计算序列除以零误差

问题描述

我正在尝试计算序列，但遇到了一个我不知道为什么会发生的问题。

“ RuntimeWarning：除以double_scalars中的零”

当我检查代码时，它似乎没有任何奇异之处，所以我很困惑。这是当前代码（对数代表自然对数）（编辑：如果有帮助，扩展代码）：

from numpy import pi,log


#Create functions to calculate the sums

def phi(z: int):
    k = 0
    phi = 0

    #Loop through 1000 times to try to approximate the series value as if it went to infinity

    while k <= 100:
        phi += ((1/(k+1)) - (1/(k+(2*z))))
        k += 1

    return phi

def psi(z: int):
    psi = 0
    k = 1

    while k <= 101:
        psi += ((log(k))/( k**(2*z)))
        k += 1
    
    return psi

def sig(z: int):
    sig = 0
    k = 1

    while k <= 101:
        sig += ((log(k))**2)/(k^(2*z))
        k += 1

    return sig

def beta(z: int):
    beta = 0
    k = 1

    while k <= 101:
        beta += (1/(((2*z)+k)^2))
        k += 1
    
    return beta


#Create the formula to approximate the value. For higher accuracy,either calculate more derivatives of Bernoulli numbers or increase the boundry of k.

def Bern(z :int):
    #Define Euler–Mascheroni constant

    c = 0.577215664901532860606512

    #Begin computations (only approximation)

    B = (pi/6) * (phi(1) - c - 2 * log(2 * pi) - 1) - z * ((pi/6) * ((phi(1)- c - (2 * log(2 * pi)) - 1) * (phi(1) - c) + beta(1) - 2 * psi(1)) - 2 * (psi(1) * (phi(1) - c) + sig(1) + 2 * psi(1) * log(2 * pi)))

    #output

    return B

A = int(input("Choose any value: "))
print("The answer is",Bern(A + 1))

任何帮助将不胜感激。

解决方法

确定要使用^ 按位互斥或运算符而不是**吗？我尝试用输入参数z = 1运行您的代码。在第二次迭代中，k^(2*z)的结果等于0，所以零除法误差从哪里来（2 ^ 2 * 1 = 0 ）。