SO 46296263

from math import pi
from scipy import optimize
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import numpy as np

x = np.array([
  0.0, 5.0, 10.0, 15.0, 20.0, 25.0, 30.0, 35.0, 40.0, 45.0, 50.0, 55.0, 60.0,
  65.0, 70.0, 75.0, 80.0, 85.0, 90.0, 95.0, 100.0, 105.0, 110.0, 115.0, 120.0,
  125.0, 130.0, 135.0, 140.0, 145.0, 150.0, 155.0, 160.0, 165.0, 170.0, 175.0,
  180.0, 185.0, 190.0, 195.0, 200.0, 205.0, 210.0, 215.0, 220.0, 225.0, 230.0,
  235.0, 240.0, 245.0, 250.0, 255.0, 260.0, 265.0, 270.0, 275.0, 280.0, 285.0,
  290.0, 295.0, 300.0, 305.0, 310.0, 315.0, 320.0, 325.0, 330.0, 335.0, 340.0,
  345.0, 350.0, 355.0, 360.0
])


y = np.array([
  1.69000000e-05, 2.80000000e-05, 4.14000000e-05, 5.89000000e-05,
  7.97000000e-05, 9.79000000e-05, 1.23000000e-04, 1.47500000e-04,
  1.69800000e-04, 1.94000000e-04, 2.17400000e-04, 2.40200000e-04,
  2.55400000e-04, 2.70500000e-04, 2.81900000e-04, 2.87600000e-04,
  2.91500000e-04, 2.90300000e-04, 2.83500000e-04, 2.76200000e-04,
  2.62100000e-04, 2.41800000e-04, 2.24200000e-04, 1.99500000e-04,
  1.74100000e-04, 1.49300000e-04, 1.35600000e-04, 1.11500000e-04,
  9.00000000e-05, 6.87000000e-05, 4.98000000e-05, 3.19000000e-05,
  2.07000000e-05, 1.31000000e-05, 9.90000000e-06, 1.03000000e-05,
  1.49000000e-05, 2.34000000e-05, 3.65000000e-05, 5.58000000e-05,
  7.56000000e-05, 9.65000000e-05, 1.19400000e-04, 1.46900000e-04,
  1.73000000e-04, 1.99200000e-04, 2.24600000e-04, 2.38700000e-04,
  2.60700000e-04, 2.74800000e-04, 2.84000000e-04, 2.91200000e-04,
  2.93400000e-04, 2.90300000e-04, 2.86400000e-04, 2.77900000e-04,
  2.63600000e-04, 2.45900000e-04, 2.25500000e-04, 2.03900000e-04,
  1.79100000e-04, 1.51800000e-04, 1.32400000e-04, 1.07000000e-04,
  8.39000000e-05, 6.20000000e-05, 4.41000000e-05, 3.01000000e-05,
  1.93000000e-05, 1.24000000e-05, 1.00000000e-05, 1.13000000e-05,
  1.77000000e-05
])

def form(theta, I_0, theta0, offset):
    return I_0 * np.cos(np.radians(theta - theta0)) ** 2 + offset

param, covariance = optimize.curve_fit(form, x, y, [3e-4, 90, 0])
print 'I_0: {0:e} / theta_0: {1} degrees / offset: {2:e}'.format(*param)
print covariance

plt.scatter(x, y, label='data')
plt.ylim(0, 3e-4)
plt.xlim(0, 360)
plt.plot(x, form(x, *param), 'b-')
plt.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
plt.axes().xaxis.set_major_locator(ticker.MultipleLocator(45))
plt.show()