问题描述
我有一个橙色峰值，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,sigma] # a = max(spec_peak)
popt,pcov = curve_fit(Gauss,x,y,p0,maxfev=100000)
但拟合不起作用，我尝试使用猜测值，但我找不到它不起作用的任何原因。任何帮助都会非常感激。 x 轴由以下数据给出：
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
解决方法
失败的典型原因是：错误的启动参数。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，n 的使用没有意义。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 )
总尺度 n 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。它相当，但拟合收敛而不增加 maxfev