我正在尝试对某些数据拟合经过指数修改的高斯函数。顶部提供数据。
我有以下代码：
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
from scipy.special import erfc
bins = [-46.82455, -46.41738, -46.01021, -45.60304, -45.19587, -44.7887, -44.38153,
-43.97436, -43.56719, -43.16002, -42.75285, -42.34568, -41.93851, -41.53134,
-41.12417, -40.717, -40.30983, -39.90266, -39.49549, -39.08832, -38.68115,
-38.27398, -37.86681, -37.45964, -37.05247, -36.6453, -36.23813, -35.83096,
-35.42379, -35.01662, -34.60945, -34.20228, -33.79511, -33.38794, -32.98077,
-32.5736, -32.16643, -31.75926, -31.35209, -30.94492, -30.53775, -30.13058,
-29.72341, -29.31624, -28.90907, -28.5019, -28.09473, -27.68756, -27.28039,
-26.87322, -26.46605, -26.05888, -25.65171, -25.24454, -24.83737, -24.4302,
-24.02303, -23.61586, -23.20869, -22.80152, -22.39435, -21.98718, -21.58001,
-21.17284, -20.76567, -20.3585, -19.95133, -19.54416, -19.13699, -18.72982,
-18.32265, -17.91548, -17.50831, -17.10114, -16.69397, -16.2868, -15.87963,
-15.47246, -15.06529, -14.65812, -14.25095, -13.84378, -13.43661, -13.02944,
-12.62227, -12.2151, -11.80793, -11.40076, -10.99359, -10.58642, -10.17925,
-9.77208, -9.36491, -8.95774, -8.55057, -8.1434, -7.73623, -7.32906,
-6.92189, -6.51472, -6.10755, -5.70038, -5.29321, -4.88604, -4.47887,
-4.0717, -3.66453, -3.25736, -2.85019, -2.44302, -2.03585, -1.62868,
-1.22151, -0.81434, -0.40717, 0.0, 0.40717, 0.81434, 1.22151,
1.62868, 2.03585, 2.44302, 2.85019, 3.25736, 3.66453, 4.0717,
4.47887, 4.88604, 5.29321, 5.70038, 6.10755, 6.51472, 6.92189,
7.32906, 7.73623, 8.1434, 8.55057, 8.95774, 9.36491, 9.77208,
10.17925, 10.58642, 10.99359, 11.40076, 11.80793, 12.2151, 12.62227,
13.02944, 13.43661, 13.84378, 14.25095, 14.65812, 15.06529, 15.47246,
15.87963, 16.2868, 16.69397, 17.10114, 17.50831, 17.91548, 18.32265,
18.72982, 19.13699, 19.54416, 19.95133, 20.3585, 20.76567, 21.17284,
21.58001, 21.98718, 22.39435, 22.80152, 23.20869, 23.61586, 24.02303,
24.4302, 24.83737, 25.24454, 25.65171, 26.05888, 26.46605, 26.87322,
27.28039, 27.68756, 28.09473, 28.5019, 28.90907, 29.31624, 29.72341,
30.13058, 30.53775, 30.94492, 31.35209, 31.75926, 32.16643, 32.5736,
32.98077, 33.38794, 33.79511, 34.20228, 34.60945, 35.01662, 35.42379,
35.83096, 36.23813, 36.6453, 37.05247, 37.45964, 37.86681, 38.27398,
38.68115, 39.08832, 39.49549, 39.90266, 40.30983, 40.717, 41.12417,
41.53134, 41.93851, 42.34568, 42.75285, 43.16002, 43.56719, 43.97436,
44.38153, 44.7887, 45.19587, 45.60304, 46.01021, 46.41738]
counts = [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
9.82318271e-04, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
9.82318271e-04, 0.00000000e+00, 9.82318271e-04, 0.00000000e+00,
0.00000000e+00, 9.82318271e-04, 0.00000000e+00, 9.82318271e-04,
9.82318271e-04, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
9.82318271e-04, 0.00000000e+00, 0.00000000e+00, 9.82318271e-04,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 9.82318271e-04, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 9.82318271e-04,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 9.82318271e-04,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 9.82318271e-04, 0.00000000e+00, 0.00000000e+00,
1.96463654e-03, 9.82318271e-04, 9.82318271e-04, 0.00000000e+00,
9.82318271e-04, 1.96463654e-03, 9.82318271e-04, 9.82318271e-04,
7.85854617e-03, 9.82318271e-03, 1.27701375e-02, 1.47347741e-02,
1.76817289e-02, 2.75049116e-02, 3.14341847e-02, 4.32220039e-02,
