A variety of libraries can be used in Python to fit equations, the most commonly used of which are NumPy and SciPy. NumPy is a library for processing arrays and matrices, while SciPy provides a large number of scientific computing functions, including fitting algorithms.
1 Fitting of a linear equation of one variable
It should be noted that our equation here needs to be defined by ourselves, and then we can use curve_fit to find the parameters (coefficients) and covariance matrix in the equation.
def linear_equation_with_one_unknown():
# 需要自己定义方程
mpl.rcParams['font.sans-serif'] = ['SimHei'] # 显示中文
plt.rcParams['axes.unicode_minus'] = False # 解决负数坐标显示问题
x = np.array([1, 2, 3, 4, 5])
y = np.array([4, 6, 7, 9, 13])
def func(x1, a, b): # 定义拟合方程
return a*x1 + b
p_opt, p_cov = curve_fit(func, x, y) # p0 = 1是因为只有a一参数
print("方程参数最佳值为：", p_opt.astype(np.int64)) # 参数最佳值,np.round(popt, 4)
print("拟合方程协方差矩阵：\n", p_cov) # 协方差矩阵,popt[0],popt[1],popt[2]分别代表参数a b c
y_predict = func(x, p_opt[0], p_opt[1])
plt.scatter(x, y, marker='x', lw=1, label='原始数据')
plt.plot(x, y_predict, c='r', label='拟合曲线')
plt.legend() # 显示label
plt.show()
2 Fitting of quadratic equation of one variable
The code here is no different from the above. It just needs to change the defined function into a function of a quadratic equation. If it is other functions, such as exponential function and logarithmic function, you can modify it here.
def Uni_quadratic_equation():
# 需要自己定义方程
mpl.rcParams['font.sans-serif'] = ['SimHei'] # 显示中文
plt.rcParams['axes.unicode_minus'] = False # 解决负数坐标显示问题
# x = np.a range(0, 20)
# y = 2 * x ** 2 + np.random.randint(0, 100, 20)
x = np.array([1, 2, 3, 4, 5])
y = np.array([1, 4, 9, 16, 25])
def func(x1, a, b, c): # 定义拟合方程
return a*x1**2 + b*x1 + c
p_opt, p_cov = curve_fit(func, x, y) # p0 = 1是因为只有a一参数
print("方程参数最佳值为：", p_opt.astype(np.int64)) # 参数最佳值,np.round(popt, 4)
print("拟合方程协方差矩阵：\n", p_cov) # 协方差矩阵,popt[0],popt[1],popt[2]分别代表参数a b c
y_predict = func(x, p_opt[0], p_opt[1], p_opt[2])
plt.scatter(x, y, marker='x', lw=1, label='原始数据')
plt.plot(x, y_predict, c='r', label='拟合曲线')
plt.legend() # 显示label
plt.show()
3 Summary
Today I only share the fitting of linear and quadratic equations of one variable. There is no difference in the code. It is just a matter of changing the initially defined equation. Theoretically, this code can be used directly as long as x and y are single. If there are multiple independent variables (multivariate), you cannot use this code directly. At present, I have not studied the problem of multiple regression. I will write it down and share it with you later.