Trying to fit a trig function to data with scipy

问题

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 data which is simple, 2D data which looks approximately like a trig function. I want to fit it with a general trig function using scipy.

My approach is as follows:

from __future__ import division
import numpy as np
from scipy.optimize import curve_fit



#Load the data
data = np.loadtxt('example_data.txt')
t = data[:,0]
y = data[:,1]


#define the function to fit
def func_cos(t,A,omega,dphi,C):
    # A is the amplitude, omega the frequency, dphi and C the horizontal/vertical shifts
    return A*np.cos(omega*t + dphi) + C

#do a scipy fit
popt, pcov = curve_fit(func_cos, t,y)

#Plot fit data and original data
fig = plt.figure(figsize=(14,10))
ax1 = plt.subplot2grid((1,1), (0,0))

ax1.plot(t,y)
ax1.plot(t,func_cos(t,*popt))

This outputs:

where blue is the data orange is the fit. Clearly I am doing something wrong. Any pointers?

回答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:

来源：https://stackoverflow.com/questions/59293054/trying-to-fit-a-trig-function-to-data-with-scipy