| 1 | |
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| 2 | import sys |
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| 3 | import os |
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| 4 | import functools |
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| 5 | import math |
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| 6 | import statistics |
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| 7 | import gzip |
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| 8 | import random |
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| 9 | try: |
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| 10 | import numpy |
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| 11 | except: |
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| 12 | sys.stderr.write('ERROR: Could not import numpy module. Ensure it is installed.\n') |
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| 13 | sys.stderr.write(' Under Debian, the package name is "python3-numpy"\n.') |
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| 14 | sys.exit(1) |
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| 15 | |
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| 16 | # Don't trust numpy's seeding |
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| 17 | numpy.random.seed(random.SystemRandom().randint(0,2**32-1)) |
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| 18 | |
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| 19 | |
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| 20 | def mad(arr): |
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| 21 | """ Median Absolute Deviation: a "Robust" version of standard deviation. |
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| 22 | Indices variabililty of the sample. |
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| 23 | https://en.wikipedia.org/wiki/Median_absolute_deviation |
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| 24 | """ |
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| 25 | arr = numpy.ma.array(arr).compressed() # should be faster to not use masked arrays. |
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| 26 | med = numpy.median(arr) |
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| 27 | return numpy.median(numpy.abs(arr - med)) |
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| 28 | |
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| 29 | |
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| 30 | def cov(x,y): |
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| 31 | mx = statistics.mean(x) |
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| 32 | my = statistics.mean(y) |
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| 33 | products = [] |
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| 34 | for i in range(0,len(x)): |
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| 35 | products.append((x[i] - mx)*(y[i] - my)) |
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| 36 | |
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| 37 | return statistics.mean(products) |
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| 38 | |
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| 39 | |
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| 40 | def OLSRegression(x,y): |
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| 41 | #print(x,y) |
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| 42 | x = numpy.array(x) |
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| 43 | y = numpy.array(y) |
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| 44 | #A = numpy.vstack([x, numpy.ones(len(x))]).T |
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| 45 | #m, c = numpy.linalg.lstsq(A, y)[0] # broken |
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| 46 | #c,m = numpy.polynomial.polynomial.polyfit(x, y, 1) # less accurate |
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| 47 | c,m = numpy.polynomial.Polynomial.fit(x,y,1).convert().coef |
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| 48 | |
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| 49 | #print(m,c) |
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| 50 | |
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| 51 | #import matplotlib.pyplot as plt |
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| 52 | #plt.clf() |
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| 53 | #plt.scatter(x, y) |
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| 54 | #plt.plot(x, m*x + c, 'r', label='Fitted line') |
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| 55 | #plt.show() |
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| 56 | |
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| 57 | return (m,c) |
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| 58 | |
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| 59 | |
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| 60 | def difference(ls): |
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| 61 | return ls[0]-ls[1] |
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| 62 | |
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| 63 | def product(ls): |
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| 64 | return ls[0]*ls[1] |
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| 65 | |
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| 66 | def hypotenuse(ls): |
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| 67 | return math.hypot(ls[0],ls[1]) |
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| 68 | |
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| 69 | def trustValues(derived, trustFunc): |
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| 70 | ret_val = [] |
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| 71 | for k,v in derived.items(): |
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| 72 | ret_val.append((trustFunc((v['long'],v['short'])), k)) |
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| 73 | |
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| 74 | ret_val.sort() |
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| 75 | return ret_val |
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| 76 | |
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| 77 | |
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| 78 | def prunedWeights(derived, trust, alpha): |
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| 79 | weights = {} |
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| 80 | |
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| 81 | threshold = len(trust)*(1.0-alpha) |
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| 82 | for i in range(0,len(trust)): |
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| 83 | if i < threshold: |
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| 84 | weights[trust[i][1]] = 1.0 |
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| 85 | else: |
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| 86 | weights[trust[i][1]] = 0.0 |
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| 87 | |
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| 88 | return weights |
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| 89 | |
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| 90 | |
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| 91 | def linearWeights(derived, trust, alpha): |
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| 92 | x1 = trust[0][0] |
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| 93 | y1 = 1.0 + (alpha*10) |
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| 94 | x2 = trust[(len(trust)-1)//3][0] |
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| 95 | y2 = 1.0 |
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| 96 | m = (y1-y2)/(x1-x2) |
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| 97 | b = y1 - m*x1 |
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| 98 | |
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| 99 | weights = {} |
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| 100 | for t,k in trust: |
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| 101 | weights[k] = m*t+b |
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| 102 | if weights[k] < 0.0: |
