#! /usr/bin/env python

from __future__ import print_function
from openturns import *
from math import *

TESTPREAMBLE()
RandomGenerator.SetSeed(0)

try:
    # Instanciate one distribution object
    dim = 2
    copula = FarlieGumbelMorgensternCopula(0.7)
    copula.setName("a farlieGumbelMorgenstern copula")
    print("Copula ", repr(copula))
    print("Copula ", copula)
    print("Mean ", copula.getMean())
    print("Covariance ", copula.getCovariance())
    # Is this copula an elliptical distribution?
    print("Elliptical distribution= ", copula.isElliptical())

    # Is this copula elliptical ?
    print("Elliptical copula= ", copula.hasEllipticalCopula())

    # Is this copula independent ?
    print("Independent copula= ", copula.hasIndependentCopula())

    # Test for realization of copula
    oneRealization = copula.getRealization()
    print("oneRealization=", oneRealization)

    # Test for sampling
    size = 10
    oneSample = copula.getSample(size)
    print("oneSample=", oneSample)

    # Test for sampling
    size = 10000
    anotherSample = copula.getSample(size)
    print("anotherSample mean=", anotherSample.computeMean())
    print("anotherSample covariance=", anotherSample.computeCovariance())

    # Define a point
    point = NumericalPoint(dim, 0.2)

    # Show PDF and CDF of zero point
    zeroPDF = copula.computePDF(point)
    zeroCDF = copula.computeCDF(point)
    print("point= ", point, " pdf=", zeroPDF, " cdf= %.12g" % zeroCDF)

    # Get 50% quantile
    quantile = copula.computeQuantile(0.5)
    print("Quantile=", quantile)
    print("CDF(quantile)= %.12g" % copula.computeCDF(quantile))
    # Get 95% survival function
    inverseSurvival = NumericalPoint(copula.computeInverseSurvivalFunction(0.95))
    print("InverseSurvival=", repr(inverseSurvival))
    print("Survival(inverseSurvival)=%.6f" % copula.computeSurvivalFunction(inverseSurvival))

    # Confidence regions
    interval, threshold = copula.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
    print("Minimum volume interval=", interval)
    print("threshold=", NumericalPoint(1, threshold))
    levelSet, beta = copula.computeMinimumVolumeLevelSetWithThreshold(0.95)
    print("Minimum volume level set=", levelSet)
    print("beta=", NumericalPoint(1, beta))
    interval, beta = copula.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
    print("Bilateral confidence interval=", interval)
    print("beta=", NumericalPoint(1, beta))
    interval, beta = copula.computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, False)
    print("Unilateral confidence interval (lower tail)=", interval)
    print("beta=", NumericalPoint(1, beta))
    interval, beta = copula.computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, True)
    print("Unilateral confidence interval (upper tail)=", interval)
    print("beta=", NumericalPoint(1, beta))

    # Extract the marginals
    for i in range(dim):
        margin = copula.getMarginal(i)
        print("margin=", margin)
        print("margin PDF=", margin.computePDF(NumericalPoint(1, 0.25)))
        print("margin CDF=", margin.computeCDF(NumericalPoint(1, 0.25)))
        print("margin quantile=", margin.computeQuantile(0.95))
        print("margin realization=", margin.getRealization())

    # Extract a 2-D marginal
    indices = Indices(2, 0)
    indices[0] = 1
    indices[1] = 0
    print("indices=", indices)
    margins = copula.getMarginal(indices)
    print("margins=", margins)
    print("margins PDF=", margins.computePDF(NumericalPoint(2, 0.25)))
    print("margins CDF= %.12g" % margins.computeCDF(NumericalPoint(2, 0.25)))
    quantile = margins.computeQuantile(0.95)
    print("margins quantile=", quantile)
    print("margins CDF(quantile)= %.12g" % margins.computeCDF(quantile))
    print("margins realization=", margins.getRealization())

except:
    import sys
    print("t_FarlieGumbelMorgensternCopula_std.py",
          sys.exc_info()[0], sys.exc_info()[1])
