Mercurial Hosting > traffic-intelligence
annotate python/utils.py @ 376:2e6b8610bcaa
work on indicator similarity
author | Nicolas Saunier <nicolas.saunier@polymtl.ca> |
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date | Wed, 17 Jul 2013 18:19:08 -0400 |
parents | 2ea8584aa80a |
children | 387cc0142211 |
rev | line source |
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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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10 |
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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 # simple statistics |
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26 ######################### |
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27 |
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28 def confidenceInterval(mean, stdev, nSamples, percentConfidence, printLatex = False): |
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29 from math import sqrt |
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30 from scipy.stats.distributions import norm |
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31 k = round(norm.ppf(0.5+percentConfidence/200., 0, 1)*100)/100. # 1.-(100-percentConfidence)/200. |
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32 e = k*stdev/sqrt(nSamples) |
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33 if printLatex: |
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34 print('${0} \pm {1}\\frac{{{2}}}{{\sqrt{{{3}}}}}$'.format(mean, k, stdev, nSamples)) |
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35 return mean-e, mean+e |
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36 |
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37 def computeChi2(expected, observed): |
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38 '''Returns the Chi2 statistics''' |
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39 result = 0. |
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40 for e, o in zip(expected, observed): |
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41 result += ((e-o)*(e-o))/e |
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42 return result |
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43 |
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44 class EmpiricalDistribution: |
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45 def nSamples(self): |
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46 return sum(self.counts) |
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47 |
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48 def cumulativeDensityFunction(sample): |
276 | 49 '''Returns the cumulative density function of the sample of a random variable''' |
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50 from numpy.core.multiarray import array |
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51 from numpy.lib.function_base import unique |
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52 from numpy.core.fromnumeric import sum |
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53 a = array(sample) |
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54 a.sort() |
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55 xaxis = unique(a) |
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56 counts = [sum(a <= x) for x in xaxis] |
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57 return xaxis, counts |
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58 |
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59 class EmpiricalDiscreteDistribution(EmpiricalDistribution): |
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60 '''Class to represent a sample of a distribution for a discrete random variable |
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61 ''' |
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62 from numpy.core.fromnumeric import sum |
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63 |
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64 def __init__(self, categories, counts): |
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65 self.categories = categories |
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66 self.counts = counts |
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67 |
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68 def mean(self): |
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69 result = [float(x*y) for x,y in zip(self.categories, self.counts)] |
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70 return sum(result)/self.nSamples() |
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71 |
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72 def var(self, mean = None): |
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73 if not mean: |
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74 m = self.mean() |
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75 else: |
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76 m = mean |
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77 result = 0. |
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78 squares = [float((x-m)*(x-m)*y) for x,y in zip(self.categories, self.counts)] |
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79 return sum(squares)/(self.nSamples()-1) |
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80 |
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81 def referenceCounts(self, probability): |
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82 '''probability is a function that returns the probability of the random variable for the category values''' |
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83 refProba = [probability(c) for c in self.categories] |
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84 refProba[-1] = 1-sum(refProba[:-1]) |
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85 refCounts = [r*self.nSamples() for r in refProba] |
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86 return refCounts, refProba |
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87 |
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88 class EmpiricalContinuousDistribution(EmpiricalDistribution): |
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89 '''Class to represent a sample of a distribution for a continuous random variable |
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90 with the number of observations for each interval |
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91 intervals (categories variable) are defined by their left limits, the last one being the right limit |
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92 categories contain therefore one more element than the counts''' |
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93 def __init__(self, categories, counts): |
276 | 94 # todo add samples for initialization and everything to None? (or setSamples?) |
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95 self.categories = categories |
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96 self.counts = counts |
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97 |
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98 def mean(self): |
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99 result = 0. |
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100 for i in range(len(self.counts)-1): |
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101 result += self.counts[i]*(self.categories[i]+self.categories[i+1])/2 |
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102 return result/self.nSamples() |
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103 |
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104 def var(self, mean = None): |
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105 if not mean: |
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106 m = self.mean() |
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107 else: |
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108 m = mean |
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109 result = 0. |
