Mercurial Hosting > traffic-intelligence
annotate python/utils.py @ 552:ca6bded754ac
corrected more bugs from merging (caught in regression tests)
author | Nicolas Saunier <nicolas.saunier@polymtl.ca> |
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date | Tue, 08 Jul 2014 17:04:55 -0400 |
parents | 97c5fef5b2d6 |
children | 3622a5653ee9 |
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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 from datetime import time, datetime |
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7 |
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8 __metaclass__ = type |
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9 |
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10 datetimeFormat = "%Y-%m-%d %H:%M:%S" |
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11 |
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12 ######################### |
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13 # Enumerations |
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14 ######################### |
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15 |
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16 def inverseEnumeration(l): |
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17 'Returns the dictionary that provides for each element in the input list its index in the input list' |
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18 result = {} |
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19 for i,x in enumerate(l): |
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20 result[x] = i |
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21 return result |
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22 |
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23 ######################### |
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24 # simple statistics |
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25 ######################### |
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26 |
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27 def sampleSize(stdev, tolerance, percentConfidence, printLatex = False): |
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28 from scipy.stats.distributions import norm |
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29 k = round(norm.ppf(0.5+percentConfidence/200., 0, 1)*100)/100. # 1.-(100-percentConfidence)/200. |
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30 if printLatex: |
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31 print('${0}^2\\frac{{{1}^2}}{{{2}^2}}$'.format(k, stdev, tolerance)) |
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32 return (k*stdev/tolerance)**2 |
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33 |
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34 def confidenceInterval(mean, stdev, nSamples, percentConfidence, trueStd = True, printLatex = False): |
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35 '''if trueStd, use normal distribution, otherwise, Student |
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36 |
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37 Use otherwise t.interval or norm.interval |
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38 ex: norm.interval(0.95, loc = 0., scale = 2.3/sqrt(11)) |
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39 t.interval(0.95, 10, loc=1.2, scale = 2.3/sqrt(nSamples)) |
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40 loc is mean, scale is sigma/sqrt(n) (for Student, 10 is df)''' |
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41 from math import sqrt |
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42 from scipy.stats.distributions import norm, t |
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43 if trueStd: |
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44 k = round(norm.ppf(0.5+percentConfidence/200., 0, 1)*100)/100. # 1.-(100-percentConfidence)/200. |
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45 else: # use Student |
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46 k = round(t.ppf(0.5+percentConfidence/200., nSamples-1)*100)/100. |
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47 e = k*stdev/sqrt(nSamples) |
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48 if printLatex: |
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49 print('${0} \pm {1}\\frac{{{2}}}{{\sqrt{{{3}}}}}$'.format(mean, k, stdev, nSamples)) |
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50 return mean-e, mean+e |
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51 |
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52 def computeChi2(expected, observed): |
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53 '''Returns the Chi2 statistics''' |
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54 result = 0. |
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55 for e, o in zip(expected, observed): |
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56 result += ((e-o)*(e-o))/e |
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57 return result |
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58 |
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59 class EmpiricalDistribution: |
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60 def nSamples(self): |
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61 return sum(self.counts) |
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62 |
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63 def cumulativeDensityFunction(sample): |
276 | 64 '''Returns the cumulative density function of the sample of a random variable''' |
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65 from numpy.core.multiarray import array |
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66 from numpy.lib.function_base import unique |
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67 from numpy.core.fromnumeric import sum |
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68 a = array(sample) |
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69 a.sort() |
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70 xaxis = unique(a) |
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71 counts = [sum(a <= x) for x in xaxis] |
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72 return xaxis, counts |
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73 |
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74 class EmpiricalDiscreteDistribution(EmpiricalDistribution): |
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75 '''Class to represent a sample of a distribution for a discrete random variable |
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76 ''' |
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77 from numpy.core.fromnumeric import sum |
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78 |
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79 def __init__(self, categories, counts): |
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80 self.categories = categories |
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81 self.counts = counts |
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82 |
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83 def mean(self): |
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84 result = [float(x*y) for x,y in zip(self.categories, self.counts)] |
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85 return sum(result)/self.nSamples() |
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86 |
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87 def var(self, mean = None): |
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88 if not mean: |
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89 m = self.mean() |
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90 else: |
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91 m = mean |
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92 result = 0. |
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93 squares = [float((x-m)*(x-m)*y) for x,y in zip(self.categories, self.counts)] |
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94 return sum(squares)/(self.nSamples()-1) |
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95 |
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96 def referenceCounts(self, probability): |