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| 103 | weights[k] = 0.0 |
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| 104 | |
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| 105 | return weights |
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| 106 | |
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| 107 | |
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| 108 | def invertedWeights(derived,trust,alpha): |
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| 109 | # (x+1-first_sample)^(-alpha) |
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| 110 | #scale = trust[0][0] |
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| 111 | |
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| 112 | #weights = {} |
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| 113 | #for t,k in trust: |
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| 114 | # weights[k] = (t+1-scale)**(-1.0*alpha) |
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| 115 | # if weights[k] < 0.0: |
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| 116 | # weights[k] = 0.0 |
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| 117 | |
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| 118 | weights = {} |
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| 119 | for i in range(len(trust)): |
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| 120 | w = 10.0/(i+2.0)-0.2 |
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| 121 | if w < 0.0: |
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| 122 | w = 0.0 |
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| 123 | weights[trust[i][1]] = w |
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| 124 | |
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| 125 | |
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| 126 | return weights |
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| 127 | |
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| 128 | |
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| 129 | |
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| 130 | def arctanWeights(derived,trust,alpha): |
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| 131 | shift = trust[int((len(trust)-1)*(1.0-alpha))][0] |
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| 132 | minimum = trust[0][0] |
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| 133 | |
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| 134 | weights = {} |
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| 135 | for i in range(len(trust)): |
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| 136 | w = math.pi/2.0 - math.atan(2*(trust[i][0] - shift)/(shift-minimum)) |
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| 137 | if w < 0.0: |
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| 138 | w = 0.0 |
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| 139 | weights[trust[i][1]] = w |
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| 140 | |
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| 141 | return weights |
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| 142 | |
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| 143 | |
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| 144 | def arctanWeights2(derived,trust,alpha): |
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| 145 | shift = trust[int((len(trust)-1)*(1.0-alpha))][0] |
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| 146 | minimum = trust[0][0] |
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| 147 | stretch = trust[int((len(trust)-1)*0.5)][0] - minimum # near median |
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| 148 | |
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| 149 | weights = {} |
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| 150 | for i in range(len(trust)): |
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| 151 | w = math.pi/2.0 - math.atan(3*(trust[i][0] - shift)/(shift-minimum)) |
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| 152 | if w < 0.0: |
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| 153 | w = 0.0 |
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| 154 | weights[trust[i][1]] = w |
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| 155 | |
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| 156 | return weights |
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| 157 | |
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| 158 | |
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| 159 | def midsummary(values, distance=25): |
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| 160 | #return (numpy.percentile(values, 50-distance) + numpy.percentile(values, 50+distance))/2.0 |
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| 161 | l,h = numpy.percentile(values, (50-distance,50+distance)) |
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| 162 | return (l+h)/2.0 |
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| 163 | |
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| 164 | def trimean(values, distance=25): |
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| 165 | return (midsummary(values, distance) + statistics.median(values))/2 |
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| 166 | |
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| 167 | def ubersummary(values, distance=25): |
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| 168 | left2 = 50-distance |
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| 169 | left3 = 50-(distance/2.0) |
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| 170 | left1 = left2/2.0 |
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| 171 | right2 = 50+distance |
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| 172 | right3 = 50+(distance/2.0) |
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| 173 | right1 = (right2+100)/2.0 |
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| 174 | l1,l2,l3,r3,r2,r1 = numpy.percentile(values, (left1,left2,left3,right3,right2,right1)) |
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| 175 | #print(l1,l2,l3,m,r3,r2,r1) |
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| 176 | return (l1+l2*4+l3+r3+r2*4+r1)/12.0 |
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| 177 | #return statistics.mean((l1,l2,l3,m,r3,r2,r1)) |
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| 178 | |
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| 179 | |
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| 180 | def quadsummary(values, distance=25): |
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| 181 | left1 = 50-distance |
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| 182 | left2 = (left1+50)/2.0 |
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| 183 | right1 = 50+distance |
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| 184 | right2 = (right1+50)/2.0 |
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| 185 | l1,l2,r2,r1 = numpy.percentile(values, (left1,left2,right2,right1)) |
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| 186 | #print(left1,left2,left3,50,right3,right2,right1) |
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| 187 | #print(l1,l2,l3,m,r3,r2,r1) |
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| 188 | return (l1+l2+r2+r1)/4.0 |
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| 189 | #return statistics.mean((l1,l2,l3,m,r3,r2,r1)) |
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| 190 | |
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| 191 | |
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| 192 | def septasummary(values, distance=25): |
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| 193 | left2 = 50-distance |
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| 194 | left3 = 50-(distance/2.0) |
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| 195 | left1 = left2/2.0 |
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| 196 | right2 = 50+distance |
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| 197 | right3 = 50+(distance/2.0) |
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| 198 | right1 = (right2+100)/2.0 |
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| 199 | l1,l2,l3,m,r3,r2,r1 = numpy.percentile(values, (left1,left2,left3,50,right3,right2,right1)) |
