189 lines
8.5 KiB
HTML
189 lines
8.5 KiB
HTML
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
|||
|
|
"http://www.w3.org/TR/REC-html40/loose.dtd">
|
|||
|
|
<html>
|
|||
|
|
<head>
|
|||
|
|
<title>Description of generalized_cholesky2</title>
|
|||
|
|
<meta name="keywords" content="generalized_cholesky2">
|
|||
|
|
<meta name="description" content="/*">
|
|||
|
|
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
|||
|
|
<meta name="generator" content="m2html © 2003 Guillaume Flandin">
|
|||
|
|
<meta name="robots" content="index, follow">
|
|||
|
|
<link type="text/css" rel="stylesheet" href="../m2html.css">
|
|||
|
|
</head>
|
|||
|
|
<body>
|
|||
|
|
<a name="_top"></a>
|
|||
|
|
<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > generalized_cholesky2.m</div>
|
|||
|
|
|
|||
|
|
<!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td>
|
|||
|
|
<td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="../right.png"></a></td></tr></table>-->
|
|||
|
|
|
|||
|
|
<h1>generalized_cholesky2
|
|||
|
|
</h1>
|
|||
|
|
|
|||
|
|
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
|
|||
|
|
<div class="box"><strong>/*</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_cholesky2(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"> /*
|
|||
|
|
** By Jeff Gill, April 2002.
|
|||
|
|
**
|
|||
|
|
** This procedure produces:
|
|||
|
|
**
|
|||
|
|
** y = chol(A+E), where E is a diagonal matrix with each element as small
|
|||
|
|
** as possible, and A and E are the same size. E diagonal values are
|
|||
|
|
** constrained by iteravely updated Gerschgorin bounds.
|
|||
|
|
**
|
|||
|
|
** REFERENCES:
|
|||
|
|
**
|
|||
|
|
** Jeff Gill and Gary King. 1998. "`Hessian not Invertable.' Help!"
|
|||
|
|
** manuscript in progress, Harvard University.
|
|||
|
|
**
|
|||
|
|
** Robert B. Schnabel and Elizabeth Eskow. 1990. "A New Modified Cholesky
|
|||
|
|
** Factorization," SIAM Journal of Scientific Statistical Computating,
|
|||
|
|
** 11, 6: 1136-58.
|
|||
|
|
**
|
|||
|
|
**
|
|||
|
|
**
|
|||
|
|
** Stphane Adjemian (2003): translation from Gauss to Matlab.
|
|||
|
|
*/</pre></div>
|
|||
|
|
|
|||
|
|
<!-- crossreference -->
|
|||
|
|
<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)">
|
|||
|
|
</ul>
|
|||
|
|
This function is called by:
|
|||
|
|
<ul style="list-style-image:url(../matlabicon.gif)">
|
|||
|
|
</ul>
|
|||
|
|
<!-- crossreference -->
|
|||
|
|
|
|||
|
|
|
|||
|
|
<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">% /*</span>
|
|||
|
|
0002 <span class="comment">% ** By Jeff Gill, April 2002.</span>
|
|||
|
|
0003 <span class="comment">% **</span>
|
|||
|
|
0004 <span class="comment">% ** This procedure produces:</span>
|
|||
|
|
0005 <span class="comment">% **</span>
|
|||
|
|
0006 <span class="comment">% ** y = chol(A+E), where E is a diagonal matrix with each element as small</span>
|
|||
|
|
