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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
# We create a numerical math function
myFunction = ot.SymbolicFunction(["x0", "x1"], ["-(6+x0^2-x1)"])
dim = myFunction.getInputDimension()
# We create a normal distribution point of dimension 1
mean = [5.0, 2.1]
sigma = [3.3, 3.0]
R = ot.IdentityMatrix(dim)
#
testDistributions = ot.DistributionCollection(2)
testDistributions[0] = ot.Normal(mean, sigma, R)
marginals = ot.DistributionCollection(2)
marginals[0] = testDistributions[0].getMarginal(0)
marginals[1] = testDistributions[0].getMarginal(1)
testDistributions[1] = ot.JointDistribution(marginals, ot.NormalCopula(R))
for i in range(1):
myDistribution = testDistributions[i]
myDistribution.setDescription(["Marginal 1", "Marginal 2"])
# We create a 'usual' RandomVector from the Distribution
vect = ot.RandomVector(myDistribution)
# We create a composite random vector
output = ot.CompositeRandomVector(myFunction, vect)
output.setDescription(["Interest Variable 1"])
# We create an Event from this RandomVector
myEvent = ot.ThresholdEvent(output, ot.Greater(), 0.0)
# We create a NearestPoint algorithm
myCobyla = ot.Cobyla()
myCobyla.setStartingPoint(mean)
myCobyla.setMaximumCallsNumber(200)
myCobyla.setMaximumAbsoluteError(1.0e-10)
myCobyla.setMaximumRelativeError(1.0e-10)
myCobyla.setMaximumResidualError(1.0e-10)
myCobyla.setMaximumConstraintError(1.0e-10)
print("myCobyla=", myCobyla)
# We create a FORM algorithm
# The first parameter is an OptimizationAlgorithm
# The second parameter is an event
# The third parameter is a starting point for the design point research
myAlgo = ot.FORM(myCobyla, myEvent)
print("FORM=", myAlgo)
# Perform the simulation
myAlgo.run()
# Stream out the result
result = ot.FORMResult(myAlgo.getResult())
print("importance factors=", result.getImportanceFactors())
print("Hasofer reliability index=%.6f" % result.getHasoferReliabilityIndex())
print("result=", result)
# Hasofer Reliability Index Sensitivity
hasoferReliabilityIndexSensitivity = result.getHasoferReliabilityIndexSensitivity()
print(
"hasoferReliabilityIndexSensitivity = ",
repr(hasoferReliabilityIndexSensitivity),
)
# Event Probability Sensitivity
eventProbabilitySensitivity = result.getEventProbabilitySensitivity()
print("eventProbabilitySensitivity = ", repr(eventProbabilitySensitivity))
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