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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Multivariate case
coll2 = ot.DistributionCollection(0)
coll2.add(ot.Dirac(1))
coll2.add(ot.Dirac(2))
coll2.add(ot.Bernoulli(0.7))
coll2.add(ot.Uniform(3.0, 4.0))
d2 = ot.JointDistribution(coll2)
coll1 = ot.DistributionCollection(0)
coll1.add(ot.Uniform())
coll1.add(ot.Uniform())
d1 = ot.JointDistribution(coll1)
# Test the different DOE
ot.ResourceMap.SetAsUnsignedInteger(
"DeconditionedDistribution-MarginalIntegrationNodesNumber", 256
)
ot.ResourceMap.SetAsUnsignedInteger(
"DeconditionedDistribution-MaximumIntegrationNodesNumber", 10000
)
for method in ["GaussProduct", "QMC", "MC"]:
print("#" * 50)
print("method=", method)
ot.ResourceMap.SetAsString(
"DeconditionedDistribution-ContinuousDiscretizationMethod", method
)
distribution = ot.DeconditionedDistribution(d1, d2)
dim = distribution.getDimension()
print("distribution=", distribution)
print("Parameters ", distribution.getParametersCollection())
print("Mean ", distribution.getMean())
cov = distribution.getCovariance()
cov_ref = ot.CovarianceMatrix([[0.0833333, 0.0], [0.0, 0.751111]])
ott.assert_almost_equal(cov, cov_ref, 1e-3, 1e-3)
# Is this distribution an elliptical distribution?
print("Elliptical distribution= ", distribution.isElliptical())
# Has this distribution an elliptical copula?
print("Elliptical copula= ", distribution.hasEllipticalCopula())
# Has this distribution an independent copula?
print("Independent copula= ", distribution.hasIndependentCopula())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", oneRealization)
# Test for sampling
size = 10
oneSample = distribution.getSample(size)
print("oneSample=", oneSample)
# Test for sampling
size = 10000
anotherSample = distribution.getSample(size)
print("anotherSample mean=", anotherSample.computeMean())
print("anotherSample covariance=", anotherSample.computeCovariance())
# Define a point
zero = ot.Point(dim, 0.0)
# Show PDF and CDF of zero point
zeroPDF = distribution.computePDF(zero)
zeroCDF = distribution.computeCDF(zero)
print("Zero point= ", zero, " pdf=", zeroPDF, " cdf=", zeroCDF)
# Get 95% quantile
quantile = distribution.computeQuantile(0.95)
print("Quantile=", quantile)
print("CDF(quantile)= %.5g" % distribution.computeCDF(quantile))
# Get 95% survival function
inverseSurvival = ot.Point(distribution.computeInverseSurvivalFunction(0.95))
print("InverseSurvival=", repr(inverseSurvival))
print(
"Survival(inverseSurvival)=%.6f"
% distribution.computeSurvivalFunction(inverseSurvival)
)
# Confidence regions
# interval, threshold = distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
# print("Minimum volume interval=", interval)
# print("threshold=", Point(1, threshold))
# levelSet, beta = distribution.computeMinimumVolumeLevelSetWithThreshold(0.95)
# print("Minimum volume level set=", levelSet)
# print("beta=", Point(1, beta))
# interval, beta = distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
# print("Bilateral confidence interval=", interval)
# print("beta=", Point(1, beta))
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, False
)
print("Unilateral confidence interval (lower tail)=", interval)
print("beta=", ot.Point(1, beta))
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, True
)
print("Unilateral confidence interval (upper tail)=", interval)
print("beta=", ot.Point(1, beta))
# "
# 1D tests
# Create a collection of distribution
conditionedDistribution = ot.Normal()
conditioningDistributionCollection = ot.DistributionCollection(0)
# First conditioning distribution: continuous/continuous
atoms = ot.DistributionCollection(0)
atoms.add(ot.Uniform(0.0, 1.0))
atoms.add(ot.Uniform(1.0, 2.0))
conditioningDistributionCollection.add(ot.JointDistribution(atoms))
# Second conditioning distribution: discrete/continuous
atoms = ot.DistributionCollection(0)
atoms.add(ot.Binomial(3, 0.5))
atoms.add(ot.Uniform(1.0, 2.0))
conditioningDistributionCollection.add(ot.JointDistribution(atoms))
# Third conditioning distribution: dirac/continuous
atoms = ot.DistributionCollection(0)
atoms.add(ot.Dirac(0.5))
atoms.add(ot.Uniform(1.0, 2.0))
conditioningDistributionCollection.add(ot.JointDistribution(atoms))
for i in range(conditioningDistributionCollection.getSize()):
print("conditioning distribution=", conditioningDistributionCollection[i])
distribution = ot.DeconditionedDistribution(
conditionedDistribution, conditioningDistributionCollection[i]
)
dim = distribution.getDimension()
print("Distribution ", distribution)
print("Parameters ", distribution.getParametersCollection())
print("Mean ", distribution.getMean())
print("Covariance ", distribution.getCovariance())
# Is this distribution an elliptical distribution?
print("Elliptical distribution= ", distribution.isElliptical())
# Has this distribution an elliptical copula?
print("Elliptical copula= ", distribution.hasEllipticalCopula())
# Has this distribution an independent copula?
print("Independent copula= ", distribution.hasIndependentCopula())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", oneRealization)
# Test for sampling
size = 10
oneSample = distribution.getSample(size)
print("oneSample=", oneSample)
# Test for sampling
size = 10000
anotherSample = distribution.getSample(size)
print("anotherSample mean=", anotherSample.computeMean())
print("anotherSample covariance=", anotherSample.computeCovariance())
# Define a point
zero = ot.Point(dim, 0.0)
# Show PDF and CDF of zero point
zeroPDF = distribution.computePDF(zero)
zeroCDF = distribution.computeCDF(zero)
print("Zero point= ", zero, " pdf=%.6f" % zeroPDF, " cdf=%.6f" % zeroCDF)
# Get 95% quantile
quantile = distribution.computeQuantile(0.95)
print("Quantile=", quantile)
print("CDF(quantile)= %.12g" % distribution.computeCDF(quantile))
# Get 95% survival function
inverseSurvival = ot.Point(distribution.computeInverseSurvivalFunction(0.95))
print("InverseSurvival=", repr(inverseSurvival))
print(
"Survival(inverseSurvival)=%.6f"
% distribution.computeSurvivalFunction(inverseSurvival)
)
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