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110 for i in range(len(self.counts)-1): |
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111 mid = (self.categories[i]+self.categories[i+1])/2 |
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112 result += self.counts[i]*(mid - m)*(mid - m) |
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113 return result/(self.nSamples()-1) |
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114 |
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115 def referenceCounts(self, cdf): |
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116 '''cdf is a cumulative distribution function |
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117 returning the probability of the variable being less that x''' |
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118 # refCumulativeCounts = [0]#[cdf(self.categories[0][0])] |
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119 # for inter in self.categories: |
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120 # refCumulativeCounts.append(cdf(inter[1])) |
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121 refCumulativeCounts = [cdf(x) for x in self.categories[1:-1]] |
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122 |
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123 refProba = [refCumulativeCounts[0]] |
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124 for i in xrange(1,len(refCumulativeCounts)): |
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125 refProba.append(refCumulativeCounts[i]-refCumulativeCounts[i-1]) |
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126 refProba.append(1-refCumulativeCounts[-1]) |
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127 refCounts = [p*self.nSamples() for p in refProba] |
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128 |
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129 return refCounts, refProba |
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130 |
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131 def printReferenceCounts(self, refCounts=None): |
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132 if refCounts: |
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133 ref = refCounts |
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134 else: |
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135 ref = self.referenceCounts |
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136 for i in xrange(len(ref[0])): |
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137 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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138 |
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139 |
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140 ######################### |
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141 # maths section |
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142 ######################### |
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143 |
370
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144 def argMaxDict(d): |
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145 return max(d.iterkeys(), key=(lambda key: d[key])) |
279
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146 |
248
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147 def framesToTime(nFrames, frameRate, initialTime = (0.,0.,0.)): |
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148 'returns hour, minutes and seconds' |
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149 from math import floor |
261
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150 from datetime import time |
262
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151 seconds = int(floor(float(nFrames)/float(frameRate))+initialTime[0]*3600+initialTime[1]*60+initialTime[2]) |
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152 h = int(floor(seconds/3600.)) |
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153 seconds = seconds - h*3600 |
261
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154 m = int(floor(seconds/60)) |
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155 seconds = seconds - m*60 |
262
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156 return time(h, m, seconds) |
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157 |
241
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158 def sortXY(X,Y): |
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159 'returns the sorted (x, Y(x)) sorted on X' |
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160 D = {} |
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161 for x, y in zip(X,Y): |
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162 D[x]=y |
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163 xsorted = sorted(D.keys()) |
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164 return xsorted, [D[x] for x in xsorted] |
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165 |
32 | 166 def ceilDecimals(v, nDecimals): |
167 '''Rounds the number at the nth decimal | |
168 eg 1.23 at 0 decimal is 2, at 1 decimal is 1.3''' | |
169 from math import ceil,pow | |
170 tens = pow(10,nDecimals) | |
171 return ceil(v*tens)/tens | |
172 | |
152
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173 def inBetween(bound1, bound2, x): |
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174 return bound1 <= x <= bound2 or bound2 <= x<= bound1 |
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175 |
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176 def crossProduct(l1, l2): |
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177 return l1[0]*l2[1]-l1[1]*l2[0] |
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178 |
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179 def filterMovingWindow(input, halfWidth): |
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180 '''Returns an array obtained after the smoothing of the input by a moving average |
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181 The first and last points are copied from the original.''' |
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182 width = float(halfWidth*2+1) |
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183 win = ones(width,'d') |
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184 result = convolve(win/width,array(inputSignal),'same') |
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185 result[:halfWidth] = inputSignal[:halfWidth] |
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186 result[-halfWidth:] = inputSignal[-halfWidth:] |
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187 return result |
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188 |
199
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189 def linearRegression(x, y, deg = 1, plotData = False): |
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190 '''returns the least square estimation of the linear regression of y = ax+b |
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191 as well as the plot''' |
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192 from numpy.lib.polynomial import polyfit |
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193 from matplotlib.pyplot import plot |
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194 from numpy.core.multiarray import arange |
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195 coef = polyfit(x, y, deg) |
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196 if plotData: |
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197 def poly(x): |
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198 result = 0 |
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199 for i in range(len(coef)): |
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200 result += coef[i]*x**(len(coef)-i-1) |
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201 return result |
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202 plot(x, y, 'x') |
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203 xx = arange(min(x), max(x),(max(x)-min(x))/1000) |
