# Copyright (c) 2007 RADLogic

# 

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# The above copyright notice and this permission notice shall be included in

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# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

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"""Provide various handy Python functions.

Running this script directly will execute the doctests.

Functions:

int2bin(i, n) -- Convert integer to binary string.

bin2int(bin_string) -- Convert binary string to integer.

reverse(input_string) -- Reverse a string.

transpose(matrix) -- Transpose a list of lists.

polygon_area(points_list) -- Calculate the area of an arbitrary polygon.

timestamp() -- Return string containing current time stamp.

pt2str(point) -- Return prettier string version of point tuple.

gcf(a, b) -- Return the greatest common factor of two numbers.

lcm(a, b) -- Return the least common multiple of two numbers.

permutations(input_list) -- Generate all permutations of a list of items.

reduce_fraction(fraction) -- Reduce fraction (num, denom) to simplest form.

quantile(l, p) -- Return p quantile of list l. E.g. p=0.25 for q1.

trim(l) -- Discard values in list more than 1.5*IQR outside IQR.

nice_units(value) -- Return value converted to human readable units.

uniquify(seq) -- Return sequence with duplicate items in sequence seq removed.

reverse_dict(d) -- Return the dictionary with the items as keys and vice-versa.

lsb(x, n) -- Return the n least significant bits of x.

gray_encode(i) -- Gray encode the given integer.

random_vec(bits, max_value=None) -- Return a random binary vector.

binary_range(bits) -- Return list of all possible binary numbers width=bits.

float_range([start], stop, [step]) -- Return range of floats.

find_common_fixes(s1, s2) -- Find common (prefix, suffix) of two strings.

is_rotated(seq1, seq2) -- Return true if the list is a rotation of other list.

getmodule(obj) -- Return the module that contains the object definition of obj.

                  (use inspect.getmodule instead, though)

get_args(argv) -- Store command-line args in a dictionary.

This module requires Python >= 2.2

"""

__author__ = 'Tim Wegener <twegener@radlogic.com.au>'

__date__ = '$Date: 2007/03/27 03:15:06 $'

__version__ = '$Revision: 0.45 $'

__credits__ = """

              David Chandler, for polygon area algorithm.

               (http://www.davidchandler.com/AreaOfAGeneralPolygon.pdf)

              """

import re

import sys

import time

import random

try:

    True, False

except NameError:

    True, False = (1==1, 0==1)

def int2bin(i, n):

    """Convert decimal integer i to n-bit binary number (string).

    >>> int2bin(0, 8)

    '00000000'

    >>> int2bin(123, 8)

    '01111011'

    >>> int2bin(123L, 8)

    '01111011'

    >>> int2bin(15, 2)

    Traceback (most recent call last):

    ValueError: Value too large for given number of bits.

    """

    hex2bin = {'0': '0000', '1': '0001', '2': '0010', '3': '0011',

               '4': '0100', '5': '0101', '6': '0110', '7': '0111',

               '8': '1000', '9': '1001', 'a': '1010', 'b': '1011',

               'c': '1100', 'd': '1101', 'e': '1110', 'f': '1111'}

    # Convert to hex then map each hex digit to binary equivalent.

    result = ''.join([hex2bin[x] for x in hex(i).lower().replace('l','')[2:]])

    # Shrink result to appropriate length.

    # Raise an error if the value is changed by the truncation.

    if '1' in result[:-n]:

        raise ValueError("Value too large for given number of bits.")

    result = result[-n:]

    # Zero-pad if length longer than mapped result.

    result = '0'*(n-len(result)) + result

    return result

def bin2int(bin_string):

    """Convert binary number string to decimal integer.

    Note: Python > v2 has int(bin_string, 2)

    >>> bin2int('1111')

    15

    >>> bin2int('0101')

    5

    """

##     result = 0

##     bin_list = list(bin_string)

##     if len(filter(lambda x: x in ('1','0'), bin_list)) < len(bin_list):

##         raise Exception ("bin2int: Error - not a binary number: %s"

##                          % bin_string)

##     bit_list = map(int, bin_list)

##     bit_list.reverse()  # Make most significant bit have highest index.

##     for bit_place in range(len(bit_list)):

##         result = result + ((2**bit_place) * bit_list[bit_place])

##     return result

    return int(bin_string, 2)

def reverse(input_string):

    """Reverse a string. Useful for strings of binary numbers.

