File size: 3,161 Bytes
ed7d493 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | function [ OMEGA ] = create_OMEGA( n_x,varargin )
%The function creates sparse matrices OMEGA1,..,OMEGA9, that are used for
%the high-order multivariate chain rules described in Levintal, Oren,
%"Fifth Order Perturbation Solution to DSGE Models", 2014.
%
% � Copyright, Oren Levintal, June 13, 2016.
if length(varargin)==1
order=varargin{1}; % do only specified order
else
order=0; % do orders 3,4,5
end
if order==3 || order==0
ind=[1:n_x^3];
M=reshape(ind,1,n_x,n_x,n_x);
Ix=speye(n_x^3);
OMEGA.OMEGA1=Ix(:,ipermute(M,[1,3,4,2]))+Ix(:,ipermute(M,[1,2,4,3]))+Ix(:,ipermute(M,[1,2,3,4]));
end
if order==4 || order==0
ind=[1:n_x^4];
M=reshape(ind,1,n_x,n_x,n_x,n_x);
Ix=speye(n_x^4);
OMEGA.OMEGA2=Ix(:,ipermute(M,[1,4,5,3,2]))+Ix(:,ipermute(M,[1,3,5,4,2]))+Ix(:,ipermute(M,[1,2,5,4,3]))...
+Ix(:,ipermute(M,[1,3,4,5,2]))+Ix(:,ipermute(M,[1,2,4,5,3]))+Ix(:,ipermute(M,[1,2,3,5,4]));
OMEGA.OMEGA3=Ix(:,ipermute(M,[1,3,4,5,2]))+Ix(:,ipermute(M,[1,2,4,5,3]))+Ix(:,ipermute(M,[1,2,3,5,4]))+Ix(:,ipermute(M,[1,2,3,4,5]));
OMEGA.OMEGA4=Ix(:,ipermute(M,[1,3,4,2,5]))+Ix(:,ipermute(M,[1,2,4,3,5]))+Ix(:,ipermute(M,[1,2,3,4,5]));
end
if order==5 || order==0
ind=[1:n_x^5];
M=reshape(ind,1,n_x,n_x,n_x,n_x,n_x);
Ix=speye(n_x^5);
OMEGA.OMEGA5=Ix(:,ipermute(M,[1,5,6,4,3,2]))+Ix(:,ipermute(M,[1,4,6,5,3,2]))+Ix(:,ipermute(M,[1,3,6,5,4,2]))+Ix(:,ipermute(M,[1,2,6,5,4,3]))...
+Ix(:,ipermute(M,[1,4,5,6,3,2]))+Ix(:,ipermute(M,[1,3,5,6,4,2]))...
+Ix(:,ipermute(M,[1,2,5,6,4,3]))+Ix(:,ipermute(M,[1,3,4,6,5,2]))+Ix(:,ipermute(M,[1,2,4,6,5,3]))+Ix(:,ipermute(M,[1,2,3,6,5,4]));
OMEGA.OMEGA6=Ix(:,ipermute(M,[1,4,5,6,3,2]))+Ix(:,ipermute(M,[1,3,5,6,4,2]))+Ix(:,ipermute(M,[1,2,5,6,4,3]))+Ix(:,ipermute(M,[1,3,4,6,5,2]))...
+Ix(:,ipermute(M,[1,2,4,6,5,3]))+Ix(:,ipermute(M,[1,2,3,6,5,4]))+Ix(:,ipermute(M,[1,3,4,5,6,2]))...
+Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))+Ix(:,ipermute(M,[1,2,3,4,6,5]));
OMEGA.OMEGA7=Ix(:,ipermute(M,[1,4,5,3,6,2]))+Ix(:,ipermute(M,[1,3,5,4,6,2]))+Ix(:,ipermute(M,[1,2,5,4,6,3]))...
+Ix(:,ipermute(M,[1,3,4,5,6,2]))+Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))...
+Ix(:,ipermute(M,[1,4,5,2,6,3]))+Ix(:,ipermute(M,[1,3,5,2,6,4]))+Ix(:,ipermute(M,[1,2,5,3,6,4]))...
+Ix(:,ipermute(M,[1,3,4,2,6,5]))+Ix(:,ipermute(M,[1,2,4,3,6,5]))+Ix(:,ipermute(M,[1,2,3,4,6,5]))...
+Ix(:,ipermute(M,[1,3,4,2,5,6]))+Ix(:,ipermute(M,[1,2,4,3,5,6]))+Ix(:,ipermute(M,[1,2,3,4,5,6]));
OMEGA.OMEGA8=Ix(:,ipermute(M,[1,3,4,5,6,2]))+Ix(:,ipermute(M,[1,2,4,5,6,3]))+Ix(:,ipermute(M,[1,2,3,5,6,4]))+Ix(:,ipermute(M,[1,2,3,4,6,5]))+Ix(:,ipermute(M,[1,2,3,4,5,6]));
OMEGA.OMEGA9=Ix(:,ipermute(M,[1,3,4,5,2,6]))+Ix(:,ipermute(M,[1,2,4,5,3,6]))+Ix(:,ipermute(M,[1,2,3,5,4,6]))+Ix(:,ipermute(M,[1,2,3,4,5,6]))...
+Ix(:,ipermute(M,[1,3,4,6,2,5]))+Ix(:,ipermute(M,[1,2,4,6,3,5]))+Ix(:,ipermute(M,[1,2,3,6,4,5]))...
+Ix(:,ipermute(M,[1,2,5,6,3,4]))+Ix(:,ipermute(M,[1,3,5,6,2,4]))+Ix(:,ipermute(M,[1,4,5,6,2,3]));
end
end
|