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#! /usr/bin/env python
import sys
import openturns as ot
ot.TESTPREAMBLE()
def progress(percent):
sys.stderr.write("-- progress=" + str(percent) + "%\n")
def stop():
sys.stderr.write("-- stop?\n")
return False
# We create a numerical math function
myFunction = ot.SymbolicFunction(["E", "F", "L", "I"], ["-F*L^3/(3*E*I)"])
dim = myFunction.getInputDimension()
# We create a normal distribution point of dimension 1
mean = [0.0] * dim
# E
mean[0] = 50.0
# F
mean[1] = 1.0
# L
mean[2] = 10.0
# I
mean[3] = 5.0
sigma = [1.0] * dim
R = ot.IdentityMatrix(dim)
myDistribution = ot.Normal(mean, sigma, R)
# We create a 'usual' RandomVector from the Distribution
vect = ot.RandomVector(myDistribution)
# We create a composite random vector
output = ot.CompositeRandomVector(myFunction, vect)
# We create an Event from this RandomVector
myEvent = ot.ThresholdEvent(output, ot.Less(), -3.0)
# Monte Carlo
experiments = [ot.MonteCarloExperiment()]
# Quasi Monte Carlo
experiments.append(ot.LowDiscrepancyExperiment())
# Randomized Quasi Monte Carlo
experiment = ot.LowDiscrepancyExperiment()
experiment.setRandomize(True)
experiments.append(experiment)
# Importance sampling
mean[0] = 4.99689645939288809018e01
mean[1] = 1.84194175946153282375e00
mean[2] = 1.04454036676956398821e01
mean[3] = 4.66776215562709406726e00
myImportance = ot.Normal(mean, sigma, R)
experiments.append(ot.ImportanceSamplingExperiment(myImportance))
# Randomized LHS
experiment = ot.LHSExperiment()
experiment.setAlwaysShuffle(True)
experiments.append(experiment)
for experiment in experiments:
ot.RandomGenerator.SetSeed(0)
myAlgo = ot.ProbabilitySimulationAlgorithm(myEvent, experiment)
myAlgo.setMaximumOuterSampling(250)
myAlgo.setBlockSize(4)
myAlgo.setMaximumCoefficientOfVariation(0.1)
print("algo=", myAlgo)
# Perform the simulation
myAlgo.run()
# Stream out the result
print("algo result=", myAlgo.getResult())
print("probability distribution=", myAlgo.getResult().getProbabilityDistribution())
# Use the standard deviation as a stopping rule
experiment = ot.MonteCarloExperiment()
myAlgo = ot.ProbabilitySimulationAlgorithm(myEvent, experiment)
myAlgo.setMaximumOuterSampling(250)
myAlgo.setBlockSize(4)
myAlgo.setMaximumCoefficientOfVariation(0.0)
myAlgo.setMaximumStandardDeviation(0.1)
myAlgo.setProgressCallback(progress)
myAlgo.setStopCallback(stop)
print("algo=", myAlgo)
# Perform the simulation
myAlgo.run()
# Stream out the result
print("algo result=", myAlgo.getResult())
print("probability distribution=", myAlgo.getResult().getProbabilityDistribution())
print("-" * 32)
ot.RandomGenerator.SetSeed(0)
description = ot.Description()
description.add("composite vector/comparison event")
dim = 2
distribution = ot.Normal(dim)
Xvector = ot.RandomVector(distribution)
f = ot.SymbolicFunction(["x0", "x1"], ["x0+x1"])
Yvector = ot.CompositeRandomVector(f, Xvector)
s = 1.0
event1 = ot.ThresholdEvent(Yvector, ot.Greater(), s)
description.add("composite vector/domain event")
domain1D = ot.LevelSet(ot.SymbolicFunction(["x0"], ["sin(x0)"]), ot.LessOrEqual(), -0.5)
event2 = ot.DomainEvent(Yvector, domain1D)
description.add("composite vector/interval event")
interval = ot.Interval(0.5, 1.5)
event3 = ot.ThresholdEvent(Yvector, interval)
description.add("process/domain event")
Xprocess = ot.WhiteNoise(distribution, ot.RegularGrid(0.0, 0.1, 10))
domain2D = ot.LevelSet(
ot.SymbolicFunction(["x0", "x1"], ["(x0-1)^2+x1^2"]), ot.LessOrEqual(), 1.0
)
event4 = ot.ProcessEvent(Xprocess, domain2D)
all_events = [event1, event2, event3, event4]
for i, event in enumerate(all_events):
print(description[i])
if event.isComposite():
experiment = ot.MonteCarloExperiment()
myAlgo = ot.ProbabilitySimulationAlgorithm(event, experiment)
else:
myAlgo = ot.ProbabilitySimulationAlgorithm(event)
myAlgo.setMaximumOuterSampling(250)
myAlgo.setBlockSize(4)
myAlgo.setMaximumCoefficientOfVariation(0.1)
myAlgo.run()
print("MonteCarlo result=", myAlgo.getResult())
print("probability distribution=", myAlgo.getResult().getProbabilityDistribution())
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