Golden Section Interval Update

Problem

Given a bracket [a, b] with interior probe points, one golden section iteration keeps the subinterval around the smaller probe: keep [a, d] when f(c) < f(d) and [c, b] otherwise, where c and d are the probes.

The probe offsets are r * (b - a) with r = (sqrt(5) - 1) / 2. Given a, b, f(c), and f(d), return the new bracket [lo, hi].

Hint

The probe ordering depends on the interval orientation; use b - r*(b-a) and a + r*(b-a).

Test cases

case 1

in: [0,1,1,2]

expected: [0,0.6180339887498949]

case 2

in: [0,1,3,2]

expected: [0.3819660112501051,1]

case 3

in: [-2,2,0.5,0.5]

expected: [-0.4721359549995796,2]

Starter codePython

def golden_section_interval_update(a, b, fc, fd):
    # Your code here
    pass

3 test cases · run your code against them in the editor