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Sep 29th, 2018
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Python 1.60 KB | None | 0 0
  1. def F(C):
  2.     x2 = x**2  
  3.     C5_2, C3_2, C1_2 = C
  4.     y = (((C5_2 * x2) + C3_2) * x2 + C1_2) * x
  5.     y *= 2        # scaling
  6.     return y
  7.  
  8. def Hrms(C):
  9.     return 1E+08 * ((F(C) - truth)**2).sum()
  10.  
  11. def Hmax(C):
  12.     return 1E+06 * np.abs((F(C)-truth)).max()
  13.  
  14. import numpy as np
  15. from scipy.special import factorial
  16. from scipy.optimize import minimize
  17. import matplotlib.pyplot as plt
  18.  
  19. quarterpi, halfpi, pi, twopi = [f*np.pi for f in (0.25, 0.5, 1, 2)]
  20.  
  21. C5_2 =  0.03635510    # per https://space.stackexchange.com/a/30955/12102
  22. C3_2 = -0.32161470
  23. C1_2 =  0.78531340
  24.  
  25. C0   = np.array([C5_2, C3_2, C1_2])
  26.  
  27. Cnom = np.array([halfpi**5 /(2.*factorial(5)),
  28.                  halfpi**3 /(2.*factorial(3)),
  29.                  halfpi**1 /(2.*factorial(1))]) # if expanding about 0
  30.  
  31. angle = np.linspace(0, halfpi, 1001)
  32. truth = np.sin(angle)
  33. x     = angle/halfpi   # scaling
  34.  
  35. Cst = np.array([0.1, 0.0, 0.5])  # arbitrary starting point
  36.  
  37. opts = {'xtol': 1E-12, 'disp': False, 'maxiter':1000, 'maxfev':2000}
  38.  
  39. resrms = minimize(Hrms, Cst, method='Nelder-Mead', options=opts)
  40. Crms   = resrms['x']
  41.  
  42. resmax = minimize(Hmax, Cst, method='Nelder-Mead', options=opts)
  43. Cmax   = resmax['x']
  44.  
  45. np.set_printoptions(precision=6)
  46.  
  47. print ("C0:   {}, Hmax(C0):   {:0.2f}, Hmrms(C0):   {:0.2f}".format(C0, Hmax(C0), Hrms(C0)))
  48. print ("Cnom: {}, Hmax(Cnom): {:0.2f}, Hmrms(Cnom): {:0.2f}".format(Cnom, Hmax(Cnom), Hrms(Cnom)))
  49. print ("Crms: {}, Hmax(Crms): {:0.2f}, Hmrms(Crms): {:0.2f}".format(Crms, Hmax(Crms), Hrms(Crms)))
  50. print ("Cmax: {}, Hmax(Cmax): {:0.2f}, Hmrms(Cmax): {:0.2f}".format(Cmax, Hmax(Cmax), Hrms(Cmax)))
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