_structure.block(i).variable(j),:));
+ else
+ fprintf('| %10s | %10s | %30s | %14d | %30s |\n','','','',M_.block_structure.block(i).equation(j),M_.endo_names(M_.block_structure.block(i).variable(j),:));
+ end;
+ end;
+ end;
+ fprintf('==============================================================================================================\n');
+ fprintf('\n');
+ for k=1:M_.maximum_endo_lag+M_.maximum_endo_lead+1
+ if(k==M_.maximum_endo_lag+1)
+ fprintf('%-30s %s','the variable','is used in equations contemporously');
+ elseif(k0)
+ IM=sortrows(M_.block_structure.incidence(k).sparse_IM,2);
+ else
+ IM=[];
+ end;
+ size_IM=size(IM,1);
+ last=0;
+ for i=1:size_IM
+ if(last~=IM(i,2))
+ fprintf('\n%-30s',M_.endo_names(IM(i,2),:));
+ end;
+ fprintf(' %5d',IM(i,1));
+ last=IM(i,2);
+ end;
+ fprintf('\n\n');
+ end;
+ else
+ fprintf('There is no block decomposition of the model.\nUse ''sparse'' or ''sparse_dll'' model''s option.\n');
+ end;
+
+
+function ret=Sym_type(type);
+ EVALUATE_FOREWARD=0;
+ EVALUATE_BACKWARD=1;
+ SOLVE_FOREWARD_SIMPLE=2;
+ SOLVE_BACKWARD_SIMPLE=3;
+ SOLVE_TWO_BOUNDARIES_SIMPLE=4;
+ SOLVE_FOREWARD_COMPLETE=5;
+ SOLVE_BACKWARD_COMPLETE=6;
+ SOLVE_TWO_BOUNDARIES_COMPLETE=7;
+ EVALUATE_FOREWARD_R=8;
+ EVALUATE_BACKWARD_R=9;
+ switch (type)
+ case {EVALUATE_FOREWARD,EVALUATE_FOREWARD_R},
+ ret='EVALUATE FOREWARD ';
+ case {EVALUATE_BACKWARD,EVALUATE_BACKWARD_R},
+ ret='EVALUATE BACKWARD ';
+ case SOLVE_FOREWARD_SIMPLE,
+ ret='SOLVE FOREWARD SIMPLE ';
+ case SOLVE_BACKWARD_SIMPLE,
+ ret='SOLVE BACKWARD SIMPLE ';
+ case SOLVE_TWO_BOUNDARIES_SIMPLE,
+ ret='SOLVE TWO BOUNDARIES SIMPLE ';
+ case SOLVE_FOREWARD_COMPLETE,
+ ret='SOLVE FOREWARD COMPLETE ';
+ case SOLVE_BACKWARD_COMPLETE,
+ ret='SOLVE BACKWARD COMPLETE ';
+ case SOLVE_TWO_BOUNDARIES_COMPLETE,
+ ret='SOLVE TWO BOUNDARIES COMPLETE';
+ end;
+
+
+
+
diff --git a/matlab/resol.m b/matlab/resol.m
index e453bbcc7..937d6e0d2 100644
--- a/matlab/resol.m
+++ b/matlab/resol.m
@@ -98,8 +98,11 @@ if check1
end
dr.fbias = zeros(M_.endo_nbr,1);
-[dr,info,M_,options_,oo_] = dr1(dr,check_flag,M_,options_,oo_);
-
+if(options_.model_mode==1)
+ [dr,info,M_,options_,oo_] = dr1_sparse(dr,check_flag,M_,options_,oo_);
+else
+ [dr,info,M_,options_,oo_] = dr1(dr,check_flag,M_,options_,oo_);
+end
if info(1)
return
end
diff --git a/matlab/transition_matrix.m b/matlab/transition_matrix.m
index 2a2895ffc..3894ae9e8 100644
--- a/matlab/transition_matrix.m
+++ b/matlab/transition_matrix.m
@@ -1,10 +1,11 @@
-function [A,B] = transition_matrix(dr)
+function [A,B] = transition_matrix(dr, varargin)
-% function [A,B] = transition_matrix(dr)
+% function [A,B] = transition_matrix(dr, varargin)
% Makes transition matrices out of ghx and ghu
%
% INPUTS
% dr: structure of decision rules for stochastic simulations
+% varargin: {1}: M_
%
% OUTPUTS
% A: matrix of effects of predetermined variables in linear solution (ghx)
@@ -30,7 +31,12 @@ function [A,B] = transition_matrix(dr)
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see .
- global M_
+ if(length(varargin)<=0)
+ global M_
+ else
+ M_=varargin{1};
+ end;
+
exo_nbr = M_.exo_nbr;
ykmin_ = M_.maximum_endo_lag;
@@ -43,7 +49,9 @@ function [A,B] = transition_matrix(dr)
i0 = find(k0(:,2) == ykmin_+1);
A(i0,:) = dr.ghx(ikx,:);
B = zeros(nx,exo_nbr);
- B(i0,:) = dr.ghu(ikx,:);
+ if(isfield(dr,'ghu'))
+ B(i0,:) = dr.ghu(ikx,:);
+ end;
for i=ykmin_:-1:2
i1 = find(k0(:,2) == i);
n1 = size(i1,1);
@@ -54,3 +62,4 @@ function [A,B] = transition_matrix(dr)
A(i1,i0(j))=eye(n1);
i0 = i1;
end
+
\ No newline at end of file