# Copyright 2003-2009 Bill Manaris, Dana Hughes, J.R. Armstrong, Thomas Zalonis, Luca Pellicoro, # Chris Wagner, Chuck McCormick # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # # zipf.py Version 1.5 24-Dec-2008 # # This module encapsulates functions that may be used to calculate # the slope and r2 (fit) of a trendline # of a Zipf distribution (byRank or bySize). # # The byRank distribution plots the values (y-axis) # against the ranks of the values from largest to smallest # (x-axis) in log-log scale. The ranks are generated automatically. # # The bySize distribution plots the values (y-axis) # against the supplied keys (x-axis) in log-log scale. # # Usage: Call bySize(sizes, counts) and/or byRank(counts) functions # Output: slope and R2 # # WARNING: If an error occurs the current code will NOT raise an exception; # it will only print an error message (for ShedSkin compatibility). # This may cause problems, if the error messages go undetected # (e.g., this code is run in batch mode). # # Authors: Chris Wagner and Bill Manaris (based on VB code by Chuck McCormick and Bill Manaris) # # version 1.5 (December 24, 2008) J.R. Armstrong and Bill Manaris # - Now we are differentiating between monotonous and random phenomena (vertical vs. horizontal trendlines). # In the first case, we return slope = 0 and r2 = 0. # In the second case, we return slope = 0 and r2 = 1. # Also, some variable names have been updated. # # version 1.4 (October 1, 2008) Bill Manaris # - Added more unit-testing code (i.e., if __name__=='__main__') for Shed Skin Python-to-C++ conversion to work. # - Updated some variable names for usability/readability # # version 1.3 (March 23, 2007) Thomas Zalonis # - Added code to the getSlopeR2() function that calculates the y-intercept for the trendline. # - getSlopeR2() now returns 3 values, slope, r2 and the trendline y-intercept # # version 1.2 (Feb 03, 2007) Luca Pellicoro # -Translation from Java to Python # -Raise exceptions with erroneous user inputs (such as zero keys or values) # # version 1.1 (July 30, 2005) # # version 1.0 (May 10, 2003) # # for logarithmic calculations from math import * def byRank(counts): ''' Calculate the slope and R^2 of the counts. Sorting the counts in descending order. ''' newCounts = [] # to hold the deep copy newRanks = [] # the newly created ranks numberOfCounts = len(counts) for index in range(numberOfCounts): newCounts.append(counts[index]) # deep copy the counts newRanks.append(numberOfCounts - index) # create the ranks: highest frequency has smallest rank newCounts.sort() checkRanksAndCounts(newRanks, newCounts) return getSlopeR2(newRanks, newCounts) def bySize(sizes, counts): ''' Calculate the slope and r2 of the counts without ordering the ranks. Keys contains the desired ranking. ''' checkRanksAndCounts(sizes,counts) return getSlopeR2(sizes, counts) ###################################### ######### SUPPORTING METHODS ######### ###################################### def checkRanksAndCounts(ranks, counts): ''' Verify that: - ranks and counts contain at least one element - ranks and counts have the same length - both ranks and counts do not contain any negative or zero element ''' if len(counts) == 0: raise ValueError, 'Counts should contain at least one element' if min(counts) <= 0.0: raise ValueError, 'Counts should be strictly positive: %f' % (min(counts)) if len(ranks) == 0: raise ValueError, 'Ranks should contain at least one element' if min(ranks) <= 0.0 : raise ValueError, 'Ranks should be strictly positive: %f' % (min(ranks)) if len(ranks) != len(counts): raise ValueError,'Ranks (length: %d) and counts (length: %d) should have the same size.' % (len(ranks), len(counts)) ## # Comment the above exception code, and uncomment the code below, ## # for ShedSkin compatibility. ## if len(counts) == 0: print "Zipf ValueError: ", 