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Commit 1b3aa73c authored by MichelJuillard's avatar MichelJuillard
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adapted dyn_first_order_solver.m for models without lagged variables 

and singular coefficient matrix for current variables
parent 1732db84
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matlab/dyn_first_order_solver.m
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......@@ -64,8 +64,11 @@ function [dr,info] = dyn_first_order_solver(jacobia,DynareModel,dr,DynareOptions
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
persistent reorder_jacobian_columns innovations_idx index_s index_m index_c index_p row_indx index_0m index_0p k1 k2 j3 j4 state_var
persistent ndynamic nstatic nfwrd npred nboth nd nyf n
persistent reorder_jacobian_columns innovations_idx index_s index_m index_c
persistent index_p row_indx index_0m index_0p k1 k2 state_var
persistent ndynamic nstatic nfwrd npred nboth nd nyf n_current index_d
persistent index_e index_d1 index_d2 index_e1 index_e2 row_indx_de_1
persistent row_indx_de_2 cols_b
if ~nargin
......@@ -76,8 +79,11 @@ if ~nargin
return
end
if isempty(reorder_jacobian_columns)
exo_nbr = DynareModel.exo_nbr;
if isempty(reorder_jacobian_columns)
maximum_lag = DynareModel.maximum_endo_lag;
kstate = dr.kstate;
nfwrd = dr.nfwrd;
nboth = dr.nboth;
......@@ -85,7 +91,7 @@ if isempty(reorder_jacobian_columns)
nstatic = dr.nstatic;
ndynamic = npred+nfwrd+nboth;
nyf = nfwrd + nboth;
n = ndynamic+nstatic;
n = DynareModel.endo_nbr;
k1 = 1:(npred+nboth);
k2 = 1:(nfwrd+nboth);
......@@ -95,44 +101,60 @@ if isempty(reorder_jacobian_columns)
lead_lag_incidence = DynareModel.lead_lag_incidence;
nz = nnz(lead_lag_incidence);
%lead variables actually present in the model
j4 = nstatic+npred+1:nstatic+npred+nboth+nfwrd; % Index on the forward and both variables
j3 = nonzeros(lead_lag_incidence(2,j4)) - nstatic - 2 * npred - nboth; % Index on the non-zeros forward and both variables
j4 = find(lead_lag_incidence(2,j4));
no_lead_id = find(lead_lag_incidence(3,:)==0);
no_lag_id = find(lead_lag_incidence(1,:)==0);
static_id = intersect(no_lead_id,no_lag_id);
lag_id = setdiff(no_lead_id,static_id);
lead_id = setdiff(no_lag_id,static_id);
both_id = intersect(setdiff(1:n,no_lead_id),setdiff(1:n,no_lag_id));
lead_idx = lead_lag_incidence(3,lead_id);
lag_idx = lead_lag_incidence(1,lag_id);
both_lagged_idx = lead_lag_incidence(1,both_id);
both_leaded_idx = lead_lag_incidence(3,both_id);
innovations_idx = (size(jacobia,2)-DynareModel.exo_nbr+1):size(jacobia,2);
state_var = [lag_idx, both_lagged_idx];
indexi_0 = 0;
if DynareModel.maximum_endo_lag > 0 && (npred > 0 || nboth > 0)
indexi_0 = min(lead_lag_incidence(2,:));
lead_id = find(lead_lag_incidence(maximum_lag+2,:));
lead_idx = lead_lag_incidence(maximum_lag+2,lead_id);
if maximum_lag
lag_id = find(lead_lag_incidence(1,:));
lag_idx = lead_lag_incidence(1,lag_id);
static_id = find((lead_lag_incidence(1,:) == 0) & ...