    >>> reverse('abc')

    'cba'

    """

    str_list = list(input_string)

    str_list.reverse()

    return ''.join(str_list)

def transpose(matrix):

    """Transpose a list of lists.

    >>> transpose([['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']])

    [['a', 'd', 'g'], ['b', 'e', 'h'], ['c', 'f', 'i']]

    >>> transpose([['a', 'b', 'c'], ['d', 'e', 'f']])

    [['a', 'd'], ['b', 'e'], ['c', 'f']]

    >>> transpose([['a', 'b'], ['d', 'e'], ['g', 'h']])

    [['a', 'd', 'g'], ['b', 'e', 'h']]

    """

    result = zip(*matrix)

    # Convert list of tuples to list of lists.

    # map is faster than a list comprehension since it is being used with

    # a built-in function as an argument.

    result = map(list, result)

    return result

def polygon_area(points_list, precision=100):

    """Calculate area of an arbitrary polygon using an algorithm from the web.

    Return the area of the polygon as a positive float. 

    Arguments:

    points_list -- list of point tuples [(x0, y0), (x1, y1), (x2, y2), ...]

                   (Unclosed polygons will be closed automatically.

    precision -- Internal arithmetic precision (integer arithmetic).

    >>> polygon_area([(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 0), (0, 0)])

    3.0

    Credits:

    Area of a General Polygon by David Chandler

    http://www.davidchandler.com/AreaOfAGeneralPolygon.pdf

    """

    # Scale up co-ordinates and convert them to integers.

    for i in range(len(points_list)):

        points_list[i] = (int(points_list[i][0] * precision),

                          int(points_list[i][1] * precision))

    # Close polygon if not closed.

    if points_list[-1] != points_list[0]:

        points_list.append(points_list[0])

    # Calculate area.

    area = 0

    for i in range(len(points_list)-1):

        (x_i, y_i) = points_list[i]

        (x_i_plus_1, y_i_plus_1) = points_list[i+1]

        area = area + (x_i_plus_1 * y_i) - (y_i_plus_1 * x_i)

    area = abs(area / 2)

    # Unscale area.

    area = float(area)/(precision**2)

    return area

def timestamp():

    """Return string containing current time stamp.

    Note: In Python 2 onwards can use time.asctime() with no arguments.

    """

    return time.asctime()

def pt2str(point):

    """Return prettier string version of point tuple.

    >>> pt2str((1.8, 1.9))

    '(1.8, 1.9)'

    """

    return "(%s, %s)" % (str(point[0]), str(point[1]))

def gcf(a, b, epsilon=1e-16):

    """Return the greatest common factor of a and b, using Euclidean algorithm.

    Arguments:

    a, b -- two numbers

            If both numbers are integers return an integer result, 

            otherwise return a float result.

    epsilon -- floats less than this magnitude are considered to be zero

               (default: 1e-16)

    Examples:

    >>> gcf(12, 34)

    2

    >>> gcf(13.5, 4)

    0.5

    >>> gcf(-2, 4)

    2

    >>> gcf(5, 0)

    5

    By (a convenient) definition:

    >>> gcf(0, 0)

    0

    """

    result = max(a, b)

    remainder = min(a, b)

    while remainder and abs(remainder) > epsilon:

        new_remainder = result % remainder

        result = remainder

        remainder = new_remainder

    return abs(result)

def lcm(a, b, precision=None):

    """Return the least common multiple of a and b, using the gcf function.

    Arguments:

    a, b -- two numbers. If both are integers return an integer result, 

            otherwise a return a float result.

    precision -- scaling factor if a and/or b are floats.

