lambert_newton

lambert_newton:
  Use Newton's method to seek a root of the lambert function.
it = 2: alpha = 0.108328, log(alpha)= -2.2226
it = 3: alpha = 0.991943, log(alpha)= -0.00808959, r = 0.00363971
it = 4: alpha = 0.988803, log(alpha)= -0.0112604, r = 1.39197
it = 5: alpha = 0.982003, log(alpha)= -0.0181604, r = 1.61276
it = 6: alpha = 0.965831, log(alpha)= -0.0347668, r = 1.91442
it = 7: alpha = 0.925889, log(alpha)= -0.0770008, r = 2.21478
it = 8: alpha = 0.83009, log(alpha)= -0.186221, r = 2.41843
it = 9: alpha = 0.630036, log(alpha)= -0.461978, r = 2.48081
it = 10: alpha = 0.331472, log(alpha)= -1.10421, r = 2.39018
it = 11: alpha = 0.0889238, log(alpha)= -2.41998, r = 2.19159
it = 12: alpha = 0.00718688, log(alpha)= -4.9355, r = 2.03948
it = 13: alpha = 5.11763e-05, log(alpha)= -9.88023, r = 2.00187

  Number of steps = 13
  f(5) = 0
diary off