99 lines
4.7 KiB
HTML
99 lines
4.7 KiB
HTML
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<title>Description of hessian</title>
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<meta name="keywords" content="hessian">
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<meta name="description" content="Copyright (C) 2001 Michel Juillard">
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > hessian.m</div>
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<!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td>
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<td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="../right.png"></a></td></tr></table>-->
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<h1>hessian
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</h1>
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>Copyright (C) 2001 Michel Juillard</strong></div>
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<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function hessian_mat = hessian(func,x,varargin) </strong></div>
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<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre class="comment"> Copyright (C) 2001 Michel Juillard
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% computes second order partial derivatives
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uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884</pre></div>
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<!-- crossreference -->
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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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This function calls:
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<ul style="list-style-image:url(../matlabicon.gif)">
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</ul>
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This function is called by:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="dr1.html" class="code" title="function [dr,info]=dr1(dr,task)">dr1</a> Copyright (C) 2001 Michel Juillard</li><li><a href="dynare_estimation.html" class="code" title="function dynare_estimation(var_list_)">dynare_estimation</a> </li><li><a href="mode_check.html" class="code" title="function mode_check(x,fval,hessian,gend,data,lb,ub)">mode_check</a> </li></ul>
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<!-- crossreference -->
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<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre>0001 <span class="comment">% Copyright (C) 2001 Michel Juillard</span>
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0002 <span class="comment">%% computes second order partial derivatives</span>
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0003 <span class="comment">% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884</span>
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0004
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0005 <a name="_sub0" href="#_subfunctions" class="code">function hessian_mat = hessian(func,x,varargin)</a>
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0006 <span class="keyword">global</span> options_
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0007 func = str2func(func);
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0008 n=size(x,1);
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0009 <span class="comment">%h1=max(abs(x),options_.gstep*ones(n,1))*eps^(1/3);</span>
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0010 h1=max(abs(x),sqrt(options_.gstep)*ones(n,1))*eps^(1/6);
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0011 h_1=h1;
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0012 xh1=x+h1;
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0013 h1=xh1-x;
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0014 xh1=x-h_1;
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0015 h_1=x-xh1;
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0016 xh1=x;
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0017 f0=feval(func,x,varargin{:});
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0018 f1=zeros(size(f0,1),n);
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0019 f_1=f1;
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0020 <span class="keyword">for</span> i=1:n
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0021 xh1(i)=x(i)+h1(i);
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0022 f1(:,i)=feval(func,xh1,varargin{:});
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0023 xh1(i)=x(i)-h_1(i);
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0024 f_1(:,i)=feval(func,xh1,varargin{:});
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0025 xh1(i)=x(i);
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0026 i=i+1;
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0027 <span class="keyword">end</span>
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0028 xh_1=xh1;
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0029 hessian_mat = zeros(size(f0,1),n*n);
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0030 <span class="keyword">for</span> i=1:n
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0031 <span class="keyword">if</span> i > 1
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0032 k=[i:n:n*(i-1)];
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0033 hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k);
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0034 <span class="keyword">end</span>
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0035 hessian_mat(:,(i-1)*n+i)=(f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i));
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0036 temp=f1+f_1-f0*ones(1,n);
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0037 <span class="keyword">for</span> j=i+1:n
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0038 xh1(i)=x(i)+h1(i);
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0039 xh1(j)=x(j)+h_1(j);
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0040 xh_1(i)=x(i)-h1(i);
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0041 xh_1(j)=x(j)-h_1(j);
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0042 hessian_mat(:,(i-1)*n+j)=-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j));
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0043 xh1(i)=x(i);
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0044 xh1(j)=x(j);
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0045 xh_1(i)=x(i);
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0046 xh_1(j)=x(j);
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0047 j=j+1;
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0048 <span class="keyword">end</span>
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0049 i=i+1;
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0050 <span class="keyword">end</span>
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0051 <span class="comment">% 11/25/03 SA Created from Hessian_sparse (removed sparse)</span></pre></div>
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<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>
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