(lead_lag_incidence(3,:) == 0));
else
lag_id = [];
lag_idx = [];
static_id = find(lead_lag_incidence(2,:)==0);
end
index_c = lead_lag_incidence(2,:); % Index of all endogenous variables present at time=t
index_s = lead_lag_incidence(2,1:nstatic); % Index of all static endogenous variables present at time=t
index_0m = (nstatic+1:nstatic+npred)+indexi_0-1;
index_0p = (nstatic+npred+1:n)+indexi_0-1;
index_m = 1:(npred+nboth);
index_p = lead_lag_incidence(3,find(lead_lag_incidence(3,:)));
row_indx = nstatic+1:n;
both_id = intersect(lead_id,lag_id);
if maximum_lag
no_both_lag_id = setdiff(lag_id,both_id);
else
no_both_lag_id = [];
end
innovations_idx = nz+(1:exo_nbr);
state_var = [lag_id, both_id];
reorder_jacobian_columns = [lag_idx, both_lagged_idx, npred+nboth+[static_id lag_id both_id lead_id], both_leaded_idx, lead_idx, innovations_idx ];
index_c = nonzeros(lead_lag_incidence(maximum_lag+1,:)); % Index of all endogenous variables present at time=t
n_current = length(index_c);
end
index_s = npred+nboth+(1:nstatic); % Index of all static
% endogenous variables
% present at time=t
indexi_0 = npred+nboth;
info = 0;
npred0 = nnz(lead_lag_incidence(maximum_lag+1,no_both_lag_id));
index_0m = indexi_0+nstatic+(1:npred0);
nfwrd0 = nnz(lead_lag_incidence(2,lead_id));
index_0p = indexi_0+nstatic+npred0+(1:nfwrd0);
index_m = 1:(npred+nboth);
index_p = npred+nboth+n_current+(1:(nfwrd+nboth));
row_indx_de_1 = 1:ndynamic;
row_indx_de_2 = ndynamic+1:nboth;
row_indx = nstatic+row_indx_de_1;
index_d = [index_0m index_p];
llx = lead_lag_incidence(:,order_var);
index_d1 = [find(llx(maximum_lag+1,nstatic+(1:npred))), npred+nboth+(1:nyf) ];
index_d2 = npred+1:nboth;
index_e = [index_m index_0p];
index_e1 = [1:(npred+nboth), npred+nboth+find(llx(maximum_lag+1,nstatic+npred+(1: ...
nyf)))];
index_e2 = npred+nboth+nfwrd+1:nboth;
[junk,cols_b] = find(lead_lag_incidence(maximum_lag+1, order_var));
reorder_jacobian_columns = [nonzeros(lead_lag_incidence(:,order_var)'); ...
nz+(1:exo_nbr)'];
end
dr.ghx = [];
dr.ghu = [];
......@@ -149,32 +171,49 @@ else
end
A = aa(:,index_m); % Jacobain matrix for lagged endogeneous variables
B = aa(:,index_c); % Jacobian matrix for contemporaneous endogeneous variables
B(:,cols_b) = aa(:,index_c); % Jacobian matrix for contemporaneous endogeneous variables
C = aa(:,index_p); % Jacobain matrix for led endogeneous variables
info = 0;
info1 = 1;
if task ~= 1 && (DynareOptions.dr_cycle_reduction || DynareOptions.dr_logarithmic_reduction)
if n_current < DynareModel.endo_nbr
if DynareOptions.dr_cycle_reduction
error(['The cycle reduction algorithme can''t be used when the ' ...
'coefficient matrix for current variables is singular'])
elseif DynareOptions.dr_logarithmic_reduction
error(['The logarithmic reduction algorithme can''t be used when the ' ...
'coefficient matrix for current variables is singular'])
end
end
A1 = [aa(row_indx,index_m ) zeros(ndynamic,nfwrd)];
B1 = [aa(row_indx,index_0m) aa(row_indx,index_0p) ];
C1 = [zeros(ndynamic,npred) aa(row_indx,index_p)];
if DynareOptions.dr_cycle_reduction == 1
[ghx, info] = cycle_reduction(A1, B1, C1, DynareOptions.dr_cycle_reduction_tol);
[ghx, info1] = cycle_reduction(A1, B1, C1, DynareOptions.dr_cycle_reduction_tol);
else
[ghx, info] = logarithmic_reduction(C1, B1, A1, DynareOptions.dr_logarithmic_reduction_tol, DynareOptions.dr_logarithmic_reduction_maxiter);
[ghx, info1] = logarithmic_reduction(C1, B1, A1, DynareOptions.dr_logarithmic_reduction_tol, DynareOptions.dr_logarithmic_reduction_maxiter);
end
ghx = ghx(:,index_m);
hx = ghx(1:npred+nboth,:);
gx = ghx(1+npred:end,:);
end
if (task ~= 1 && ((DynareOptions.dr_cycle_reduction == 1 && info ==1) || DynareOptions.dr_cycle_reduction == 0)) || task == 1
D = [[aa(row_indx,index_0m) zeros(ndynamic,nboth) aa(row_indx,index_p)] ; [zeros(nboth, npred) eye(nboth) zeros(nboth, nboth + nfwrd)]];