'Counts should contain at least one element' ## if min(counts) <= 0.0: print "Zipf ValueError: ", 'Counts should be strictly positive: %f' % (min(counts)) ## ## if len(ranks) == 0: print "Zipf ValueError: ", 'Ranks should contain at least one element' ## if min(ranks) <= 0.0 : print "Zipf ValueError: ", 'Ranks should be strictly positive: %f' % (min(ranks)) ## ## if len(ranks) != len(counts): ## print "Zipf ValueError: ",'Ranks (length: %d) and counts (length: %d) should have the same size.' % (len(ranks), len(values)) def getSlopeR2(ranks, counts): ''' Calculates the Zipf Slope and R^2(fit) of a set of ranks and counts. If slope and/or R^2 cannot be calculated, a zero is returned. ''' assert len(ranks) == len(counts) , 'Ranks and counts must have the same length.' sumX = sumY = sumXY = sumX2 = sumY2 = 0.0 numberOfRanks = len(ranks) # one exterme case: # if the phenomenon is monotonous (only one type of event, e.g., ['a', 'a', 'a']), # then the slope is negative infinity (cannot draw a line with only one data point), # so indicate this with slope = 0 AND r2 = 0 if numberOfRanks == 1: slope = 0.0 r2 = 0.0 else: # the other extreme case: # if the phenomenon is uniformly distributed (several types of events, # but all having the same number of instances, e.g., ['a', 'b', 'a', 'b', 'a', 'b']), # then the slope = 0 and r2 = 1 (a horizontal line). # check if all counts are equal i = 0 allCountsEqual = True # assume they are all equal while allCountsEqual and i < numberOfRanks-1: allCountsEqual = (counts[i] == counts[i + 1]) # update hypothesis i = i + 1 if allCountsEqual: # is phenomenon uniformly distributed? slope = 0.0 r2 = 1.0 # general case, so calculate actual slope and r2 values else: # Sum up the values for the calculations for index in range(numberOfRanks): sumX += log(ranks[index],10) sumY += log(counts[index],10) sumXY += log(ranks[index],10) * log(counts[index],10) sumX2 += log(ranks[index],10)**2 sumY2 += log(counts[index],10)**2 # calculate the slope if ((numberOfRanks * sumX2 - sumX * sumX) == 0.0): slope = 0.0 else: slope = ((numberOfRanks * sumXY - sumX * sumY) / (numberOfRanks * sumX2 - sumX * sumX)) # calculate the r2 if(sqrt((numberOfRanks * sumX2 - sumX * sumX) * (numberOfRanks * sumY2 - sumY * sumY)) == 0.0): r2 = 0.0 else: r = (numberOfRanks * sumXY - sumX * sumY) / sqrt((numberOfRanks * sumX2 - sumX * sumX) * (numberOfRanks * sumY2 - sumY * sumY)) r2 = r * r # calulate y-intercept yint = (sumY - slope * sumX) / len(ranks) return slope, r2, yint if __name__ == '__main__': #print "Enter sequence of numbers to calculate its Zipfian distribution." #print "The rank-frequency distribution is calculated based on how many times each number appears." #print "The size-frequency distribution is calculated based on how many times each number appears; also the actual number is treated as if it represents 'size'." #phenomenon = input("Enter sequence of numbers (e.g., [50, 100, 50]): ") #phenomenon = [1, 1, 1] # check monotonous #phenomenon = [2, 2, 2, 3, 3, 3] # check uniformly distributed (white noise) #phenomenon = [1, 1, 2] # check truly zipfian (pink noise) #phenomenon = [1, 1, 1, 1, 2] # check brown noise phenomenon = [1, 2, 2, 3, 3, 3, 3] # check general case print "Given the sequence", phenomenon # calculate frequency of occurrence of each symbol histogram = {} for event in phenomenon: histogram[event] = histogram.get(event, 0) + 1 # now, the histogram contains the frequencies # next, extract the counts and calculate their rank-frequency (Zipfian) distribution counts = histogram.values() slope, r2, yint = byRank(counts) print "The byRank slope is", slope, "and the R^2 is", r2 # now, extract the sizes calculate their side-frequency (Zipfian) distribution sizes = histogram.keys() slope, r2, yint = bySize(sizes, counts) print "The bySize slope is", slope, "and the R^2 is", r2