python实现数值积分的Simpson方法实例分析

#coding = utf-8#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 Ndef GenerateData(a,b,n,width): datas = [] r=a for i in range(0,n):  datas.append(func(r))  r = r+width return datasdef 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/3.0if __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)