使用lmfit拟合洛伦兹模型后，如何生成多数据点平滑曲线？

问题描述 #

使用lmfit的LorentzianModel拟合数据时，绘制的最佳拟合曲线仅在原始数据的x值点显示，尝试用np.linspace生成平滑x序列绘制拟合曲线时结果异常。

原始数据与代码 #

数据 #

y_means = [2.32070822e-06, 1.90175015e-06, 2.09473380e-06, 2.80934411e-06,
   2.38255275e-06, 3.02204121e-06, 3.84290466e-06, 3.84136311e-06,
   7.53941486e-06, 8.68364774e-06, 1.20078494e-05, 2.20557048e-05,
   3.73314724e-05, 6.03141332e-05, 9.84530711e-05, 1.58565010e-04,
   3.61269554e-04, 7.53586472e-04, 3.56518897e-04, 1.60734633e-04,
   1.06442283e-04, 5.41622644e-05, 2.73085592e-05, 2.54361900e-05,
   9.10802093e-06, 4.81356192e-06, 6.49884117e-06, 4.94871197e-06,
   3.27389990e-06, 2.65197533e-06, 2.52672943e-06, 2.56496345e-06,
   2.11445845e-06, 1.96091323e-06, 2.60823301e-06]

all_xslices = [ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
   17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
   34]

原始代码 #

# lorentzian fit
from lmfit.models import LorentzianModel

model = LorentzianModel()
params = model.guess(y_means, x=all_xslices)
all_xslices_fit = np.linspace(min(all_xslices), max(all_xslices), 100)
result = model.fit(y_means, params, x=all_xslices)
result_smooth = model.eval(x=all_xslices_fit)


# plotting the decay along y-axis: log axis
plt.figure(figsize=(8, 5), dpi=300)
plt.scatter(all_xslices, y_means, marker = '.', s = 200, c = 'g', label = "")      
# plt.plot(all_xslices,lorentzian(all_xslices,*popt), 'g', label='Lorentz 1')
plt.plot(all_xslices, result.best_fit, 'g', label='Lorentz')
plt.plot(all_xslices_fit, result_smooth, 'r', label='Lorentz')
plt.xlabel("y length", fontsize = 15)
plt.ylabel("FFT amplitude", fontsize = 15)
plt.xticks(fontsize = 15)
plt.yticks(fontsize = 15)
plt.yscale('log')
plt.subplots_adjust(right=0.96,left=0.15,top=0.96,bottom=0.12)
plt.legend(loc = 'best')
plt.show()

问题原因 #

生成平滑拟合曲线时，直接调用model.eval()但未传入拟合后的最优参数，导致使用初始猜测的params而非拟合得到的结果，这是平滑曲线异常的核心原因。

修正后的代码 #

import numpy as np
import matplotlib.pyplot as plt
from lmfit.models import LorentzianModel

# 数据
y_means = [2.32070822e-06, 1.90175015e-06, 2.09473380e-06, 2.80934411e-06,
           2.38255275e-06, 3.02204121e-06, 3.84290466e-06, 3.84136311e-06,
           7.53941486e-06, 8.68364774e-06, 1.20078494e-05, 2.20557048e-05,
           3.73314724e-05, 6.03141332e-05, 9.84530711e-05, 1.58565010e-04,
           3.61269554e-04, 7.53586472e-04, 3.56518897e-04, 1.60734633e-04,
           1.06442283e-04, 5.41622644e-05, 2.73085592e-05, 2.54361900e-05,
           9.10802093e-06, 4.81356192e-06, 6.49884117e-06, 4.94871197e-06,
           3.27389990e-06, 2.65197533e-06, 2.52672943e-06, 2.56496345e-06,
           2.11445845e-06, 1.96091323e-06, 2.60823301e-06]

all_xslices = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
               17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34]

# Lorentzian拟合
model = LorentzianModel()
params = model.guess(y_means, x=all_xslices)
result = model.fit(y_means, params, x=all_xslices)

# 生成平滑x序列并计算拟合值（使用拟合后的最优参数）
all_xslices_fit = np.linspace(min(all_xslices), max(all_xslices), 100)
result_smooth = result.eval(x=all_xslices_fit)  # 重点：用result.eval而非model.eval

# 绘图
plt.figure(figsize=(8, 5), dpi=300)
plt.scatter(all_xslices, y_means, marker='.', s=200, c='g', label='原始数据')
plt.plot(all_xslices, result.best_fit, 'g--', label='原始点拟合曲线')
plt.plot(all_xslices_fit, result_smooth, 'r-', label='平滑拟合曲线')

plt.xlabel("y length", fontsize=15)
plt.ylabel("FFT amplitude", fontsize=15)
plt.xticks(fontsize=15)
plt.yticks(fontsize=15)
plt.yscale('log')
plt.subplots_adjust(right=0.96, left=0.15, top=0.96, bottom=0.12)
plt.legend(loc='best')
plt.show()

# 可选：打印拟合结果
print(result.fit_report())

关键修改点 #

• 替换model.eval(x=all_xslices_fit)为result.eval(x=all_xslices_fit)：result对象包含拟合后的最优参数，调用其eval方法才能得到基于最优参数的平滑拟合曲线。
• 补充缺失的numpy和matplotlib导入语句，保证代码可直接运行。
• 给图例添加明确标签，区分原始数据、原始点拟合曲线和平滑拟合曲线，提升可读性。

内容的提问来源于stack exchange，提问作者Abhinav Kumar