Examples

Often the first step of a function optimisation is to find an interval within which a solution is believed to exist. The following example shows how brent_search.bracket() can be used to attain that task.

>>> from brent_search import bracket
>>> def f(x):
...     return (x-2)**2
>>>
>>> (x0, x1, x2, f0, f1, f2), e = bracket(f)
>>> print("Left point: {:.2f}".format(x0))
Left point: 1.25
>>> print("Best point: {:.2f}".format(x1))
Best point: 2.50
>>> print("Right point: {:.2f}".format(x2))
Right point: 5.00
>>> print("{:.2f}".format(f0))
0.56
>>> print("{:.2f}".format(f1))
0.25
>>> print("{:.2f}".format(f2))
9.00

The brent_search.brent() function can then be applied to find a minimum within the interval.

>>> from brent_search import brent
>>> (x, fx, exit_code) = brent(f, x0, x2, x1, f1)
>>> print("({:.1f}, {:.1f}, {})".format(x, fx, exit_code))
(2.0, 0.0, 6)