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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)
# First test: comparison with a Normal distribution with block-diagonal
# correlation
R0 = ot.CorrelationMatrix(2)
R0[0, 1] = 0.5
R1 = ot.CorrelationMatrix(3)
R1[0, 1] = 0.2
R1[0, 2] = 0.1
R1[1, 2] = 0.15
R2 = ot.CorrelationMatrix(2)
R2[0, 1] = 0.3
collection = [
ot.Normal([0.0] * 2, [1.0] * 2, R0),
ot.Normal([0.0] * 3, [1.0] * 3, R1),
ot.Normal([0.0] * 2, [1.0] * 2, R2),
]
distribution = ot.BlockIndependentDistribution(collection)
copulaCollection = [ot.NormalCopula(R0), ot.NormalCopula(R1), ot.NormalCopula(R2)]
copula = ot.BlockIndependentCopula(copulaCollection)
ref = ot.JointDistribution([ot.Normal(0.0, 1.0)] * 7, copula)
# Define a point
point = [0.3] * distribution.getDimension()
print("Point= ", point)
# Show PDF and CDF of point
DDF = distribution.computeDDF(point)
print("ddf =", DDF)
print("ddf (ref)=", ref.computeDDF(point))
PDF = distribution.computePDF(point)
print("pdf =%.5f" % PDF)
print("pdf (ref)=%.5f" % ref.computePDF(point))
CDF = distribution.computeCDF(point)
print("cdf =%.5f" % CDF)
print("cdf (ref)=%.5f" % ref.computeCDF(point))
Survival = distribution.computeSurvivalFunction(point)
print("Survival =%.5f" % Survival)
print("Survival (ref)=%.5f" % ref.computeSurvivalFunction(point))
InverseSurvival = distribution.computeInverseSurvivalFunction(0.95)
print("Inverse survival =", InverseSurvival)
print("Inverse survival (ref)=", ref.computeInverseSurvivalFunction(0.95))
print(
"Survival(inverse survival)=%.5f"
% distribution.computeSurvivalFunction(InverseSurvival)
)
# Get 50% quantile
quantile = distribution.computeQuantile(0.5)
print("Quantile =", quantile)
print("Quantile (ref)=", ref.computeQuantile(0.5))
print("CDF(quantile) =%.5f" % distribution.computeCDF(quantile))
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.setPDFTolerance(4e-3) # for conditional PDF
validation.run()
# Instantiate one distribution object
R = ot.CorrelationMatrix(3)
R[0, 1] = 0.5
R[0, 2] = 0.25
collection = [
ot.JointDistribution([ot.Normal()] * 2, ot.AliMikhailHaqCopula(0.5)),
ot.Normal([1.0] * 3, [2.0] * 3, R),
ot.JointDistribution([ot.Exponential()] * 2, ot.FrankCopula(0.5)),
]
distribution = ot.BlockIndependentDistribution(collection)
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical distribution= ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Has this distribution an elliptical copula ?
print("Elliptical = ", distribution.hasEllipticalCopula())
