Page 299 - MATLAB an introduction with applications

284 ——— MATLAB: An Introduction with Applications

[a,b] = goldBracket(@fLine,0.0,h);
[s,fMin] = goldSearch(@fLine,a,b);
X = X + s*V;
g1 = –feval(DFUNC,X);
if sqrt(dot(g1,g1)) <= tol
xMin = X; nCyc = i; return
end
gamma = dot((g1 – g0),g1)/dot(g0,g0);
V = g1 + gamma*V;
g0 = g1;
end
error(‘Method did not converge’)
function z = fLine(s)
global X FUNC V
z = feval(FUNC,X+s*V);

function [a,b] = goldBracket(func,x1,h)
% Brackets the minimum point of f(x)
% func = returns f(x)
% x1= starting value of x
% h = initial step size
% a, b = limits on x
c = 1.618033989;
f1 = feval(func,x1);
x2 = x1 + h; f2 = feval(func,x2);
if f2 > f1
h = –h;
x2 = x1 + h; f2 = feval(func,x2);
if f2 > f1
a = x2; b = x1 – h; return
end
end
% Search loop
for i = 1:100
h = c*h;
x3 = x2 + h; f3 = feval(func,x3);
if f3 > f2
a = x1; b = x3; return
end
x1 = x2; f1 = f2; x2 = x3; f2 = f3;
end
error(‘Failed to find minimum’)