[Mathematical Model] Python fitting multivariate equations (linear regression)

        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.

        The fitting of linear/quadratic equations of one variable has been shared before. If you are interested, you can check out: Fitting of Univariate Equations in Python . Today I will share with you how to use Python to fit multivariate equations.

1 Python code

        The same functions used here are curve_fit, so I won’t introduce them in detail. The binary implementation is implemented using a two-dimensional array. See the code for details. In addition, code for three-dimensional visualization has been added.

# -*- coding: utf-8 -*-
"""
@Time ： 2023/12/25 9:21
@Auth ： RS迷途小书童
@File ：Regressive Analysis.py
@IDE ：PyCharm
@Purpose：线性回归
@Web：博客地址:https://blog.csdn.net/m0_56729804
"""
import numpy as np
import pylab as mpl
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit


def binary_linear_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.array([[1, 4], [2, 1], [3, 1], [4, 2],  [5, 1], [9, 3]])
    y = np.array([33, 4, 5, 12, 7, 27])

    def func(x1, a, b, c):
        return a * b * x1.T[0] + c * x1.T[1] ** 2
    p_opt, p_cov = curve_fit(func, x, y)
    print("方程参数最佳值为：", p_opt.astype(np.int64))  # 参数最佳值,np.round(p_opt, 4)
    print("拟合方程协方差矩阵：\n", p_cov)
    y_fit = func(x, *p_opt)  # 使用拟合参数计算对应的y值
    # ------------------可视化------------------
    mpl.rcParams['legend.fontsize'] = 12  # 将图例的字体大小设置为12
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    ax.scatter(x.T[0], x.T[1], y, marker='x', lw=2, label='原始数据')
    ax.plot(x.T[0], x.T[1], y_fit, c='r', label='拟合曲线')
    plt.legend()  # 显示label
    plt.tight_layout()  # 自动调整子图参数，使其内部组件（例如轴、标题、标签等）之间以及与子图边缘之间没有重叠。
    plt.show()


if __name__ == "__main__":
    # linear_equation_with_one_unknown()
    # Uni_quadratic_equation()
    binary_linear_equation()

2 Summary

        The blog post on fitting equations will not be updated from now on, because I have no need for this yet. Logarithmic, exponential, idempotent equations can also be implemented with the above code, so I won’t be verbose anymore. Other aspects of code and theory will be updated later. If you are interested, you can follow me!