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functions.py
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functions.py
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import numpy as np
import scipy.stats as stats
import pprint
import time
import datetime
from json_tricks import dumps, load
def rand_with_sum(rand, n):
while n > 0:
r = rand()
if ( r > n ):
return
yield r
n -= r
def processNextInQueue(absArrival, prevServiceEnd):
if(absArrival < prevServiceEnd):
return prevServiceEnd
else:
return absArrival
def processQueue(arrivalTimes, serviceTimes):
absStartService = np.zeros(arrivalTimes.shape)
absEndService = np.zeros(arrivalTimes.shape)
absStartService[0] = arrivalTimes[0]
absEndService[0] = absStartService[0] + serviceTimes[0]
for i in range(1, arrivalTimes.size):
absStartService[i] = processNextInQueue(arrivalTimes[i], absEndService[i-1])
absEndService[i] = absStartService[i] + serviceTimes[i]
return absStartService, absEndService
def lastIndexOfValue(arr, value, defaultValue):
indices = np.argwhere(arr == value)
if(indices.size > 0):
return indices[-1]
else:
return defaultValue
def processMultipleQueues(arrivalTimes, serviceTimes, numQueues):
absStartService = np.zeros(arrivalTimes.shape)
absEndService = np.zeros(arrivalTimes.shape)
affinity = -np.ones(arrivalTimes.shape, np.int)
absStartService[0] = arrivalTimes[0]
absEndService[0] = absStartService[0] + serviceTimes[0]
affinity[0] = 0
for i in range(1, arrivalTimes.size):
###
# For everyone coming:
# - Find the number of people waiting in each queue when this person arrives.
# Which means sum people with absEndService > arrivalTimes[i] in each queue
# - Set person i to the queue with the least number of people at that time
# - calculate absStartService and absEndService for person i depending on
# serving values for previous people.
##
queueCount = []
for q in range(numQueues):
queueCount.append(
np.sum(
(affinity == q) &
(absEndService > arrivalTimes[i])
)
)
chosenQueue = np.argmin(queueCount)
lastServedIndex = lastIndexOfValue(affinity, chosenQueue, -1)
affinity[i] = chosenQueue
if( lastServedIndex >= 0):
absStartService[i] = processNextInQueue(arrivalTimes[i], absEndService[lastServedIndex])
else:
absStartService[i] = arrivalTimes[i]
absEndService[i] = absStartService[i] + serviceTimes[i]
return absStartService, absEndService, affinity
def queueCountPerTime(arrivalTimes, serviceEndTimes):
queueCountTimes = np.concatenate((arrivalTimes, serviceEndTimes))
values = np.concatenate((np.ones(arrivalTimes.shape), -np.ones(serviceEndTimes.shape)))
sortedIndices = np.argsort(queueCountTimes)
sortedQueueCountTimes = queueCountTimes[sortedIndices]
sortedValues = values[sortedIndices]
sortedValues = np.add.accumulate(sortedValues)
return sortedQueueCountTimes, sortedValues
def timeAverage(times, values):
diff = np.diff(times)
integral = diff.dot(values[:-1])
# TODO or T = sum of diff ???
T = times[-1]
avg = integral / T
return avg
def separateByAffinity(values, affinity):
result = {}
for key in np.unique(affinity):
result[key] = values[affinity == key]
return result
def meanEstimate(values, alpha=0.05):
pointEstimate = np.mean(values)
replicationsCount = values.size
S2 = np.var(values, ddof=1)
degreesOfFreedom = replicationsCount - 1
if degreesOfFreedom <= 0 :
degreesOfFreedom = 1
confidenceHalfInterval = stats.t.ppf(1 - alpha/2, df=degreesOfFreedom) * np.sqrt(S2/replicationsCount)
return pointEstimate, confidenceHalfInterval
def collectStats(collectedStats, stats):
for key, value in stats.items():
if not key in collectedStats:
collectedStats[key] = np.array([])
collectedStats[key] = np.append(collectedStats[key], value)
def satisfyConfidenceHalfIntervals(collectedStats, targetConfidenceHalfInterval, alpha):
for key, values in collectedStats.items():
if key in targetConfidenceHalfInterval:
pointEstimate, confidenceHalfInterval = meanEstimate(values, alpha)
# print(key, "pointEstimate", pointEstimate, "confidenceHalfInterval", confidenceHalfInterval)
type, value = targetConfidenceHalfInterval[key]
if type == "absolute" :
if confidenceHalfInterval > value:
return False
elif type == "relative":
if (confidenceHalfInterval/pointEstimate) > value:
return False
return True
def achieveTargetConfigenceHalfIntervals(systemModelRunner, targetConfidenceHalfInterval, alpha):
collectedStats = {}
# initial steps
for i in range(5):
stats = systemModelRunner()
collectStats(collectedStats, stats)
i = 5
while not satisfyConfidenceHalfIntervals(collectedStats, targetConfidenceHalfInterval, alpha):
stats = systemModelRunner()
