The method of gold segmentation in Python

Source: Internet
Author: User
Tags scalar

This article mainly introduces the implementation of the Golden section in Python, involving techniques related to the calculation of Python's mathematics, the need for friends can refer to the

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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 This is the ; > "' A,b = bracket (f,xstart,h) finds the brackets (a,b) of a minimum point of the user-supplied scalar function f (x). The search starts downhill from Xstart and a step length h. x,fmin = Search (f,a,b,tol=1.0e-6) Golden section method for D Etermining x that minimizes the user-supplied scalar function f (x). The minimum must is bracketed in (A,B). ' From math import log, Ceil def bracket (f,x1,h): c = 1.618033989 f1 = f (x1) x2 = x1 + H; F2 = f (x2) # Determine downhill direction and change sign of H if needed if F2 > f1:h =-H x2 = x1 + H; F2 = f (x2) # Check If minimum between x1-h and X1 + H if F2 > F1:return x2,x1-h # Search loop for I in range (100) : h = c*h x3 = x2 + H; F3 = f (x3) If F3 > F2:return x1,x3 x1 = x2; x2 = x3 F1 = F2; F2 = f3 print "Bracket did not find a mimimum" Def search (f,a,b,tol=1.0e-9): niter = Int (ceil ( -2.078087*log (tol/abs)) # Eq. (10.4) R = 0.618033989 C = 1.0-r # I telescoping x1 = r*a + c*b; x2 = c*a + R*b f1 = f (x1); F2 = f (x2) # Main loop for I in range (niter): If f1 > f2:a = x1 x1 = x2; F1 = F2 x2 = c*a + r*b; F2 = f (x2) else:b = x2 x2 = x1; F2 = f1 X1 = r*a + c*b; F1 = f (x1) If F1 < F2:return x1,f1 Else:return x2,f2

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