使用lambdify将硬积分转换为lambda函数 [英] Converting hard integral to lambda function with lambdify

问题描述

我想对函数 Integral(t ** t，(t，0，x))进行lambdize.它可以工作，但是由 lambdify 返回的我的新函数不返回数字，而仅返回 sympy.integrals.integrals.Integral 类.但我不希望这样，我希望它返回一个浮点数.

I would like to lambdify the function Integral(t**t,(t,0,x)). It works, but my new function, which was returned by lambdify, doesn't return a number but only sympy.integrals.integrals.Integral class. But I don't want that, I want it to return a float number.

这是我的代码:

import sympy as sp
import numpy as np
f = sp.lambdify(x,sp.integrate(t**t,(t,0,x)))
print(f(2)) #return Integral(t**t, (t, 0, 2))
#but i want 2.83387674524687

推荐答案

lambdify 不直接支持 scipy.integrate.quad

lambdify doesn't support scipy.integrate.quad directly yet, but it's not difficult to add the appropiate definition. One simply needs to tell lambdify how to print Integral:

def integral_as_quad(expr, lims):
    var, a, b = lims
    return scipy.integrate.quad(lambdify(var, expr), a, b)

f = lambdify(x, Integral(t**t,(t,0,x)), modules={"Integral": integral_as_quad})

结果是

In [42]: f(2)
Out[42]: (2.8338767452468625, 2.6601787439517466e-10)

我们在这里正在定义一个函数 integral_as_quad ，该函数将SymPy Integral 转换为 scipy.integrate.quad 调用，递归地对被积数进行lambd化(如果您有更复杂或符号化的积分限制，那么您也将希望递归地对这些被积数进行lambdize).

What we're doing here is defining a function integral_as_quad, which translates a SymPy Integral into a scipy.integrate.quad call, recursively lambdifying the integrand (if you have more complicated or symbolic integration limits, you'll want to recursively lambdify those as well).

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