0007 <span class="comment">% ** as possible, and A and E are the same size. E diagonal values are</span>
|
|||
|
|
0008 <span class="comment">% ** constrained by iteravely updated Gerschgorin bounds.</span>
|
|||
|
|
0009 <span class="comment">% **</span>
|
|||
|
|
0010 <span class="comment">% ** REFERENCES:</span>
|
|||
|
|
0011 <span class="comment">% **</span>
|
|||
|
|
0012 <span class="comment">% ** Jeff Gill and Gary King. 1998. "`Hessian not Invertable.' Help!"</span>
|
|||
|
|
0013 <span class="comment">% ** manuscript in progress, Harvard University.</span>
|
|||
|
|
0014 <span class="comment">% **</span>
|
|||
|
|
0015 <span class="comment">% ** Robert B. Schnabel and Elizabeth Eskow. 1990. "A New Modified Cholesky</span>
|
|||
|
|
0016 <span class="comment">% ** Factorization," SIAM Journal of Scientific Statistical Computating,</span>
|
|||
|
|
0017 <span class="comment">% ** 11, 6: 1136-58.</span>
|
|||
|
|
0018 <span class="comment">% **</span>
|
|||
|
|
0019 <span class="comment">% **</span>
|
|||
|
|
0020 <span class="comment">% **</span>
|
|||
|
|
0021 <span class="comment">% ** Stphane Adjemian (2003): translation from Gauss to Matlab.</span>
|
|||
|
|
0022 <span class="comment">% */</span>
|
|||
|
|
0023 <a name="_sub0" href="#_subfunctions" class="code">function AA = generalized_cholesky2(A)</a>
|
|||
|
|
0024
|
|||
|
|
0025 n = size(A,1);
|
|||
|
|
0026 L = zeros(n,n);
|
|||
|
|
0027 deltaprev = 0;
|
|||
|
|
0028 gamm = max(abs(diag(A)));
|
|||
|
|
0029 tau = eps^(1/3);
|
|||
|
|
0030
|
|||
|
|
0031 <span class="keyword">if</span> min(eig(A)) > 0;
|
|||
|
|
0032 tau = -1000000;
|
|||
|
|
0033 <span class="keyword">end</span>;
|
|||
|
|
0034
|
|||
|
|
0035 norm_A = max(sum(abs(A))');
|
|||
|
|
0036 gamm = max(abs(diag(A)));
|
|||
|
|
0037 delta = max([eps*norm_A;eps]);
|
|||
|
|
0038 Pprod = eye(n);
|
|||
|
|
0039
|
|||
|
|
0040 <span class="keyword">if</span> n > 2;
|
|||
|
|
0041 <span class="keyword">for</span> k = 1,n-2;
|
|||
|
|
0042 <span class="keyword">if</span> min((diag(A(k+1:n,k+1:n))' - A(k,k+1:n).^2/A(k,k))') < tau*gamm <span class="keyword">...</span>
|
|||
|
|
0043 & min(eig(A((k+1):n,(k+1):n))) < 0;
|
|||
|
|
0044 [tmp,dmax] = max(diag(A(k:n,k:n)));
|
|||
|
|
0045 <span class="keyword">if</span> A(k+dmax-1,k+dmax-1) > A(k,k);
|
|||
|
|
0046 P = eye(n);
|
|||
|
|
0047 Ptemp = P(k,:);
|
|||
|
|
0048 P(k,:) = P(k+dmax-1,:);
|
|||
|
|
0049 P(k+dmax-1,:) = Ptemp;
|
|||
|
|
0050 A = P*A*P;
|
|||
|
|
0051 L = P*L*P;
|
|||
|
|
0052 Pprod = P*Pprod;
|
|||
|
|
0053 <span class="keyword">end</span>;
|
|||
|
|
0054 g = zeros(n-(k-1),1);
|
|||
|
|
0055 <span class="keyword">for</span> i=k:n;
|
|||
|
|
0056 <span class="keyword">if</span> i == 1;
|
|||
|
|
0057 sum1 = 0;
|
|||
|
|
0058 <span class="keyword">else</span>;
|
|||
|
|
0059 sum1 = sum(abs(A(i,k:(i-1)))');
|
|||
|
|
0060 <span class="keyword">end</span>;
|
|||
|
|
0061 <span class="keyword">if</span> i == n;
|
|||
|
|