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97 '''probability is a function that returns the probability of the random variable for the category values''' |
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98 refProba = [probability(c) for c in self.categories] |
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99 refProba[-1] = 1-sum(refProba[:-1]) |
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100 refCounts = [r*self.nSamples() for r in refProba] |
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101 return refCounts, refProba |
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102 |
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103 class EmpiricalContinuousDistribution(EmpiricalDistribution): |
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104 '''Class to represent a sample of a distribution for a continuous random variable |
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105 with the number of observations for each interval |
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106 intervals (categories variable) are defined by their left limits, the last one being the right limit |
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107 categories contain therefore one more element than the counts''' |
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108 def __init__(self, categories, counts): |
276 | 109 # todo add samples for initialization and everything to None? (or setSamples?) |
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110 self.categories = categories |
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111 self.counts = counts |
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112 |
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113 def mean(self): |
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114 result = 0. |
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115 for i in range(len(self.counts)-1): |
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116 result += self.counts[i]*(self.categories[i]+self.categories[i+1])/2 |
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117 return result/self.nSamples() |
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118 |
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119 def var(self, mean = None): |
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120 if not mean: |
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121 m = self.mean() |
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122 else: |
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123 m = mean |
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124 result = 0. |
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125 for i in range(len(self.counts)-1): |
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126 mid = (self.categories[i]+self.categories[i+1])/2 |
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127 result += self.counts[i]*(mid - m)*(mid - m) |
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128 return result/(self.nSamples()-1) |
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129 |
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130 def referenceCounts(self, cdf): |
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131 '''cdf is a cumulative distribution function |
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132 returning the probability of the variable being less that x''' |
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133 # refCumulativeCounts = [0]#[cdf(self.categories[0][0])] |
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134 # for inter in self.categories: |
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135 # refCumulativeCounts.append(cdf(inter[1])) |
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136 refCumulativeCounts = [cdf(x) for x in self.categories[1:-1]] |
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137 |
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138 refProba = [refCumulativeCounts[0]] |
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139 for i in xrange(1,len(refCumulativeCounts)): |
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140 refProba.append(refCumulativeCounts[i]-refCumulativeCounts[i-1]) |
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141 refProba.append(1-refCumulativeCounts[-1]) |
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142 refCounts = [p*self.nSamples() for p in refProba] |
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143 |
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144 return refCounts, refProba |
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145 |
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146 def printReferenceCounts(self, refCounts=None): |
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147 if refCounts: |
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148 ref = refCounts |
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149 else: |
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150 ref = self.referenceCounts |
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151 for i in xrange(len(ref[0])): |
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152 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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153 |
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154 |
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155 ######################### |
370
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156 # maths section |
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157 ######################### |
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158 |
433
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159 # def kernelSmoothing(sampleX, X, Y, weightFunc, halfwidth): |
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160 # '''Returns a smoothed weighted version of Y at the predefined values of sampleX |
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161 # Sum_x weight(sample_x,x) * y(x)''' |
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162 # from numpy import zeros, array |
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163 # smoothed = zeros(len(sampleX)) |
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164 # for i,x in enumerate(sampleX): |
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165 # weights = array([weightFunc(x,xx, halfwidth) for xx in X]) |
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166 # if sum(weights)>0: |
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167 # smoothed[i] = sum(weights*Y)/sum(weights) |
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168 # else: |
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169 # smoothed[i] = 0 |
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170 # return smoothed |
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171 |
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172 def kernelSmoothing(x, X, Y, weightFunc, halfwidth): |
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173 '''Returns the smoothed estimate of (X,Y) at x |
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174 Sum_x weight(sample_x,x) * y(x)''' |
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175 from numpy import zeros, array |
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176 weights = array([weightFunc(x,observedx, halfwidth) for observedx in X]) |
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177 if sum(weights)>0: |
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178 return sum(weights*Y)/sum(weights) |
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179 else: |
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180 return 0 |
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181 |
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182 def uniform(center, x, halfwidth): |
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183 if abs(center-x)<halfwidth: |
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184 return 1. |
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185 else: |
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186 return 0. |
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187 |
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188 def gaussian(center, x, halfwidth): |
