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simplified intervales in empiricalDistribution
author Nicolas Saunier <nicolas.saunier@polymtl.ca>
date Thu, 10 Feb 2011 22:15:54 -0500
parents 46ec876ce90e
children 5e6cd36a991c
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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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7 import moving
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8
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9 __metaclass__ = type
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10
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11 commentChar = '#'
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13 delimiterChar = '%';
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15 #########################
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16 # simple statistics
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17 #########################
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18
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19 def computeChi2(expected, observed):
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20 '''Returns the Chi2 statistics'''
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21 result = 0.
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22 for e, o in zip(expected, observed):
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23 result += ((e-o)*(e-o))/e
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24 return result
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25
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26 class empiricalDistribution:
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27 '''Class to represent a sample of a distribution for a continuous random variable
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28 with the number of observations for each interval
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29 intervals (categories variable) are defined by their left limits, the last one being the right limit
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30 categories contain therefore one more element than the counts'''
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31 def __init__(self, categories, counts):
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32 self.categories = categories
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33 self.counts = counts
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34
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35 def mean(self):
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36 result = 0.
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37 for i in range(len(self.counts)-1):
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38 result += self.counts[i]*(self.categories[i]+self.categories[i+1])/2
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39 return result/self.nSamples()
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40
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41 def var(self, mean = None):
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42 if not mean:
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43 m = self.mean()
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44 else:
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45 m = mean
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46 result = 0.
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47 for i in range(len(self.counts)-1):
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48 mid = (self.categories[i]+self.categories[i+1])/2
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49 result += self.counts[i]*(mid - m)*(mid - m)
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50 return result/(self.nSamples()-1)
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51
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52 def nSamples(self):
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53 return sum(self.counts)
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55 def referenceCounts(self, cdf):
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56 '''cdf is a cumulative distribution function
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57 returning the probability of the variable being less that x'''
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58 # refCumulativeCounts = [0]#[cdf(self.categories[0][0])]
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59 # for inter in self.categories:
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60 # refCumulativeCounts.append(cdf(inter[1]))
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61 refCumulativeCounts = [cdf(x) for x in self.categories[1:-1]]
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62
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63 refProba = [refCumulativeCounts[0]]
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64 for i in xrange(1,len(refCumulativeCounts)):
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65 refProba.append(refCumulativeCounts[i]-refCumulativeCounts[i-1])
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66 refProba.append(1-refCumulativeCounts[-1])
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67 refCounts = [p*self.nSamples() for p in refProba]
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68
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69 return refCounts, refProba
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70
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71 #########################
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72 # maths section
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73 #########################
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74
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75 def ceilDecimals(v, nDecimals):
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76 '''Rounds the number at the nth decimal
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77 eg 1.23 at 0 decimal is 2, at 1 decimal is 1.3'''
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78 from math import ceil,pow
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79 tens = pow(10,nDecimals)
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80 return ceil(v*tens)/tens
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81
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82 def segmentIntersection(p1, p2, p3, p4):
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83 '''Returns the intersecting point of the segments [p1, p2] and [p3, p4], None otherwise'''
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84 from numpy import matrix
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85 from numpy.linalg import linalg, det
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86
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87 dp1 = p2-p1#[s1[0][1]-s1[0][0], s1[1][1]-s1[1][0]]
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88 dp2 = p4-p3#[s2[0][1]-s2[0][0], s2[1][1]-s2[1][0]]
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89
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90 A = matrix([[dp1.y, -dp1.x],
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91 [dp2.y, -dp2.x]])
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92 B = matrix([[dp1.y*p1.x-dp1.x*p1.y],
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93 [dp2.y*p3.x-dp2.x*p3.y]])
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94
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95 if linalg.det(A) == 0:#crossProduct(ds1, ds2) == 0:
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96 return None
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97 else:
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98 intersection = linalg.solve(A,B)
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99 if (moving.Interval(p1.x, p2.x, True).contains(intersection[0,0])
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100 and moving.Interval(p3.x, p4.x, True).contains(intersection[0,0])
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101 and moving.Interval(p1.y, p2.y, True).contains(intersection[1,0])
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102 and moving.Interval(p3.y, p4.y, True).contains(intersection[1,0])):
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103 return moving.Point(intersection[0,0], intersection[1,0])
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104 else:
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105 return None
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106
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107 def crossProduct(l1, l2):
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108 return l1[0]*l2[1]-l1[1]*l2[0]
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109
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110 def filterMovingWindow(input, halfWidth):
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111 '''Returns an array obtained after the smoothing of the input by a moving average
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112 The first and last points are copied from the original.'''
