257 lines
14 KiB
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257 lines
14 KiB
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<title>Description of csminit</title>
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<meta name="description" content="[fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,...">
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > csminit.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>csminit
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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>[fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,...</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 [fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,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"> [fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,...
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P1,P2,P3,P4,P5,P6,P7,P8)
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retcodes: 0, normal step. 5, largest step still improves too fast.
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4,2 back and forth adjustment of stepsize didn't finish. 3, smallest
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stepsize still improves too slow. 6, no improvement found. 1, zero
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gradient.
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---------------------
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Modified 7/22/96 to omit variable-length P list, for efficiency and compilation.
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Places where the number of P's need to be altered or the code could be returned to
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its old form are marked with ARGLIST comments.
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Fixed 7/17/93 to use inverse-hessian instead of hessian itself in bfgs
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update.
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Fixed 7/19/93 to flip eigenvalues of H to get better performance when
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it's not psd.
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tailstr = ')';
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for i=nargin-6:-1:1
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tailstr=[ ',P' num2str(i) tailstr];
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end
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ANGLE = .03;</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="csminwel.html" class="code" title="function [fh,xh,gh,H,itct,fcount,retcodeh] = csminwel(fcn,x0,H0,grad,crit,nit,varargin)">csminwel</a> [fhat,xhat,ghat,Hhat,itct,fcount,retcodehat] = csminwel(fcn,x0,H0,grad,crit,nit,varargin)</li><li><a href="mr_gstep.html" class="code" title="function [f0, x] = mr_gstep(func0,x,htol0,varargin)">mr_gstep</a> Copyright (C) 2005 Marco Ratto</li><li><a href="newrat.html" class="code" title="function [xparam1, hh, gg, fval, igg] = newrat(func0, x, hh, gg, igg, ftol0, nit, flagg, varargin)">newrat</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 <a name="_sub0" href="#_subfunctions" class="code">function [fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,varargin)</a>
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0002 <span class="comment">% [fhat,xhat,fcount,retcode] = csminit(fcn,x0,f0,g0,badg,H0,...</span>
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0003 <span class="comment">% P1,P2,P3,P4,P5,P6,P7,P8)</span>
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0004 <span class="comment">% retcodes: 0, normal step. 5, largest step still improves too fast.</span>
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0005 <span class="comment">% 4,2 back and forth adjustment of stepsize didn't finish. 3, smallest</span>
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0006 <span class="comment">% stepsize still improves too slow. 6, no improvement found. 1, zero</span>
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0007 <span class="comment">% gradient.</span>
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0008 <span class="comment">%---------------------</span>
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0009 <span class="comment">% Modified 7/22/96 to omit variable-length P list, for efficiency and compilation.</span>
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0010 <span class="comment">% Places where the number of P's need to be altered or the code could be returned to</span>
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0011 <span class="comment">% its old form are marked with ARGLIST comments.</span>
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0012 <span class="comment">%</span>
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0013 <span class="comment">% Fixed 7/17/93 to use inverse-hessian instead of hessian itself in bfgs</span>
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0014 <span class="comment">% update.</span>
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0015 <span class="comment">%</span>
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0016 <span class="comment">% Fixed 7/19/93 to flip eigenvalues of H to get better performance when</span>
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0017 <span class="comment">% it's not psd.</span>
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0018 <span class="comment">%</span>
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0019 <span class="comment">%tailstr = ')';</span>
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0020 <span class="comment">%for i=nargin-6:-1:1</span>
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0021 <span class="comment">% tailstr=[ ',P' num2str(i) tailstr];</span>
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0022 <span class="comment">%end</span>
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0023 <span class="comment">%ANGLE = .03;</span>
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0024 ANGLE = .005;
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0025 <span class="comment">%THETA = .03;</span>
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0026 THETA = .3; <span class="comment">%(0<THETA<.5) THETA near .5 makes long line searches, possibly fewer iterations.</span>
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0027 FCHANGE = 1000;
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0028 MINLAMB = 1e-9;
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0029 <span class="comment">% fixed 7/15/94</span>
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0030 <span class="comment">% MINDX = .0001;</span>
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0031 <span class="comment">% MINDX = 1e-6;</span>
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0032 MINDFAC = .01;
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0033 fcount=0;
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0034 lambda=1;
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0035 xhat=x0;
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0036 f=f0;
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0037 fhat=f0;
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0038 g = g0;
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0039 gnorm = norm(g);
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0040 <span class="comment">%</span>
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0041 <span class="keyword">if</span> (gnorm < 1.e-12) & ~badg <span class="comment">% put ~badg 8/4/94</span>
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0042 retcode =1;
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0043 dxnorm=0;
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0044 <span class="comment">% gradient convergence</span>
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0045 <span class="keyword">else</span>
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0046 <span class="comment">% with badg true, we don't try to match rate of improvement to directional</span>
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0047 <span class="comment">% derivative. We're satisfied just to get some improvement in f.</span>
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0048 <span class="comment">%</span>
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0049 <span class="comment">%if(badg)</span>
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0050 <span class="comment">% dx = -g*FCHANGE/(gnorm*gnorm);</span>
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0051 <span class="comment">% dxnorm = norm(dx);</span>
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0052 <span class="comment">% if dxnorm > 1e12</span>
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0053 <span class="comment">% disp('Bad, small gradient problem.')</span>
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0054 <span class="comment">% dx = dx*FCHANGE/dxnorm;</span>
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0055 <span class="comment">% end</span>
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0056 <span class="comment">%else</span>
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0057 <span class="comment">% Gauss-Newton step;</span>
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0058 <span class="comment">%---------- Start of 7/19/93 mod ---------------</span>
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0059 <span class="comment">%[v d] = eig(H0);</span>
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0060 <span class="comment">%toc</span>
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0061 <span class="comment">%d=max(1e-10,abs(diag(d)));</span>
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0062 <span class="comment">%d=abs(diag(d));</span>
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0063 <span class="comment">%dx = -(v.*(ones(size(v,1),1)*d'))*(v'*g);</span>
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0064 <span class="comment">% toc</span>
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0065 dx = -H0*g;
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0066 <span class="comment">% toc</span>
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0067 dxnorm = norm(dx);
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0068 <span class="keyword">if</span> dxnorm > 1e12
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0069 disp(<span class="string">'Near-singular H problem.'</span>)
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0070 dx = dx*FCHANGE/dxnorm;
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0071 <span class="keyword">end</span>
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0072 dfhat = dx'*g0;
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0073 <span class="comment">%end</span>
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0074 <span class="comment">%</span>
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0075 <span class="comment">%</span>
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0076 <span class="keyword">if</span> ~badg
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0077 <span class="comment">% test for alignment of dx with gradient and fix if necessary</span>
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0078 a = -dfhat/(gnorm*dxnorm);
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0079 <span class="keyword">if</span> a<ANGLE
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0080 dx = dx - (ANGLE*dxnorm/gnorm+dfhat/(gnorm*gnorm))*g;
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0081 dfhat = dx'*g;
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0082 dxnorm = norm(dx);
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0083 disp(sprintf(<span class="string">'Correct for low angle: %g'</span>,a))
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0084 <span class="keyword">end</span>
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0085 <span class="keyword">end</span>
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0086 disp(sprintf(<span class="string">'Predicted improvement: %18.9f'</span>,-dfhat/2))
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0087 <span class="comment">%</span>
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0088 <span class="comment">% Have OK dx, now adjust length of step (lambda) until min and</span>
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0089 <span class="comment">% max improvement rate criteria are met.</span>
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0090 done=0;
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0091 factor=3;
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0092 shrink=1;
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0093 lambdaMin=0;
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0094 lambdaMax=inf;
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0095 lambdaPeak=0;
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0096 fPeak=f0;
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0097 lambdahat=0;
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0098 <span class="keyword">while</span> ~done
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0099 <span class="keyword">if</span> size(x0,2)>1
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0100 dxtest=x0+dx'*lambda;
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0101 <span class="keyword">else</span>
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0102 dxtest=x0+dx*lambda;
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0103 <span class="keyword">end</span>
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0104 <span class="comment">% home</span>
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0105 f = eval([fcn <span class="string">'(dxtest,varargin{:})'</span>]);
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0106 <span class="comment">%ARGLIST</span>
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0107 <span class="comment">%f = feval(fcn,dxtest,P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11,P12,P13);</span>
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0108 <span class="comment">% f = feval(fcn,x0+dx*lambda,P1,P2,P3,P4,P5,P6,P7,P8);</span>
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0109 disp(sprintf(<span class="string">'lambda = %10.5g; f = %20.7f'</span>,lambda,f ))
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0110 <span class="comment">%debug</span>
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0111 <span class="comment">%disp(sprintf('Improvement too great? f0-f: %g, criterion: %g',f0-f,-(1-THETA)*dfhat*lambda))</span>
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0112 <span class="keyword">if</span> f<fhat