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204 plot(xx, [poly(z) for z in xx]) |
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205 return coef |
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206 |
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207 ######################### |
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208 # sequence section |
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209 ######################### |
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210 |
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211 class LCSS: |
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212 '''Class that keeps the LCSS parameters |
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213 and puts together the various computations''' |
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214 def __init__(self, similarityFunc, delta = float('inf'), aligned = False, lengthFunc = min): |
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215 self.similarityFunc = similarityFunc |
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216 self.aligned = aligned |
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217 self.delta = delta |
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218 self.lengthFunc = lengthFunc |
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219 self.alignmentShift = 0 |
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220 |
373
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221 def similarities(self, l1, l2, jshift=0): |
370
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222 from numpy import zeros, int as npint |
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223 n1 = len(l1) |
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224 n2 = len(l2) |
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225 self.similarityTable = zeros((n1+1,n2+1), dtype = npint) |
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226 for i in xrange(1,n1+1): |
374
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227 for j in xrange(max(1,i-jshift-self.delta),min(n2,i-jshift+self.delta)+1): |
370
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228 if self.similarityFunc(l1[i-1], l2[j-1]): |
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229 self.similarityTable[i,j] = self.similarityTable[i-1,j-1]+1 |
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230 else: |
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231 self.similarityTable[i,j] = max(self.similarityTable[i-1,j], self.similarityTable[i,j-1]) |
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232 |
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233 def subSequence(self, i, j): |
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234 '''Returns the subsequence of two sequences |
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235 http://en.wikipedia.org/wiki/Longest_common_subsequence_problem''' |
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236 if i == 0 or j == 0: |
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237 return [] |
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238 elif self.similarityTable[i][j] == self.similarityTable[i][j-1]: |
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239 return self.subSequence(i, j-1) |
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240 elif self.similarityTable[i][j] == self.similarityTable[i-1][j]: |
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241 return self.subSequence(i-1, j) |
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242 else: |
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243 return self.subSequence(i-1, j-1) + [(i-1,j-1)] |
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244 |
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245 def _compute(self, _l1, _l2, computeSubSequence = False): |
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246 '''returns the longest common subsequence similarity |
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247 based on the threshold on distance between two elements of lists l1, l2 |
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248 similarityFunc returns True or False whether the two points are considered similar |
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249 |
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250 if aligned, returns the best matching if using a finite delta by shiftinig the series alignments |
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251 |
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252 eg distance(p1, p2) < epsilon |
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253 ''' |
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254 if len(_l2) < len(_l1): # l1 is the shortest |
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255 l1 = _l2 |
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256 l2 = _l1 |
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257 revertIndices = True |
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258 else: |
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259 l1 = _l1 |
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260 l2 = _l2 |
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261 revertIndices = False |
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262 n1 = len(l1) |
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263 n2 = len(l2) |
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264 |
370
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265 if self.aligned: |
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266 lcssValues = {} |
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267 similarityTables = {} |
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268 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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269 self.similarities(l1, l2, i) |
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270 lcssValues[i] = self.similarityTable.max() |
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271 similarityTables[i] = self.similarityTable |
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272 #print self.similarityTable |
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273 self.alignmentShift = argMaxDict(lcssValues) # ideally get the medium alignment shift, the one that minimizes distance |
372
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274 self.similarityTable = similarityTables[self.alignmentShift] |
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275 else: |
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276 self.alignmentShift = 0 |
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277 self.similarities(l1, l2) |
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278 |
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279 # threshold values for the useful part of the similarity table are n2-n1-delta and n1-n2-delta |
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280 self.similarityTable = self.similarityTable[:min(n1, n2+self.alignmentShift+self.delta)+1, :min(n2, n1-self.alignmentShift+self.delta)+1] |
373
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281 |
372
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282 if computeSubSequence: |
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283 self.subSequenceIndices = self.subSequence(self.similarityTable.shape[0]-1, self.similarityTable.shape[1]-1) |
371
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284 if revertIndices: |
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285 self.subSequenceIndices = [(j,i) for i,j in self.subSequenceIndices] |
372
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286 return self.similarityTable[-1,-1] |
370
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287 |
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288 def compute(self, l1, l2, computeSubSequence = False): |
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289 '''get methods are to be shadowed in child classes ''' |
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290 return self._compute(l1, l2, computeSubSequence) |
