#! /usr/bin/env python

import openturns as ot
import openturns.testing as ott

ot.TESTPREAMBLE()

# Instantiate one distribution object
distribution = ot.Rayleigh(2.5, -0.5)
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(), 1.0)
print("Point= ", repr(point))

# Show PDF and CDF of point
DDF = distribution.computeDDF(point)
print("ddf     =", repr(DDF))

PDF = distribution.computePDF(point)
print("pdf     = %.12g" % PDF)

CDF = distribution.computeCDF(point)
print("cdf= %.12g" % CDF)
CF = distribution.computeCharacteristicFunction(point[0])
print("characteristic function= (%.12g%+.12gj)" % (CF.real, CF.imag))
PDFgr = distribution.computePDFGradient(point)
print("pdf gradient     =", repr(PDFgr))

CDFgr = distribution.computeCDFGradient(point)
print("cdf gradient     =", repr(CDFgr))

quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=", 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
)
ott.assert_almost_equal(interval.getLowerBound(), [-0.2238], 1e-3, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [5.7505], 1e-3, 0.0)
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))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
parameters = distribution.getParametersCollection()
print("parameters=", repr(parameters))
print("Standard representative=", distribution.getStandardRepresentative())

# Specific to this distribution
gamma = distribution.getGamma()
print("gamma=", gamma)
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", repr(standardDeviation))
skewness = distribution.getSkewness()
print("skewness=", repr(skewness))
kurtosis = distribution.getKurtosis()
print("kurtosis=", repr(kurtosis))
beta = distribution.getBeta()
print("beta=", beta)

ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.run()
