误差非线性回归python曲线拟合

问题描述

大家好，我想用曲线拟合在 python 中进行非线性回归 这是我的代码：

#fit a fourth degree polynomial to the economic data
from numpy import arange
from scipy.optimize import curve_fit
from matplotlib import pyplot
import math

x = [17.47,20.71,21.08,18.08,17.12,14.16,14.06,12.44,11.86,11.19,10.65]
y = [5,35,65,95,125,155,185,215,245,275,305]

# define the true objective function
def objective(x,a,b,c,d,e):
    return ((a)-((b)*(x/3-5)))+((c)*(x/305)**2)-((d)*(math.log(305))-math.log(x))+((e)*(math.log(305)-(math.log(x))**2))

popt,_ = curve_fit(objective,x,y)
# summarize the parameter values
a,e = popt
# plot input vs output
pyplot.scatter(x,y)
# define a sequence of inputs between the smallest and largest kNown inputs
x_line = arange(min(x),max(x),1)
# calculate the output for the range
y_line = objective(x_line,e)
# create a line plot for the mapping function
pyplot.plot(x_line,y_line,'--',color='red')
pyplot.show()

这是我的错误：

回溯（最近一次调用最后一次）： 文件“C:\Users\Fahmi\PycharmProjects\pythonProject\main.py”，第 16 行，在 弹出，_ = 曲线拟合（目标，x，y） 文件“C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py”，第784行，在curve_fit中 res = leastsq(func,p0,Dfun=jac,full_output=1,**kwargs) 文件 "C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py",line 410,in leastsq 形状,dtype = _check_func('leastsq','func',func,x0,args,n) 文件“C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py”，第 24 行，在 _check_func res = atleast_1d(thefunc(((x0[:numinputs],) + args))) 文件“C:\Users\Fahmi\PycharmProjects\pythonProject\venv\lib\site-packages\scipy\optimize\minpack.py”，第 484 行，在 func_wrapped 返回 func(xdata,params) - ydata 文件“C:\Users\Fahmi\PycharmProjects\pythonProject\main.py”，第 13 行，目标 返回 ((a)-((b)(x/3-5)))+((c)(x/305)**2)-((d)( math.log(305))-math.log(x))+((e)(math.log(305)-(math.log(x))**2)) 类型错误：只有大小为 1 的数组可以转换为 Python 标量

谢谢

解决方法

这是数学库的一个已知问题。只需使用 numpy 即可解决您的问题，因为 numpy 函数支持标量和数组。

#fit a fourth degree polynomial to the economic data
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

x = [17.47,20.71,21.08,18.08,17.12,14.16,14.06,12.44,11.86,11.19,10.65]
y = [5,35,65,95,125,155,185,215,245,275,305]

# define the true objective function
def objective(x,a,b,c,d,e):
    return ((a)-((b)*(x/3-5)))+((c)*(x/305)**2)-((d)*(np.log(305))-np.log(x))+((e)*(np.log(305)-(np.log(x))**2))

popt,_ = curve_fit(objective,x,y)
# summarize the parameter values
a,e = popt
# plot input vs output
plt.scatter(x,y)
# define a sequence of inputs between the smallest and largest known inputs
x_line = np.arange(np.min(x),np.max(x),1)
# calculate the output for the range
y_line = objective(x_line,e)
# create a line plot for the mapping function
plt.plot(x_line,y_line,'--',color='red')
plt.show()