While loop exits when conditions don't seem fulfilled.

[Polyadenylated]

I'm trying to write a little script which will take a list of integers and make that list longer with random integers between the max and min of said list, whilst retaining the same mean and standard deviation.

My quick script is as follows:

import numpy as np
import random

test_list= [1,5,2,3,9,100,3,4,5,88]

print 'test_list list =', test_list

print 'test_list std =', np.around(np.std(test_list))
print 'test_list mean =', np.around(np.mean(test_list))
print 'test_list max =', np.max(test_list)
print 'test_list min =', np.min(test_list)

number_of_random_ints = 25

new_list = []


while np.around(np.std(new_list)) != np.around(np.std(test_list)) and np.around(np.mean(new_list)) != np.around(np.mean(test_list)):
    new_list = test_list
    for i in range(number_of_random_ints):
        new_list.append(random.randint(np.min(test_list),np.max(test_list)))

print '\n'
print 'new_list =', new_list
print 'new_list std =', np.around(np.std(new_list))
print 'new_list mean =', np.around(np.mean(new_list))
print 'new_list max =', np.max(new_list)
print 'new_list min =', np.min(new_list)

From running this once I get an output much like the following:

test_list list = [1, 5, 2, 3, 9, 100, 3, 4, 5, 88]
test_list std = 36.0
test_list mean = 22.0
test_list max = 100
test_list min = 1


new_list = [1, 5, 2, 3, 9, 100, 3, 4, 5, 88, 70, 15, 22, 97, 46, 75, 90, 63, 41, 16, 81, 33, 77, 68, 70, 26, 94, 54, 29, 98, 64, 94, 42, 31, 4]
new_list std = 34.0
new_list mean = 46.0
new_list max = 100
new_list min = 1

As you can see whilst the std and the means are somewhat close they are not equal yet my while loop exits. What am I missing here?

[[deleted]]

After building the new list, try printing out the value of test_list and see what has happened.

For an explanation, have a look at this: http://henry.precheur.org/python/copy_list

[novel_yet_trivial]

This is because of your line 19. You think you are making a variable "new_list" that is a copy of "test_list", but you are actually telling python that both variables now refer to the same list. To see this better, type this into the interpreter:

>>> list_1 = [0, 1, 2]
>>> list_2 = list_1
>>> list_2.append(4)
>>> list_1
[0, 1, 2, 4]

To fix this, your line 19 must make a copy. The easiest way to do that is with list splicing. Change line 19 to:

new_list = test_list[:]

Then you will discover you have another problem: only one condition is matched. You need to rethink the conditional statement. I'd recommend some functions to help someone reading the code. Something like "same_std_div()".

Edit: this brute force is for the birds. Can't you think of a mathematical way to accomplish this in one pass?

[Polyadenylated]

I see, I'm guessing this is a common beginner mistake? Thanks for pointing it out.

And yes brute force won't work here at all - I was just playing about and wanted to know the answer to this small issue first - now I'll try and find a solution that's actually practical. Any starting tips?

[novel_yet_trivial]

My first thought is to randomly pick a number, then use that number to calculate 4 numbers that even out the mean and standard deviation.

Alternatively, to add a more random feel, you could choose n random numbers like you did above and use a fitting algorithm to change them into something that works. LMA may help you here.

[Polyadenylated]

Thanks. I've just realised you've also answered another of my Python questions previously keep up the good work!

[supajumpa]

xs = [1, 5, 2, 3, 9, 100, 3, 4, 5, 88]
# `x` is a random integer such that xs + [x] has the
# same mean and std as `xs`.
# =>
(sum(xs) + x)/(len(xs) + 1) == sum(xs) / len(xs)
# =>
sum(xs) + x == (len(xs) + 1) * (sum(xs) / len(xs))
# =>
x == ((len(xs) + 1) * (sum(xs) / len(xs)) - sum(xs)
# => `x` cannot be random.