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291 |
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292 def computeAlignment(self): |
370
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293 from numpy import mean |
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294 return mean([j-i for i,j in self.subSequenceIndices]) |
370
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295 |
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296 def _computeNormalized(self, l1, l2, computeSubSequence = False): |
370
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297 ''' compute the normalized LCSS |
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298 ie, the LCSS divided by the min or mean of the indicator lengths (using lengthFunc) |
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299 lengthFunc = lambda x,y:float(x,y)/2''' |
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300 return float(self._compute(l1, l2, computeSubSequence))/self.lengthFunc(len(l1), len(l2)) |
370
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301 |
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302 def computeNormalized(self, l1, l2, computeSubSequence = False): |
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303 return self._computeNormalized(l1, l2, computeSubSequence) |
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304 |
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305 def _computeDistance(self, l1, l2, computeSubSequence = False): |
370
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306 ''' compute the LCSS distance''' |
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307 return 1-self._computeNormalized(l1, l2, computeSubSequence) |
370
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308 |
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309 def computeDistance(self, l1, l2, computeSubSequence = False): |
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310 return self._computeDistance(l1, l2, computeSubSequence) |
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311 |
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312 ######################### |
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313 # plotting section |
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314 ######################### |
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315 |
332
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316 def plotPolygon(poly, options = ''): |
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317 'Plots shapely polygon poly' |
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318 from numpy.core.multiarray import array |
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319 from matplotlib.pyplot import plot |
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320 from shapely.geometry import Polygon |
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321 |
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322 tmp = array(poly.exterior) |
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323 plot(tmp[:,0], tmp[:,1], options) |
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324 |
324 | 325 def stepPlot(X, firstX, lastX, initialCount = 0, increment = 1): |
326 '''for each value in X, increment by increment the initial count | |
297
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327 returns the lists that can be plotted |
324 | 328 to obtain a step plot increasing by one for each value in x, from first to last value |
329 firstX and lastX should be respectively smaller and larger than all elements in X''' | |
297
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330 |
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331 sortedX = [] |
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332 counts = [initialCount] |
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333 for x in sorted(X): |
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334 sortedX += [x,x] |
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335 counts.append(counts[-1]) |
324 | 336 counts.append(counts[-1]+increment) |
297
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337 counts.append(counts[-1]) |
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338 return [firstX]+sortedX+[lastX], counts |
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339 |
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340 class PlottingPropertyValues: |
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341 def __init__(self, values): |
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342 self.values = values |
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343 |
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344 def __getitem__(self, i): |
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345 return self.values[i%len(self.values)] |
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346 |
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347 markers = PlottingPropertyValues(['+', '*', ',', '.', 'x', 'D', 's', 'o']) |
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348 scatterMarkers = PlottingPropertyValues(['s','o','^','>','v','<','d','p','h','8','+','x']) |
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349 |
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350 linestyles = PlottingPropertyValues(['-', '--', '-.', ':']) |
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351 |
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352 colors = PlottingPropertyValues('brgmyck') # 'w' |
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353 |
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354 def plotIndicatorMap(indicatorMap, squareSize, masked = True, defaultValue=-1): |
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355 from numpy import array, arange, ones, ma |
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356 from matplotlib.pyplot import pcolor |
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357 coords = array(indicatorMap.keys()) |
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358 minX = min(coords[:,0]) |
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359 minY = min(coords[:,1]) |
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360 X = arange(minX, max(coords[:,0])+1.1)*squareSize |
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361 Y = arange(minY, max(coords[:,1])+1.1)*squareSize |
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362 C = defaultValue*ones((len(Y), len(X))) |
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363 for k,v in indicatorMap.iteritems(): |
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364 C[k[1]-minY,k[0]-minX] = v |
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365 if masked: |
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366 pcolor(X, Y, ma.masked_where(C==defaultValue,C)) |
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367 else: |
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368 pcolor(X, Y, C) |
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369 |
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370 ######################### |
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371 # file I/O section |
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372 ######################### |
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373 |
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374 def openCheck(filename, option = 'r', quit = False): |
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375 '''Open file filename in read mode by default |
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376 and checks it is open''' |
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377 try: |
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378 return open(filename, option) |
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379 except IOError: |
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380 print 'File %s could not be opened.' % filename |
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381 if quit: |