    >>> lcm(21, 6)

    42

    >>> lcm(2.5, 3.5)

    17.5

    >>> str(lcm(1.5e-8, 2.5e-8, precision=1e9))

    '7.5e-08'

    By (an arbitary) definition:

    >>> lcm(0, 0)

    0

    """

    # Note: Dummy precision argument is for backwards compatibility.

    # Do the division first.

    # (See http://en.wikipedia.org/wiki/Least_common_multiple )

    denom = gcf(a, b)

    if denom == 0:

        result = 0

    else:

        result = a * (b / denom)

    return result

def permutations(input_list):

    """Return a list containing all permutations of the input list.

    Note: This is a recursive function.

    >>> perms = permutations(['a', 'b', 'c'])

    >>> perms.sort()

    >>> for perm in perms:

    ...     print perm

    ['a', 'b', 'c']

    ['a', 'c', 'b']

    ['b', 'a', 'c']

    ['b', 'c', 'a']

    ['c', 'a', 'b']

    ['c', 'b', 'a']

    """

    out_lists = []

    if len(input_list) > 1:

        # Extract first item in list.

        item = input_list[0]

        # Find all permutations of remainder of list. (Recursive call.)

        sub_lists = permutations(input_list[1:])

        # For every permutation of the sub list...

        for sub_list in sub_lists:

            # Insert the extracted first item at every position of the list.

            for i in range(len(input_list)):

                new_list = sub_list[:]

                new_list.insert(i, item)

                out_lists.append(new_list)

    else:

        # Termination condition: only one item in input list.

        out_lists = [input_list]

    return out_lists

def reduce_fraction(fraction):

    """Reduce fraction tuple to simplest form. fraction=(num, denom)

    >>> reduce_fraction((14, 7))

    (2, 1)

    >>> reduce_fraction((-2, 4))

    (-1, 2)

    >>> reduce_fraction((0, 4))

    (0, 1)

    >>> reduce_fraction((4, 0))

    (1, 0)

    """

    (numerator, denominator) = fraction

    common_factor = abs(gcf(numerator, denominator))

    result = (numerator/common_factor, denominator/common_factor)

    return result

def quantile(l, p):

    """Return p quantile of list l. E.g. p=0.25 for q1.

    See:

    http://rweb.stat.umn.edu/R/library/base/html/quantile.html

    """

    l_sort = l[:]

    l_sort.sort()

    n = len(l)

    r = 1 + ((n - 1) * p)

    i = int(r)

    f = r - i

    if i < n:

        result =  (1-f)*l_sort[i-1] + f*l_sort[i]

    else:

        result = l_sort[i-1]

    return result

def trim(l):

    """Discard values in list more than 1.5*IQR outside IQR.

    (IQR is inter-quartile-range)

    This function uses rad_util.quantile

    1.5*IQR -- mild outlier

    3*IQR -- extreme outlier

    See:

    http://wind.cc.whecn.edu/~pwildman/statnew/section_7_-_exploratory_data_analysis.htm

    """

    l_sort = l[:]

    l_sort.sort()

    # Calculate medianscore  (based on stats.py lmedianscore by Gary Strangman)

    if len(l_sort) % 2 == 0:

        # If even number of scores, average middle 2.

        index = int(len(l_sort) / 2)  # Integer division correct

        median = float(l_sort[index] + l_sort[index-1]) / 2

    else:

        # int divsion gives mid value when count from 0

        index = int(len(l_sort) / 2)

        median = l_sort[index]

    # Calculate IQR.

    q1 = quantile(l_sort, 0.25)

    q3 = quantile(l_sort, 0.75)

    iqr = q3 - q1

    iqr_extra = iqr * 1.5

    def in_interval(x, i=iqr_extra, q1=q1, q3=q3):

        return (x >= q1-i and x <= q3+i)

    l_trimmed = [x for x in l_sort if in_interval(x)]

    return l_trimmed

def nice_units(value, dp=0, sigfigs=None, suffix='', space=' ',

               use_extra_prefixes=False, use_full_name=False, mode='si'):

    """Return value converted to human readable units eg milli, micro, etc.

    Arguments:

    value -- number in base units

    dp -- number of decimal places to display (rounded)

    sigfigs -- number of significant figures to display (rounded)

               This overrides dp if set.

    suffix -- optional unit suffix to append to unit multiplier

    space -- seperator between value and unit multiplier (default: ' ')

    use_extra_prefixes -- use hecto, deka, deci and centi as well if set.

