python - scipy curve_fit 在拟合大值曲线时失败

Question

我正在尝试将一些水平风数据拟合到余弦曲线，以估计不同高度的风向和风速(速度方位角显示)，但似乎每当我尝试使用 > ~1 的值时，曲线显得太平，拟合的输出低于预期。

import numpy as np
import scipy.optimize as sc

azimuth = np.full((8), 60) #All values = 60 deg.
velocity = [5.6261001,6.6962662,3.9316666,-0.88413334,-5.4323335,-6.5153003,-3.2538002,1.0269333]
#Function that defines curve that data will be fitted to
def cos_Wave(x,a, b, c):
    return a * np.cos(x-b) + c

azimuthData = np.deg2rad(azimuth)
coeffs, matcov = sc.curve_fit(cos_Wave, azimuthData, velocity, p0 = (1,0,0)

plt.scatter(azimuthData, velocity)
plt.plot(azimuthData, cos_Wave(azimuthData, *coeffs))
plt.show()
print(coeffs)

coeffs 输出为:[ 1., 0., 0.13705066] 并附有绘图:

Python 曲线拟合

我使用 IDL 的内置曲线拟合函数执行了类似的曲线拟合，并收到了更实际的值，产生 [ 7.0348234, 0.59962606, 0.079354301] 并提供了合适的拟合。为什么会这样？我假设它可能与初始估计 (P0) 有关，但是，在 IDL 实现中使用初始初始估计仍然提供更合理的结果。

Answer 1

您需要解决一些问题:

import numpy as np
import scipy.optimize as sc
import matplotlib.pyplot as plt

azimuth = np.linspace(0, 360, 8)  # deg values from 0 to 360
velocity = [5.6261001, 6.6962662, 3.9316666, -0.88413334, -5.4323335,
            -6.5153003, -3.2538002, 1.0269333]


def cos_Wave(x, a, b, c):
    """Function that defines curve that data will be fitted to"""
    return a * np.cos(x-b) + c


azimuthData = np.deg2rad(azimuth)
coeffs, matcov = sc.curve_fit(cos_Wave, azimuthData, velocity, p0=[1, 0, 0])

plt.scatter(azimuthData, velocity)
nx = np.linspace(0, 2 * np.pi, 100)
plt.plot(nx, cos_Wave(nx, *coeffs))
plt.savefig("plot.png")
print(coeffs)

[ 6.63878549 1.03148322 -0.27674095]