108 lines
3.5 KiB
Matlab
108 lines
3.5 KiB
Matlab
function [b,rts,ia,nexact,nnumeric,lgroots,aimcode] = ...
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SPAmalg(h,neq,nlag,nlead,condn,uprbnd)
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% [b,rts,ia,nexact,nnumeric,lgroots,aimcode] = ...
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% SPAmalg(h,neq,nlag,nlead,condn,uprbnd)
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%
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% Solve a linear perfect foresight model using the matlab eig
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% function to find the invariant subspace associated with the big
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% roots. This procedure will fail if the companion matrix is
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% defective and does not have a linearly independent set of
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% eigenvectors associated with the big roots.
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%
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% Input arguments:
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%
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% h Structural coefficient matrix (neq,neq*(nlag+1+nlead)).
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% neq Number of equations.
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% nlag Number of lags.
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% nlead Number of leads.
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% condn Zero tolerance used as a condition number test
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% by numeric_shift and reduced_form.
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% uprbnd Inclusive upper bound for the modulus of roots
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% allowed in the reduced form.
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%
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% Output arguments:
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%
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% b Reduced form coefficient matrix (neq,neq*nlag).
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% rts Roots returned by eig.
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% ia Dimension of companion matrix (number of non-trivial
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% elements in rts).
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% nexact Number of exact shiftrights.
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% nnumeric Number of numeric shiftrights.
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% lgroots Number of roots greater in modulus than uprbnd.
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% aimcode Return code: see function aimerr.
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% Original author: Gary Anderson
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% Original file downloaded from:
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% http://www.federalreserve.gov/Pubs/oss/oss4/code.html
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% Adapted for Dynare by Dynare Team, in order to deal
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% with infinite or nan values.
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%
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% This code is in the public domain and may be used freely.
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% However the authors would appreciate acknowledgement of the source by
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% citation of any of the following papers:
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%
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% Anderson, G. and Moore, G.
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% "A Linear Algebraic Procedure for Solving Linear Perfect Foresight
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% Models."
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% Economics Letters, 17, 1985.
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%
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% Anderson, G.
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% "Solving Linear Rational Expectations Models: A Horse Race"
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% Computational Economics, 2008, vol. 31, issue 2, pages 95-113
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%
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% Anderson, G.
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% "A Reliable and Computationally Efficient Algorithm for Imposing the
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% Saddle Point Property in Dynamic Models"
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% Journal of Economic Dynamics and Control, 2010, vol. 34, issue 3,
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% pages 472-489
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b=[];rts=[];ia=[];nexact=[];nnumeric=[];lgroots=[];aimcode=[];
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if(nlag<1 || nlead<1)
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error('Aim_eig: model must have at least one lag and one lead');
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end
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% Initialization.
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nexact=0;nnumeric=0;lgroots=0;iq=0;aimcode=0;b=0;qrows=neq*nlead;qcols=neq*(nlag+nlead);
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bcols=neq*nlag;q=zeros(qrows,qcols);rts=zeros(qcols,1);
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[h,q,iq,nexact]=SPExact_shift(h,q,iq,qrows,qcols,neq);
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if (iq>qrows)
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aimcode = 61;
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return
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end
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[h,q,iq,nnumeric]=SPNumeric_shift(h,q,iq,qrows,qcols,neq,condn);
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if (iq>qrows)
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aimcode = 62;
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return
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end
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[a,ia,js] = SPBuild_a(h,qcols,neq);
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if (ia ~= 0)
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if any(any(isnan(a))) || any(any(isinf(a)))
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disp('A is NAN or INF')
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aimcode=63;
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return
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end
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[w,rts,lgroots,flag_trouble]=SPEigensystem(a,uprbnd,min(length(js),qrows-iq+1));
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if flag_trouble==1
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disp('Problem in SPEIG');
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aimcode=64;
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return
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end
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q = SPCopy_w(q,w,js,iq,qrows);
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end
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test=nexact+nnumeric+lgroots;
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if (test > qrows)
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aimcode = 3;
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elseif (test < qrows)
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aimcode = 4;
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end
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if(aimcode==0)
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[nonsing,b]=SPReduced_form(q,qrows,qcols,bcols,neq,condn);
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if ( nonsing && aimcode==0)
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aimcode = 1;
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elseif (~nonsing && aimcode==0)
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aimcode = 5;
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elseif (~nonsing && aimcode==3)
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aimcode = 35;
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elseif (~nonsing && aimcode==4)
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aimcode = 45;
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end
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end |