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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Instantiate one distribution object
for dim in range(1, 2):
theta = ot.Point(dim + 1)
for i in range(dim + 1):
theta[i] = (i + 1.0) / 4.0
distribution = ot.Dirichlet(theta)
description = [""] * dim
for j in range(1, dim + 1):
oss = "Marginal " + str(j)
description[j - 1] = oss
distribution.setDescription(description)
print("Distribution ", repr(distribution))
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", repr(oneRealization))
# Define a point
point = ot.Point(distribution.getDimension(), 0.5 / distribution.getDimension())
print("Point= ", repr(point))
# Show PDF and CDF of point
LPDF = distribution.computeLogPDF(point)
print("log pdf= %.8g" % LPDF)
PDF = distribution.computePDF(point)
print("pdf = %.8g" % PDF)
CDF = distribution.computeCDF(point)
print("cdf= %.8g" % CDF)
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)= %.6f" % 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)
)
print("entropy=%.6f" % distribution.computeEntropy())
# Confidence regions
(
interval,
threshold,
) = distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
print("Minimum volume interval=", interval)
print("threshold=", ot.Point(1, threshold))
levelSet, beta = distribution.computeMinimumVolumeLevelSetWithThreshold(0.95)
print("Minimum volume level set=", levelSet)
print("beta=", ot.Point(1, beta))
(
interval,
beta,
) = distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
print("Bilateral confidence interval=", interval)
print("beta=", ot.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))
mean = distribution.getMean()
print("mean=", repr(mean))
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", repr(standardDeviation))
skewness = distribution.getSkewness()
print("skewness=", repr(skewness))
kurtosis = distribution.getKurtosis()
print("kurtosis=", repr(kurtosis))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % distribution.computeConditionalPDF(x, y))
print("conditional CDF=%.6f" % distribution.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % distribution.computeConditionalQuantile(x, y))
pt = ot.Point([0.1 * i + 0.15 for i in range(dim)])
print(
"sequential conditional PDF=",
distribution.computeSequentialConditionalPDF(point),
)
resCDF = distribution.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
distribution.computeSequentialConditionalQuantile(resCDF),
)
# Ticket #2306
if dim == 2:
condPDF = distribution.computeConditionalPDF(-0.1, [0.5])
assert ot.SpecFunc.IsNormal(condPDF), "condPDF is not normal"
condPDF = distribution.computeConditionalPDF(0.5, [0.5])
assert ot.SpecFunc.IsNormal(condPDF), "condPDF is not normal"
condPDF = distribution.computeConditionalPDF(0.6, [0.5])
assert ot.SpecFunc.IsNormal(condPDF), "condPDF is not normal"
condPDF = distribution.computeSequentialConditionalPDF([0.5, -0.1])
assert ot.SpecFunc.IsNormal(condPDF), "condPDF is not normal"
condPDF = distribution.computeSequentialConditionalPDF([0.5, 0.5])
assert ot.SpecFunc.IsNormal(condPDF), "condPDF is not normal"
condPDF = distribution.computeSequentialConditionalPDF([0.5, 0.6])
assert ot.SpecFunc.IsNormal(condPDF), "condPDF is not normal"
# Extract the marginals
for i in range(dim):
margin = distribution.getMarginal(i)
print("margin=", margin)
print("margin PDF= %.8g" % margin.computePDF(ot.Point(1, 0.5)))
print("margin CDF= %.8g" % margin.computeCDF(ot.Point(1, 0.5)))
print("margin quantile=", repr(margin.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
if dim >= 2:
# Extract a 2-D marginal
indices = [1, 0]
print("indices=", indices)
margins = distribution.getMarginal(indices)
print("margins=", margins)
print("margins PDF=", margins.computePDF(ot.Point(2, 0.5)))
print("margins CDF= %.8g" % margins.computeCDF(ot.Point(2, 0.5)))
quantile = margins.computeQuantile(0.95)
print("margins quantile=", repr(quantile))
print("margins CDF(quantile)= %.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipCDF()
validation.skipGradient()
validation.skipMoments()
validation.run()
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