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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# 1D tests
distribution = ot.Dirac(0.7)
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=", oneRealization)
# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", oneSample[0], " last=", oneSample[size - 1])
print("mean=", oneSample.computeMean())
sampleCovariance = oneSample.computeCovariance()[0, 0]
if abs(sampleCovariance) < 1.0e-16:
sampleCovariance = 0.0
print("covariance=", sampleCovariance)
# Define a point
point = ot.Point(distribution.getDimension(), 0.0)
print("Point= ", point)
# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf =", PDF)
print(
"pdf (FD)=",
(
distribution.computeCDF(point + ot.Point(1, 0))
- distribution.computeCDF(point + ot.Point(1, -1))
),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)
# Define a point
point = ot.Point(distribution.getSupport(distribution.getRange())[0])
print("Point= ", point)
# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf =", PDF)
print(
"pdf (FD)=",
(
distribution.computeCDF(point + ot.Point(1, 0))
- distribution.computeCDF(point + ot.Point(1, -1))
),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)
CF = distribution.computeCharacteristicFunction(0.5)
print("characteristic function= (%.12g%+.12gj)" % (CF.real, CF.imag))
GF = distribution.computeGeneratingFunction(0.5 + 0.3j)
print("generating function= (%.12g%+.12gj)" % (GF.real, GF.imag))
quantile = distribution.computeQuantile(0.95)
# Test invalid quantile
try:
q12 = distribution.computeScalarQuantile(1.2)
raise ValueError(f"Expected a TypeError but got quantile(1.2) = {q12}")
except TypeError:
pass
print("quantile=", quantile)
print("cdf(quantile)=", distribution.computeCDF(quantile))
print("entropy=%.6f" % distribution.computeEntropy())
mean = distribution.getMean()
print("mean=", mean)
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", standardDeviation)
skewness = distribution.getSkewness()
print("skewness=", skewness)
kurtosis = distribution.getKurtosis()
print("kurtosis=", kurtosis)
covariance = distribution.getCovariance()
print("covariance=", covariance)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
print("Standard representative=", distribution.getStandardRepresentative())
# N-D tests
dim = 4
distribution = ot.Dirac(ot.Point(dim, 2.3))
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=", oneRealization)
# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", oneSample[0], " last=", oneSample[size - 1])
print("mean=", oneSample.computeMean())
sampleCovariance = oneSample.computeCovariance()
for i in range(dim):
for j in range(i + 1):
if abs(sampleCovariance[i, j]) < 1.0e-16:
sampleCovariance[i, j] = 0.0
print("covariance=", sampleCovariance)
# Define a point
point = ot.Point(dim, 0.0)
print("Point= ", point)
# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf =", PDF)
print(
"pdf (FD)=",
(
distribution.computeCDF(point + ot.Point(dim, 0))
- distribution.computeCDF(point + ot.Point(dim, -1))
),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)
# Define a point
point = ot.Point(distribution.getSupport(distribution.getRange())[0])
print("Point= ", point)
# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf =", PDF)
print(
"pdf (FD)=",
(
distribution.computeCDF(point + ot.Point(dim, 0))
- distribution.computeCDF(point + ot.Point(dim, -1))
),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)
quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
print("cdf(quantile)=", distribution.computeCDF(quantile))
mean = distribution.getMean()
print("mean=", mean)
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", standardDeviation)
skewness = distribution.getSkewness()
print("skewness=", skewness)
kurtosis = distribution.getKurtosis()
print("kurtosis=", kurtosis)
covariance = distribution.getCovariance()
print("covariance=", covariance)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
print("Standard representative=", distribution.getStandardRepresentative())
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipMoments()
validation.skipCorrelation()
validation.skipConditional() # FIXME
validation.run()
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