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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
import math as m
def cleanPoint(inPoint):
dim = inPoint.getDimension()
for i in range(dim):
if m.fabs(inPoint[i]) < 1.0e-10:
inPoint[i] = 0.0
return inPoint
def cleanCovariance(inCovariance):
dim = inCovariance.getDimension()
for j in range(dim):
for i in range(dim):
if m.fabs(inCovariance[i, j]) < 1.0e-10:
inCovariance[i, j] = 0.0
return inCovariance
# Instantiate one distribution object
referenceDistribution = [
ot.TruncatedNormal(2.0, 1.5, 1.0, 4.0),
ot.TruncatedNormal(2.0, 1.5, 1.0, 200.0),
ot.TruncatedNormal(2.0, 1.5, -200.0, 4.0),
ot.TruncatedNormal(2.0, 1.5, 1.0, 4.0),
]
distribution = [
ot.TruncatedDistribution(ot.Normal(2.0, 1.5), 1.0, 4.0),
ot.TruncatedDistribution(ot.Normal(2.0, 1.5), 1.0, ot.TruncatedDistribution.LOWER),
ot.TruncatedDistribution(ot.Normal(2.0, 1.5), 4.0, ot.TruncatedDistribution.UPPER),
ot.TruncatedDistribution(
ot.Normal(2.0, 1.5), ot.Interval([1.0], [4.0], [True], [True])
),
]
# add a 2-d test
dimension = 2
# This distribution takes too much time for the test
# size = 70
# ref = ot.Normal(dimension)
# sample = ref.getSample(size)
# ks = ot.KernelSmoothing().build(sample)
# Use a multivariate Normal distribution instead
ks = ot.Normal(2)
truncatedKS = ot.TruncatedDistribution(
ks, ot.Interval([-0.5] * dimension, [2.0] * dimension)
)
distribution.append(truncatedKS)
referenceDistribution.append(ks) # N/A
# Add a non-truncated example
weibull = ot.WeibullMin(2.0, 3.0)
distribution.append(ot.TruncatedDistribution(weibull))
referenceDistribution.append(weibull)
ot.RandomGenerator.SetSeed(0)
for testCase in range(len(distribution)):
print("Distribution ", distribution[testCase])
# Is this distribution elliptical ?
print("Elliptical = ", distribution[testCase].isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution[testCase].isContinuous())
# Test for realization of distribution
oneRealization = distribution[testCase].getRealization()
print("oneRealization=", repr(oneRealization))
# Test for sampling
size = 10000
oneSample = distribution[testCase].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(distribution[testCase].getDimension(), 1.5)
print("Point= ", repr(point))
# Show PDF and CDF of point
eps = 1e-5
DDF = distribution[testCase].computeDDF(point)
print("ddf =", repr(DDF))
print("ddf (ref)=", repr(referenceDistribution[testCase].computeDDF(point)))
PDF = distribution[testCase].computePDF(point)
print("pdf =%.6f" % PDF)
print("pdf (ref)=%.6f" % referenceDistribution[testCase].computePDF(point))
CDF = distribution[testCase].computeCDF(point)
print("cdf=%.6f" % CDF)
CCDF = distribution[testCase].computeComplementaryCDF(point)
print("ccdf=%.6f" % CCDF)
print("cdf (ref)=%.6f" % referenceDistribution[testCase].computeCDF(point))
PDFgr = distribution[testCase].computePDFGradient(point)
print("pdf gradient =", repr(cleanPoint(PDFgr)))
CDFgr = distribution[testCase].computeCDFGradient(point)
print("cdf gradient =", repr(cleanPoint(CDFgr)))
# quantile
quantile = distribution[testCase].computeQuantile(0.95)
print("quantile=", repr(quantile))
print("quantile=", repr(referenceDistribution[testCase].computeQuantile(0.95)))
print("cdf(quantile)=%.6f" % distribution[testCase].computeCDF(quantile))
# Get 95% survival function
inverseSurvival = ot.Point(
distribution[testCase].computeInverseSurvivalFunction(0.95)
)
print("InverseSurvival=", repr(inverseSurvival))
print(
"Survival(inverseSurvival)=%.6f"
% distribution[testCase].computeSurvivalFunction(inverseSurvival)
)
print("entropy=%.6f" % distribution[testCase].computeEntropy())
# Confidence regions
if distribution[testCase].getDimension() == 1:
interval, threshold = distribution[
testCase
].computeMinimumVolumeIntervalWithMarginalProbability(0.95)
print("Minimum volume interval=", interval)
print("threshold=", ot.Point(1, threshold))
levelSet, beta = distribution[
testCase
].computeMinimumVolumeLevelSetWithThreshold(0.95)
print("Minimum volume level set=", levelSet)
print("beta=", ot.Point(1, beta))
interval, beta = distribution[
testCase
].computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
print("Bilateral confidence interval=", interval)
print("beta=", ot.Point(1, beta))
interval, beta = distribution[
testCase
].computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, False)