if info1 == 1
D = zeros(ndynamic+nboth);
E = zeros(ndynamic+nboth);
D(row_indx_de_1,index_d1) = aa(row_indx,index_d);
D(row_indx_de_2,index_d2) = eye(nboth);
E(row_indx_de_1,index_e1) = -aa(row_indx,index_e);
E(row_indx_de_2,index_e2) = eye(nboth);
E = [-aa(row_indx,[index_m index_0p]) ; [zeros(nboth,nboth+npred) eye(nboth,nboth+nfwrd) ] ];
[err, ss, tt, w, sdim, dr.eigval, info1] = mjdgges(E,D,DynareOptions.qz_criterium);
[err, ss, tt, w, sdim, dr.eigval, info2] = mjdgges(E,D,DynareOptions.qz_criterium);
mexErrCheck('mjdgges', err);
if info1
if info1 == -30
if info2
if info2 == -30
% one eigenvalue is close to 0/0
info(1) = 7;
else
......@@ -211,65 +250,64 @@ if (task ~= 1 && ((DynareOptions.dr_cycle_reduction == 1 && info ==1) || DynareO
end
%First order approximation
if task ~= 1
indx_stable_root = 1: (nd - nyf); %=> index of stable roots
indx_explosive_root = npred + nboth + 1:nd; %=> index of explosive roots
% derivatives with respect to dynamic state variables
% forward variables
Z = w';
Z11t = Z(indx_stable_root, indx_stable_root)';
Z21 = Z(indx_explosive_root, indx_stable_root);
Z22 = Z(indx_explosive_root, indx_explosive_root);
if ~isfloat(Z21) && (condest(Z21) > 1e9)
info(1) = 5;
info(2) = condest(Z21);
return;
else
gx = - Z22 \ Z21;
end
% predetermined variables
hx = Z11t * inv(tt(indx_stable_root, indx_stable_root)) * ss(indx_stable_root, indx_stable_root) * inv(Z11t);
ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
end;
end
indx_stable_root = 1: (nd - nyf); %=> index of stable roots
indx_explosive_root = npred + nboth + 1:nd; %=> index of explosive roots
% derivatives with respect to dynamic state variables
% forward variables
Z = w';
Z11t = Z(indx_stable_root, indx_stable_root)';
Z21 = Z(indx_explosive_root, indx_stable_root);
Z22 = Z(indx_explosive_root, indx_explosive_root);
if ~isfloat(Z21) && (condest(Z21) > 1e9)
info(1) = 5;
info(2) = condest(Z21);
return;
else
gx = - Z22 \ Z21;
end
% predetermined variables
hx = Z11t * inv(tt(indx_stable_root, indx_stable_root)) * ss(indx_stable_root, indx_stable_root) * inv(Z11t);
ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
if task~= 1
end
if nstatic > 0
B_static = B(:,1:nstatic); % submatrix containing the derivatives w.r. to static variables
else
B_static = [];
end;
%static variables, backward variable, mixed variables and forward variables
B_pred = B(:,nstatic+1:nstatic+npred+nboth);
B_fyd = B(:,nstatic+npred+nboth+1:end);
dr.gx = gx;
% static variables
if nstatic > 0
temp = - C(1:nstatic,j3)*gx(j4,:)*hx;
b = aa(:,index_c);
b10 = b(1:nstatic, 1:nstatic);
b11 = b(1:nstatic, nstatic+1:n);
temp(:,index_m) = temp(:,index_m)-A(1:nstatic,:);
temp = b10\(temp-b11*ghx);
ghx = [temp; ghx];
temp = [];
end
if nstatic > 0
B_static = B(:,1:nstatic); % submatrix containing the derivatives w.r. to static variables
else
B_static = [];
end;
%static variables, backward variable, mixed variables and forward variables
B_pred = B(:,nstatic+1:nstatic+npred+nboth);
B_fyd = B(:,nstatic+npred+nboth+1:end);
A_ = real([B_static C(:,j3)*gx+B_pred B_fyd]); % The state_variable of the block are located at [B_pred B_both]
% static variables
if nstatic > 0
temp = - C(1:nstatic,:)*gx*hx;
b(:,cols_b) = aa(:,index_c);
b10 = b(1:nstatic, 1:nstatic);
b11 = b(1:nstatic, nstatic+1:end);
temp(:,index_m) = temp(:,index_m)-A(1:nstatic,:);
temp = b10\(temp-b11*ghx);
ghx = [temp; ghx];
temp = [];
end
if DynareModel.exo_nbr
if nstatic > 0
fu = Q' * jacobia(:,innovations_idx);
else
fu = jacobia(:,innovations_idx);
end;
A_ = real([B_static C*gx+B_pred B_fyd]); % The state_variable of the block are located at [B_pred B_both]
ghu = - A_ \ fu;
if exo_nbr
if nstatic > 0
fu = Q' * jacobia(:,innovations_idx);
else
ghu = [];
fu = jacobia(:,innovations_idx);
end;
end
ghu = - A_ \ fu;
else
ghu = [];
end;
dr.ghx = ghx;
......
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