SPBuild_a

  [a,ia,js] = SPBuild_a(h,qcols,neq)

  Build the companion matrix, deleting inessential lags.
  Solve for x_{t+nlead} in terms of x_{t+nlag},...,x_{t+nlead-1}.

0001 %  [a,ia,js] = SPBuild_a(h,qcols,neq)
0002 %
0003 %  Build the companion matrix, deleting inessential lags.
0004 %  Solve for x_{t+nlead} in terms of x_{t+nlag},...,x_{t+nlead-1}.
0005 
0006 % Original author: Gary Anderson
0007 % Original file downloaded from:
0008 % http://www.federalreserve.gov/Pubs/oss/oss4/code.html
0009 % Adapted for Dynare by Dynare Team.
0010 %
0011 % This code in the public domain and may be used freely.
0012 % However the authors would appreciate acknowledgement of the source by
0013 % citation of any of the following papers:
0014 %
0015 % Anderson, G. and Moore, G.
0016 % "A Linear Algebraic Procedure for Solving Linear Perfect Foresight
0017 % Models."
0018 % Economics Letters, 17, 1985.
0019 %
0020 % Anderson, G.
0021 % "Solving Linear Rational Expectations Models: A Horse Race"
0022 % Computational Economics, 2008, vol. 31, issue 2, pages 95-113
0023 %
0024 % Anderson, G.
0025 % "A Reliable and Computationally Efficient Algorithm for Imposing the
0026 % Saddle Point Property in Dynamic Models"
0027 % Journal of Economic Dynamics and Control, 2010, vol. 34, issue 3,
0028 % pages 472-489
0029 
0030 function [a,ia,js] = SPBuild_a(h,qcols,neq)
0031 
0032 left  = 1:qcols;
0033 right = qcols+1:qcols+neq;
0034 %hs=SPSparse(h);
0035 hs=sparse(h);
0036 
0037 hs(:,left) = -hs(:,right)\hs(:,left);
0038 
0039 %  Build the big transition matrix.
0040 
0041 a = zeros(qcols,qcols);
0042 
0043 if(qcols > neq)
0044   eyerows = 1:qcols-neq;
0045   eyecols = neq+1:qcols;
0046   a(eyerows,eyecols) = eye(qcols-neq);
0047 end
0048 hrows      = qcols-neq+1:qcols;
0049 a(hrows,:) = hs(:,left);
0050 
0051 %  Delete inessential lags and build index array js.  js indexes the
0052 %  columns in the big transition matrix that correspond to the
0053 %  essential lags in the model.  They are the columns of q that will
0054 %  get the unstable left eigenvectors.
0055 
0056 js       = 1:qcols;
0057 zerocols = sum(abs(a)) == 0;
0058 while( any(zerocols) )
0059   a(:,zerocols) = [];
0060   a(zerocols,:) = [];
0061   js(zerocols)  = [];
0062   zerocols = sum(abs(a)) == 0;
0063 end
0064 ia = length(js);