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
|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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