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【数值积分】scipy.integrate
source link: https://www.guofei.site/2017/06/06/scipyintegrate.html
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【数值积分】scipy.integrate
2017年06月06日Author: Guofei
文章归类: 5-5-数值计算 ，文章编号: 7512
版权声明：本文作者是郭飞。转载随意，但需要标明原文链接，并通知本人
原文链接：https://www.guofei.site/2017/06/06/scipyintegrate.html
定积分
step1：生成数据
import numpy as np
def func(x):
return np.sin(x**2)
import numpy as np
x=np.linspace(-1,1,1000)
y=func(x)
step2：计算定积分
- 矩形法计算定积分，最不准确但最方便的一种
S1=(x[1]-x[0])*sum(y) - 梯形法。比矩形法准一些
S2=np.trapz(y,x) - 貌似是simpson算法？
from scipy import integrate S3,err=integrate.quad(func,-1,1)
二重积分dblquad()
例如，要算这个定积分：
∫0.5−0.5∫1−x2√−1−x2√sin((xy)2)dydx∫−0.50.5∫−1−x21−x2sin((xy)2)dydx
import numpy as np
from scipy import integrate
def fun(x,y):#被积函数
return np.sin((x*y)**2)
def bound(x):#用来生成积分上界和下界
return (1-x**2)**0.5
S,err=integrate.dblquad(fun,-0.5,0.5,lambda x:-bound(x),lambda x:bound(x))
或者另一种形式：
import numpy as np
from scipy import integrate
def fun(x,y):#被积函数
return np.sin((x*y)**2)
def bound1(x):#积分上界
return -(1-x**2)**0.5
def bound2(x):#积分下界
return (1-x**2)**0.5
S,err=integrate.dblquad(fun,-0.5,0.5,bound1,bound2)
三重积分tplquad()
三重积分tplquad，非分方程odeint() 略
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