ValueError：调用函数时数学域错误，但单独运行正常

Question

我知道这个问题可能是个新手问题，所以提前道个歉。我读过几本关于基础Python使用的书，现在正在做《编程集体智慧》里的教程，但我在我的代码块中遇到了一个错误：

ValueError: math domain error

我在谷歌上看到过很多类似的错误，但我不太明白为什么会发生。这个程序基本上是处理一个包含电影评论家及其评论的字典，然后第一个函数（sim_pearson）会告诉你两个评论家有多相似。这部分单独运行是没问题的。问题出在我尝试将一个用户与其他所有人进行比较，以便对评论家进行排名时。

这是代码：

# A dictionary of movie critics and their ratings of a small
# set of movies
critics={'Lisa Rose': {'Lady in the Water': 2.5, 'Snakes on a Plane': 3.5,
'Just My Luck': 3.0, 'Superman Returns': 3.5, 'You, Me and Dupree': 2.5,
'The Night Listener': 3.0},
'Gene Seymour': {'Lady in the Water': 3.0, 'Snakes on a Plane': 3.5,
'Just My Luck': 1.5, 'Superman Returns': 5.0, 'The Night Listener': 3.0,
'You, Me and Dupree': 3.5},
'Michael Phillips': {'Lady in the Water': 2.5, 'Snakes on a Plane': 3.0,
'Superman Returns': 3.5, 'The Night Listener': 4.0},
'Claudia Puig': {'Snakes on a Plane': 3.5, 'Just My Luck': 3.0,
'The Night Listener': 4.5, 'Superman Returns': 4.0,
'You, Me and Dupree': 2.5},
'Mick LaSalle': {'Lady in the Water': 3.0, 'Snakes on a Plane': 4.0,
'Just My Luck': 2.0, 'Superman Returns': 3.0, 'The Night Listener': 3.0,
'You, Me and Dupree': 2.0},
'Jack Matthews': {'Lady in the Water': 3.0, 'Snakes on a Plane': 4.0,
'The Night Listener': 3.0, 'Superman Returns': 5.0, 'You, Me and Dupree': 3.5},
'Toby': {'Snakes on a Plane':4.5,'You, Me and Dupree':1.0,'Superman Returns':4.0}}

from math import sqrt
#now lets use the pearson correlation score to see if we can get better results
#Returns the pearson correlation coefficient for p1 and p2
def sim_pearson(prefs, p1, p2):
    #get the list of mutually rated items
    si={}
    for item in prefs[p1]:
        if item in prefs[p2]:
            si[item]=1

    #find the number of elements
    n=len(si)

    # if they have no rating in common, return 0
    if n == 0: return 0

    #add up all the preferences
    sum1=sum([prefs[p1][it] for it in si])
    sum2=sum([prefs[p2][it] for it in si])

    #sum up the squares
    sum1Sq=sum([pow(prefs[p1][it],2) for it in si])
    sum2Sq=sum([pow(prefs[p2][it],2) for it in si])

    #sum up the products
    pSum=sum([prefs[p1][it]*prefs[p2][it] for it in si])

    #Calculate Pearson score
    num=pSum-(sum1*sum2/n)
    den=sqrt((sum1Sq-pow(sum1,2)/n)* sum2Sq-pow(sum2,2)/n)

    if den == 0: return 0
    r=num/den

    return r


#lets check out the results
print 'here are the results from the Pearson algo:'
print sim_pearson(critics, 'Lisa Rose', 'Gene Seymour')
print sim_pearson(critics, 'Mick LaSalle', 'Jack Matthews')

#now lets rank critics to see who is the most simlair
#Returns the best matches for person from prefs dictionary
#Number of results and similarity functions are optional params.

def topMatches(prefs, person, n=5, similarity=sim_pearson):
    scores=[(similarity(prefs, person, other),other)
            for other in prefs if other != person]
    #sort the list so the highest scores appear at the top
    scores.sort()
    scores.reverse()
    return scores[0:n]


#lets see the ranking
print 'here are the top matches:'
print topMatches(critics, 'Toby', n=3)

错误追踪信息显示有3行代码出现了问题：追踪信息（最近的调用在最后）：

print topMatches(critics, 'Toby', n=3)
for other in prefs if other != person]
den=sqrt((sum1Sq-pow(sum1,2)/n)* sum2Sq-pow(sum2,2)/n)

我不太明白这里发生了什么。这里是书中预期的答案：

[(0.9912, 'Lisa Rose')], (0.9244, 'Mick LaSalle'), (0.8934, 'Claudia Puig')

提前谢谢你们

（坦白说：我数学不好，还在学习Python，所以可能有一些我没注意到的基本问题，但我仔细检查了书中的代码，觉得没有打错字或者其他问题）。

函数调用数据处理错误追踪值错误编程新手相似度计算数学域错误电影评论分析

ValueError：调用函数时数学域错误，但单独运行正常

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