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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
# Instantiate one distribution object
R = ot.CorrelationMatrix(3)
R[0, 1] = 0.5
R[0, 2] = 0.25
collection = [ot.FrankCopula(3.0), ot.NormalCopula(R), ot.ClaytonCopula(2.0)]
copula = ot.BlockIndependentCopula(collection)
print("Copula ", repr(copula))
print("Copula ", copula)
# Is this copula elliptical ?
print("Elliptical distribution= ", copula.isElliptical())
# Is this copula continuous ?
print("Continuous = ", copula.isContinuous())
# Is this copula elliptical ?
print("Elliptical = ", copula.hasEllipticalCopula())
# Is this copula independent ?
print("Independent = ", copula.hasIndependentCopula())
# Test for realization of copula
oneRealization = copula.getRealization()
print("oneRealization=", repr(oneRealization))
# Test for sampling
size = 10000
oneSample = copula.getSample(size)
print("oneSample first=", repr(oneSample[0]), " last=", repr(oneSample[size - 1]))
print("mean=", repr(oneSample.computeMean()))
print("covariance=", repr(oneSample.computeCovariance()))
# Define a point
point = ot.Point(copula.getDimension(), 0.6)
print("Point= ", repr(point))
# Show PDF and CDF of point
# Scalar eps(1e-5)
DDF = copula.computeDDF(point)
print("ddf =", repr(DDF))
PDF = copula.computePDF(point)
print("pdf =%.6f" % PDF)
CDF = copula.computeCDF(point)
print("cdf=%.6f" % CDF)
# Point PDFgr = copula.computePDFGradient( point )
# print "pdf gradient =", PDFgr
# Point CDFgr = copula.computeCDFGradient( point )
# print "cdf gradient =", CDFgr
quantile = copula.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=%.6f" % copula.computeCDF(quantile))
# Get 95% survival function
inverseSurvival = ot.Point(copula.computeInverseSurvivalFunction(0.95))
print("InverseSurvival=", repr(inverseSurvival))
print(
"Survival(inverseSurvival)=%.6f" % copula.computeSurvivalFunction(inverseSurvival)
)
print("entropy=%.6f" % copula.computeEntropy())
# Confidence regions
if copula.getDimension() <= 2:
threshold = ot.Point()
print(
"Minimum volume interval=", copula.computeMinimumVolumeInterval(0.95, threshold)
)
print("threshold=", threshold)
beta = ot.Point()
levelSet = copula.computeMinimumVolumeLevelSet(0.95, beta)
print("Minimum volume level set=", levelSet)
print("beta=", beta)
print(
"Bilateral confidence interval=",
copula.computeBilateralConfidenceInterval(0.95, beta),
)
print("beta=", beta)
print(
"Unilateral confidence interval (lower tail)=",
copula.computeUnilateralConfidenceInterval(0.95, False, beta),
)
print("beta=", beta)
print(
"Unilateral confidence interval (upper tail)=",
copula.computeUnilateralConfidenceInterval(0.95, True, beta),
)
print("beta=", beta)
mean = copula.getMean()
print("mean=", repr(mean))
covariance = copula.getCovariance()
print("covariance=", repr(covariance))
parameters = copula.getParametersCollection()
print("parameters=", repr(parameters))
# Covariance and correlation
precision = ot.PlatformInfo.GetNumericalPrecision()
ot.PlatformInfo.SetNumericalPrecision(4)
covariance = copula.getCovariance()
print("covariance=", covariance)
correlation = copula.getCorrelation()
print("correlation=", correlation)
spearman = copula.getSpearmanCorrelation()
print("spearman=", spearman)
kendall = copula.getKendallTau()
print("kendall=", kendall)
ot.PlatformInfo.SetNumericalPrecision(precision)
dim = copula.getDimension()
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % copula.computeConditionalPDF(x, y))
print("conditional CDF=%.6f" % copula.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % copula.computeConditionalQuantile(x, y))
pt = ot.Point([0.1 * i + 0.05 for i in range(dim)])
print("sequential conditional PDF=", copula.computeSequentialConditionalPDF(point))
resCDF = copula.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
copula.computeSequentialConditionalQuantile(resCDF),
)
# Specific to this copula
# Extract a 5-D marginal
dim = 5
point = ot.Point(dim, 0.25)
indices = ot.Indices(dim, 0)
indices[0] = 1
indices[1] = 2
indices[2] = 3
indices[3] = 5
indices[4] = 6
print("indices=", repr(indices))
margins = copula.getMarginal(indices)
print("margins=", repr(margins))
print("margins PDF=%.6f" % margins.computePDF(point))
print("margins CDF=%.6f" % margins.computeCDF(point))
quantile = margins.computeQuantile(0.95)
print("margins quantile=", repr(quantile))
print("margins CDF(quantile)=%.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
# Tests the isoprobabilistic transformation
# General case with normal standard distribution
print(
"isoprobabilistic transformation (general normal)=",
copula.getIsoProbabilisticTransformation(),
)
# General case with non-normal standard distribution
collection[0] = ot.SklarCopula(
ot.Student(3.0, ot.Point(2, 1.0), ot.Point(2, 3.0), ot.CorrelationMatrix(2))
)
copula = ot.BlockIndependentCopula(collection)
print(
"isoprobabilistic transformation (general non-normal)=",
copula.getIsoProbabilisticTransformation(),
)
dim = copula.getDimension()
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % copula.computeConditionalPDF(x, y))
print("conditional CDF=%.6f" % copula.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % copula.computeConditionalQuantile(x, y))
pt = ot.Point([0.1 * i + 0.05 for i in range(dim)])
print("sequential conditional PDF=", copula.computeSequentialConditionalPDF(pt))
resCDF = copula.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
copula.computeSequentialConditionalQuantile(resCDF),
)
# Special case, independent copula
collection[0] = ot.SklarCopula(ot.Normal(2))
collection[1] = ot.IndependentCopula(2)
collection[2] = ot.NormalCopula(ot.CorrelationMatrix(2))
copula = ot.BlockIndependentCopula(collection)
print(
"isoprobabilistic transformation (independent)=",
copula.getIsoProbabilisticTransformation(),
)
dim = copula.getDimension()
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % copula.computeConditionalPDF(x, y))
print("conditional CDF=%.6f" % copula.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % copula.computeConditionalQuantile(x, y))
pt = ot.Point([0.1 * i + 0.05 for i in range(dim)])
print("sequential conditional PDF=", copula.computeSequentialConditionalPDF(pt))
resCDF = copula.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
copula.computeSequentialConditionalQuantile(resCDF),
)
# Special case, single contributor
collection = [
ot.SklarCopula(
ot.Student(3.0, ot.Point(2, 1.0), ot.Point(2, 3.0), ot.CorrelationMatrix(2))
)
]
copula = ot.BlockIndependentCopula(collection)
print(
"isoprobabilistic transformation (single contributor)=",
copula.getIsoProbabilisticTransformation(),
)
dim = copula.getDimension()
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % copula.computeConditionalPDF(x, y))
print("conditional CDF=%.6f" % copula.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % copula.computeConditionalQuantile(x, y))
pt = ot.Point([0.1 * i + 0.05 for i in range(dim)])
print("sequential conditional PDF=", copula.computeSequentialConditionalPDF(pt))
resCDF = copula.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
copula.computeSequentialConditionalQuantile(resCDF),
)
# test BlockIndependentCopula.getMarginal in reverse
copula = ot.BlockIndependentCopula([ot.IndependentCopula(2), ot.NormalCopula(2)])
print(copula.getMarginal([3, 2, 1, 0]))
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