collectStats(collectedStats, stats)
i = i+1
print('.', end='', flush=True)
print(' ')
return collectedStats, i
def calculateMeanEstimate(stats, alpha):
results = {}
for key, values in stats.items():
results[key] = meanEstimate(values, alpha)
# print(results)
return results
def writeStatesToFile(stats, filename):
with open(filename, 'w') as file:
file.write(dumps(stats))
def writeMultipleStatesToFile(multipleStats):
for key, stats in multipleStats.items():
writeStatesToFile(stats, "data/"+key+".json")
def readMultipleStats(dirname, cases):
multipleStats = {}
for case in cases:
with open(dirname + case + ".json", 'r') as file:
multipleStats[case] = load(file)
return multipleStats
def printSummaryPdf(multipleEstimates, filename):
estimateStr = ''
confidenceStr = ''
headerStr = '------\t\t'
headerDone = False
for key, estimates in multipleEstimates.items():
estimateStr += key + '\t\t'
confidenceStr += key + '\t\t'
for estimateKey, (estimate, confidence) in estimates.items():
estimateStr += str(estimate.item()) + '\t\t'
confidenceStr += str(confidence.item()) + '\t\t'
if not headerDone:
headerStr += estimateKey + '\t\t'
estimateStr += '\n'
confidenceStr += '\n'
headerDone = True
with open(filename, 'w') as file:
file.write(headerStr)
file.write('\n')
file.write(estimateStr)
file.write('\n')
file.write('\n')
file.write(headerStr)
file.write('\n')
file.write(confidenceStr)
file.write('\n')
def simulateWithTargetConfidence(cafeteriaModel, name, targetConfidenceHalfInterval, alpha, itersPerTime=10):
stats, N = achieveTargetConfigenceHalfIntervals(lambda:cafeteriaModel.runManySeparate(itersPerTime), targetConfidenceHalfInterval, alpha)
return stats, N * itersPerTime
def simulateMore(cafeteriaModel, collectedStats, N, alpha):
stats = cafeteriaModel.runManySeparate(N)
collectStats(collectedStats, stats)
return collectedStats
def pairedTTest(baseValues, newValues, alpha):
diff = baseValues - newValues
return meanEstimate(diff)
def welchTest(baseValues, newValues, alpha):
baseN = baseValues.size
baseMean = np.mean(baseValues)
baseS2 = np.var(baseValues, ddof=1)
newN = newValues.size
newMean = np.mean(newValues)
newS2 = np.var(newValues, ddof=1)
# Estimated Degrees of Freedom
estimatedDOF = ( baseS2/baseN + newS2/newN )**2 / ( (baseS2/baseN)**2/(baseN-1) + (newS2/newN)**2/(newN-1) )
diffEstimate = baseMean - newMean
confidenceHalfInterval = stats.t.ppf(1 - alpha/2, df=estimatedDOF) * np.sqrt(baseS2/baseN + newS2/newN)
return diffEstimate, confidenceHalfInterval
def testMany(testFunc, baseStats, newStats, alpha):
diffEstimates = {}
for key, baseValues in baseStats.items():
newValues = newStats[key]
diffEstimates[key] = testFunc(baseValues, newValues, alpha)
return diffEstimates
def printElapsed(startTime):
elapsed_time = time.time() - startTime
elapsed_time = str(datetime.timedelta(seconds=elapsed_time))[:-7]
print(elapsed_time)
def calcComparison(estimate, confidenceHalfInterval):
if estimate < 0:
if estimate + confidenceHalfInterval < 0:
return -1
else:
return 0
elif estimate > 0:
if estimate - confidenceHalfInterval > 0:
return 1
else:
return 0
else:
return 0
def judgeDiffEstimates(diffEstimatesDict):
judgedDiffEstimatesDict = {}
for case, caseDiffEstimates in diffEstimatesDict.items():
judgedDiffEstimatesDict[case] = {}
for testName, diffEstimates in caseDiffEstimates.items():
judgedDiffEstimatesDict[case][testName] = {}
for estimateKey, (estimate, confidence) in diffEstimates.items():
comp = calcComparison(estimate, confidence)
judgedDiffEstimatesDict[case][testName][estimateKey] = (estimate, confidence, comp)
return judgedDiffEstimatesDict
def compareWithBase(multipleStates, baseCase, newCases, alpha):
diffEstimatesDict = {}
for newCase in newCases:
print("Running tests for {} ...".format(newCase))
diffEstimatesDict[newCase] = {}
diffEstimatesDict[newCase]["paired_t"] = testMany(pairedTTest, multipleStates[newCase], multipleStates[baseCase], alpha)
diffEstimatesDict[newCase]["welch"] = testMany(welchTest, multipleStates[newCase], multipleStates[baseCase], alpha)
return diffEstimatesDict
def computeEstimates(multipleStates, alpha):
print("Computing estimates ...")
multipleEstimates = {}
for key, stats in multipleStates.items():
multipleEstimates[key] = calculateMeanEstimate(stats, alpha)
return multipleEstimates
def extractEqualStats(multipleStats, N):
equalMultipleStats = {}
for caseName, caseStats in multipleStats.items():
equalMultipleStats[caseName] = {}
for measure, values in caseStats.items():
equalMultipleStats[caseName][measure] = values[:N]
return equalMultipleStats