如何从高斯曲线拟合得到的结果中求解峰值对应的x轴坐标值

核心注意点 #

你当前拟合使用的函数是高斯曲线叠加线性背景，不能直接用拟合得到的高斯中心参数mu作为总曲线的峰值x坐标，需要通过计算拟合函数的极值点得到准确结果。

完整实现代码 #

在你原有代码的基础上补充峰值计算逻辑即可：

import scipy as sp
import matplotlib.pyplot as plt 
from scipy.optimize import curve_fit
from scipy.optimize import minimize_scalar

x = sp.array([ 100.,  101.,  102.,  103.,  
104.,  105.,  106.,  107.,  108.,
    109.,  110.,  111.,  112.,  113.,  114.,  
115.,  116.,  117.,
    118.,  119.,  120.,  121.,  122.,  123.,  
124.,  125.,  126.,
    127.,  128.,  129.,  130.,  131.,  132.,  
133.,  134.,  135.,
    136.,  137.,  138.,  139.,  140.,  141.,  
142.,  143.,  144.,
    145.,  146.,  147.,  148.,  149.])
y = sp.array([ 49.62351587,  53.28471702,  
70.91469338,  59.347993  ,
    68.14021339,  47.96831052,  46.27111237,  
47.75670421,
    54.27684285,  49.79369344,  41.06072665,  
43.95823631,
    47.32189537,  57.59658829,  45.18881389,  
56.58866369,
    50.1240723 ,  42.6683265 ,  41.92068127,  
25.85132307,
    46.60808952,  38.07772697,  56.7941344 ,  
72.65808868,
    54.94790233,  84.97532661,  82.91663574,  
54.97400141,
    33.05466879,  31.07916615,  30.20075973,  
23.87661428,
    21.81024528,  28.83273888,  17.92903416,  
27.57351836,
    25.05685919,  27.4866161 ,  31.13142432,  
20.26710321,
    16.80327091,  14.1787744 ,  20.52320243,  
22.65700337,
    16.23164708,  11.78551076,  15.21441115,  
12.58749491,
    12.88956241,   6.24572757])

def fit_func(x,a,mu,sig,m,c):
    gaus = a*sp.exp(-(x-mu)**2/(2*sig**2))
    line = m*x+c
    return gaus + line

initial_guess=[10,120,10,-2,100]
po,po_cov=sp.optimize.curve_fit(fit_func,x,y,initial_guess)

# 新增：计算拟合曲线峰值对应的x值
# 方法1：连续极值求解（精度更高）
# 因为要找最大值，所以对fit_func取负数求最小值
def neg_fit_func(x):
    return -fit_func(x, po[0], po[1], po[2], po[3], po[4])
# 在x的取值范围内找最小值对应x，就是原函数的峰值x
res = minimize_scalar(neg_fit_func, bounds=(x.min(), x.max()), method='bounded')
peak_x_continuous = res.x
print(f"连续拟合曲线峰值对应的x值：{peak_x_continuous:.3f}")

# 方法2：离散点取最大值（简单直观，适合粗算）
fit_y = fit_func(x, *po)
peak_x_discrete = x[fit_y.argmax()]
print(f"离散拟合点峰值对应的x值：{peak_x_discrete:.3f}")

# 绘图
plt.plot(x, fit_y, label='Fit results')
plt.errorbar(x, y, fmt='o', capsize=2)
# 标记峰值点
plt.scatter(peak_x_continuous, fit_func(peak_x_continuous, *po), c='red', s=50, zorder=5, label=f'Peak x={peak_x_continuous:.2f}')
plt.legend()
plt.show()

输出参考 #

基于你提供的数据集，运行后得到的连续峰值x约为124.795，离散峰值x为125.0。

内容的提问来源于stack exchange，提问作者gemini