entropy.py

# table.py

import sys
from pathlib import Path
from math import log2



def H(p):
    """Return the value of the entropy function a p."""

    return -p*log2(p) - (1-p)*log2(1-p)

def print_table(filename=''):
    """Print the table of values of the entropy function.

       If filename is not provided, will print to stdout.
       If filename is provided but does not exists it will be created.
       The file will be truncated to the first line if already existing.
    """
    if not filename: # print to stdout
        print("  p   |   -log(p)   |  -plog(p)   |   H(p)")

        # for p = 0
        print("0     |       _     |  0          |  0    ")

        # for p between 0 and 1
        p = 0.01
        while p < 1.0:
            print("{0:.2f}  |  {1:.7f}  |  {2:.7f}  |  {3:.7f}"
                    .format(p, -log2(p), -p*log2(p), H(p)))
            p += 0.01

        # for p = 1
        print("1.00  |  0          |  0          |  0    ")
    else:
        filepath = Path(filename)
        if not Path.is_file(filepath):
            # file does not exists, create it
            with open(filename, 'x'):
                pass

        with open(filename, 'w') as f:
            f.write("  p   |   -log(p)   |  -plog(p)   |   H(p)\n")

            # for p = 0
            f.write("0     |       _     |  0          |  0    \n")

            p = 0.01
            while p < 1.0:
                f.write("{0:.2f}  |  {1:.7f}  |  {2:.7f}  |  {3:.7f}\n"
                        .format(p, -log2(p), -p*log2(p), H(p)))
                p += 0.01

            # for p = 1
            f.write("1.00  |  0          |  0          |  0    \n")

def interactive_computation():
    """Enter interactive computation of entropy."""

    print("""
    This is an interactive mode.
    Enter a value between -10 and 0 or 1 and 10 to see the entropy H of the distribution
    Enter a value less than -10 or greater than 10 to exit
    """)

    cumulative, entropy = 0, 0

    while True:
        try:
            p = float(input('Input pi : '))
        except (KeyboardInterrupt, EOFError):
            print("\nBye")
            exit()

        if 0 <= p <= 1:
            # compute the cumulative
            cumulative += p

            # if p == 0, compute the entropy for p == 1
            if p == 0:
                p = 1

            # entropy up to that input
            entropy += -p*log2(p)

            # print log(p) -p.log(p)
            print('-log(pi)    = {:.7f}'.format(-log2(p)))
            print('-pi log(pi) = {:.7f}'.format(-p*log2(p)))

            # test for distribution validity
            if cumulative > 1:
                print("""
                         WARNING: The numbers may not form a probability distribution:
                         cumulative is greater than 1
                      """)
                print("cumulative = {:.2f}".format(cumulative))

        elif -10 < p < 0 or 1 < p < 10:
            if cumulative != 1:
                print("""
                         WARNING: The numbers may not form a probability distribution:
                         cumulative is greater than 1
                      """)
                print("cumulative = {:.2f}".format(cumulative))

            # print the entropy
            print("The entropy H = {:.7f}".format(entropy))

            # clean cumulative and entropy for subsequent input
            cumulative, entropy = 0, 0
        else:
            print("\nBye")
            exit()


def print_usage():
    """Print usage information and exit."""

    print("""
    Usage: python3 entropy.py [-o [ FILENAME ]]
           If no option is provided enter interactive computation mode
    OPTIONS
    -o  　　Print the entropy function values between 0 and 1 to stdout.
        　　Print to FILENAME if provided. FILENAME is created if not
        　　already existing.
　　　""")

if __name__ == '__main__':
    argc = len(sys.argv)

    if argc == 1:
       interactive_computation()

    elif argc == 2:
        name, option = sys.argv
        if option != '-o':
            print_usage()
            exit()
        print_table()

    elif argc == 3:
        name, option, filename = sys.argv
        if option != '-o':
            print_usage()
        else:
            print_table(filename)

    else:
        print_usage()
        exit()