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189 from numpy import exp |
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190 return exp(-((center-x)/halfwidth)**2/2) |
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191 |
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192 def epanechnikov(center, x, halfwidth): |
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193 diff = abs(center-x) |
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194 if diff<halfwidth: |
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195 return 1.-(diff/halfwidth)**2 |
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196 else: |
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197 return 0. |
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198 |
434 | 199 def triangular(center, x, halfwidth): |
200 diff = abs(center-x) | |
201 if diff<halfwidth: | |
202 return 1.-abs(diff/halfwidth) | |
203 else: | |
204 return 0. | |
433
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205 |
518
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206 def medianSmoothing(x, X, Y, halfwidth): |
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207 '''Returns the media of Y's corresponding to X's in the interval [x-halfwidth, x+halfwidth]''' |
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208 from numpy import median |
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209 return median([y for observedx, y in zip(X,Y) if abs(x-observedx)<halfwidth]) |
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210 |
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211 def argmaxDict(d): |
370
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212 return max(d.iterkeys(), key=(lambda key: d[key])) |
279
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213 |
395
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214 def framesToTime(nFrames, frameRate, initialTime = time()): |
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215 '''returns a datetime.time for the time in hour, minutes and seconds |
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216 initialTime is a datetime.time''' |
248
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217 from math import floor |
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218 seconds = int(floor(float(nFrames)/float(frameRate))+initialTime.hour*3600+initialTime.minute*60+initialTime.second) |
261
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219 h = int(floor(seconds/3600.)) |
248
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220 seconds = seconds - h*3600 |
261
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221 m = int(floor(seconds/60)) |
248
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222 seconds = seconds - m*60 |
262
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223 return time(h, m, seconds) |
248
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224 |
381
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225 def timeToFrames(t, frameRate): |
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226 return frameRate*(t.hour*3600+t.minute*60+t.second) |
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227 |
241
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228 def sortXY(X,Y): |
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229 'returns the sorted (x, Y(x)) sorted on X' |
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230 D = {} |
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231 for x, y in zip(X,Y): |
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232 D[x]=y |
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233 xsorted = sorted(D.keys()) |
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234 return xsorted, [D[x] for x in xsorted] |
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235 |
32 | 236 def ceilDecimals(v, nDecimals): |
237 '''Rounds the number at the nth decimal | |
238 eg 1.23 at 0 decimal is 2, at 1 decimal is 1.3''' | |
239 from math import ceil,pow | |
240 tens = pow(10,nDecimals) | |
241 return ceil(v*tens)/tens | |
242 | |
152
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243 def inBetween(bound1, bound2, x): |
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244 return bound1 <= x <= bound2 or bound2 <= x<= bound1 |
24
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245 |
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246 def crossProduct(l1, l2): |
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247 return l1[0]*l2[1]-l1[1]*l2[0] |
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248 |
547 | 249 def filterMovingWindow(inputSignal, halfWidth): |
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250 '''Returns an array obtained after the smoothing of the input by a moving average |
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251 The first and last points are copied from the original.''' |
547 | 252 from numpy import ones,convolve,array |
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253 width = float(halfWidth*2+1) |
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254 win = ones(width,'d') |
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255 result = convolve(win/width,array(inputSignal),'same') |
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256 result[:halfWidth] = inputSignal[:halfWidth] |
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257 result[-halfWidth:] = inputSignal[-halfWidth:] |
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258 return result |
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259 |
199
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260 def linearRegression(x, y, deg = 1, plotData = False): |
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261 '''returns the least square estimation of the linear regression of y = ax+b |
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262 as well as the plot''' |
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263 from numpy.lib.polynomial import polyfit |
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264 from matplotlib.pyplot import plot |
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265 from numpy.core.multiarray import arange |
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266 coef = polyfit(x, y, deg) |
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267 if plotData: |
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268 def poly(x): |
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269 result = 0 |
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270 for i in range(len(coef)): |
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271 result += coef[i]*x**(len(coef)-i-1) |
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272 return result |
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273 plot(x, y, 'x') |
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274 xx = arange(min(x), max(x),(max(x)-min(x))/1000) |
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275 plot(xx, [poly(z) for z in xx]) |
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276 return coef |
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277 |
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278 ######################### |
455
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279 # iterable section |
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280 ######################### |
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281 |
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282 def mostCommon(L): |
456 | 283 '''Returns the most frequent element in a iterable |
284 | |
285 taken from http://stackoverflow.com/questions/1518522/python-most-common-element-in-a-list''' | |
455
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286 from itertools import groupby |
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287 from operator import itemgetter |
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288 # get an iterable of (item, iterable) pairs |
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289 SL = sorted((x, i) for i, x in enumerate(L)) |
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290 # print 'SL:', SL |
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291 groups = groupby(SL, key=itemgetter(0)) |
