Merge remote-tracking branch 'rcc02007/master'

lecture_08/goldmin.m

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+function [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,varargin)
+% goldmin: minimization golden section search
+%   [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,p1,p2,...):
+%     uses golden section search to find the minimum of f
+% input:
+%   f = name of function
+%   xl, xu = lower and upper guesses
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by f
+% output:
+%   x = location of minimum
+%   fx = minimum function value
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+phi=(1+sqrt(5))/2;
+iter=0;
+while(1)
+  d = (phi-1)*(xu - xl);
+  x1 = xl + d;
+  x2 = xu - d;
+  if f(x1,varargin{:}) < f(x2,varargin{:})
+    xopt = x1;
+    xl = x2;
+  else
+    xopt = x2;
+    xu = x1;
+  end
+  iter=iter+1;
+  if xopt~=0, ea = (2 - phi) * abs((xu - xl) / xopt) * 100;end
+  if ea <= es | iter >= maxit,break,end
+end
+x=xopt;fx=f(xopt,varargin{:});