Metoda lui fibonacci

function fib(n)
    a = b = i = 1
    while (i < n)
        c = a  + b
        a = b
        b = c
        i = i + 1
    end
    if (i == n)
        return a
    end
end

function find_fib(n)
    i = 1
    while (fib(i) < n)
        i = i + 1
    end
    return i
end

function fibonacci_method(f, interval, epsilon)
    a = first(interval)
    b = last(interval)
    n = find_fib((abs(b-a))/epsilon)
    lambda = a + (fib(n-2)/fib(n)) * (b-a)
    miu = a + (fib(n-1)/fib(n)) * (b-a)
    while (abs(b-a) > epsilon)
        if (f(lambda) > f(miu))
            a = lambda
            lambda = miu
            miu = a + (fib(n-1)/fib(n)) * (b-a)
        else
            b = miu
            lambda = a + (fib(n-2)/fib(n)) * (b-a)
            miu = lambda
        end
    end
    x_optim = (a+b)/2
    return x_min
end

f(x) = x^4 - 14*x^3 + 60*x^2 - 70*x
interval = range(0, stop=2)
epsilon = 0.3
x_optim = fibonacci_method(f, interval, epsilon)