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function [dr,info] = k_order_pert(dr,M,options)
% Compute decision rules using the k-order DLL from Dynare++
% Copyright (C) 2009-2013 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 <http://www.gnu.org/licenses/>.
info = 0;
M.var_order_endo_names = M.endo_names(dr.order_var,:);
order = options.order;
endo_nbr = M.endo_nbr;
exo_nbr = M.exo_nbr;
nspred = M.nspred;
if order>1 && options.loglinear
error('The loglinear-option currently only works at order 1')
end
if M.maximum_endo_lead == 0 && order>1
error(['2nd and 3rd order approximation not implemented for purely ' ...
'backward models'])
end
switch(order)
case 1
[err, g_1] = k_order_perturbation(dr,M,options);
if err
info(1)=9;
return;
end
dr.g_1 = g_1;
case 2
[err, g_0, g_1, g_2] = k_order_perturbation(dr,M,options);
if err
info(1)=9;
return;
end
dr.g_0 = g_0;
dr.g_1 = g_1;
dr.g_2 = g_2;
case 3
if options.pruning
[err, g_0, g_1, g_2, g_3, derivs] = k_order_perturbation(dr, ...
M,options);
if err
info(1)=9;
return;
end
else
[err, g_0, g_1, g_2, g_3] = k_order_perturbation(dr, ...
M,options);
if err
info(1)=9;
return;
end
end
dr.g_0 = g_0;
dr.g_1 = g_1;
dr.g_2 = g_2;
dr.g_3 = g_3;
otherwise
error('order > 3 isn''t implemented')
end
% Now fill in dr.ghx, dr.ghu...
if options.pruning && order == 3
dr.ghx = derivs.gy;
dr.ghu = derivs.gu;
dr.ghxx = unfold2(derivs.gyy,nspred);
dr.ghxu = derivs.gyu;
dr.ghuu = unfold2(derivs.guu,exo_nbr);
dr.ghs2 = derivs.gss;
dr.ghxxx = unfold3(derivs.gyyy,nspred);
dr.ghxxu = unfold21(derivs.gyyu,nspred,exo_nbr);
dr.ghxuu = unfold12(derivs.gyuu,nspred,exo_nbr);
dr.ghuuu = unfold3(derivs.guuu,exo_nbr);
dr.ghxss = derivs.gyss;
dr.ghuss = derivs.guss;
else
nspred = M.nspred;
dr.ghx = dr.g_1(:,1:nspred);
dr.ghu = dr.g_1(:,nspred+1: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
if order > 1
dr.ghs2 = 2*g_0;
s0 = 0;
s1 = 0;
ghxx=zeros(endo_nbr, nspred^2);
ghxu=zeros(endo_nbr, nspred*exo_nbr);
ghuu=zeros(endo_nbr, exo_nbr^2);
for i=1:size(g_2,2)
if s0 < nspred && s1 < nspred
ghxx(:,s0*nspred+s1+1) = 2*g_2(:,i);
if s1 > s0
ghxx(:,s1*nspred+s0+1) = 2*g_2(:,i);
end
elseif s0 < nspred && s1 < nspred+exo_nbr
ghxu(:,(s0*exo_nbr+s1-nspred+1)) = 2*g_2(:,i);
elseif s0 < nspred+exo_nbr && s1 < nspred+exo_nbr
ghuu(:,(s0-nspred)*exo_nbr+s1-nspred +1) = 2*g_2(:,i);
if s1 > s0
ghuu(:,(s1-nspred)*exo_nbr+s0-nspred+1) = 2*g_2(:,i);
end
else
error('dr1:k_order_perturbation:g_2','Unaccounted columns in g_2');
end
s1 = s1+1;
if s1 == nspred+exo_nbr
s0 = s0+1;
s1 = s0;
end
end % for loop
dr.ghxx = ghxx;
dr.ghxu = ghxu;
dr.ghuu = ghuu;
end
end
function y = unfold2(x,n)
y=zeros(size(x,1),n*n);
m = 1;
for i=1:n
for j=i:n
y(:,(i-1)*n+j)=x(:,m);
if j ~= i
y(:,(j-1)*n+i)=x(:,m);
end
m = m+1;
end
end
function y = unfold3(x,n)
y = zeros(size(x,1),n*n*n);
m = 1;
for i=1:n
for j=i:n
for k=j:n
xx = x(:,m);
y(:,(i-1)*n*n+(j-1)*n+k) = xx;
y(:,(i-1)*n*n+(k-1)*n+j) = xx;
y(:,(j-1)*n*n+(k-1)*n+i) = xx;
y(:,(j-1)*n*n+(i-1)*n+k) = xx;
y(:,(k-1)*n*n+(i-1)*n+j) = xx;
y(:,(k-1)*n*n+(j-1)*n+i) = xx;
m = m + 1;
end
end
end
function y = unfold21(x,n1,n2)
y = zeros(size(x,1),n1*n1*n2);
m = 1;
for i=1:n1
for j=i:n1
for k=1:n2
xx = x(:,m);
y(:,(i-1)*n1*n2+(j-1)*n2+k) = xx;
if j ~= i
y(:,(j-1)*n1*n2+(i-1)*n2+k) = xx;
end
m = m + 1;
end
end
end
function y = unfold12(x,n1,n2)
y = zeros(size(x,1),n1*n2*n2);
m = 1;
for i=1:n1
for j=1:n2
for k=j:n2
xx = x(:,m);
y(:,(i-1)*n2*n2+(j-1)*n2+k) = xx;
if k ~= j
y(:,(i-1)*n2*n2+(k-1)*n2+j) = xx;
end
m = m + 1;
end
end
end
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