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292 # auxiliary function to get "quality" for an item |
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293 def _auxfun(g): |
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294 item, iterable = g |
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295 count = 0 |
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296 min_index = len(L) |
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297 for _, where in iterable: |
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298 count += 1 |
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299 min_index = min(min_index, where) |
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300 # print 'item %r, count %r, minind %r' % (item, count, min_index) |
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301 return count, -min_index |
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302 # pick the highest-count/earliest item |
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303 return max(groups, key=_auxfun)[0] |
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304 |
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305 ######################### |
370
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306 # sequence section |
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307 ######################### |
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308 |
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309 class LCSS: |
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310 '''Class that keeps the LCSS parameters |
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311 and puts together the various computations''' |
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312 def __init__(self, similarityFunc, delta = float('inf'), aligned = False, lengthFunc = min): |
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313 self.similarityFunc = similarityFunc |
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314 self.aligned = aligned |
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315 self.delta = delta |
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316 self.lengthFunc = lengthFunc |
389
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317 self.subSequenceIndices = [(0,0)] |
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318 |
373
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319 def similarities(self, l1, l2, jshift=0): |
370
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320 from numpy import zeros, int as npint |
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321 n1 = len(l1) |
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322 n2 = len(l2) |
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323 self.similarityTable = zeros((n1+1,n2+1), dtype = npint) |
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324 for i in xrange(1,n1+1): |
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325 for j in xrange(max(1,i-jshift-self.delta),min(n2,i-jshift+self.delta)+1): |
370
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326 if self.similarityFunc(l1[i-1], l2[j-1]): |
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327 self.similarityTable[i,j] = self.similarityTable[i-1,j-1]+1 |
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328 else: |
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329 self.similarityTable[i,j] = max(self.similarityTable[i-1,j], self.similarityTable[i,j-1]) |
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330 |
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331 def subSequence(self, i, j): |
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332 '''Returns the subsequence of two sequences |
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333 http://en.wikipedia.org/wiki/Longest_common_subsequence_problem''' |
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334 if i == 0 or j == 0: |
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335 return [] |
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336 elif self.similarityTable[i][j] == self.similarityTable[i][j-1]: |
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337 return self.subSequence(i, j-1) |
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338 elif self.similarityTable[i][j] == self.similarityTable[i-1][j]: |
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339 return self.subSequence(i-1, j) |
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340 else: |
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341 return self.subSequence(i-1, j-1) + [(i-1,j-1)] |
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342 |
373
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343 def _compute(self, _l1, _l2, computeSubSequence = False): |
370
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344 '''returns the longest common subsequence similarity |
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345 based on the threshold on distance between two elements of lists l1, l2 |
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346 similarityFunc returns True or False whether the two points are considered similar |
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347 |
373
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348 if aligned, returns the best matching if using a finite delta by shiftinig the series alignments |
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349 |
370
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350 eg distance(p1, p2) < epsilon |
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351 ''' |
372
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352 if len(_l2) < len(_l1): # l1 is the shortest |
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353 l1 = _l2 |
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354 l2 = _l1 |
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355 revertIndices = True |
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356 else: |
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357 l1 = _l1 |
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358 l2 = _l2 |
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359 revertIndices = False |
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360 n1 = len(l1) |
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361 n2 = len(l2) |
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362 |
370
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363 if self.aligned: |
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364 lcssValues = {} |
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365 similarityTables = {} |
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366 for i in xrange(-n2-self.delta+1, n1+self.delta): # interval such that [i-shift-delta, i-shift+delta] is never empty, which happens when i-shift+delta < 1 or when i-shift-delta > n2 |
373
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367 self.similarities(l1, l2, i) |
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368 lcssValues[i] = self.similarityTable.max() |
370
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369 similarityTables[i] = self.similarityTable |
374
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370 #print self.similarityTable |
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371 alignmentShift = argmaxDict(lcssValues) # ideally get the medium alignment shift, the one that minimizes distance |
389
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372 self.similarityTable = similarityTables[alignmentShift] |
372
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373 else: |
389
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374 alignmentShift = 0 |
372
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375 self.similarities(l1, l2) |
373
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376 |
374
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377 # threshold values for the useful part of the similarity table are n2-n1-delta and n1-n2-delta |
389
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378 self.similarityTable = self.similarityTable[:min(n1, n2+alignmentShift+self.delta)+1, :min(n2, n1-alignmentShift+self.delta)+1] |
373
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379 |
372
