47 lines
7.3 KiB
HTML
47 lines
7.3 KiB
HTML
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<title>Description of hessian_sparse</title>
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<meta name="description" content="Copyright (C) 2001 Michel Juillard%% computes second order partial derivatives% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884function hessian_mat = hessian_sparse(func,x,varargin)global options_func = str2func(func);n=size(x,1);%h1=max(abs(x),options_.gstep*ones(n,1))*eps^(1/3);h1=max(abs(x),sqrt(options_.gstep)*ones(n,1))*eps^(1/6);h_1=h1;xh1=x+h1;h1=xh1-x;xh1=x-h_1;h_1=x-xh1;xh1=x;f0=feval(func,x,varargin{:});nf = size(f0,1);f1=zeros(nf,n);f_1=f1;for i=1:n xh1(i)=x(i)+h1(i); f1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i)-h_1(i); f_1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i); i=i+1;endxh_1=xh1;hessian_mat = spalloc(nf,n*n,3*nf*n);for i=1:n if i > 1 k=[i:n:n*(i-1)]; hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k); end hessian_mat(:,(i-1)*n+i)=sparse((f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i))); temp=f1+f_1-f0*ones(1,n); for j=i+1:n xh1(i)=x(i)+h1(i); xh1(j)=x(j)+h_1(j); xh_1(i)=x(i)-h1(i); xh_1(j)=x(j)-h_1(j); hessian_mat(:,(i-1)*n+j)=sparse(-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j))); xh1(i)=x(i); xh1(j)=x(j); xh_1(i)=x(i); xh_1(j)=x(j); j=j+1; end i=i+1;end% 10/03/02 MJ used the 7 points formula">
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > hessian_sparse.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_sparse
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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%% computes second order partial derivatives% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884function hessian_mat = hessian_sparse(func,x,varargin)global options_func = str2func(func);n=size(x,1);%h1=max(abs(x),options_.gstep*ones(n,1))*eps^(1/3);h1=max(abs(x),sqrt(options_.gstep)*ones(n,1))*eps^(1/6);h_1=h1;xh1=x+h1;h1=xh1-x;xh1=x-h_1;h_1=x-xh1;xh1=x;f0=feval(func,x,varargin{:});nf = size(f0,1);f1=zeros(nf,n);f_1=f1;for i=1:n xh1(i)=x(i)+h1(i); f1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i)-h_1(i); f_1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i); i=i+1;endxh_1=xh1;hessian_mat = spalloc(nf,n*n,3*nf*n);for i=1:n if i > 1 k=[i:n:n*(i-1)]; hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k); end hessian_mat(:,(i-1)*n+i)=sparse((f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i))); temp=f1+f_1-f0*ones(1,n); for j=i+1:n xh1(i)=x(i)+h1(i); xh1(j)=x(j)+h_1(j); xh_1(i)=x(i)-h1(i); xh_1(j)=x(j)-h_1(j); hessian_mat(:,(i-1)*n+j)=sparse(-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j))); xh1(i)=x(i); xh1(j)=x(j); xh_1(i)=x(i); xh_1(j)=x(j); j=j+1; end i=i+1;end% 10/03/02 MJ used the 7 points formula</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>This is a script file. </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%% computes second order partial derivatives% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884function hessian_mat = hessian_sparse(func,x,varargin)global options_func = str2func(func);n=size(x,1);%h1=max(abs(x),options_.gstep*ones(n,1))*eps^(1/3);h1=max(abs(x),sqrt(options_.gstep)*ones(n,1))*eps^(1/6);h_1=h1;xh1=x+h1;h1=xh1-x;xh1=x-h_1;h_1=x-xh1;xh1=x;f0=feval(func,x,varargin{:});nf = size(f0,1);f1=zeros(nf,n);f_1=f1;for i=1:n xh1(i)=x(i)+h1(i); f1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i)-h_1(i); f_1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i); i=i+1;endxh_1=xh1;hessian_mat = spalloc(nf,n*n,3*nf*n);for i=1:n if i > 1 k=[i:n:n*(i-1)]; hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k); end hessian_mat(:,(i-1)*n+i)=sparse((f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i))); temp=f1+f_1-f0*ones(1,n); for j=i+1:n xh1(i)=x(i)+h1(i); xh1(j)=x(j)+h_1(j); xh_1(i)=x(i)-h1(i); xh_1(j)=x(j)-h_1(j); hessian_mat(:,(i-1)*n+j)=sparse(-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j))); xh1(i)=x(i); xh1(j)=x(j); xh_1(i)=x(i); xh_1(j)=x(j); j=j+1; end i=i+1;end% 10/03/02 MJ used the 7 points formula</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>
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This function calls:
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This function is called by:
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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%% computes second order partial derivatives% uses Abramowitz and Stegun (1965) formulas 25.3.24 and 25.3.27 p. 884function hessian_mat = hessian_sparse(func,x,varargin)global options_func = str2func(func);n=size(x,1);%h1=max(abs(x),options_.gstep*ones(n,1))*eps^(1/3);h1=max(abs(x),sqrt(options_.gstep)*ones(n,1))*eps^(1/6);h_1=h1;xh1=x+h1;h1=xh1-x;xh1=x-h_1;h_1=x-xh1;xh1=x;f0=feval(func,x,varargin{:});nf = size(f0,1);f1=zeros(nf,n);f_1=f1;for i=1:n xh1(i)=x(i)+h1(i); f1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i)-h_1(i); f_1(:,i)=feval(func,xh1,varargin{:}); xh1(i)=x(i); i=i+1;endxh_1=xh1;hessian_mat = spalloc(nf,n*n,3*nf*n);for i=1:n if i > 1 k=[i:n:n*(i-1)]; hessian_mat(:,(i-1)*n+1:(i-1)*n+i-1)=hessian_mat(:,k); end hessian_mat(:,(i-1)*n+i)=sparse((f1(:,i)+f_1(:,i)-2*f0)./(h1(i)*h_1(i))); temp=f1+f_1-f0*ones(1,n); for j=i+1:n xh1(i)=x(i)+h1(i); xh1(j)=x(j)+h_1(j); xh_1(i)=x(i)-h1(i); xh_1(j)=x(j)-h_1(j); hessian_mat(:,(i-1)*n+j)=sparse(-(-feval(func,xh1,varargin{:})-feval(func,xh_1,varargin{:})+temp(:,i)+temp(:,j))./(2*h1(i)*h_1(j))); xh1(i)=x(i); xh1(j)=x(j); xh_1(i)=x(i); xh_1(j)=x(j); j=j+1; end i=i+1;end% 10/03/02 MJ used the 7 points formula</span></pre></div>
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