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74 lines
1.8 KiB
Python
74 lines
1.8 KiB
Python
"""Python program for golden section search (straight-up copied from Wikipedia).
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This implementation reuses function evaluations, saving 1/2 of the evaluations per
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iteration, and returns a bounding interval."""
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import logging
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import math
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logging.basicConfig(level=logging.INFO)
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logger = logging.getLogger(__name__)
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invphi = (math.sqrt(5) - 1) / 2 # 1 / phi
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invphi2 = (3 - math.sqrt(5)) / 2 # 1 / phi^2
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def gss(f, a, b, tol=1e-4):
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"""Golden-section search.
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Given a function f with a single local minimum in
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the interval [a,b], gss returns a subset interval
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[c,d] that contains the minimum with d-c <= tol.
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Example:
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>>> f = lambda x: (x-2)**2
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>>> a = 1
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>>> b = 5
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>>> tol = 1e-5
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>>> (c,d) = gss(f, a, b, tol)
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>>> print(c, d)
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1.9999959837979107 2.0000050911830893
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"""
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(a, b) = (min(a, b), max(a, b))
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h = b - a
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if h <= tol:
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return a, b
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# Required steps to achieve tolerance
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n = int(math.ceil(math.log(tol / h) / math.log(invphi)))
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logger.info(
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"About to perform %d iterations of golden section search to find the best framerate",
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n,
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)
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def f_wrapped(x, is_last_iter):
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try:
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return f(x, is_last_iter)
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except TypeError:
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return f(x)
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c = a + invphi2 * h
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d = a + invphi * h
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yc = f_wrapped(c, n == 1)
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yd = f_wrapped(d, n == 1)
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for k in range(n - 1):
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if yc < yd:
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b = d
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d = c
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yd = yc
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h = invphi * h
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c = a + invphi2 * h
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yc = f_wrapped(c, k == n - 2)
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else:
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a = c
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c = d
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yc = yd
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h = invphi * h
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d = a + invphi * h
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yd = f(d, k == n - 2)
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if yc < yd:
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return a, d
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else:
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return c, b
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