python与计算物理：实现数值积分的Simpson方法

"""
作者：皮蛋编程(https://www.pidancode.com)
创建日期：2022/3/24
功能描述：python与计算物理：实现数值积分的Simpson方法
"""

# simpson 法计算积分，数值积分，效果非常理想
from math import *


def func(x):
    """
    定义被积分函数
    """
    return x * sin(x)

def Get_N(a, b, width):
    # width为步长
    N = int((b - a) / width + 1)
    if N % 2 == 0:
        N = N + 1
    return N


def GenerateData(a, b, n, width):
    datas = []
    r = a
    for i in range(0, n):
        datas.append(func(r))
        r = r + width
    return datas


def simpson_integral(datas, width, n):
    sum = datas[0] + datas[n - 1]
    for i in range(2, n):
        if i % 2 == 0:
            sum = sum + 4 * datas[i - 1]
        else:
            sum = sum + 2 * datas[i - 1]
    return sum * width / 3.0


if __name__ == "__main__":
    a = 1.0  # 积分上限
    b = 3.0  # 积分下限
    width = 0.0625  # 步长
    N = Get_N(a, b, width)
    datas = GenerateData(a, b, N, width)
    print(simpson_integral(datas, width, N))