如何使用pylab和numpy将正弦曲线拟合到数据？

Question

我试图表明，经济体遵循一种相对正弦的增长模式。我正在构建一个python模拟，以表明即使我们让某种程度的随机性占据主导地位，我们仍然可以产生一些相对正弦的东西

我对我生成的数据很满意，但现在我想找到一些方法来获得与数据非常接近的正弦图。我知道你能做多项式拟合，但你能做正弦拟合吗

Answer 1

对我们来说更友好的是函数curvefit。这里有一个例子：

import numpy as np
from scipy.optimize import curve_fit
import pylab as plt

N = 1000 # number of data points
t = np.linspace(0, 4*np.pi, N)
data = 3.0*np.sin(t+0.001) + 0.5 + np.random.randn(N) # create artificial data with noise

guess_freq = 1
guess_amplitude = 3*np.std(data)/(2**0.5)
guess_phase = 0
guess_offset = np.mean(data)

p0=[guess_freq, guess_amplitude,
    guess_phase, guess_offset]

# create the function we want to fit
def my_sin(x, freq, amplitude, phase, offset):
    return np.sin(x * freq + phase) * amplitude + offset

# now do the fit
fit = curve_fit(my_sin, t, data, p0=p0)

# we'll use this to plot our first estimate. This might already be good enough for you
data_first_guess = my_sin(t, *p0)

# recreate the fitted curve using the optimized parameters
data_fit = my_sin(t, *fit[0])

plt.plot(data, '.')
plt.plot(data_fit, label='after fitting')
plt.plot(data_first_guess, label='first guess')
plt.legend()
plt.show()