如何在Python中自动绘制数据框中的多条线性方程？

需求说明 #

批量绘制存储在DataFrame中的线性约束方程，方程形式为 λ₁x₁ + λ₂x₂ = b，需区分<=和>=两种约束类型，自动处理参数为0的边界场景。

优化实现代码 #

以下是修复了原代码注释错误、补充约束区域填充逻辑的实现：

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

# 示例DataFrame，替换为你的实际数据
df = pd.DataFrame([
    {'λ1': 2, 'λ2': 3, 'b': 6, 'Restrições': '<='},
    {'λ1': 0, 'λ2': 2, 'b': 4, 'Restrições': '>='},
    {'λ1': 3, 'λ2': 0, 'b': 3, 'Restrições': '<='},
    {'λ1': 1, 'λ2': -1, 'b': 0, 'Restrições': '>='}
])

plt.figure(figsize=(8, 6))

for _, row in df.iterrows():
    b = row['b']
    λ1 = row['λ1']
    λ2 = row['λ2']
    restricao = row['Restrições']
    
    # 情况1：λ1为0，方程为 λ₂x₂ = b
    if λ1 == 0:
        if λ2 == 0:
            continue  # λ1和λ2都为0时无有效约束
        y_intercept = b / λ2
        # 绘制直线
        plt.axvline(x=0, ymin=0, ymax=y_intercept/10, linestyle='solid', 
                    label=f'0x₁+{λ2}x₂ {restricao} {b}')
        # 填充约束区域
        if restricao == '<=':
            plt.fill_betweenx([0, y_intercept], 0, 10, color='lightblue', alpha=0.3)
        else:
            plt.fill_betweenx([y_intercept, 10], 0, 10, color='lightgreen', alpha=0.3)
    
    # 情况2：λ2为0，方程为 λ₁x₁ = b
    elif λ2 == 0:
        x_intercept = b / λ1
        # 绘制直线
        plt.axhline(y=0, xmin=0, xmax=x_intercept/10, linestyle='solid', 
                    label=f'{λ1}x₁+0x₂ {restricao} {b}')
        # 填充约束区域
        if restricao == '<=':
            plt.fill_between([0, x_intercept], 0, 10, color='lightblue', alpha=0.3)
        else:
            plt.fill_between([x_intercept, 10], 0, 10, color='lightgreen', alpha=0.3)
    
    # 情况3：b为0，方程为 λ₁x₁ + λ₂x₂ = 0（过原点）
    elif b == 0:
        x = np.linspace(0, 10, 100)
        y = (-λ1 / λ2) * x
        plt.plot(x, y, linestyle='solid', label=f'{λ1}x₁+{λ2}x₂ {restricao} 0')
        # 填充约束区域
        if restricao == '<=':
            plt.fill_between(x, 0, y, color='lightblue', alpha=0.3)
        else:
            plt.fill_between(x, y, 10, color='lightgreen', alpha=0.3)
    
    # 情况4：常规场景，λ1、λ2、b均不为0
    else:
        x_intercept = b / λ1
        y_intercept = b / λ2
        # 绘制直线
        plt.plot([x_intercept, 0], [0, y_intercept], linestyle='solid', 
                 label=f'{λ1}x₁+{λ2}x₂ {restricao} {b}')
        # 填充约束区域
        x = np.linspace(0, x_intercept, 100)
        y_line = (-λ1 / λ2) * x + b / λ2
        if restricao == '<=':
            plt.fill_between(x, 0, y_line, color='lightblue', alpha=0.3)
        else:
            plt.fill_between(x, y_line, 10, color='lightgreen', alpha=0.3)

plt.xlabel('x₁')
plt.ylabel('x₂')
plt.title('线性约束方程可视化')
plt.xlim(0, 10)
plt.ylim(0, 10)
plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(True)
plt.show()

代码说明 #

• 遍历DataFrame逐行提取约束参数，分4种场景处理边界情况，避免报错
• 新增约束区域填充（浅蓝色对应<=，浅绿色对应>=），直观展示约束范围
• 优化图表布局，添加坐标轴标签、标题、网格和错位图例，提升可读性

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