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#! /usr/bin/env python
import openturns as ot
def printPoint(point, digits):
oss = "["
eps = pow(0.1, digits)
for i in range(point.getDimension()):
if i == 0:
sep = ""
else:
sep = ","
if abs(point[i]) < eps:
oss += sep + "%.6f" % abs(point[i])
else:
oss += sep + "%.6f" % point[i]
sep = ","
oss += "]"
return oss
ot.TESTPREAMBLE()
# We create a numerical math function
# Analytical construction
inputFunc = ot.Description(2)
inputFunc[0] = "x0"
inputFunc[1] = "x1"
formulas = ot.Description(1)
formulas[0] = "-(6+x0^2-x1)"
print("formulas=", formulas)
myFunction = ot.SymbolicFunction(inputFunc, formulas)
dim = myFunction.getInputDimension()
# We create a normal distribution point of dimension 1
mean = ot.Point(dim, 0.0)
# x0
mean[0] = 5.0
# x1
mean[1] = 2.1
sigma = ot.Point(dim, 0.0)
# x0
sigma[0] = 3.3
# x1
sigma[1] = 3.0
R = ot.CorrelationMatrix(dim)
myDistribution = ot.Normal(mean, sigma, R)
# we name the components of the distribution
componentDescription = ot.Description(dim)
componentDescription[0] = "Marginal 1"
componentDescription[1] = "Marginal 2"
myDistribution.setDescription(componentDescription)
# We create a 'usual' RandomVector from the Distribution
vect = ot.RandomVector(myDistribution)
# We create a composite random vector
output = ot.CompositeRandomVector(myFunction, vect)
outputDescription = ot.Description(1)
outputDescription[0] = "Interest Variable 1"
output.setDescription(outputDescription)
# We create an Event from this RandomVector
myEvent = ot.ThresholdEvent(output, ot.Greater(), 0.0)
# We create a NearestPoint algorithm
myCobyla = ot.Cobyla()
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, mean)
print("FORM=", myAlgo)
# Perform the simulation
myAlgo.run()
# Stream out the result
result = ot.FORMResult(myAlgo.getResult())
digits = 5
print("importance factors=", printPoint(result.getImportanceFactors(), digits))
# Graph 1 : Importance Factors graph
importanceFactorsGraph = result.drawImportanceFactors()
# Graph 2 : Hasofer Reliability Index Sensitivity Graphs graph
reliabilityIndexSensitivityGraphs = result.drawHasoferReliabilityIndexSensitivity()
graph2a = reliabilityIndexSensitivityGraphs[0]
graph2b = reliabilityIndexSensitivityGraphs[1]
# Graph 3 : FORM Event Probability Sensitivity Graphs graph
eventProbabilitySensitivityGraphs = result.drawEventProbabilitySensitivity()
graph3a = eventProbabilitySensitivityGraphs[0]
graph3b = eventProbabilitySensitivityGraphs[1]
# Graph 4 : Convergence history
graph4 = result.getOptimizationResult().drawErrorHistory()
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