5.79567780e-02, 6.77799607e-02, 9.43025540e-02, 1.29666012e-01,
1.48330059e-01, 1.87622790e-01, 2.07269155e-01, 2.54420432e-01,
3.00589391e-01, 3.33005894e-01, 4.03732809e-01, 4.72495088e-01,
5.22593320e-01, 5.99214145e-01, 6.34577603e-01, 7.04322200e-01,
8.18271120e-01, 8.58546169e-01, 9.26326130e-01, 9.65618861e-01,
9.35166994e-01, 9.76424361e-01, 9.39096267e-01, 1.00000000e+00,
9.67583497e-01, 9.36149312e-01, 9.13555992e-01, 9.38113949e-01,
8.35952849e-01, 8.31041257e-01, 8.33988212e-01, 7.54420432e-01,
7.17092338e-01, 6.12966601e-01, 6.22789784e-01, 5.37328094e-01,
4.76424361e-01, 4.35166994e-01, 3.89980354e-01, 3.53634578e-01,
3.47740668e-01, 3.51669941e-01, 2.87819253e-01, 2.67190570e-01,
3.04518664e-01, 2.60314342e-01, 2.70137525e-01, 2.65225933e-01,
2.65225933e-01, 2.67190570e-01, 3.06483301e-01, 2.72102161e-01,
2.61296660e-01, 2.57367387e-01, 2.45579568e-01, 2.67190570e-01,
2.25933202e-01, 2.28880157e-01, 2.21021611e-01, 2.23968566e-01,
1.95481336e-01, 1.80746562e-01, 1.56188605e-01, 1.53241650e-01,
1.23772102e-01, 1.47347741e-01, 1.26719057e-01, 8.93909627e-02,
7.17092338e-02, 8.84086444e-02, 6.28683694e-02, 6.97445972e-02,
6.58153242e-02, 4.61689587e-02, 4.51866405e-02, 4.61689587e-02,
4.32220039e-02, 4.61689587e-02, 4.22396857e-02, 3.92927308e-02,
3.43811395e-02, 3.14341847e-02, 2.45579568e-02, 3.53634578e-02,
2.94695481e-02, 3.53634578e-02, 2.75049116e-02, 2.16110020e-02,
3.14341847e-02, 3.63457760e-02, 1.96463654e-02, 2.94695481e-02,
2.35756385e-02, 2.84872299e-02, 2.35756385e-02, 2.55402750e-02,
2.06286837e-02, 1.86640472e-02, 3.33988212e-02, 1.96463654e-02,
2.35756385e-02, 1.86640472e-02, 1.96463654e-02, 2.25933202e-02,
2.45579568e-02, 2.84872299e-02, 1.96463654e-02, 1.96463654e-02,
1.86640472e-02, 1.76817289e-02, 1.47347741e-02, 1.96463654e-02,
2.65225933e-02, 2.06286837e-02, 2.45579568e-02, 2.06286837e-02,
2.35756385e-02, 1.47347741e-02, 2.06286837e-02, 6.87622790e-03,
1.27701375e-02, 1.86640472e-02, 1.66994106e-02, 2.35756385e-02,
1.17878193e-02, 1.96463654e-02, 9.82318271e-03, 1.47347741e-02,
1.08055010e-02, 1.17878193e-02, 1.27701375e-02, 1.27701375e-02,
1.37524558e-02, 1.08055010e-02, 1.27701375e-02, 5.89390963e-03,
1.08055010e-02, 9.82318271e-03]
def exp_mod_gauss(x, m, s, l):
y = 0.5*l*np.exp(0.5*l*(2*m+l*s*s-2*x))*erfc((m+l*s*s-x)/(np.sqrt(2)*s))
return y
#l=Lambda, s=Sigma, m=Mu
bins=np.asarray(bins, dtype='float')
counts=np.asarray(counts, dtype='float')
popt, pcov = curve_fit(exp_mod_gauss, bins, counts, p0=[-3.5,2.8736,0.1548])
fitted_func = exp_mod_gauss(bins, popt[0], popt[1], popt[2])
#fitted_func = exp_mod_gauss(bins, -3.5, 2.8736, 0.1548) #used for manual example
plt.plot(bins, counts, 'o', markersize=1) #plot actual counts
plt.plot(bins, fitted_func/max(fitted_func), '-') #plot fitted func/scaled
plt.show()
如果按编写的方式使用scipy拟合运行代码，则会得到以下结果：
这显然不是很好。
但是，如果我注释掉了使用curve_fit中的参数并使用我在初始猜测中提供的参数（-3.5、2.876、0.1548）的fit_func行，那么我得到以下结果：
因此，即使我为curve_fit提供了最初的猜测，这基本上就是我要寻找的答案，但它还是失败了。通过在Matlab中执行完全相同的过程，我得到了很好的拟合参数，但是我不想使用Matlab。我想使用Python。
有人知道这是怎么回事吗？
非常感谢。
最佳答案
因此，事实证明，该配件在EMG功能运行时需要额外的自由度。以便可以扩展到数据。如果我将EMG函数修改为：
def exp_mod_gauss(x, b, m, s, l):
y = b*(0.5*l*np.exp(0.5*l*(2*m+l*s*s-2*x))*erfc((m+l*s*s-x)/(np.sqrt(2)*s)))
return y
#l=Lambda, s=Sigma, m=Mu, #b=scaling
因此，添加b项以缩放峰进行了排序。我提供了猜测[1，-1,1,0]现在适合我期望的各种数据。
关于python - scipy curve_fit即使提供了很好的猜测也根本无法正确拟合？，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/58802378/