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0113 fhat=f;
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0114 xhat=dxtest;
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0115 lambdahat = lambda;
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0116 <span class="keyword">end</span>
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0117 fcount=fcount+1;
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0118 shrinkSignal = (~badg & (f0-f < max([-THETA*dfhat*lambda 0]))) | (badg & (f0-f) < 0) ;
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0119 growSignal = ~badg & ( (lambda > 0) & (f0-f > -(1-THETA)*dfhat*lambda) );
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0120 <span class="keyword">if</span> shrinkSignal & ( (lambda>lambdaPeak) | (lambda<0) )
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0121 <span class="keyword">if</span> (lambda>0) & ((~shrink) | (lambda/factor <= lambdaPeak))
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0122 shrink=1;
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0123 factor=factor^.6;
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0124 <span class="keyword">while</span> lambda/factor <= lambdaPeak
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0125 factor=factor^.6;
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0126 <span class="keyword">end</span>
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0127 <span class="comment">%if (abs(lambda)*(factor-1)*dxnorm < MINDX) | (abs(lambda)*(factor-1) < MINLAMB)</span>
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0128 <span class="keyword">if</span> abs(factor-1)<MINDFAC
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0129 <span class="keyword">if</span> abs(lambda)<4
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0130 retcode=2;
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0131 <span class="keyword">else</span>
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0132 retcode=7;
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0133 <span class="keyword">end</span>
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0134 done=1;
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0135 <span class="keyword">end</span>
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0136 <span class="keyword">end</span>
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0137 <span class="keyword">if</span> (lambda<lambdaMax) & (lambda>lambdaPeak)
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0138 lambdaMax=lambda;
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0139 <span class="keyword">end</span>
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0140 lambda=lambda/factor;
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0141 <span class="keyword">if</span> abs(lambda) < MINLAMB
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0142 <span class="keyword">if</span> (lambda > 0) & (f0 <= fhat)
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0143 <span class="comment">% try going against gradient, which may be inaccurate</span>
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0144 lambda = -lambda*factor^6
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0145 <span class="keyword">else</span>
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0146 <span class="keyword">if</span> lambda < 0
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0147 retcode = 6;
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0148 <span class="keyword">else</span>
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0149 retcode = 3;
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0150 <span class="keyword">end</span>
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0151 done = 1;
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0152 <span class="keyword">end</span>
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0153 <span class="keyword">end</span>
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0154 <span class="keyword">elseif</span> (growSignal & lambda>0) | (shrinkSignal & ((lambda <= lambdaPeak) & (lambda>0)))
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0155 <span class="keyword">if</span> shrink
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0156 shrink=0;
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0157 factor = factor^.6;
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0158 <span class="comment">%if ( abs(lambda)*(factor-1)*dxnorm< MINDX ) | ( abs(lambda)*(factor-1)< MINLAMB)</span>
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0159 <span class="keyword">if</span> abs(factor-1)<MINDFAC
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0160 <span class="keyword">if</span> abs(lambda)<4
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0161 retcode=4;
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0162 <span class="keyword">else</span>
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0163 retcode=7;
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0164 <span class="keyword">end</span>
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0165 done=1;
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0166 <span class="keyword">end</span>
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0167 <span class="keyword">end</span>
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0168 <span class="keyword">if</span> ( f<fPeak ) & (lambda>0)
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0169 fPeak=f;
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0170 lambdaPeak=lambda;
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0171 <span class="keyword">if</span> lambdaMax<=lambdaPeak
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0172 lambdaMax=lambdaPeak*factor*factor;
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0173 <span class="keyword">end</span>
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0174 <span class="keyword">end</span>
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0175 lambda=lambda*factor;
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0176 <span class="keyword">if</span> abs(lambda) > 1e20;
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0177 retcode = 5;
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0178 done =1;
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0179 <span class="keyword">end</span>
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0180 <span class="keyword">else</span>
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0181 done=1;
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0182 <span class="keyword">if</span> factor < 1.2
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0183 retcode=7;
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0184 <span class="keyword">else</span>
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0185 retcode=0;
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0186 <span class="keyword">end</span>
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0187 <span class="keyword">end</span>
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0188 <span class="keyword">end</span>
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0189 <span class="keyword">end</span>
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0190 disp(sprintf(<span class="string">'Norm of dx %10.5g'</span>, dxnorm))</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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