Implementation of the Golden Segmentation Method in python

Implementation of the Golden Segmentation Method in python

This article mainly introduces the implementation of the Golden division method in python, involving the related skills of Python mathematical computation. For more information, see

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'''A, B = bracket (f, xStart, h) Finds the brackets (a, B) of a minimum point of 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

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