使用 scipy.integrate.dblquad 在 Python 中对 x*np.log(x) 进行双重积分 [英] Double integration of x*np.log(x) in Python using scipy.integrate.dblquad

问题描述

下面的代码使用与 scipy.integrate.dblquad 的双重积分来计算 copula 密度函数的微分熵 c*np.log(c)code>c，它有一个依赖参数，theta，通常为正.可以在

将 numpy 导入为 np从 scipy 导入集成def copula_entropy(theta):c = lambda v, u: ((1+theta)*(u*v)**(-1-theta)) * (u**(-theta)+ v**(-theta) -1)**(-1/theta-2)返回 -integrate.dblquad(c*np.log(c), 0, 1, lambda u: 0, lambda u: 1)[0]

调用函数

copula_entropy(1)

返回错误

TypeError: ufunc 的循环不支持没有可调用日志方法的函数类型的参数 0

如何使函数起作用?

解决方案

第一个参数必须是可调用的，所以只需将它包装在 lambda 本身中:

将 numpy 导入为 np从 scipy 导入集成def copula_entropy(theta):c = lambda v, u: ((1+theta)*(u*v)**(-1-theta)) * (u**(-theta)+v**(-theta)-1)**(-1/theta-2)return -integrate.dblquad(lambda u,v: c(v,u)*np.log(c(v,u)), 0, 1, lambda u: 0, lambda u: 1)[0]

(请注意，我还根据您提供的公式更改了 c 的表达式).

The code below uses double integration with scipy.integrate.dblquad to calculate the differential entropy, c*np.log(c), of a copula density function c, which has one dependence parameter, theta, usually positive. Formula can be found here.

import numpy as np
from scipy import integrate 

def copula_entropy(theta):
    c = lambda v, u: ((1+theta)*(u*v)**(-1-theta)) * (u**(-theta) 
        + v**(-theta) -1)**(-1/theta-2)
    return -integrate.dblquad(c*np.log(c), 0, 1, lambda u: 0, lambda u: 1)[0] 

Calling the function with

copula_entropy(1)

returns the error

TypeError: loop of ufunc does not support argument 0 of type function which has no callable log method

How can the function be made to work?

解决方案

The first argument must be a callable, so just wrap it in a lambda itself:

import numpy as np
from scipy import integrate 

def copula_entropy(theta):
    c = lambda v, u: ((1+theta)*(u*v)**(-1-theta)) * (u**(-theta)+v**(-theta)-1)**(-1/theta-2)
    return -integrate.dblquad(lambda u,v: c(v,u)*np.log(c(v,u)), 0, 1, lambda u: 0, lambda u: 1)[0] 

(Please note that I also changed the expression for c according to the formula you gave).

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