python:积分未知的上限内含未知的fsolve [英] python: fsolve with unknown inside the upper limit of an integral

问题描述

是否可以将fsolve方法应用于上限和被积分数未知的积分???我正在使用Quad方法在python中进行集成.

Is it possible to apply fsolve method for an integral with the unknown in the upper limit and in the integrand??? I am ussing quad method for integration in python.

提前谢谢！

推荐答案

可以.

假设您要查找x，使得t *(1-x * t)的从t = 0到t = x的t上的积分为0.您可以通过定义两个函数来做到这一点. integrand(t, x)将计算t *(1-x * t)，func(x)将使用quad对integrand进行积分，其中x既是积分的上限，又是被积分数的额外参数.这是一个演示:

Suppose you want to find x such that the integral over t from t=0 to t=x of t*(1-x*t) is 0. You can do this by defining two functions. integrand(t, x) will evaluate t*(1-x*t), and func(x) will integrate integrand using quad, with x as both the upper limit of the integration, and as the extra argument of the integrand. Here's a demo:

import numpy as np
from scipy.integrate import quad
from scipy.optimize import fsolve


def integrand(t, x):
    return t*(1 - x*t)


def func(x):
    y, err = quad(integrand, 0, x, args=(x,))
    return y


# Use 1.0 as the initial guess.  Note that a bad initial guess
# might generate a warning and return the degenerate solution at x=0.
sol = fsolve(func, 1.0)

print "Solution:      ", sol[0]

# The exact solution that we want is sqrt(3/2)
print "Exact solution:", np.sqrt(1.5)

输出:

Solution:       1.22474487139
Exact solution: 1.22474487139

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