Sum of products of pairs in a list

Question

This is the problem I have. Given a list

xList = [9, 13, 10, 5, 3]

I would like to calculate for sum of each element multiplied by subsequent elements

sum([9*13, 9*10, 9*5 , 9*3]) + 
sum([13*10, 13*5, 13*3]) + 
sum([10*5, 10*3]) + 
sum ([5*3])

in this case the answer is 608.

Is there a way to do this perhaps with itertools or natively with numpy?

Below is a function I came up with. It does the job but it is far from ideal as I would like to add other stuff as well.

    def SumProduct(xList):
        ''' compute the sum of the product 
        of a list 
        e.g. 
        xList = [9, 13, 10, 5, 3]
        the result will be 
        sum([9*13, 9*10, 9*5 , 9*3]) + 
        sum([13*10, 13*5, 13*3]) + 
        sum([10*5, 10*3]) + 
        sum ([5*3])
        '''
        xSum = 0
        for xnr, x in enumerate(xList):
            #print xnr, x
            xList_1 = np.array(xList[xnr+1:])
            #print x * xList_1
            xSum = xSum + sum(x * xList_1)
        return xSum

Any help appreciated.

N.B: In case you wonder, I am trying to implement Krippendorf's alpha with pandas

Answer 1

Here's one way:

In [14]: x = [9, 13, 10, 5, 3]

In [15]: np.triu(np.outer(x, x), k=1).sum()
Out[15]: 608

but I'd go with @user2357112's answer.