65 lines
1.8 KiB
Matlab
65 lines
1.8 KiB
Matlab
function [a,ia,js] = SPBuild_a(h,qcols,neq)
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% [a,ia,js] = SPBuild_a(h,qcols,neq)
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%
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% Build the companion matrix, deleting inessential lags.
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% Solve for x_{t+nlead} in terms of x_{t+nlag},...,x_{t+nlead-1}.
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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.
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%
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% This code 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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left = 1:qcols;
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right = qcols+1:qcols+neq;
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%hs=SPSparse(h);
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hs=sparse(h);
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hs(:,left) = -hs(:,right)\hs(:,left);
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% Build the big transition matrix.
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a = zeros(qcols,qcols);
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if(qcols > neq)
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eyerows = 1:qcols-neq;
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eyecols = neq+1:qcols;
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a(eyerows,eyecols) = eye(qcols-neq);
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end
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hrows = qcols-neq+1:qcols;
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a(hrows,:) = hs(:,left);
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% Delete inessential lags and build index array js. js indexes the
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% columns in the big transition matrix that correspond to the
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% essential lags in the model. They are the columns of q that will
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% get the unstable left eigenvectors.
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js = 1:qcols;
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zerocols = sum(abs(a)) == 0;
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while( any(zerocols) )
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a(:,zerocols) = [];
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a(zerocols,:) = [];
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js(zerocols) = [];
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zerocols = sum(abs(a)) == 0;
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end
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ia = length(js);
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