Styjun

I am trying to write a python function that takes an index of a list as an input n1, then in an interval of size w, selects [n1-w,n1+w] selects another index n2 with probability that decays as a function of the separation between n1 and n2 and returns the index n2 and the element of the list corresponding to n2.

In my current implementation ("Attempt 1"), first I compute all the probabilities using, then select an index with the weights.

This works fine (I think) given a list [0,1,2,3,4,5,6,7,8,9]
and if my n1 is somewhere in the middle say 5 and w=2, then an element is being chosen from the interval
[3 4 5 6 7] with probability weights [0.16666667 0.33333333 0. 0.33333333 0.16666667].

The problem I am dealing with is if I am selecting an element from the ends, for example, choosing n2choice(8) gives

[6 7 8 9]#indices interval
[0.2 0.4 0. 0.4]#weights

Instead I would like an interval

[6 7 8 9 0]# indices interval
[0.16666667 0.33333333 0. 0.33333333 0.16666667]#weights

Or similarly, at the other end, n2choice(1) gives [0 1 2 3]#interval
[0.2 0.4 0. 0.4]#weights

Instead I would like to get

[9 0 1 2 3]# indices interval
[0.16666667 0.33333333 0. 0.33333333 0.16666667]#weights

Essentially, I would like to convert the current "absorbing" boundary conditions I have implemented to "periodic boundaries" wherein the 1D list is in fact treated as a 1D ring.

To do so i used i tried using the % operator (see attempt 2). However this throws an "IndexError: list index out of range". I could use some help troubleshooting this code, and also suggestion on a fast, pythonic way to do this. I would like to be able to do this for arrays of arbitrary length, and with arbitrary w, instead of this simple test case presented here.

#Attempt 1
import numpy as np
import random
a = [0,1,2,3,4,5,6,7,8,9]
w =2
mylist = np.array(a)
indices_list = np.arange(mylist.size)
def n2choice(n1):
 prob_wts = [0 if i+(n1-w) == n1 else 1/(abs(i+(n1-w)-n1))**(1.) for i in np.arange(mylist[max(n1-w,0):n1+w+1].size)]
 prob_wts = np.array(prob_wts)/sum(prob_wts)
 #for i in np.arange(mylist[max(n1-w,0):n1+w+1].size):
 #print(i, i+(n1-w))

 print(prob_wts)
 print(sum(prob_wts))
 print(indices_list[max(n1-w,0):n1+w+1])
 n2 = random.choices(indices_list[max(n1-w,0):n1+w+1], weights=prob_wts,k=1)
 print(prob_wts[max(n1-w,0):n1+w+1])
 n2_c = (n2[0], mylist[n2[0]])
 return np.array(n2_c) 
n2choice(5)

#Attempt 2
import numpy as np
import random
import itertools
a = [0,1,2,3,4,5,6,7,8,9]
w =2
mylist = np.array(a)
indices_list = np.arange(mylist.size)
def n2choice(n1):
 prob_wts = [0 if i+(n1-w) == n1 else 1/(abs(i+(n1-w)-n1))**(1.) for i in np.arange(mylist[(n1 - w)%len(mylist):(n1+w+1)%len(mylist)].size)]
 prob_wts = np.array(prob_wts)/sum(prob_wts)
 #for i in np.arange(mylist[max(n1-w,0):n1+w+1].size):
 #print(i, i+(n1-w))

 print(prob_wts)
 print(sum(prob_wts))
 print(indices_list[(n1 - w)%len(mylist):(n1+w+1)%len(mylist)])
 n2 = random.choices(indices_list[(n1 - w)%len(mylist):(n1+w+1)%len(mylist)], weights=prob_wts,k=1)
 #print(prob_wts[max(n1-w,0):n1+w+1])
 n2_c = (n2[0], mylist[n2[0]])
 return np.array(n2_c) 
n2choice(1)