#! /usr/bin/env python

from __future__ import print_function
from openturns import *

TESTPREAMBLE()
RandomGenerator.SetSeed(0)


# Instanciate one distribution object
distribution = Wishart(CovarianceMatrix(1), 3.0)
print("Distribution ", repr(distribution))
print("Distribution ", distribution)

# Get mean and covariance
print("Mean= ", repr(distribution.getMean()))
print("Covariance= ", repr(distribution.getCovariance()))

# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())

# 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 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 = NumericalPoint(distribution.getDimension(), 9.1)
print("Point= ", repr(point))

# Show PDF and CDF of point
eps = 1e-5
#max = distribution.getB() + distribution.getA()
#min = distribution.getB() - distribution.getA()
# derivative of PDF with regards its arguments
DDF = distribution.computeDDF(point)
print("ddf     =", repr(DDF))
# by the finite difference technique
print("ddf (FD)=", repr(NumericalPoint(1, (distribution.computePDF(point + NumericalPoint(1, eps)) -
                                           distribution.computePDF(point + NumericalPoint(1, -eps))) / (2.0 * eps))))

# PDF value
LPDF = distribution.computeLogPDF(point)
print("log pdf=%.6f" % LPDF)
PDF = distribution.computePDF(point)
print("pdf     =%.6f" % PDF)
# by the finite difference technique from CDF
print("pdf (FD)=%.6f" % ((distribution.computeCDF(point + NumericalPoint(1, eps)) -
                          distribution.computeCDF(point + NumericalPoint(1, -eps))) / (2.0 * eps)))

# derivative of the PDF with regards the parameters of the distribution
CDF = distribution.computeCDF(point)
print("cdf=%.6f" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf=%.6f" % CCDF)
PDFgr = distribution.computePDFGradient(point)
print("pdf gradient     =", repr(PDFgr))
# by the finite difference technique
#PDFgrFD = NumericalPoint(2)
#PDFgrFD[0] = (Arcsine(distribution.getA() + eps, distribution.getB()).computePDF(point) -
              #Arcsine(distribution.getA() - eps, distribution.getB()).computePDF(point)) / (2.0 * eps)
#PDFgrFD[1] = (Arcsine(distribution.getA(), distribution.getB() + eps).computePDF(point) -
              #Arcsine(distribution.getA(), distribution.getB() - eps).computePDF(point)) / (2.0 * eps)
#print("pdf gradient (FD)=", repr(PDFgrFD))

# derivative of the PDF with regards the parameters of the distribution
CDFgr = distribution.computeCDFGradient(point)
print("cdf gradient     =", repr(CDFgr))
#CDFgrFD = NumericalPoint(2)
#CDFgrFD[0] = (Arcsine(distribution.getA() + eps, distribution.getB()).computeCDF(point) -
              #Arcsine(distribution.getA() - eps, distribution.getB()).computeCDF(point)) / (2.0 * eps)
#CDFgrFD[1] = (Arcsine(distribution.getA(), distribution.getB() + eps).computeCDF(point) -
              #Arcsine(distribution.getA(), distribution.getB() - eps).computeCDF(point)) / (2.0 * eps)
#print("cdf gradient (FD)=",  repr(CDFgrFD))

# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile))
# Get 95% survival function
inverseSurvival = NumericalPoint(distribution.computeInverseSurvivalFunction(0.95))
print("InverseSurvival=", repr(inverseSurvival))
print("Survival(inverseSurvival)=%.6f" % distribution.computeSurvivalFunction(inverseSurvival))

# Confidence regions
interval, threshold = distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
print("Minimum volume interval=", interval)
print("threshold=", NumericalPoint(1, threshold))
levelSet, beta = distribution.computeMinimumVolumeLevelSetWithThreshold(0.95)
print("Minimum volume level set=", levelSet)
print("beta=", NumericalPoint(1, beta))
interval, beta = distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
print("Bilateral confidence interval=", interval)
print("beta=", NumericalPoint(1, beta))
interval, beta = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, False)
print("Unilateral confidence interval (lower tail)=", interval)
print("beta=", NumericalPoint(1, beta))
interval, beta = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(0.95, True)
print("Unilateral confidence interval (upper tail)=", interval)
print("beta=", NumericalPoint(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))
for i in range(6):
    print("standard moment n=", i, " value=",
          distribution.getStandardMoment(i))
print("Standard representative=", distribution.getStandardRepresentative())
