Trying To Fit A Trig Function To Data With Scipy

I am trying to fit some data using scipy.optimize.curve_fit. I have read the documentation and also this StackOverflow post, but neither seem to answer my question. I have some da

Solution 1:

If no values are provided for initial guess of the parameters p0 then a value of 1 is assumed for each of them. From the docs:

p0 : array_like, optional Initial guess for the parameters (length N). If None, then the initial values will all be 1 (if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised).

Since your data has very large x-values and very small y-values an initial guess of 1 is far from the actual solution and hence the optimizer does not converge. You can help the optimizer by providing suitable initial parameter values that can be guessed / approximated from the data:

• Amplitude: A = (y.max() - y.min()) / 2
• Offset: C = (y.max() + y.min()) / 2
• Frequency: Here we can estimate the number of zero crossing by multiplying consecutive y-values and check which products are smaller than zero. This number divided by the total x-range gives the frequency and in order to get it in units of pi we can multiply that number by pi: y_shifted = y - offset; oemga = np.pi * np.sum(y_shifted[:-1] * y_shifted[1:] < 0) / (t.max() - t.min())
• Phase shift: can be set to zero, dphi = 0

So in summary, the following initial parameter guess can be used:

offset= (y.max() + y.min()) /2
y_shifted = y -offset
p0 = (
    (y.max() - y.min()) /2,
    np.pi * np.sum(y_shifted[:-1] * y_shifted[1:] <0) / (t.max() - t.min()),
    0,
    offset
)
popt, pcov = curve_fit(func_cos, t, y, p0=p0)

Which gives me the following fit function: