Day-of-year temperature take two

The quadratic polynomial approximation for the day-of-the-year temperature fit can be improved upon. We haven't used any of the NumPy trigonometric functions until now. Those should be a good fit for this problem. So, let's try a trigonometric function and fit again using a function from the scipy.optimize module (leastsq to be precise) as follows:

1. Set up a simple model function and an error function to be minimized, as shown in the following code snippet:

   def model(p, d):
      a, b, w, c = p
      return a + b * np.cos(w * d + c)
    
   def error(p, d, t):
      return t - model(p, d)

2. Give the initial guess and fit the data:

   p0 = [.1, 1, .01, .01]
   params = leastsq(error, p0, args=(days, temp))[0]
   print params

   We get the following parameters:

   [ 9.6848106  -7.59870042 -0.01766333 -5.83349705]
   

Note

Here, -2 pi over 365 is equal to the third parameter. I believe that the first parameter is equal to the average of all the temperatures, and we can come up with similar explanations...