Python scipy.optimize.curve\u拟合与数据不匹配
我试图用高斯曲线拟合我的数据。这是我的密码:Python scipy.optimize.curve\u拟合与数据不匹配,python,optimization,scipy,Python,Optimization,Scipy,我试图用高斯曲线拟合我的数据。这是我的密码: import numpy as np from scipy import optimize # The independent variable where the data is measured x_coord = np.array([-0.1216 , -0.11692308, -0.11224615, -0.10756923, -0.10289231, -0.09821538, -0.09353846, -0.08886
import numpy as np
from scipy import optimize
# The independent variable where the data is measured
x_coord = np.array([-0.1216 , -0.11692308, -0.11224615, -0.10756923, -0.10289231,
-0.09821538, -0.09353846, -0.08886154, -0.08418462, -0.07950769,
-0.07483077, -0.07015385, -0.06547692, -0.0608 , -0.05612308,
-0.05144615, -0.04676923, -0.04209231, -0.03741538, -0.03273846,
-0.02806154, -0.02338462, -0.01870769, -0.01403077, -0.00935385,
-0.00467692, 0. , 0.00467692, 0.00935385, 0.01403077,
0.01870769, 0.02338462, 0.02806154, 0.03273846, 0.03741538,
0.04209231, 0.04676923, 0.05144615, 0.05612308, 0.0608 ,
0.06547692, 0.07015385, 0.07483077, 0.07950769, 0.08418462,
0.08886154, 0.09353846, 0.09821538, 0.10289231, 0.10756923,
0.11224615, 0.11692308])
# The dependent data — nominally f(x_coord)
y = np.array([-0.0221931 , -0.02323915, -0.02414913, -0.0255389 , -0.02652465,
-0.02888672, -0.03075954, -0.03355392, -0.03543005, -0.03839526,
-0.040933 , -0.0456585 , -0.04849097, -0.05038776, -0.0466699 ,
-0.04202133, -0.034239 , -0.02667525, -0.01404582, -0.00122683,
0.01703862, 0.03992694, 0.06704549, 0.11362071, 0.28149172,
0.6649422 , 1. , 0.6649422 , 0.28149172, 0.11362071,
0.06704549, 0.03992694, 0.01703862, -0.00122683, -0.01404582,
-0.02667525, -0.034239 , -0.04202133, -0.0466699 , -0.05038776,
-0.04849097, -0.0456585 , -0.040933 , -0.03839526, -0.03543005,
-0.03355392, -0.03075954, -0.02888672, -0.02652465, -0.0255389 ,
-0.02414913, -0.02323915])
# define a gaussian function to fit the data
def gaussian(x, a, b, c):
val = a * np.exp(-(x - b)**2 / c**2)
return val
# fit the data
popt, pcov = optimize.curve_fit(gaussian, x_coord, y, sigma = np.array([0.01] * len(x_coord)))
# plot the data and the fitting curve
plt.plot(x_coord, y, 'b-', x_coord, gaussian(x_coord, popt[0], popt[1], popt[2]), 'r:')
如图所示,拟合曲线完全错误:
我应该怎么做才能得到一条很好的拟合曲线呢?这实际上是一个很好的问题,说明找到正确的局部最优可能非常困难 通过p0参数,您可以给优化例程一个提示,其中大致是您期望的最佳值 如果从[1,0,0.1]的初始猜测开始: 您将得到以下结果:
# fit the data
popt, pcov = optimize.curve_fit(gaussian, x_coord, y)
# plot the data and the fitting curve
plt.plot(x_coord, y, 'b-', x_coord, gaussian(x_coord, *popt), 'r:')
需要注意的是:您强制使用曲线拟合来拟合没有常数项的钟形曲线。这让事情有点尴尬
如果允许偏移量d,则得到:
# define a gaussian function to fit the data
def gaussian(x, a, b, c, d):
val = a* np.exp(-(x - b)**2 / c**2) + d
return val
并得到如下结果:
# fit the data
popt, pcov = optimize.curve_fit(gaussian, x_coord, y)
# plot the data and the fitting curve
plt.plot(x_coord, y, 'b-', x_coord, gaussian(x_coord, *popt), 'r:')
这看起来更像是一种合理的搭配。虽然高斯分布似乎与数据不太吻合
非常尖峰的形状表明拉普拉斯人可能更适合:
# define a laplacian function to fit the data
def laplacian(x, a, b, c, d):
val = a* np.exp(-np.abs(x - b) / c) + d
return val
# fit the data
popt, pcov = optimize.curve_fit(laplacian, x_coord, y, p0=[1,0,0.01,-0.1])
# plot the data and the fitting curve
plt.plot(x_coord, y, 'b-', x_coord, laplacian(x_coord, *popt), 'r:')
结果是: