编码西格玛公式？

Question

Python初学者,运行2.7

我找不到Pythonic方法来编写以下公式.我的目标是有一个单一的功能,我可以输入值(在以前的尝试我只发现了一个高度重复的暴力解决方案).

必要的信息:

如果您不知道sigma符号的含义:请看这里

# '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".在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,我认为你在这里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)