                          (default: False)

    use_full_name -- use full name for multiplier symbol,

                     e.g. milli instead of m

                     (default: False)

    mode -- 'si' for SI prefixes, 'bin' for binary multipliers (1024, etc.)

            (Default: 'si')

    SI prefixes from:

    http://physics.nist.gov/cuu/Units/prefixes.html

    (Greek mu changed to u.)

    Binary prefixes based on:

    http://physics.nist.gov/cuu/Units/binary.html

    >>> nice_units(2e-11)

    '20 p'

    >>> nice_units(2e-11, space='')

    '20p'

    """

    si_prefixes = {1e24:  ('Y', 'yotta'),

                   1e21:  ('Z', 'zetta'),

                   1e18:  ('E', 'exa'),

                   1e15:  ('P', 'peta'),

                   1e12:  ('T', 'tera'),

                   1e9:   ('G', 'giga'),

                   1e6:   ('M', 'mega'),

                   1e3:   ('k', 'kilo'),

                   1e-3:  ('m', 'milli'),

                   1e-6:  ('u', 'micro'),

                   1e-9:  ('n', 'nano'),

                   1e-12: ('p', 'pico'),

                   1e-15: ('f', 'femto'),

                   1e-18: ('a', 'atto'),

                   1e-21: ('z', 'zepto'),

                   1e-24: ('y', 'yocto')

                   }

    if use_extra_prefixes:

        si_prefixes.update({1e2:  ('h', 'hecto'),

                            1e1:  ('da', 'deka'),

                            1e-1: ('d', 'deci'),

                            1e-2: ('c', 'centi')

                            })

    bin_prefixes = {2**10: ('K', 'kilo'),

                    2**20: ('M', 'mega'),

                    2**30: ('G', 'mega'),

                    2**40: ('T', 'tera'),

                    2**50: ('P', 'peta'),

                    2**60: ('E', 'exa')

                    }

    if mode == 'bin':

        prefixes = bin_prefixes

    else:

        prefixes = si_prefixes

    prefixes[1] = ('', '')  # Unity.

    # Determine appropriate multiplier.

    multipliers = prefixes.keys()

    multipliers.sort()

    mult = None

    for i in range(len(multipliers) - 1):

        lower_mult = multipliers[i]

        upper_mult = multipliers[i+1]

        if lower_mult <= value < upper_mult:

            mult_i = i

            break

    if mult is None:

        if value < multipliers[0]:

            mult_i = 0

        elif value >= multipliers[-1]:

            mult_i = len(multipliers) - 1

    mult = multipliers[mult_i]

    # Convert value for this multiplier.

    new_value = value / mult

    # Deal with special case due to rounding.

    if sigfigs is None:

        if mult_i < (len(multipliers) - 1) and \

               round(new_value, dp) == \

               round((multipliers[mult_i+1] / mult), dp):

            mult = multipliers[mult_i + 1]

            new_value = value / mult

    # Concatenate multiplier symbol.

    if use_full_name:

        label_type = 1

    else:

        label_type = 0

    # Round and truncate to appropriate precision.

    if sigfigs is None:

        str_value = eval('"%.'+str(dp)+'f" % new_value', locals(), {})

    else:

        str_value = eval('"%.'+str(sigfigs)+'g" % new_value', locals(), {})

    return str_value + space + prefixes[mult][label_type] + suffix

def uniquify(seq, preserve_order=False):

    """Return sequence with duplicate items in sequence seq removed.

    The code is based on usenet post by Tim Peters.

    This code is O(N) if the sequence items are hashable, O(N**2) if not.

    Peter Bengtsson has a blog post with an empirical comparison of other

    approaches:

    http://www.peterbe.com/plog/uniqifiers-benchmark

    If order is not important and the sequence items are hashable then

    list(set(seq)) is readable and efficient.

    If order is important and the sequence items are hashable generator

    expressions can be used (in py >= 2.4) (useful for large sequences):

    seen = set()

    do_something(x for x in seq if x not in seen or seen.add(x))