這篇文章主要介紹了python中黃金分割法實現方法,涉及Python數學計算的相關技巧,需要的朋友可以參考下
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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 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 ''' 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 with a step length h. x,fMin = search(f,a,b,tol=1.0e-6) Golden section method for determining x that minimizes the user-supplied scalar function f(x). The minimum must be 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(b-a)))) # Eq. (10.4) R = 0.618033989 C = 1.0 - R # First 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希望本文所述對大家的Python程序設計有所幫助。
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