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113 width = float(halfWidth*2+1)
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114 win = ones(width,'d')
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115 result = convolve(win/width,array(inputSignal),'same')
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116 result[:halfWidth] = inputSignal[:halfWidth]
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117 result[-halfWidth:] = inputSignal[-halfWidth:]
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118 return result
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119
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120 #########################
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121 # plotting section
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122 #########################
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123
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124 class PlottingPropertyValues:
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125 def __init__(self, values):
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126 self.values = values
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127
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128 def get(self,i):
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129 return self.values[i%len(self.values)]
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130
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131 markers = PlottingPropertyValues(['+', '*', ',', '.', 'x', 'D', 's', 'o'])
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132
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133 linestyles = PlottingPropertyValues(['-', '--', '-.', ':'])
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134
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135 colors = PlottingPropertyValues('brgmyck') # 'w'
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136
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137 def plotIndicatorMap(indicatorMap, squareSize):
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138 from numpy import array, arange, ones, ma
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139 from matplotlib.pyplot import pcolor
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140 coords = array(indicatorMap.keys())
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141 minX = min(coords[:,0])
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142 minY = min(coords[:,1])
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143 X = arange(minX, max(coords[:,0])+1.1)*squareSize
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144 Y = arange(minY, max(coords[:,1])+1.1)*squareSize
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145 C = -ones((len(Y), len(X)))
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146 for k,v in indicatorMap.iteritems():
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147 C[k[1]-minY,k[0]-minX] = v
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148 masked = ma.masked_where(C<0,C)
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149 pcolor(X, Y, masked)
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150
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151 #########################
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152 # file I/O section
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153 #########################
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154
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155 def openCheck(filename, option = 'r', quit = False):
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156 '''Open file filename in read mode by default
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157 and checks it is open'''
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158 try:
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159 return open(filename, option)
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160 except IOError:
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161 print 'File %s could not be opened.' % filename
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162 if quit:
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163 from sys import exit
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164 exit()
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165 return None
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166
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167 def readline(f, commentCharacter = commentChar):
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168 '''Modified readline function to skip comments.'''
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169 s = f.readline()
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170 while (len(s) > 0) and s.startswith(commentCharacter):
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171 s = f.readline()
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172 return s.strip()
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173
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174 def getLines(f, delimiterCharacter = delimiterChar):
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175 '''Gets a complete entry (all the lines) in between delimiterChar.'''
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176 dataStrings = []
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177 s = readline(f)
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178 while (len(s) > 0) and (not s.startswith(delimiterCharacter)):
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179 dataStrings += [s.strip()]
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180 s = readline(f)
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181 return dataStrings
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182
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183 def removeExtension(filename, delimiter = '.'):
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184 '''Returns the filename minus the extension (all characters after last .)'''
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185 i = filename.rfind(delimiter)
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186 if i>0:
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187 return filename[:i]
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188 else:
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189 return filename
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190
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191 def cleanFilename(s):
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192 'cleans filenames obtained when contatenating figure characteristics'
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193 return s.replace(' ','-').replace('.','')
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194
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195 def listfiles(dirname, extension, remove = False):
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196 '''Returns the list of files with the extension in the directory dirname
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197 If remove is True, the filenames are stripped from the extension'''
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198 from os import listdir
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199 tmp = [f for f in listdir(dirname) if f.endswith(extension)]
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200 tmp.sort()
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201 if remove:
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202 return [removeExtension(f, extension) for f in tmp]
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203 else:
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204 return tmp
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205
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206 def removeFile(filename):
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207 '''Deletes the file while avoiding raising an error
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208 if the file does not exist'''
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209 if (os.path.exists(filename)):
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210 os.remove(filename)
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211
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212 def plotPolygon(poly, options = ''):
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213 from numpy.core.multiarray import array
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214 from matplotlib.pyplot import plot
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215 from shapely.geometry import Polygon
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216
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217 tmp = array(poly.exterior)
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218 plot(tmp[:,0], tmp[:,1], options)
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219
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220 def line2Floats(l, separator=' '):
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221 '''Returns the list of floats corresponding to the string'''
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222 return [float(x) for x in l.split(separator)]
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223
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224 def line2Ints(l, separator=' '):
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225 '''Returns the list of ints corresponding to the string'''
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226 return [int(x) for x in l.split(separator)]
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227
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228 #########################
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229 # running tests
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230 #########################
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231
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232 if __name__ == "__main__":
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233 import doctest
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234 import unittest
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235 suite = doctest.DocFileSuite('tests/utils.txt')
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236 #suite = doctest.DocTestSuite()
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237 unittest.TextTestRunner().run(suite)
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238 #doctest.testmod()
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239 #doctest.testfile("example.txt")