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| 200 | return (l1+l2+l3+m+r3+r2+r1)/7.0 |
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| 201 | |
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| 202 | |
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| 203 | def tsvalwmean(subseries): |
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| 204 | weights = [(s['unusual_packet']+s['other_packet'])**2 for s in subseries] |
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| 205 | normalizer = sum(weights)/len(weights) |
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| 206 | return numpy.mean([weights[i]*(subseries[i]['unusual_tsval']-subseries[i]['other_tsval'])/normalizer |
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| 207 | for i in range(len(weights))]) |
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| 208 | |
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| 209 | #def tsvalwmean(subseries): |
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| 210 | # return numpy.mean([(s['unusual_tsval']-s['other_tsval']) for s in subseries]) |
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| 211 | |
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| 212 | |
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| 213 | def weightedMean(derived, weights): |
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| 214 | normalizer = sum(weights.values())/len(weights) |
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| 215 | return statistics.mean([w*(derived[k]['long']-derived[k]['short'])/normalizer for k,w in weights.items()]) |
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| 216 | |
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| 217 | def weightedMeanTsval(derived, weights): |
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| 218 | normalizer = sum(weights.values())/len(weights) |
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| 219 | return statistics.mean([w*(derived[k]['long_tsval']-derived[k]['short_tsval'])/normalizer for k,w in weights.items()]) |
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| 220 | |
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| 221 | |
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| 222 | |
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| 223 | |
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| 224 | def estimateMean(trustFunc, weightFunc, alpha, derived): |
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| 225 | trust = trustValues(derived, trustFunc) |
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| 226 | weights = weightFunc(derived, trust, alpha) |
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| 227 | return weightedMean(derived, weights) |
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| 228 | |
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| 229 | |
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| 230 | def estimateMeanTsval(trustFunc, weightFunc, alpha, derived): |
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| 231 | trust = trustValues(derived, trustFunc) |
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| 232 | weights = weightFunc(derived, trust, alpha) |
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| 233 | return weightedMeanTsval(derived, weights) |
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| 234 | |
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| 235 | |
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| 236 | def bootstrap3(estimator, db, probe_type, unusual_case, subseries_size, num_trials): |
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| 237 | ret_val = [] |
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| 238 | for t in range(num_trials): |
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| 239 | ret_val.append(estimator(db.subseries(probe_type, unusual_case, subseries_size))) |
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| 240 | |
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| 241 | return ret_val |
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| 242 | |
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| 243 | |
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| 244 | # Returns 1 if unusual_case is unusual in the expected direction |
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| 245 | # 0 if it isn't unusual |
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| 246 | # -1 if it is unusual in the wrong direction |
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| 247 | def multiBoxTest(params, greater, samples): |
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| 248 | uc = [s['unusual_packet'] for s in samples] |
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| 249 | rest = [s['other_packet'] for s in samples] |
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| 250 | |
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| 251 | uc_high,uc_low = numpy.percentile(uc, (params['high'],params['low'])) |
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| 252 | rest_high,rest_low = numpy.percentile(rest, (params['high'],params['low'])) |
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| 253 | if uc_high < rest_low: |
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| 254 | if greater: |
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| 255 | return -1 |
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| 256 | else: |
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| 257 | return 1 |
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| 258 | |
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| 259 | if rest_high < uc_low: |
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| 260 | if greater: |
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| 261 | return 1 |
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| 262 | else: |
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| 263 | return -1 |
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| 264 | |
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| 265 | return 0 |
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| 266 | |
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| 267 | |
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| 268 | # Returns 1 if unusual_case is unusual in the expected direction |
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| 269 | # 0 otherwise |
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| 270 | def summaryTest(f, params, greater, samples): |
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| 271 | diffs = [s['unusual_packet']-s['other_packet'] for s in samples] |
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| 272 | |
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| 273 | mh = f(diffs, params['distance']) |
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| 274 | #print("estimate:", mh) |
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| 275 | if greater: |
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| 276 | if mh > params['threshold']: |
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| 277 | return 1 |
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| 278 | else: |
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| 279 | return 0 |
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| 280 | else: |
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| 281 | if mh < params['threshold']: |
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| 282 | return 1 |
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| 283 | else: |
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| 284 | return 0 |
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| 285 | |
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| 286 | |
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| 287 | midsummaryTest = functools.partial(summaryTest, midsummary) |
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| 288 | trimeanTest = functools.partial(summaryTest, trimean) |
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| 289 | ubersummaryTest = functools.partial(summaryTest, ubersummary) |
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| 290 | quadsummaryTest = functools.partial(summaryTest, quadsummary) |
