Python+Matplotlib简单示例展示泛函、变换、函数

import numpy as np
import matplotlib.pyplot as plt# 设置中文字体
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号# 创建子图
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))# 1. 函数示例：f(x) = x^2
x = np.linspace(-2, 2, 100)
y = x**2ax1.plot(x, y)
ax1.set_title('函数: f(x) = x^2')
ax1.set_xlabel('x')
ax1.set_ylabel('y')
ax1.grid(True)# 2. 变换示例：g(x) = 2f(x) + 1
y_transformed = 2*y + 1ax2.plot(x, y, label='原函数')
ax2.plot(x, y_transformed, label='变换后')
ax2.set_title('变换: g(x) = 2f(x) + 1')
ax2.set_xlabel('x')
ax2.set_ylabel('y')
ax2.legend()
ax2.grid(True)# 3. 泛函示例：计算函数在区间[-1,1]上的平均值
def functional(f, a, b):x_vals = np.linspace(a, b, 1000)y_vals = f(x_vals)return np.mean(y_vals)f_values = [x**2, x**3, np.sin(x), np.cos(x)]
f_names = ['x^2', 'x^3', 'sin(x)', 'cos(x)']
averages = [functional(lambda x: f, -1, 1) for f in f_values]ax3.bar(f_names, averages)
ax3.set_title('泛函: 函数在[-1,1]上的平均值')
ax3.set_ylabel('平均值')
ax3.grid(True)plt.tight_layout()
plt.show()