编码西格玛公式？

Question

Python初学者，运行2.7

我找不到用于编码以下公式的Pythonic方法。我的目标是拥有一个可以输入值的单一函数（在之前的尝试中我只发现了一个高度重复的暴力解决方案）。

必要信息：

如果您不知道sigma符号的含义：look here

# 'v' is the formula
# 'i' 'j' 'k' are actors with numerical attributes 'c' 's' and 'x'
# 'n' = length of the following lists (length is identical for all four lists)

values_1 = [Bob, Sue, Mary, Jo...] # i, j, and k are any 3 values drawn from this list  
                        # under the condition that i != j != k

values_2 = [5,6,7,8...] # c is drawn from this list. 
                        # if i = values_1[0], then c(i) = values_2[0]. 
                        # same for j and k

values_3 = [9,10,11,12...] # s is drawn from this list.  
                        # if i = values_1[0], then s(i) = values_3[0]

values_4 = [13,14,15, 16..] # x is drawn from this list. 
                           # if i = values_1[0], then x(i) = values_4[0].

def V (j,k):
        #this is where I need help!

v_Bob_Sue = # this is where V(Bob, Sue) should go.
            # this is what the math would look like in English:
# SUM of (c_Mary * s_Mary * ((abs(x_Mary - x_Sue) - abs(x_Mary - x_Bob)) / x's range))
# and (c_Jo * s_Jo * ((abs(x_Jo - x_Sue) - abs(x_Jo - x_Bob)) / x's range))

# Bob and Sue are the j and k value
# we do the formula with all the other actors (from values_1) who AREN'T Bob and Sue


v_Bob_Mary = # etc 
v_Bob_Jo = 
v_Sue_Bob =
v_Sue_Mary =
v_Sue_Jo =
v_Mary_Bob =
v_Mary_Sue =
v_Mary_Jo =
v_Jo_Bob =
v_Jo_Sue =
v_Jo_Mary =

Answer 1

至于“西格玛”，计算很简单，因为它也被称为“和”。 python中有一个内置函数：http://docs.python.org/library/functions.html#sum

至于你提供的公式，我认为你真正想念的是列表或数组。 i，j和k可以是n维数组的索引。 我会使用numpy包：

import numpy as np

c = np.asarray(values_2)
s = np.asarray(values_3)
x = np.asarray(values_4)

def V(j, k):
    return np.sum(c * s * (np.abs(x - x[j]) - np.abs(x - x[k])) / np.abs(x[-1] - x[0]))

这里Bob和Sue由values_1列表中的indice位置编码。这比使用字符串或类实例更容易。所以你会写：

v_Bob_Sue = V(0, 1)

如果要自动创建变量v_Bob_Sue，则需要动态定义变量名称。所以你需要exec语句如下：

for i in xrange(len(values_1)):
    for j in xrange(len(values_1)):
        exec("v_%s_%s = V(%u, %u)" % (values_1[i], values_1[j], i, j)

Answer 2

使用python 3.6.x，您可以尝试...

def sigma(lowerBound, upperBound):
    x = list(range(lowerBound, upperBound))
    print(" + ".join(str(i) for i in x) + " = " + str(sum(x)))

sigma(0, 10)

# output
0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45