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simple cumulatie function distribution computation
author Nicolas Saunier <nicolas.saunier@polymtl.ca>
date Wed, 08 Feb 2012 15:02:30 -0500
parents c06379f25ab8
children ca9d9104afba
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1 #! /usr/bin/env python
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2 ''' Generic utilities.'''
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3
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4 #from numpy import *
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5 #from pylab import *
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6
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7 __metaclass__ = type
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8
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9 commentChar = '#'
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11 delimiterChar = '%';
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12
185
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13 #########################
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14 # Enumerations
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15 #########################
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16
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17 def inverseEnumeration(l):
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18 'Returns the dictionary that provides for each element in the input list its index in the input list'
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19 result = {}
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20 for i,x in enumerate(l):
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21 result[x] = i
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22 return result
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23
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24 #########################
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25 # CLI utils
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26 #########################
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27
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28 def parseCLIOptions(helpMessage, options, cliArgs, optionalOptions=[]):
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29 ''' Simple function to handle similar argument parsing
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30 Returns the dictionary of options and their values
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31
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32 * cliArgs are most likely directly sys.argv
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33 (only the elements after the first one are considered)
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34
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35 * options should be a list of strings for getopt options,
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36 eg ['frame=','correspondences=','video=']
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37 A value must be provided for each option, or the program quits'''
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38 import sys, getopt
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39 from numpy.core.fromnumeric import all
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40 optionValues, args = getopt.getopt(cliArgs[1:], 'h', ['help']+options+optionalOptions)
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41 optionValues = dict(optionValues)
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42
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43 if '--help' in optionValues.keys() or '-h' in optionValues.keys():
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44 print(helpMessage+
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45 '\n - Compulsory options: '+' '.join([opt.replace('=','') for opt in options])+
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46 '\n - Non-compulsory options: '+' '.join([opt.replace('=','') for opt in optionalOptions]))
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47 sys.exit()
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48
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49 missingArgument = [('--'+opt.replace('=','') in optionValues.keys()) for opt in options]
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50 if not all(missingArgument):
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51 print('Missing argument')
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52 print(optionValues)
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53 sys.exit()
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54
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55 return optionValues
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56
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57 #########################
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58 # simple statistics
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59 #########################
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60
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61 def computeChi2(expected, observed):
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62 '''Returns the Chi2 statistics'''
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63 result = 0.
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64 for e, o in zip(expected, observed):
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65 result += ((e-o)*(e-o))/e
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66 return result
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67
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68 class EmpiricalDistribution:
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69 def nSamples(self):
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70 return sum(self.counts)
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71
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72 def cumulativeDensityFunction(sample):
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73 'Returns the cumulative density function of the sample of a random variable'
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74 from numpy.core.multiarray import array
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75 from numpy.lib.function_base import unique
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76 from numpy.core.fromnumeric import sum
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77 a = array(sample)
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78 a.sort()
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79 xaxis = unique(a)
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80 counts = [sum(a <= x) for x in xaxis]
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81 return xaxis, counts
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82
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83 class EmpiricalDiscreteDistribution(EmpiricalDistribution):
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84 '''Class to represent a sample of a distribution for a discrete random variable
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85 '''
86
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86 from numpy.core.fromnumeric import sum
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87
85
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88 def __init__(self, categories, counts):
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89 self.categories = categories
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90 self.counts = counts
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91
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92 def mean(self):
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93 result = [float(x*y) for x,y in zip(self.categories, self.counts)]
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94 return sum(result)/self.nSamples()
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95
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96 def var(self, mean = None):
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97 if not mean:
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98 m = self.mean()
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99 else:
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100 m = mean
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101 result = 0.
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102 squares = [float((x-m)*(x-m)*y) for x,y in zip(self.categories, self.counts)]
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103 return sum(squares)/(self.nSamples()-1)
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104
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105 def referenceCounts(self, probability):
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106 '''probability is a function that returns the probability of the random variable for the category values'''
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107 refProba = [probability(c) for c in self.categories]
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108 refProba[-1] = 1-sum(refProba[:-1])
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109 refCounts = [r*self.nSamples() for r in refProba]
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110 return refCounts, refProba
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111
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112 class EmpiricalContinuousDistribution(EmpiricalDistribution):
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113 '''Class to represent a sample of a distribution for a continuous random variable
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114 with the number of observations for each interval
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115 intervals (categories variable) are defined by their left limits, the last one being the right limit
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116 categories contain therefore one more element than the counts'''
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117 def __init__(self, categories, counts):
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118 self.categories = categories
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119 self.counts = counts
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120
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121 def mean(self):
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122 result = 0.