0062 sum2 = 0;
|
|||
|
|
0063 <span class="keyword">else</span>;
|
|||
|
|
0064 sum2 = sum(abs(A((i+1):n,i)));
|
|||
|
|
0065 <span class="keyword">end</span>;
|
|||
|
|
0066 g(i-k+1) = A(i,i) - sum1 - sum2;
|
|||
|
|
0067 <span class="keyword">end</span>;
|
|||
|
|
0068 [tmp,gmax] = max(g);
|
|||
|
|
0069 <span class="keyword">if</span> gmax ~= k;
|
|||
|
|
0070 P = eye(n);
|
|||
|
|
0071 Ptemp = P(k,:);
|
|||
|
|
0072 P(k,:) = P(k+dmax-1,:);
|
|||
|
|
0073 P(k+dmax-1,:) = Ptemp;
|
|||
|
|
0074 A = P*A*P;
|
|||
|
|
0075 L = P*L*P;
|
|||
|
|
0076 Pprod = P*Pprod;
|
|||
|
|
0077 <span class="keyword">end</span>;
|
|||
|
|
0078 normj = sum(abs(A(k+1:n,k)));
|
|||
|
|
0079 delta = max([0;deltaprev;-A(k,k)+normj;-A(k,k)+tau*gamm]);
|
|||
|
|
0080 <span class="keyword">if</span> delta > 0;
|
|||
|
|
0081 A(k,k) = A(k,k) + delta;
|
|||
|
|
0082 deltaprev = delta;
|
|||
|
|
0083 <span class="keyword">end</span>;
|
|||
|
|
0084 <span class="keyword">end</span>;
|
|||
|
|
0085 A(k,k) = sqrt(A(k,k));
|
|||
|
|
0086 L(k,k) = A(k,k);
|
|||
|
|
0087 <span class="keyword">for</span> i=k+1:n;
|
|||
|
|
0088 <span class="keyword">if</span> L(k,k) > eps;
|
|||
|
|
0089 A(i,k) = A(i,k)/L(k,k);
|
|||
|
|
0090 <span class="keyword">end</span>;
|
|||
|
|
0091 L(i,k) = A(i,k);
|
|||
|
|
0092 A(i,k+1:i) = A(i,k+1:i) - L(i,k)*L(k+1:i,k)';
|
|||
|
|
0093 <span class="keyword">if</span> A(i,i) < 0;
|
|||
|
|
0094 A(i,i) = 0;
|
|||
|
|
0095 <span class="keyword">end</span>;
|
|||
|
|
0096 <span class="keyword">end</span>;
|
|||
|
|
0097 <span class="keyword">end</span>;
|
|||
|
|
0098 <span class="keyword">end</span>;
|
|||
|
|
0099 A(n-1,n) = A(n,n-1);
|
|||
|
|
0100 eigvals = eig(A(n-1:n,n-1:n));
|
|||
|
|
0101 dlist = [ 0 ; deltaprev ;<span class="keyword">...</span>
|
|||
|
|
0102 -min(eigvals)+tau*max((inv(1-tau)*max(eigvals)-min(eigvals))|gamm) ];
|
|||
|
|
0103 <span class="keyword">if</span> dlist(1) > dlist(2);
|
|||
|
|
0104 delta = dlist(1);
|
|||
|
|
0105 <span class="keyword">else</span>;
|
|||
|
|
0106 delta = dlist(2);
|
|||
|
|
0107 <span class="keyword">end</span>;
|
|||
|
|
0108 <span class="keyword">if</span> delta < dlist(3);
|
|||
|
|
0109 delta = dlist(3);
|
|||
|
|
0110 <span class="keyword">end</span>;
|
|||
|
|
0111 <span class="keyword">if</span> delta > 0;
|
|||
|
|
0112 A(n-1,n-1) = A(n-1,n-1) + delta;
|
|||
|
|
0113 A(n,n) = A(n,n) + delta;
|
|||
|
|
0114 deltaprev = delta;
|
|||
|
|
0115 <span class="keyword">end</span>;
|
|||
|
|
0116 A(n-1,n-1) = sqrt(A(n-1,n-1));
|
|||
|
|
0117 L(n-1,n-1) = A(n-1,n-1);
|
|||
|
|
0118 A(n,n-1) = A(n,n-1)/L(n-1,n-1);
|
|||
|
|
0119 L(n,n-1) = A(n,n-1);
|
|||
|
|
0120 A(n,n) = sqrt(A(n,n) - L(n,(n-1))^2);
|
|||
|
|
0121 L(n,n) = A(n,n);
|
|||
|
|
0122 AA = Pprod'*L'*Pprod';</pre></div>
|
|||
|
|
<hr><address>Generated on Fri 16-Jun-2006 09:09:06 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address>
|
|||
|
|
</body>
|
|||
|
|
</html>
|