scipy积分 integral

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2018/5/24 15:03
# @Author  : zhang chao
# @File    : s.py

#integral积分
import numpy as np
from scipy.integrate import quad,dblquad,nquad
print(quad(lambda x:np.exp(-x),0,np.inf))#lambda x:np.exp(-x)定义函数，它的积分；定义区间为0-inf
#结果为(1.0000000000000002, 5.842606703608969e-11)
#1.0000000000000002为积分的值；5.842606703608969e-11为误差的范围
print(dblquad(lambda t,x:np.exp(-x*t)/t**3,0,np.inf,lambda x:1,lambda x:np.inf))
#dblquad为二元积分，lambda t,x:np.exp(-x*t)/t**3为积分函数；0,np.inf为t的取值范围；
#lambda x:1,lambda x:np.inf其实为x的取值范围，定义为t的函数
#结果为(0.33333333325010883, 1.3888461883425516e-08)
#nquad为多维积分，多元积分
def f(x,y):
    return x*y
def bound_y():
    return [0,0.5]
def bound_x(y):
    return [0,1-2*y]
print(nquad(f,[bound_x,bound_y]))#(0.010416666666666668, 4.101620128472366e-16)