initial commit

ptycho/+engines/+ML/brent.m

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+function [a,f] = brent(func,x0,dx,a1,a,a2,f1,f,f2,varargin)
+% one-dimensional minimization by parabolic interpolation & golden
+% section (does not use the gradient)
+%
+% [a,f] = brent(func,x0,dx,a1,a,a2,f1,f,f2,varargin)
+%
+% func = string name of objective function
+% x0 = starting point of linesearch
+% dx = direction of linesearch
+% a1,a,a2 = bracketing triplet of steplengths (a1<a<a2)
+% f1,f,f2 = objective function at steplengths a1, a, & a2
+% a = output as final steplength
+% f = output as objective function at final steplength
+
+gold = 0.3819660; % golden ratio
+itmax = 5;
+tol = 0.5;
+% check order of bracket
+if (a1>a)|(a2<a), error('brent called with bracket in wrong order'), end
+% initialize
+v = a;fv = f; % middle point on step before last
+w = a;fw = f; % middle point on last step
+e = 0; % distance moved on step before last
+% iterations
+for it = 1:itmax
+   am = 0.5*(a1+a2);
+   tol1 = tol*abs(a)+eps;
+   tol2 = 2*tol1;
+   % test for convergence
+   if abs(a-am)<=(tol2-0.5*(a2-a1)), return, end
+   % choose next point
+   if abs(e)>tol1 % construct a trial parabolic fit
+       r = (a-w)*(f-fv);
+       q = (a-v)*(f-fw);
+       p = (a-v)*q-(a-w)*r;
+       q = 2*(q-r);
+       if q>0, p = -p; end
+       q = abs(q);
+       etemp = e;
+       e = d;
+       % check acceptability of parabolic fit
+       ok = ~(abs(p)>=abs(0.5*q*etemp) | p<=q*(a1-a) | p>=q*(a2-a));
+       if ok % take parabolic step
+           d = p/q;
+           u = a+d;
+           if (u-a1)<tol2 | (a2-u)<tol2, d = sign(am-a)*tol1; end
+       else % take golden section step
+           if a>=am
+               e = a1-a;
+           else
+               e = a2-a;
+           end
+           d = gold*e;
+       end
+   else % take golden section step
+       if a>=am
+           e = a1-a;
+       else
+           e = a2-a;
+       end
+       d = gold*e;
+   end
+   % arrive here with d computed either from
+   % parabolic fit or else from golden section
+   if abs(d)>=tol1
+       u = a+d;
+   else
+       u = a+sign(d)*tol1;
+   end
+   fu = feval(func,x0+u*dx,varargin{:}); % one function evaluation per iteration
+   if fu<=f
+       if u>=a
+           a1 = a;
+       else
+           a2 = a;
+       end
+       v = w; fv = fw;
+       w = a; fw = f;
+       a = u; f = fu;
+   else
+       if u<a
+           a1 = u;
+       else
+           a2 = u;
+       end
+       if fu<=fw | w==a
+           v = w; fv = fw;
+           w = u; fw = fu;
+       elseif fu<=fv | v==a | v==w
+           v = u; fv = fu;
+       end
+   end
+end
+disp('exceeded maximum number of iterations')
+return
+end
+