# Has this distribution an independent copula ?
print("Independent = ", distribution.hasIndependentCopula())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", oneRealization)
# Define a point
point = [0.3] * distribution.getDimension()
print("Point= ", point)
# Show PDF and CDF of point
DDF = distribution.computeDDF(point)
print("ddf =", DDF)
PDF = distribution.computePDF(point)
print("pdf =%.5f" % PDF)
CDF = distribution.computeCDF(point)
print("cdf=%.5f" % CDF)
Survival = distribution.computeSurvivalFunction(point)
print("Survival =%.5f" % Survival)
print("Survival (ref)=%.5f" % distribution.computeSurvivalFunction(point))
InverseSurvival = distribution.computeInverseSurvivalFunction(0.95)
print("Inverse survival=", InverseSurvival)
print(
"Survival(inverse survival)=%.5f"
% distribution.computeSurvivalFunction(InverseSurvival)
)
# Get 50% quantile
quantile = distribution.computeQuantile(0.5)
print("Quantile=", quantile)
print("CDF(quantile)=%.5f" % distribution.computeCDF(quantile))
if distribution.getDimension() <= 2:
# Confidence regions
(
interval,
threshold,
) = distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
print("Minimum volume interval=", interval)
print("threshold=%.5f" % threshold)
levelSet, beta = distribution.computeMinimumVolumeLevelSetWithThreshold(0.95)
print("Minimum volume level set=", levelSet)
print("beta=%.5f" % beta)
(
interval,
beta,
) = distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
print("Bilateral confidence interval=", interval)
print("beta=%.5f" % beta)
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, False
)
print("Unilateral confidence interval (lower tail)=", interval)
print("beta=%.5f" % beta)
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, True
)
print("Unilateral confidence interval (upper tail)=", interval)
print("beta=%.5f" % beta)
print("entropy =%.5f" % distribution.computeEntropy())
mean = distribution.getMean()
# Ensure mean is [0,0,1,1,1,1,1]
# Following platform, the value slightly differs
ott.assert_almost_equal(distribution.getMean(), [0, 0, 1, 1, 1, 1, 1])
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", repr(standardDeviation))
skewness = distribution.getSkewness()
# print("skewness=", repr(skewness))
kurtosis = distribution.getKurtosis()
print("kurtosis=", repr(kurtosis))
dim = distribution.getDimension()
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.5f" % distribution.computeConditionalPDF(x, y))
print("conditional CDF=%.5f" % distribution.computeConditionalCDF(x, y))
print("conditional quantile=%.5f" % distribution.computeConditionalQuantile(x, y))
pt = ot.Point(dim)
for i in range(dim):
pt[i] = 0.1 * i + 0.05
print("sequential conditional PDF=", distribution.computeSequentialConditionalPDF(pt))
resCDF = distribution.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
distribution.computeSequentialConditionalQuantile(resCDF),
)
# Extract a 5-D marginal
dim = 5
point = [0.25] * dim
indices = [1, 2, 3, 5, 6]
print("indices=", indices)
margins = distribution.getMarginal(indices)
print("margins=", margins)
print("margins PDF=%.5f" % margins.computePDF(point))
print("margins CDF=%.5f" % margins.computeCDF(point))
quantile = margins.computeQuantile(0.95)
print("margins quantile=", quantile)
print("margins CDF(quantile)=%.5f" % margins.computeCDF(quantile))
print("margins realization=", margins.getRealization())
# Tests o the isoprobabilistic transformation
# General case with normal standard distribution
print(
"isoprobabilistic transformation (general normal)=",
distribution.getIsoProbabilisticTransformation(),
)
# General case with non-normal standard distribution
collection[0] = ot.SklarCopula(
ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
)
collection.append(ot.Triangular(2.0, 3.0, 4.0))
distribution = ot.BlockIndependentDistribution(collection)
print(
"isoprobabilistic transformation (general non-normal)=",
distribution.getIsoProbabilisticTransformation(),
)
dim = distribution.getDimension()
x = 2.6
y = [0.2] * (dim - 1)
q = 0.9
print("conditional PDF=%.5f" % distribution.computeConditionalPDF(x, y))
print("conditional CDF=%.5f" % distribution.computeConditionalCDF(x, y))
print("conditional quantile=%.5f" % distribution.computeConditionalQuantile(q, y))
pt = ot.Point(dim)
for i in range(dim):
pt[i] = 0.1 * i + 0.05
print("sequential conditional PDF=", distribution.computeSequentialConditionalPDF(pt))
resCDF = distribution.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
distribution.computeSequentialConditionalQuantile(resCDF),
)
print("range=", distribution.getRange())
# getStandardDeviation vs Dirac
distribution2 = ot.BlockIndependentDistribution([ot.Normal(), ot.Dirac(1800)])
ott.assert_almost_equal(distribution2.getStandardDeviation(), [1, 0])
# check marginal from a group is not uselessly wrapped in BlockIndependent
margins = distribution.getMarginal([0, 1])
ott.assert_almost_equal(margins, collection[0])
# check getSupport
distribution = ot.BlockIndependentDistribution(
[ot.Multinomial(5, ot.Point(2, 0.25))] * 2
)
support = distribution.getSupport(ot.Interval([2] * 4, [5] * 4))
print(support)
assert support.getSize() == 9
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