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| 291 | septasummaryTest = functools.partial(summaryTest, septasummary) |
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| 292 | |
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| 293 | def rmse(expected, measurements): |
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| 294 | s = sum([(expected-m)**2 for m in measurements])/len(measurements) |
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| 295 | return math.sqrt(s) |
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| 296 | |
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| 297 | def nrmse(expected, measurements): |
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| 298 | return rmse(expected, measurements)/(max(measurements)-min(measurements)) |
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| 299 | |
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| 300 | |
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| 301 | class KalmanFilter1D: |
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| 302 | def __init__(self, x0, P, R, Q): |
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| 303 | self.x = x0 |
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| 304 | self.P = P |
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| 305 | self.R = R |
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| 306 | self.Q = Q |
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| 307 | |
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| 308 | def update(self, z): |
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| 309 | self.x = (self.P * z + self.x * self.R) / (self.P + self.R) |
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| 310 | self.P = 1. / (1./self.P + 1./self.R) |
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| 311 | |
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| 312 | def predict(self, u=0.0): |
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| 313 | self.x += u |
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| 314 | self.P += self.Q |
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| 315 | |
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| 316 | |
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| 317 | def kfilter(params, observations): |
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| 318 | x = numpy.array(observations) |
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| 319 | movement = 0 |
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| 320 | est = [] |
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| 321 | var = [] |
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| 322 | kf = KalmanFilter1D(x0 = quadsummary(x), # initial state |
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| 323 | #P = 10000, # initial variance |
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| 324 | P = 10, # initial variance |
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| 325 | R = numpy.std(x), # msensor noise |
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| 326 | Q = 0) # movement noise |
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| 327 | for round in range(1): |
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| 328 | for d in x: |
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| 329 | kf.predict(movement) |
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| 330 | kf.update(d) |
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| 331 | est.append(kf.x) |
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| 332 | var.append(kf.P) |
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| 333 | |
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| 334 | return({'est':est, 'var':var}) |
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| 335 | |
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| 336 | |
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| 337 | def kalmanTest(params, greater, samples): |
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| 338 | diffs = [s['unusual_packet']-s['other_packet'] for s in samples] |
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| 339 | |
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| 340 | m = kfilter(params, diffs)['est'][-1] |
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| 341 | if greater: |
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| 342 | if m > params['threshold']: |
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| 343 | return 1 |
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| 344 | else: |
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| 345 | return 0 |
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| 346 | else: |
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| 347 | if m < params['threshold']: |
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| 348 | return 1 |
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| 349 | else: |
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| 350 | return 0 |
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| 351 | |
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| 352 | |
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| 353 | def tsvalwmeanTest(params, greater, samples): |
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| 354 | m = tsvalwmean(samples) |
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| 355 | if greater: |
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| 356 | if m > params['threshold']: |
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| 357 | return 1 |
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| 358 | else: |
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| 359 | return 0 |
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| 360 | else: |
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| 361 | if m < params['threshold']: |
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| 362 | return 1 |
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| 363 | else: |
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| 364 | return 0 |
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| 365 | |
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| 366 | |
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| 367 | from pykalman import KalmanFilter |
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| 368 | def pyKalman4DTest(params, greater, samples): |
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| 369 | kp = params['kparams'] |
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| 370 | #kp['initial_state_mean']=[quadsummary([s['unusual_packet'] for s in samples]), |
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| 371 | # quadsummary([s['other_packet'] for s in samples]), |
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| 372 | # numpy.mean([s['unusual_tsval'] for s in samples]), |
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| 373 | # numpy.mean([s['other_tsval'] for s in samples])] |
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| 374 | kf = KalmanFilter(n_dim_obs=4, n_dim_state=4, **kp) |
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| 375 | smooth,covariance = kf.smooth([(s['unusual_packet'],s['other_packet'],s['unusual_tsval'],s['other_tsval']) |
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| 376 | for s in samples]) |
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| 377 | m = numpy.mean(smooth) |
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| 378 | if greater: |
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| 379 | if m > params['threshold']: |
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| 380 | return 1 |
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| 381 | else: |
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| 382 | return 0 |
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| 383 | else: |
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| 384 | if m < params['threshold']: |
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| 385 | return 1 |
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| 386 | else: |
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| 387 | return 0 |
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| 388 | |
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