mirror of
https://github.com/c-sooyoung/fold_slice.git
synced 2026-09-18 01:09:10 +09:00
98 lines
2.5 KiB
Matlab
98 lines
2.5 KiB
Matlab
function [a,f] = brent(func,x0,dx,a1,a,a2,f1,f,f2,varargin)
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% one-dimensional minimization by parabolic interpolation & golden
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% section (does not use the gradient)
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%
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% [a,f] = brent(func,x0,dx,a1,a,a2,f1,f,f2,varargin)
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%
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% func = string name of objective function
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% x0 = starting point of linesearch
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% dx = direction of linesearch
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% a1,a,a2 = bracketing triplet of steplengths (a1<a<a2)
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% f1,f,f2 = objective function at steplengths a1, a, & a2
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% a = output as final steplength
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% f = output as objective function at final steplength
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gold = 0.3819660; % golden ratio
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itmax = 5;
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tol = 0.5;
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% check order of bracket
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if (a1>a)|(a2<a), error('brent called with bracket in wrong order'), end
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% initialize
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v = a;fv = f; % middle point on step before last
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w = a;fw = f; % middle point on last step
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e = 0; % distance moved on step before last
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% iterations
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for it = 1:itmax
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am = 0.5*(a1+a2);
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tol1 = tol*abs(a)+eps;
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tol2 = 2*tol1;
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% test for convergence
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if abs(a-am)<=(tol2-0.5*(a2-a1)), return, end
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% choose next point
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if abs(e)>tol1 % construct a trial parabolic fit
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r = (a-w)*(f-fv);
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q = (a-v)*(f-fw);
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p = (a-v)*q-(a-w)*r;
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q = 2*(q-r);
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if q>0, p = -p; end
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q = abs(q);
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etemp = e;
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e = d;
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% check acceptability of parabolic fit
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ok = ~(abs(p)>=abs(0.5*q*etemp) | p<=q*(a1-a) | p>=q*(a2-a));
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if ok % take parabolic step
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d = p/q;
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u = a+d;
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if (u-a1)<tol2 | (a2-u)<tol2, d = sign(am-a)*tol1; end
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else % take golden section step
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if a>=am
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e = a1-a;
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else
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e = a2-a;
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end
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d = gold*e;
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end
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else % take golden section step
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if a>=am
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e = a1-a;
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else
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e = a2-a;
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end
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d = gold*e;
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end
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% arrive here with d computed either from
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% parabolic fit or else from golden section
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if abs(d)>=tol1
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u = a+d;
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else
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u = a+sign(d)*tol1;
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end
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fu = feval(func,x0+u*dx,varargin{:}); % one function evaluation per iteration
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if fu<=f
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if u>=a
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a1 = a;
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else
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a2 = a;
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end
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v = w; fv = fw;
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w = a; fw = f;
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a = u; f = fu;
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else
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if u<a
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a1 = u;
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else
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a2 = u;
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end
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if fu<=fw | w==a
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v = w; fv = fw;
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w = u; fw = fu;
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elseif fu<=fv | v==a | v==w
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v = u; fv = fu;
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end
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end
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end
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disp('exceeded maximum number of iterations')
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return
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end
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