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380 if computeSubSequence: |
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381 self.subSequenceIndices = self.subSequence(self.similarityTable.shape[0]-1, self.similarityTable.shape[1]-1) |
371
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382 if revertIndices: |
374
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383 self.subSequenceIndices = [(j,i) for i,j in self.subSequenceIndices] |
372
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384 return self.similarityTable[-1,-1] |
370
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385 |
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386 def compute(self, l1, l2, computeSubSequence = False): |
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387 '''get methods are to be shadowed in child classes ''' |
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388 return self._compute(l1, l2, computeSubSequence) |
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389 |
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390 def computeAlignment(self): |
370
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391 from numpy import mean |
374
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392 return mean([j-i for i,j in self.subSequenceIndices]) |
370
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393 |
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394 def _computeNormalized(self, l1, l2, computeSubSequence = False): |
370
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395 ''' compute the normalized LCSS |
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396 ie, the LCSS divided by the min or mean of the indicator lengths (using lengthFunc) |
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397 lengthFunc = lambda x,y:float(x,y)/2''' |
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398 return float(self._compute(l1, l2, computeSubSequence))/self.lengthFunc(len(l1), len(l2)) |
370
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399 |
376
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400 def computeNormalized(self, l1, l2, computeSubSequence = False): |
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401 return self._computeNormalized(l1, l2, computeSubSequence) |
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402 |
376
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403 def _computeDistance(self, l1, l2, computeSubSequence = False): |
370
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404 ''' compute the LCSS distance''' |
376
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405 return 1-self._computeNormalized(l1, l2, computeSubSequence) |
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406 |
376
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407 def computeDistance(self, l1, l2, computeSubSequence = False): |
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408 return self._computeDistance(l1, l2, computeSubSequence) |
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409 |
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410 ######################### |
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411 # plotting section |
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412 ######################### |
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413 |
332
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414 def plotPolygon(poly, options = ''): |
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415 'Plots shapely polygon poly' |
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416 from numpy.core.multiarray import array |
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417 from matplotlib.pyplot import plot |
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418 from shapely.geometry import Polygon |
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419 |
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420 tmp = array(poly.exterior) |
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421 plot(tmp[:,0], tmp[:,1], options) |
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422 |
324 | 423 def stepPlot(X, firstX, lastX, initialCount = 0, increment = 1): |
424 '''for each value in X, increment by increment the initial count | |
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425 returns the lists that can be plotted |
324 | 426 to obtain a step plot increasing by one for each value in x, from first to last value |
427 firstX and lastX should be respectively smaller and larger than all elements in X''' | |
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428 |
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429 sortedX = [] |
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430 counts = [initialCount] |
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431 for x in sorted(X): |
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432 sortedX += [x,x] |
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433 counts.append(counts[-1]) |
324 | 434 counts.append(counts[-1]+increment) |
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435 counts.append(counts[-1]) |
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436 return [firstX]+sortedX+[lastX], counts |
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437 |
45
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438 class PlottingPropertyValues: |
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439 def __init__(self, values): |
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440 self.values = values |
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441 |
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442 def __getitem__(self, i): |
45
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443 return self.values[i%len(self.values)] |
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444 |
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445 markers = PlottingPropertyValues(['+', '*', ',', '.', 'x', 'D', 's', 'o']) |
116
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446 scatterMarkers = PlottingPropertyValues(['s','o','^','>','v','<','d','p','h','8','+','x']) |
45
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447 |
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448 linestyles = PlottingPropertyValues(['-', '--', '-.', ':']) |
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449 |
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450 colors = PlottingPropertyValues('brgmyck') # 'w' |
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451 |
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452 def plotIndicatorMap(indicatorMap, squareSize, masked = True, defaultValue=-1): |
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453 from numpy import array, arange, ones, ma |
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454 from matplotlib.pyplot import pcolor |
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455 coords = array(indicatorMap.keys()) |
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456 minX = min(coords[:,0]) |
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457 minY = min(coords[:,1]) |
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458 X = arange(minX, max(coords[:,0])+1.1)*squareSize |
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459 Y = arange(minY, max(coords[:,1])+1.1)*squareSize |
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460 C = defaultValue*ones((len(Y), len(X))) |
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461 for k,v in indicatorMap.iteritems(): |
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462 C[k[1]-minY,k[0]-minX] = v |
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463 if masked: |
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464 pcolor(X, Y, ma.masked_where(C==defaultValue,C)) |
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465 else: |
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466 pcolor(X, Y, C) |
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467 |
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468 ######################### |
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469 # file I/O section |
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470 ######################### |
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471 |
