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<title>Description of generalized_cholesky</title>
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<div><a href="../index.html">Home</a> &gt; <a href="index.html">.</a> &gt; generalized_cholesky.m</div>
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<h1>generalized_cholesky
</h1>
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="box"><strong>proc gmchol(A);</strong></div>
<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="box"><strong>function AA = generalized_cholesky(A); </strong></div>
<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="fragment"><pre class="comment"> proc gmchol(A);
/* calculates the Gill-Murray generalized choleski decomposition */
/* input matrix A must be non-singular and symmetric */
/* Author: Jeff Gill. Part of the Hessian Project. */
local i,j,k,n,sum,R,theta_j,norm_A,phi_j,delta,xi_j,gamm,E,beta_j;</pre></div>
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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../matlabicon.gif)">
<li><a href="rows.html" class="code" title="function nr=rows(x)">rows</a> </li></ul>
This function is called by:
<ul style="list-style-image:url(../matlabicon.gif)">
<li><a href="dynare_estimation.html" class="code" title="function dynare_estimation(var_list_)">dynare_estimation</a> </li></ul>
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<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="fragment"><pre>0001 <span class="comment">% proc gmchol(A);</span>
0002 <span class="comment">% /* calculates the Gill-Murray generalized choleski decomposition */</span>
0003 <span class="comment">% /* input matrix A must be non-singular and symmetric */</span>
0004 <span class="comment">% /* Author: Jeff Gill. Part of the Hessian Project. */</span>
0005 <span class="comment">% local i,j,k,n,sum,R,theta_j,norm_A,phi_j,delta,xi_j,gamm,E,beta_j;</span>
0006
0007 <a name="_sub0" href="#_subfunctions" class="code">function AA = generalized_cholesky(A);</a>
0008
0009 n = <a href="rows.html" class="code" title="function nr=rows(x)">rows</a>(A);
0010 R = eye(n);
0011 E = zeros(n,n);
0012 norm_A = max(transpose(sum(abs(A))));
0013 gamm = max(abs(diag(A)));
0014 delta = max([eps*norm_A;eps]);
0015
0016 <span class="keyword">for</span> j = 1:n;
0017 theta_j = 0;
0018 <span class="keyword">for</span> i=1:n;
0019 somme = 0;
0020 <span class="keyword">for</span> k=1:i-1;
0021 somme = somme + R(k,i)*R(k,j);
0022 <span class="keyword">end</span>;
0023 R(i,j) = (A(i,j) - somme)/R(i,i);
0024 <span class="keyword">if</span> (A(i,j) -somme) &gt; theta_j;
0025 theta_j = A(i,j) - somme;
0026 <span class="keyword">end</span>;
0027 <span class="keyword">if</span> i &gt; j;
0028 R(i,j) = 0;
0029 <span class="keyword">end</span>;
0030 <span class="keyword">end</span>;
0031 somme = 0;
0032 <span class="keyword">for</span> k=1:j-1;
0033 somme = somme + R(k,j)^2;
0034 <span class="keyword">end</span>;
0035 phi_j = A(j,j) - somme;
0036 <span class="keyword">if</span> j+1 &lt;= n;
0037 xi_j = max(abs(A((j+1):n,j)));
0038 <span class="keyword">else</span>;
0039 xi_j = abs(A(n,j));
0040 <span class="keyword">end</span>;
0041 beta_j = sqrt(max([gamm ; (xi_j/n) ; eps]));
0042 <span class="keyword">if</span> all(delta &gt;= [abs(phi_j);((theta_j^2)/(beta_j^2))]);
0043 E(j,j) = delta - phi_j;
0044 <span class="keyword">elseif</span> all(abs(phi_j) &gt;= [((delta^2)/(beta_j^2));delta]);
0045 E(j,j) = abs(phi_j) - phi_j;
0046 <span class="keyword">elseif</span> all(((theta_j^2)/(beta_j^2)) &gt;= [delta;abs(phi_j)]);
0047 E(j,j) = ((theta_j^2)/(beta_j^2)) - phi_j;
0048 <span class="keyword">end</span>;
0049 R(j,j) = sqrt(A(j,j) - somme + E(j,j));
0050 <span class="keyword">end</span>;
0051 AA = transpose(R)*R;</pre></div>
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