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#!/usr/bin/env python
import openturns as ot
import openturns.testing as ott
#
# Physical model
#
limitState = ot.SymbolicFunction(["u1", "u2"], ["u1-u2"])
dim = limitState.getInputDimension()
#
# Probabilistic model
#
mean = ot.Point(dim, 0.0)
mean[0] = 7.0
mean[1] = 2.0
sigma = ot.Point(dim, 1.0)
R = ot.IdentityMatrix(dim)
myDistribution = ot.Normal(mean, sigma, R)
#
# Limit state
#
vect = ot.RandomVector(myDistribution)
output = ot.CompositeRandomVector(limitState, vect)
myEvent = ot.ThresholdEvent(output, ot.Less(), 0.0)
#
# Computation
#
bs = 1
# Monte Carlo
experiment = ot.MonteCarloExperiment()
myMC = ot.ProbabilitySimulationAlgorithm(myEvent, experiment)
myMC.setMaximumOuterSampling(int(1e6) // bs)
myMC.setBlockSize(bs)
myMC.setMaximumCoefficientOfVariation(-1.0)
myMC.run()
#
# SubsetSampling
mySS = ot.SubsetSampling(myEvent)
mySS.setMaximumOuterSampling(10000 // bs)
mySS.setBlockSize(bs)
mySS.setKeepSample(True)
mySS.run()
#
# Results
#
# Monte Carlo
resultMC = myMC.getResult()
PFMC = resultMC.getProbabilityEstimate()
CVMC = resultMC.getCoefficientOfVariation()
variance_PF_MC = resultMC.getVarianceEstimate()
length90MC = resultMC.getConfidenceLength(0.90)
N_MC = resultMC.getOuterSampling() * resultMC.getBlockSize()
#
# SubsetSampling
resultSS = mySS.getResult()
PFSS = resultSS.getProbabilityEstimate()
CVSS = resultSS.getCoefficientOfVariation()
variance_PF_SS = resultSS.getVarianceEstimate()
length90SS = resultSS.getConfidenceLength(0.90)
N_SS = resultSS.getOuterSampling() * resultSS.getBlockSize()
#
print("-" * 100)
print("MONTE CARLO")
print("Pf estimation = %.5e" % PFMC)
print("Pf Variance estimation = %.5e" % variance_PF_MC)
print("CoV = %.5f" % CVMC)
print("90% Confidence Interval =", "%.5e" % length90MC)
print(
"CI at 90% =[",
"%.5e" % (PFMC - 0.5 * length90MC),
"; %.5e" % (PFMC + 0.5 * length90MC),
"]",
)
print("Limit state calls =", N_MC)
print("-" * 100)
print("SUBSET SAMPLING")
print("Pf estimation = %.5e" % PFSS)
print("Pf Variance estimation = %.5e" % variance_PF_SS)
print("CoV = %.5f" % CVSS)
print("90% Confidence Interval =", "%.5e" % length90SS)
print(
"CI at 90% =[",
"%.5e" % (PFSS - 0.5 * length90SS),
"; %.5e" % (PFSS + 0.5 * length90SS),
"]",
)
print("Limit state calls =", N_SS)
# check that the event sample is right
stepsNumber = mySS.getStepsNumber()
inputEventSample = mySS.getInputSample(stepsNumber - 1, mySS.EVENT1)
outputEventSample = mySS.getOutputSample(stepsNumber - 1, mySS.EVENT1)
outputG = limitState(inputEventSample)
diffSample = outputG - outputEventSample
ott.assert_almost_equal(diffSample.computeMean(), [0.0])
# null variance case
print("-" * 100)
f = ot.SymbolicFunction(["x"], ["x"])
X = ot.Normal()
Y = ot.CompositeRandomVector(f, ot.RandomVector(X))
event = ot.ThresholdEvent(Y, ot.Less(), 5000)
mc = ot.ProbabilitySimulationAlgorithm(event)
mc.run()
result = mc.getResult()
print("MC: ", result)
subset = ot.SubsetSampling(event)
subset.setBlockSize(18)
subset.run()
result = subset.getResult()
print("SUBSET:", result)
assert subset.getStepsNumber() == 1, "wrong steps"
assert result.getProbabilityEstimate() == 1.0, "wrong pf"
assert result.getVarianceEstimate() == 0.0, "wrong var"
# case with last step threshold close from global threshold (before)
print("-" * 100)
event = ot.ThresholdEvent(Y, ot.Less(), -3.33832)
mc = ot.ProbabilitySimulationAlgorithm(event)
mc.run()
print("MC: ", mc.getResult())
ot.RandomGenerator.SetSeed(65132)
subset = ot.SubsetSampling(event)
subset.setMaximumOuterSampling(500)
subset.run()
print("SUBSET:", subset.getResult())
print("steps=", subset.getStepsNumber())
print("T=", subset.getThresholdPerStep())
# case with last step threshold close from global threshold (after)
print("-" * 100)
event = ot.ThresholdEvent(Y, ot.Less(), -3.338325)
mc = ot.ProbabilitySimulationAlgorithm(event)
mc.run()
print("MC: ", mc.getResult())
ot.RandomGenerator.SetSeed(65132)
subset = ot.SubsetSampling(event)
subset.setConvergenceStrategy(ot.Full())
subset.setMaximumOuterSampling(500)
subset.run()
print("SUBSET:", subset.getResult())
print("steps=", subset.getStepsNumber())
print("T=", subset.getThresholdPerStep())
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