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472 def removeExtension(filename, delimiter = '.'): |
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473 '''Returns the filename minus the extension (all characters after last .)''' |
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474 i = filename.rfind(delimiter) |
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475 if i>0: |
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476 return filename[:i] |
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477 else: |
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478 return filename |
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479 |
46
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480 def cleanFilename(s): |
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481 'cleans filenames obtained when contatenating figure characteristics' |
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482 return s.replace(' ','-').replace('.','').replace('/','-') |
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483 |
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484 def listfiles(dirname, extension, remove = False): |
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485 '''Returns the list of files with the extension in the directory dirname |
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486 If remove is True, the filenames are stripped from the extension''' |
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487 from os import listdir |
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488 tmp = [f for f in listdir(dirname) if f.endswith(extension)] |
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489 tmp.sort() |
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490 if remove: |
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491 return [removeExtension(f, extension) for f in tmp] |
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492 else: |
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493 return tmp |
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494 |
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495 def mkdir(dirname): |
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496 'Creates a directory if it does not exist' |
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497 import os |
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498 if not os.path.exists(dirname): |
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499 os.mkdir(dirname) |
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500 else: |
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501 print(dirname+' already exists') |
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502 |
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503 def removeFile(filename): |
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504 '''Deletes the file while avoiding raising an error |
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505 if the file does not exist''' |
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506 import os |
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507 if (os.path.exists(filename)): |
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508 os.remove(filename) |
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509 else: |
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510 print(filename+' does not exist') |
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511 |
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512 def line2Floats(l, separator=' '): |
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513 '''Returns the list of floats corresponding to the string''' |
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514 return [float(x) for x in l.split(separator)] |
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515 |
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516 def line2Ints(l, separator=' '): |
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517 '''Returns the list of ints corresponding to the string''' |
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518 return [int(x) for x in l.split(separator)] |
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519 |
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520 ######################### |
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521 # CLI utils |
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522 ######################### |
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523 |
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524 def parseCLIOptions(helpMessage, options, cliArgs, optionalOptions=[]): |
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525 ''' Simple function to handle similar argument parsing |
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526 Returns the dictionary of options and their values |
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527 |
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528 * cliArgs are most likely directly sys.argv |
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529 (only the elements after the first one are considered) |
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530 |
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531 * options should be a list of strings for getopt options, |
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532 eg ['frame=','correspondences=','video='] |
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533 A value must be provided for each option, or the program quits''' |
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534 import sys, getopt |
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535 from numpy.core.fromnumeric import all |
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536 optionValues, args = getopt.getopt(cliArgs[1:], 'h', ['help']+options+optionalOptions) |
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537 optionValues = dict(optionValues) |
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538 |
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539 if '--help' in optionValues.keys() or '-h' in optionValues.keys(): |
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540 print(helpMessage+ |
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541 '\n - Compulsory options: '+' '.join([opt.replace('=','') for opt in options])+ |
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542 '\n - Non-compulsory options: '+' '.join([opt.replace('=','') for opt in optionalOptions])) |
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543 sys.exit() |
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544 |
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545 missingArgument = [('--'+opt.replace('=','') in optionValues.keys()) for opt in options] |
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546 if not all(missingArgument): |
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547 print('Missing argument') |
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548 print(optionValues) |
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549 sys.exit() |
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550 |
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551 return optionValues |
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552 |
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553 |
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554 ######################### |
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555 # running tests |
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556 ######################### |
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557 |
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558 if __name__ == "__main__": |
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559 import doctest |
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560 import unittest |
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561 suite = doctest.DocFileSuite('tests/utils.txt') |
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562 #suite = doctest.DocTestSuite() |
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563 unittest.TextTestRunner().run(suite) |
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564 #doctest.testmod() |
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565 #doctest.testfile("example.txt") |