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382 from sys import exit |
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383 exit() |
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384 return None |
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385 |
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386 def readline(f, commentCharacter = commentChar): |
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387 '''Modified readline function to skip comments.''' |
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388 s = f.readline() |
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389 while (len(s) > 0) and s.startswith(commentCharacter): |
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390 s = f.readline() |
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391 return s.strip() |
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392 |
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393 def getLines(f, delimiterCharacter = delimiterChar): |
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394 '''Gets a complete entry (all the lines) in between delimiterChar.''' |
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395 dataStrings = [] |
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396 s = readline(f) |
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397 while (len(s) > 0) and (not s.startswith(delimiterCharacter)): |
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398 dataStrings += [s.strip()] |
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399 s = readline(f) |
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400 return dataStrings |
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401 |
304
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402 class FakeSecHead(object): |
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403 '''Add fake section header [asection] |
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404 |
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405 from http://stackoverflow.com/questions/2819696/parsing-properties-file-in-python/2819788#2819788 |
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406 use read_file in Python 3.2+ |
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407 ''' |
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408 def __init__(self, fp): |
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409 self.fp = fp |
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410 self.sechead = '[main]\n' |
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411 |
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412 def readline(self): |
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413 if self.sechead: |
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414 try: return self.sechead |
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415 finally: self.sechead = None |
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416 else: return self.fp.readline() |
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417 |
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418 def removeExtension(filename, delimiter = '.'): |
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419 '''Returns the filename minus the extension (all characters after last .)''' |
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420 i = filename.rfind(delimiter) |
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421 if i>0: |
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422 return filename[:i] |
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423 else: |
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424 return filename |
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425 |
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426 def cleanFilename(s): |
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427 'cleans filenames obtained when contatenating figure characteristics' |
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428 return s.replace(' ','-').replace('.','').replace('/','-') |
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429 |
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430 def listfiles(dirname, extension, remove = False): |
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431 '''Returns the list of files with the extension in the directory dirname |
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432 If remove is True, the filenames are stripped from the extension''' |
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433 from os import listdir |
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434 tmp = [f for f in listdir(dirname) if f.endswith(extension)] |
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435 tmp.sort() |
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436 if remove: |
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437 return [removeExtension(f, extension) for f in tmp] |
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438 else: |
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439 return tmp |
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440 |
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441 def mkdir(dirname): |
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442 'Creates a directory if it does not exist' |
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443 import os |
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444 if not os.path.exists(dirname): |
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445 os.mkdir(dirname) |
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446 else: |
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447 print(dirname+' already exists') |
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448 |
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449 def removeFile(filename): |
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450 '''Deletes the file while avoiding raising an error |
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451 if the file does not exist''' |
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452 import os |
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453 if (os.path.exists(filename)): |
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454 os.remove(filename) |
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455 else: |
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456 print(filename+' does not exist') |
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457 |
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458 def line2Floats(l, separator=' '): |
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459 '''Returns the list of floats corresponding to the string''' |
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460 return [float(x) for x in l.split(separator)] |
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461 |
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462 def line2Ints(l, separator=' '): |
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463 '''Returns the list of ints corresponding to the string''' |
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464 return [int(x) for x in l.split(separator)] |
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465 |
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466 ######################### |
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467 # CLI utils |
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468 ######################### |
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469 |
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470 def parseCLIOptions(helpMessage, options, cliArgs, optionalOptions=[]): |
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471 ''' Simple function to handle similar argument parsing |
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472 Returns the dictionary of options and their values |
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473 |
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474 * cliArgs are most likely directly sys.argv |
