python 的一个分量高斯拟合不起作用

Question

我有一个橙色峰，我想对其进行高斯拟合，目的是获得 FWHM 和最高温度的估计值：

函数由下式给出：

def Gauss(velo_peak, a, mu0, sigma):
          res = a * np.exp(-(velo_peak - mu0)**2 / (2 * sigma**2))
          return res

我的代码是：

i1,i2 = 0,len(y)
n = len(x[i1:i2])
mu0 = sum(x[i1:i2] * y[i1:i2])/n
sigma = sum(y[i1:i2]*(x[i1:i2] - mu0)**2)/n
peak = max(y)
p0 = [peak, mu0, sigma]   # a = max(spec_peak)
popt,pcov = curve_fit(Gauss, x, y, p0, maxfev=100000)

但是拟合不起作用，我尝试过使用猜测值，但我找不到任何原因导致它不起作用。任何帮助将不胜感激。 x 轴由此数据给出：

109.774
109.774
109.774
109.774
109.774
109.774
109.774
109.774
109.774
109.774
109.774
109.774
109.775
109.775
109.775
109.775
109.775
109.775
109.775
109.775
109.775
109.775
109.775
109.775
109.775
109.776
109.776
109.776
109.776
109.776
109.776
109.776
109.776
109.776
109.776
109.776
109.776
109.776
109.777
109.777
109.777
109.777
109.777
109.777
109.777
109.777
109.777
109.777
109.777
109.777
109.777
109.778
109.778
109.778
109.778
109.778
109.778
109.778
109.778
109.778
109.778
109.778
109.778
109.778
109.779
109.779
109.779
109.779
109.779
109.779
109.779
109.779
109.779
109.779
109.779
109.779
109.779
109.78
109.78
109.78
109.78
109.78
109.78
109.78
109.78
109.78
109.78
109.78
109.78
109.78
109.781
109.781
109.781
109.781
109.781
109.781
109.781
109.781
109.781
109.781
109.781
109.781
109.781
109.782
109.782
109.782
109.782
109.782
109.782
109.782
109.782
109.782
109.782
109.782
109.782
109.782
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.783
109.784
109.784
109.784
109.784
109.784
109.784
109.784
109.784
109.784
109.784
109.784
109.784
109.784
109.785
109.785
109.785
109.785
109.785
109.785
109.785
109.785
109.785
109.785
109.785
109.785
109.785
109.786
109.786
109.786
109.786
109.786
109.786
109.786
109.786
109.786
109.786
109.786
109.786
109.786
109.787
109.787
109.787
109.787
109.787
109.787
109.787
109.787
109.787
109.787
109.787
109.787
109.787
109.788
109.788
109.788
109.788
109.788
109.788
109.788
109.788
109.788
109.788
109.788
109.788
109.788
109.789
109.789
109.789
109.789
109.789
109.789
109.789
109.789
109.789
109.789
109.789
109.789
109.789
109.79
109.79
109.79
109.79
109.79
109.79
109.79
109.79
109.79
109.79
109.79
109.79
109.79
109.791
109.791

和y轴：

-0.0693423
-0.0383312
-0.0130822
0.00771434
-0.00475569
-0.0288578
-0.00323742
0.000307108
-0.0181949
0.00129764
0.00661946
-0.0116734
0.0439911
-0.0189704
0.0134336
0.017783
-0.00059444
0.00129813
-0.0146921
-0.0178051
0.00210355
0.00739107
0.0193562
0.0177199
-0.0115096
-0.0148834
-0.0359211
0.0268527
0.0159948
0.0214348
0.015795
0.00807647
-0.0597478
-0.037623
0.000166686
0.0119881
0.0127355
0.00687692
0.00479245
-0.0207917
0.0627117
0.0133312
0.011981
0.0308865
0.0323675
-0.0353238
0.0498601
0.00484114
-0.00354253
-0.0181545
0.0476038
0.019046
0.0195323
-0.013426
-0.0154619
0.0129866
-0.0158984
0.0126304
0.0269754
-0.00217857
0.0206669
-0.0219605
-0.0224113
0.00217749
-0.0359304
0.0273953
0.0133183
0.0202708
-0.0144499
0.0351752
-0.0202478
-0.0074738
0.0127188
-0.0116596
0.00869577
-0.0234507
0.0373167
0.00263353
0.0166561
-0.0043449
-0.0229105
-0.00741182
0.0467549
-0.0235804
-0.0191783
0.0528504
-0.00901956
0.043926
0.0223436
0.0181945
-0.0400392
0.0220731
-0.0167595
0.0214929
0.028309
-0.0234769
-0.0419024
0.0131882
-0.00421679
0.00359541
-0.055839
-0.0599337
-0.0283572
0.00686772
-0.00965801
0.0164275
0.00458221
-0.00909531
0.138937
0.297971
0.247663
0.124508
0.0365572
-0.00971529
0.0238192
-0.0509615
-0.0101447
-0.0298155
-0.0196555
0.0224242
-0.0329058
-0.00786179
-0.00347346
-0.0102662
0.0111553
0.013002
-0.0375893
0.00996665
-0.0125302
-0.00829957
0.0366645
0.0219919
-0.038467
-0.0260219
-0.0375669
0.00625599
-0.0498297
0.0258702
-0.0217369
-0.0349204
-0.014657
-0.0180611
-0.0420286
-0.000379184
-0.0333805
-0.0551173
-0.0224908
0.0179898
0.020866
0.0288823
-0.0182207
-0.0413725
-0.0162658
0.00223817
0.0243006
-0.0170214
0.0320711
0.0012465
0.00344509
0.00150138
-0.00169928
-0.0139581
0.0552647
0.0229482
-0.00316584
-0.033333
0.000161762
-0.00905961
-0.00685663
-0.0162735
-0.0399026
0.0270222
0.00798811
-0.00408101
-0.0072991
0.0112089
-0.012056
0.0146916
-0.00340297
0.0217221
0.00722562
-0.0203967
-0.0150112
0.00900151
0.0322559
0.00482019
-0.000814166
-0.0225995
-0.00817639
0.0201735
-0.0285309
0.0355886
0.000298672
-0.0129141
0.0428829
-0.028223
0.0183822
-6.62023e-05
0.0358768
-0.0293772
0.0125377
-0.00919312
0.00703798
0.00537255
-0.00413266
0.0505678
-0.00586183
0.0087835
-0.0113064
-0.0198051
0.0477742
0.00607189
-0.0112695
0.0288124
0.0354801
-0.0550288
-0.00167514
-0.0440247
-0.00573284
0.0138037
0.0170393
-0.0350715
0.0333013

Answer 1

失败的典型原因是：启动参数错误。这里使用的公式在某种程度上是用于测量统计的公式，而这里的数据必须被视为相应的直方图。因此，使用n 没有意义。更像是

## smoothing the data with its own noisy Gaussian
ysmooth = np.convolve( y, y[::-1], mode="same")
mu0 = sum( x * y ) / sum( y )
## the abs() is wrong but the strong noise forces it
sigma = np.sqrt( sum( np.abs( ysmooth ) * (  ( x - mu0 ) )**2 ) / sum( np.abs(ysmooth)) )
peak = max( y )

n 的总比例未知，但x 值的相对数量作为直方图的值给出，即y。 sigma 的猜测有点混乱，但在这里有效。这是相当的，但拟合收敛而不增加maxfev