Scipy curve_fit拟合线偏移至图表顶部问题求助

我需要基于Excel文件绘制散点图及带误差的最佳拟合线，但使用Scipy的curve_fit得到的拟合线偏移至图表顶部，显示异常。已完成云盘挂载，散点图显示正常，附上代码、生成的图表及数据说明。

原代码 #

import matplotlib.pyplot as plt
import numpy as np
from sympy import S, symbols, printing
import scipy.optimize as sci
import pandas as pd
from pathlib import Path


#Importing all the relevant packages for the code, plotting, finding the best fit, analyzing our data and error analysis
file=pd.read_csv(r'/content/drive/MyDrive/Dataset 1(no offset part1 plate 1).csv',sep=";")
file = file.replace(r",", ".", regex=True).astype(float)
x_axis=file['Current I_A1 / A']
y_axis=file['Voltage U_B2 / V']


#Making an array of our calculated Indices of Refraction
plt.title("Hall Voltage vs Current for -10, mT B Field") #Giving our plot a relevant title that also explains what is being plotted so the graph is stand-alone
plt.xlabel("Current [A]") #Giving the x axis a label
plt.ylabel("Hall Voltage [V]") #Giving the y axis a label
plt.grid() #Giving the plot a grid.
def f(x,a,b):
    f=a*x+b
    return f #Defining our function that is going to be fitted through our data points
def g(x,a,b): #Definin the theoretical function
    g=a*x+b
    return g
plt.scatter(x_axis,y_axis, color='purple', label= 'measured') #Making a scatter plot of our data points with a Label
fit1, covariance1 = sci.curve_fit(f, x_axis, y_axis) #Using scipy making a best fit throug the data points
plt.plot(x_axis, f(x_axis,*fit1), label='Best Fit')  #Displaying the equation of best fit line in the plot #Displaying the equation of best fit line in the plot
plt.legend(loc='best') #Showing the labels belonging to both graphs
plt.show() #Showing the plot
print("n","=",round(fit1[0],4),"*","C" ,"+",abs(round(fit1[1],3))) #Printhing the equation of the best fit and giving the appropiate amount of decimals
print("delta a=",round(np.sqrt(covariance1[0][0]),4)) #Print the uncertainty of the slope of the best fit
print("delta b =",round(np.sqrt(covariance1[1][1]),4)) #Print the uncertainty of the y intercept of the best fit

异常图表 #

数据说明 #

数据为-10mT磁场下霍尔电压与电流的测量值，包含两列：电流（Current I_A1 / A）、霍尔电压（Voltage U_B2 / V）。

问题根源 #

拟合线偏移是因为curve_fit默认初始参数[1,1]与数据实际趋势（斜率为负、毫伏级量级）偏差过大，导致拟合收敛到局部最优解；同时数据处理环节未验证转换结果，可能隐藏格式错误。

修正步骤与代码 #

1. 先验证数据读取结果，确保小数格式转换正确
2. 手动指定符合数据趋势的初始拟合参数，引导curve_fit收敛到正确解
3. 简化冗余代码，避免不必要的模块导入

import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as sci
import pandas as pd

# 读取并验证数据
file = pd.read_csv('/content/drive/MyDrive/Dataset 1(no offset part1 plate 1).csv', sep=";")
# 转换欧洲格式小数（逗号转点），并指定列类型确保转换正确
file = file.replace(',', '.', regex=True)
file = file.astype({'Current I_A1 / A': float, 'Voltage U_B2 / V': float})
x_axis = file['Current I_A1 / A']
y_axis = file['Voltage U_B2 / V']

# 打印数据前5行，确认电压为毫伏级负数
print("数据预览：")
print(file.head())

# 绘图与拟合
plt.title("-10mT磁场下霍尔电压与电流的关系")
plt.xlabel("电流 [A]")
plt.ylabel("霍尔电压 [V]")
plt.grid()

# 定义线性拟合函数
def linear_fit(x, a, b):
    return a * x + b

# 根据散点趋势指定初始参数p0：斜率为负，截距接近0
fit_params, covariance = sci.curve_fit(linear_fit, x_axis, y_axis, p0=[-0.002, 0])

plt.scatter(x_axis, y_axis, color='purple', label='测量数据')
plt.plot(x_axis, linear_fit(x_axis, *fit_params), label='最佳拟合线')
plt.legend(loc='best')
plt.show()

# 输出拟合结果与误差
print(f"拟合方程：U = {round(fit_params[0], 6)} * I + {round(fit_params[1], 6)}")
print(f"斜率误差：δa = {round(np.sqrt(covariance[0][0]), 6)}")
print(f"截距误差：δb = {round(np.sqrt(covariance[1][1]), 6)}")

关键说明 #

• 验证数据是第一步：确保电压列数值为毫伏级负数，避免格式转换错误导致拟合基础数据异常
• 初始参数引导拟合：当数据量级与默认初始值偏差较大时，手动指定p0能避免curve_fit收敛到错误的局部最优解
• 冗余模块清理：原代码导入的sympy和Path未实际使用，可删除以简化代码

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