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475 (only the elements after the first one are considered) |
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476 |
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477 * options should be a list of strings for getopt options, |
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478 eg ['frame=','correspondences=','video='] |
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479 A value must be provided for each option, or the program quits''' |
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480 import sys, getopt |
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481 from numpy.core.fromnumeric import all |
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482 optionValues, args = getopt.getopt(cliArgs[1:], 'h', ['help']+options+optionalOptions) |
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483 optionValues = dict(optionValues) |
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484 |
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485 if '--help' in optionValues.keys() or '-h' in optionValues.keys(): |
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486 print(helpMessage+ |
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487 '\n - Compulsory options: '+' '.join([opt.replace('=','') for opt in options])+ |
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488 '\n - Non-compulsory options: '+' '.join([opt.replace('=','') for opt in optionalOptions])) |
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489 sys.exit() |
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490 |
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491 missingArgument = [('--'+opt.replace('=','') in optionValues.keys()) for opt in options] |
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492 if not all(missingArgument): |
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493 print('Missing argument') |
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494 print(optionValues) |
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495 sys.exit() |
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496 |
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497 return optionValues |
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498 |
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499 class TrackingParameters: |
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500 def loadConfigFile(self, filename): |
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501 from ConfigParser import ConfigParser |
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502 from numpy import loadtxt |
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503 from os import path |
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504 |
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505 config = ConfigParser() |
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506 config.readfp(FakeSecHead(openCheck(filename))) |
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507 self.sectionHeader = config.sections()[0] |
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508 self.videoFilename = config.get(self.sectionHeader, 'video-filename') |
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509 self.databaseFilename = config.get(self.sectionHeader, 'database-filename') |
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510 self.homographyFilename = config.get(self.sectionHeader, 'homography-filename') |
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511 if (path.exists(self.homographyFilename)): |
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512 self.homography = loadtxt(self.homographyFilename) |
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513 else: |
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514 self.homography = None |
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515 self.firstFrameNum = config.getint(self.sectionHeader, 'frame1') |
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516 self.videoFrameRate = config.getfloat(self.sectionHeader, 'video-fps') |
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517 |
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518 self.maxPredictedSpeed = config.getfloat(self.sectionHeader, 'max-predicted-speed')/3.6/self.videoFrameRate |
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519 self.predictionTimeHorizon = config.getfloat(self.sectionHeader, 'prediction-time-horizon')*self.videoFrameRate |
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520 self.collisionDistance = config.getfloat(self.sectionHeader, 'collision-distance') |
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521 self.crossingZones = config.getboolean(self.sectionHeader, 'crossing-zones') |
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522 self.predictionMethod = config.get(self.sectionHeader, 'prediction-method') |
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523 self.nPredictedTrajectories = config.getint(self.sectionHeader, 'npredicted-trajectories') |
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524 self.minAcceleration = config.getfloat(self.sectionHeader, 'min-acceleration')/self.videoFrameRate**2 |
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525 self.maxAcceleration = config.getfloat(self.sectionHeader, 'max-acceleration')/self.videoFrameRate**2 |
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526 self.maxSteering = config.getfloat(self.sectionHeader, 'max-steering')/self.videoFrameRate |
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527 self.useFeaturesForPrediction = config.getboolean(self.sectionHeader, 'use-features-prediction') |
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528 |
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529 ######################### |
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530 # sqlite |
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531 ######################### |
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532 |
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533 def printDBError(error): |
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534 print('DB Error: {}'.format(error)) |
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535 |
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536 def dropTables(connection, tableNames): |
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537 'deletes the table with names in tableNames' |
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538 import sqlite3 |
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539 try: |
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540 cursor = connection.cursor() |
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541 for tableName in tableNames: |
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542 cursor.execute('DROP TABLE '+tableName) |
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543 except sqlite3.OperationalError as error: |
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544 printDBError(error) |
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545 |
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546 ######################### |
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547 # running tests |
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548 ######################### |
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549 |
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550 if __name__ == "__main__": |
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551 import doctest |
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552 import unittest |
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553 suite = doctest.DocFileSuite('tests/utils.txt') |
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554 #suite = doctest.DocTestSuite() |
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555 unittest.TextTestRunner().run(suite) |
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556 #doctest.testmod() |
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557 #doctest.testfile("example.txt") |