print("Unilateral confidence interval (lower tail)=", interval)
print("beta=", ot.Point(1, beta))
interval, beta = distribution[
testCase
].computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, True)
print("Unilateral confidence interval (upper tail)=", interval)
print("beta=", ot.Point(1, beta))
mean = distribution[testCase].getMean()
print("mean =", repr(mean))
print("mean (ref)=", repr(referenceDistribution[testCase].getMean()))
standardDeviation = distribution[testCase].getStandardDeviation()
print("standard deviation =", repr(standardDeviation))
print(
"standard deviation (ref)=",
repr(referenceDistribution[testCase].getStandardDeviation()),
)
skewness = distribution[testCase].getSkewness()
print("skewness =", repr(skewness))
print("skewness (ref)=", repr(referenceDistribution[testCase].getSkewness()))
kurtosis = distribution[testCase].getKurtosis()
print("kurtosis =", repr(kurtosis))
print("kurtosis (ref)=", repr(referenceDistribution[testCase].getKurtosis()))
covariance = distribution[testCase].getCovariance()
print("covariance =", repr(cleanCovariance(covariance)))
print(
"covariance (ref)=",
repr(cleanCovariance(referenceDistribution[testCase].getCovariance())),
)
parameters = distribution[testCase].getParametersCollection()
print("parameters =", repr(parameters))
print(
"parameters (ref)=",
repr(referenceDistribution[testCase].getParametersCollection()),
)
print("parameter =", repr(distribution[testCase].getParameter()))
print("parameter desc =", repr(distribution[testCase].getParameterDescription()))
print("marginal 0 =", repr(distribution[testCase].getMarginal(0)))
print(
"Standard representative=",
referenceDistribution[testCase].getStandardRepresentative(),
)
mean = distribution[testCase].getMean()
cpdf = distribution[testCase].computeConditionalPDF(mean[0], [])
print(f"conditional PDF={cpdf:.6f}")
scpdf = distribution[testCase].computeSequentialConditionalPDF(mean)
print(f"sequential conditional PDF={scpdf}")
ccdf = distribution[testCase].computeConditionalCDF(mean[0], [])
print(f"conditional CDF={ccdf:.6f}")
sccdf = distribution[testCase].computeSequentialConditionalCDF(mean)
print(f"sequential conditional CDF={sccdf}")
ot.Log.Show(ot.Log.TRACE)
ot.RandomGenerator.SetSeed(1)
validation = ott.DistributionValidation(distribution[testCase])
validation.skipMinimumVolumeLevelSet() # slow
validation.run()
# Check simplification
candidates = [
ot.Normal(1.0, 2.0),
ot.Uniform(1.0, 2.0),
ot.Exponential(1.0, 2.0),
ot.TruncatedDistribution(ot.WeibullMin(), 1.5, 7.8),
ot.Beta(1.5, 6.3, -1.0, 2.0),
ot.JointDistribution([ot.Normal()] * 2),
ot.BlockIndependentDistribution([ot.Normal(2), ot.Normal(2)]),
ot.BlockIndependentCopula([ot.NormalCopula(2), ot.NormalCopula(2)]),
]
intervals = [
ot.Interval(-1.0, 4.0),
ot.Interval(0.2, 2.4),
ot.Interval(2.5, 65.0),
ot.Interval(2.5, 6.0),
ot.Interval(-2.5, 6.0),
ot.Interval(2),
ot.Interval(4),
ot.Interval(4),
]
for i in range(len(candidates)):
d = ot.TruncatedDistribution(candidates[i], intervals[i])
print("d=", d, "simplified=", d.getSimplifiedVersion())
# Check that we can set the bounds independently
truncated = ot.TruncatedDistribution()
truncated.setDistribution(ot.Normal(20.0, 7.5))
truncated.setBounds(ot.Interval([0], [80], [True], [False]))
print("after setbounds q@0.9=", truncated.computeQuantile(0.9))
# Test for issue #1190
dist = ot.Normal(6.3e-19, 2.1e-19)
dist = ot.TruncatedDistribution(dist, 4.2e-19, ot.TruncatedDistribution.LOWER)
# non-finite bound bug
bounds = ot.Interval([-2, -3], [2, 3.0], [True, False], [True, True])
dist = ot.TruncatedDistribution(ot.Normal(2), bounds)
print("proba=%.6f" % dist.computeCDF([3.0, -3.0]))
# relative range wrt quantile epsilon issue
unif = ot.Uniform(0.0, 1e12)
trunc = ot.TruncatedDistribution(unif, 0.25, 2.0)
print("q@0.1=", trunc.computeQuantile(0.1))
# n-d CDF inversion
dim = 10
unif = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * dim)
trunc = ot.TruncatedDistribution(unif, ot.Interval([0.0] * dim, [1e-6] * dim))
x = trunc.getRealization()
# marginal of truncated is not truncated marginal
R = ot.CorrelationMatrix(2)
R[1, 0] = 0.8
normal = ot.Normal([0.0] * 2, [1.0] * 2, R)
trunc = ot.TruncatedDistribution(normal, ot.Interval([-0.5] * 2, [1.0] * 2))
marginal0 = trunc.getMarginal(0)
ott.assert_almost_equal(marginal0.getMean(), [0.220527])
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