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