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:
Set up a simple
modelfunction and anerrorfunction 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)
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]