Q:

Python Sigma Sums

I have a list of values 
x=[1,-1,-1,1,1,-1,1,-1,1,-1]
and I have another blank list
y=[ ]
I am trying to create a function that will take a sigma sum of values in x and store them in y.
For instance, y[0] should be the sum of x[0]*x[0] + x[0]*x[1] + x[0]*x[2] + ... + x[0]*x[9] .
Similarly, y[1] should be the sum of x[1]*x[0] + x[1]*x[1] + x[1]*x[2]+ ... + x[1]*x[9].
This has to be done for y[0] through y[9]. 
Also, in the sums, x[i]*x[i] must be zero. So for instance in y[0], x[0]*x[0] has to be zero. Similarly, in the sum for y[1], x[1]*x[1] must be zero.
This is my code, but it always gives me some sort of error regarding indices:
x=[1,-1,-1,1,1,-1,1,-1,1,-1]
y=[]
def list_extender(parameter):
    for i in parameter:
        parameter[i]*parameter[i]==0
        variable=numpy.sum(parameter[i]*parameter[:])
        if variable>0:
            variable=1
        if variable<0:
            variable=-1
        y.append(variable)
    return y

Then i run print list_extender(x) which should print list y with the sigma sums described above, but I always get an error. What I am doing wrong?
The help will be highly appreciated!

A:

You're doing way too much typing and computation here. Your function could be shorter and simpler if you computed the sum of x first, then used that to compute the elements of y. It'd also run faster.
Just do this:
x_sum = sum(x)
y = [item * (x_sum - item) for item in x]
# or, if you really want to store the results into an existing list y
# y[:] = [item * (x_sum - item) for item in x]

Replace sum and the list comprehension with numpy operations if you're using numpy:
import numpy as np
x = np.array([1,-1,-1,1,1,-1,1,-1,1,-1])
y = x * (x.sum() - x)

