#!/usr/bin/env python

# ----------------------------------------------------------------------------------- #
#  Python/ROOT script testing randomness of single digits (i.e. [0-9]).
#  
#  Author: Troels C. Petersen (NBI)
#  Email:  petersen@nbi.dk
#  Date:   16th of September 2014
#  
# ----------------------------------------------------------------------------------- #

# Load modules here
from ROOT import *



# ----------------------------------------------------------------------------------- #
# Reading data files:
# ----------------------------------------------------------------------------------- #

# Write extensive output
verbose = True

# Define list of input files
infiles = ["./data_RandomDigits2014A.txt"]

# List containing all numbers
numbers = []

# Loop over input files open them in read mode
for ifile in infiles : 
    with open( ifile, "r" ) as current_file : 
        # Extract current file info : loop through each line in the file, loop through each character
        # in the line, demand character is not empty ("") and convert the result to an integer
        # Finally add result to the numbers list
        numbers += [int(char) for line in current_file for char in line.strip() if char is not ""]

# Print out your numbers, to see everything works correctly
if verbose : 
    for i, inumb in enumerate( numbers ) : 
        print "%d"%(inumb),
        if (i%50 == 49 and i > 0) : print ""

print
print "The total number of digits is ", len(numbers)


# ----------------------------------------------------------------------------------- #
# Your analysis:
# ----------------------------------------------------------------------------------- #








# ----------------------------------------------------------------------------------- #
# 
# First look at the random digits, and see if you see any patterns? Probably not, mostly
# because there are many numbers, and patterns of this kind are not that visible to the
# human eye. So, you will have to work a bit...  with statistical tests.
# 
# Before even looking at the above program, think about what statistical tests you
# could submit the sample to. Then consider, how to actually carry out these tests.
# We will try in class to compile and discuss a list, before we start working on it!!!
# 
# Finally, I've been so kind to put three data samples for 2014! One is from the random
# number generator TRandom3, one is a series of digits from pi, and one is from the 50
# digits that all of you put into the questionaire! Try to find out, which one is human,
# and which two are from mathematics/computers.
#
# 
# Questions:
# ----------
# 1) Are each digit represented roughly equally many times? Try to count/plot the
#    frequency of each digit, and ask yourself what the chance is, that they come
#    from a uniform distribution.
# 
# 2) Are there as many even as odd numbers? How about low (0-4) vs. high (5-9) numbers?
#    And do people have a tedency to choose an even number after an odd and vice versa?
#    And similarly for low/high numbers.
# 
# 3) Are people "afraid" of putting the same digit twice in a row? And how about three
#    or four identical digits in a row? How many would you expect to have of these, and
#    how many do you observe?
# 
# 4) Try to count, which digits follows which digits. That should be 100 counts in total.
#    If the numbers were truly random, what would you expect then? Is that what you
#    observe? Can you test this for example with a Chi-Square (think about how many
#    entries you expect in each bin) and/or a likelihood?
# 
# 5) Do you throughout the above process find out, which sample you contributed to?
#    How certain are you?
# 
# Advanced:
# 6) Were the students of 2011, 2012 and 2013 better or worse at picking random numbers?
# 
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