#! /usr/bin/env python

import openturns as ot

ot.TESTPREAMBLE()

for xi in [-0.2, 0.0, 0.2]:
    # Instantiate one distribution object
    distribution = ot.GeneralizedPareto(1.5, xi, 0.5)

    print("Distribution ", repr(distribution))
    print("Distribution ", distribution)

    if xi > 0.0:
        print("asPareto=", distribution.asPareto())

    # 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))

    # Test for sampling
    size = 10000
    oneSample = distribution.getSample(size)
    print("oneSample first=", repr(oneSample[0]), " last=", repr(oneSample[size - 1]))
    print("mean=", repr(oneSample.computeMean()))
    print("covariance=", repr(oneSample.computeCovariance()))

    size = 100
    for i in range(2):
        msg = ""
        if ot.FittingTest.Kolmogorov(
            distribution.getSample(size), distribution
        ).getBinaryQualityMeasure():
            msg = "accepted"
        else:
            msg = "rejected"
        print("Kolmogorov test for the generator, sample size=", size, " is", msg)
        size *= 10

    # Define a point
    point = ot.Point(distribution.getDimension(), 1.5)
    print("Point= ", repr(point))

    # Show PDF and CDF of point
    eps = 1e-5
    # DDF = distribution.computeDDF( point )
    # print "ddf     =", repr(DDF)
    print(
        "ddf (FD)=",
        repr(
            ot.Point(
                1,
                (
                    distribution.computePDF(point + ot.Point(1, eps))
                    - distribution.computePDF(point + ot.Point(1, -eps))
                )
                / (2.0 * eps),
            )
        ),
    )
    PDF = distribution.computePDF(point)
    print("pdf     = %.12g" % PDF)
    print(
        "pdf (FD)= %.9f"
        % (
            (
                distribution.computeCDF(point + ot.Point(1, eps))
                - distribution.computeCDF(point + ot.Point(1, -eps))
            )
            / (2.0 * eps),
        )
    )
    CDF = distribution.computeCDF(point)
    print("cdf= %.12g" % CDF)
    # CF = distribution.computeCharacteristicFunction( point[0] )
    # print "characteristic function=", CF
    PDFgr = distribution.computePDFGradient(point)
    print("pdf gradient     =", repr(PDFgr))
    PDFgrFD = ot.Point(3)
    PDFgrFD[0] = (
        ot.GeneralizedPareto(
            distribution.getSigma() + eps, distribution.getXi(), distribution.getU()
        ).computePDF(point)
        - ot.GeneralizedPareto(
            distribution.getSigma() - eps, distribution.getXi(), distribution.getU()
        ).computePDF(point)
    ) / (2.0 * eps)
    PDFgrFD[1] = (
        ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi() + eps, distribution.getU()
        ).computePDF(point)
        - ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi() - eps, distribution.getU()
        ).computePDF(point)
    ) / (2.0 * eps)
    PDFgrFD[2] = (
        ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi(), distribution.getU() + eps
        ).computePDF(point)
        - ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi(), distribution.getU() - eps
        ).computePDF(point)
    ) / (2.0 * eps)
    print("pdf gradient (FD)=", repr(PDFgrFD))
    CDFgr = distribution.computeCDFGradient(point)
    print("cdf gradient     =", repr(CDFgr))
    CDFgrFD = ot.Point(3)
    CDFgrFD[0] = (
        ot.GeneralizedPareto(
            distribution.getSigma() + eps, distribution.getXi(), distribution.getU()
        ).computeCDF(point)
        - ot.GeneralizedPareto(
            distribution.getSigma() - eps, distribution.getXi(), distribution.getU()
        ).computeCDF(point)
    ) / (2.0 * eps)
    CDFgrFD[1] = (
        ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi() + eps, distribution.getU()
        ).computeCDF(point)
        - ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi() - eps, distribution.getU()
        ).computeCDF(point)
    ) / (2.0 * eps)
    CDFgrFD[2] = (
        ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi(), distribution.getU() + eps
        ).computeCDF(point)
        - ot.GeneralizedPareto(
            distribution.getSigma(), distribution.getXi(), distribution.getU() - eps
        ).computeCDF(point)
    ) / (2.0 * eps)
    print("cdf gradient (FD)=", repr(CDFgrFD))
    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)
    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))
    parameters = distribution.getParametersCollection()
    print("parameters=", repr(parameters))
    print("Standard representative=", distribution.getStandardRepresentative())