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123 for i in range(len(self.counts)-1):
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124 result += self.counts[i]*(self.categories[i]+self.categories[i+1])/2
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125 return result/self.nSamples()
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126
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127 def var(self, mean = None):
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128 if not mean:
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129 m = self.mean()
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130 else:
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131 m = mean
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132 result = 0.
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133 for i in range(len(self.counts)-1):
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134 mid = (self.categories[i]+self.categories[i+1])/2
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135 result += self.counts[i]*(mid - m)*(mid - m)
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136 return result/(self.nSamples()-1)
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137
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138 def referenceCounts(self, cdf):
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139 '''cdf is a cumulative distribution function
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140 returning the probability of the variable being less that x'''
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141 # refCumulativeCounts = [0]#[cdf(self.categories[0][0])]
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142 # for inter in self.categories:
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143 # refCumulativeCounts.append(cdf(inter[1]))
76
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144 refCumulativeCounts = [cdf(x) for x in self.categories[1:-1]]
35
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145
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146 refProba = [refCumulativeCounts[0]]
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147 for i in xrange(1,len(refCumulativeCounts)):
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148 refProba.append(refCumulativeCounts[i]-refCumulativeCounts[i-1])
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149 refProba.append(1-refCumulativeCounts[-1])
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150 refCounts = [p*self.nSamples() for p in refProba]
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151
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152 return refCounts, refProba
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153
77
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154 def printReferenceCounts(self, refCounts=None):
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155 if refCounts:
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156 ref = refCounts
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157 else:
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158 ref = self.referenceCounts
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159 for i in xrange(len(ref[0])):
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160 print('{0}-{1} & {2:0.3} & {3:0.3} \\\\'.format(self.categories[i],self.categories[i+1],ref[1][i], ref[0][i]))
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161
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162
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163 #########################
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164 # maths section
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165 #########################
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166
32
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167 def ceilDecimals(v, nDecimals):
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168 '''Rounds the number at the nth decimal
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169 eg 1.23 at 0 decimal is 2, at 1 decimal is 1.3'''
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170 from math import ceil,pow
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171 tens = pow(10,nDecimals)
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172 return ceil(v*tens)/tens
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173
152
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174 def inBetween(bound1, bound2, x):
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175 return bound1 <= x <= bound2 or bound2 <= x<= bound1
24
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176
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177 def crossProduct(l1, l2):
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178 return l1[0]*l2[1]-l1[1]*l2[0]
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179
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180 def filterMovingWindow(input, halfWidth):
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181 '''Returns an array obtained after the smoothing of the input by a moving average
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182 The first and last points are copied from the original.'''
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183 width = float(halfWidth*2+1)
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184 win = ones(width,'d')
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185 result = convolve(win/width,array(inputSignal),'same')
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186 result[:halfWidth] = inputSignal[:halfWidth]
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187 result[-halfWidth:] = inputSignal[-halfWidth:]
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188 return result
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189
27
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190 #########################
45
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191 # plotting section
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192 #########################
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193
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194 class PlottingPropertyValues:
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195 def __init__(self, values):
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196 self.values = values
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197
116
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198 def __getitem__(self, i):
45
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199 return self.values[i%len(self.values)]
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200
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201 markers = PlottingPropertyValues(['+', '*', ',', '.', 'x', 'D', 's', 'o'])
116
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202 scatterMarkers = PlottingPropertyValues(['s','o','^','>','v','<','d','p','h','8','+','x'])
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203
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204 linestyles = PlottingPropertyValues(['-', '--', '-.', ':'])
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205
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206 colors = PlottingPropertyValues('brgmyck') # 'w'
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207
115
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208 def plotIndicatorMap(indicatorMap, squareSize, masked = True, defaultValue=-1):
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209 from numpy import array, arange, ones, ma
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210 from matplotlib.pyplot import pcolor
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211 coords = array(indicatorMap.keys())
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212 minX = min(coords[:,0])
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213 minY = min(coords[:,1])
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214 X = arange(minX, max(coords[:,0])+1.1)*squareSize
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215 Y = arange(minY, max(coords[:,1])+1.1)*squareSize
115
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216 C = defaultValue*ones((len(Y), len(X)))
65
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217 for k,v in indicatorMap.iteritems():
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218 C[k[1]-minY,k[0]-minX] = v
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219 if masked:
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220 pcolor(X, Y, ma.masked_where(C==defaultValue,C))
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221 else:
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222 pcolor(X, Y, C)
65
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diff changeset
223
45
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224 #########################
27
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225 # file I/O section
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226 #########################
24
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227
0
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228 def openCheck(filename, option = 'r', quit = False):
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229 '''Open file filename in read mode by default
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diff changeset
230 and checks it is open'''
0
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231 try:
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232 return open(filename, option)
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233 except IOError:
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234 print 'File %s could not be opened.' % filename
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235 if quit:
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236 from sys import exit
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237 exit()
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238 return None
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239
48
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240 def readline(f, commentCharacter = commentChar):
0
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241 '''Modified readline function to skip comments.'''
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242 s = f.readline()
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243 while (len(s) > 0) and s.startswith(commentCharacter):
0
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244 s = f.readline()
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245 return s.strip()
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246
48
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diff changeset
247 def getLines(f, delimiterCharacter = delimiterChar):
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248 '''Gets a complete entry (all the lines) in between delimiterChar.'''
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diff changeset
249 dataStrings = []
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diff changeset
250 s = readline(f)
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diff changeset
251 while (len(s) > 0) and (not s.startswith(delimiterCharacter)):
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diff changeset
252 dataStrings += [s.strip()]
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diff changeset
253 s = readline(f)
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254 return dataStrings
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diff changeset
255
0
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256 def removeExtension(filename, delimiter = '.'):
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diff changeset
257 '''Returns the filename minus the extension (all characters after last .)'''
0
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258 i = filename.rfind(delimiter)
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259 if i>0:
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260 return filename[:i]
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261 else:
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262 return filename
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263
46
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diff changeset
264 def cleanFilename(s):
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265 'cleans filenames obtained when contatenating figure characteristics'
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266 return s.replace(' ','-').replace('.','')
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267
0
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268 def listfiles(dirname, extension, remove = False):
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269 '''Returns the list of files with the extension in the directory dirname
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270 If remove is True, the filenames are stripped from the extension'''
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271 from os import listdir
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272 tmp = [f for f in listdir(dirname) if f.endswith(extension)]
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273 tmp.sort()
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274 if remove:
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275 return [removeExtension(f, extension) for f in tmp]
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276 else:
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277 return tmp
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278
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279 def removeFile(filename):
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280 '''Deletes the file while avoiding raising an error
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281 if the file does not exist'''
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282 if (os.path.exists(filename)):
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283 os.remove(filename)
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284
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285 def plotPolygon(poly, options = ''):
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286 from numpy.core.multiarray import array
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287 from matplotlib.pyplot import plot
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288 from shapely.geometry import Polygon
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289
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290 tmp = array(poly.exterior)
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291 plot(tmp[:,0], tmp[:,1], options)
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292
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293 def line2Floats(l, separator=' '):
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294 '''Returns the list of floats corresponding to the string'''
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295 return [float(x) for x in l.split(separator)]
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296
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297 def line2Ints(l, separator=' '):
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298 '''Returns the list of ints corresponding to the string'''
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299 return [int(x) for x in l.split(separator)]
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300
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301 #########################
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302 # running tests
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303 #########################
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304
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305 if __name__ == "__main__":
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306 import doctest
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307 import unittest
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308 suite = doctest.DocFileSuite('tests/utils.txt')
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309 #suite = doctest.DocTestSuite()
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310 unittest.TextTestRunner().run(suite)
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311 #doctest.testmod()
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312 #doctest.testfile("example.txt")