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#! /usr/bin/env python
from __future__ import print_function
from openturns import *
TESTPREAMBLE()
RandomGenerator.SetSeed(0)
try:
# Instanciate one distribution object
dim = 3
R = CorrelationMatrix(dim)
for i in range(dim - 1):
R[i, i + 1] = 0.25
copula = SklarCopula(
Distribution(Normal([1.0, 2.0, 3.0], [2.0, 3.0, 1.0], R)))
copulaRef = NormalCopula(R)
print("Copula ", repr(copula))
print("Copula ", copula)
print("Mean =", repr(copula.getMean()))
print("Mean (ref)=", repr(copulaRef.getMean()))
ResourceMap.SetAsUnsignedInteger( "GaussKronrod-MaximumSubIntervals", 20 )
ResourceMap.SetAsNumericalScalar( "GaussKronrod-MaximumError", 1.0e-4 )
print("Covariance =", repr(copula.getCovariance()))
ResourceMap.SetAsUnsignedInteger( "GaussKronrod-MaximumSubIntervals", 100 )
ResourceMap.SetAsNumericalScalar( "GaussKronrod-MaximumError", 1.0e-12 )
print("Covariance (ref)=", repr(copulaRef.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 distribution
oneRealization = copula.getRealization()
print("oneRealization=", repr(oneRealization))
# Test for sampling
size = 10
oneSample = copula.getSample(size)
print("oneSample=", repr(oneSample))
# Test for sampling
size = 1000
anotherSample = copula.getSample(size)
print("anotherSample mean=", repr(anotherSample.computeMean()))
print("anotherSample covariance=", repr(anotherSample.computeCovariance()))
# Define a point
point = NumericalPoint(dim, 0.2)
# Show PDF and CDF of point
pointPDF = copula.computePDF(point)
pointCDF = copula.computeCDF(point)
pointPDFRef = copulaRef.computePDF(point)
pointCDFRef = copulaRef.computeCDF(point)
print("Point = ", repr(point), " pdf =%.6f" %
pointPDF, " cdf =%.6f" % pointCDF)
print("Point = ", repr(point), " pdf (ref)=%.6f" %
pointPDFRef, " cdf (ref)=%.6f" % pointCDFRef)
# Get 50% quantile
quantile = copula.computeQuantile(0.5)
quantileRef = copulaRef.computeQuantile(0.5)
print("Quantile =", repr(quantile))
print("Quantile (ref)=", repr(quantileRef))
print("CDF(quantile)=%.6f" % copula.computeCDF(quantile))
# Extract the marginals
for i in range(dim):
margin = copula.getMarginal(i)
marginRef = copulaRef.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF =%.6f" %
margin.computePDF(NumericalPoint(1, 0.25)))
print("margin PDF (ref)=%.6f" %
marginRef.computePDF(NumericalPoint(1, 0.25)))
print("margin CDF =%.6f" %
margin.computeCDF(NumericalPoint(1, 0.25)))
print("margin CDF (ref)=%.6f" %
marginRef.computeCDF(NumericalPoint(1, 0.25)))
print("margin quantile =", repr(margin.computeQuantile(0.95)))
print("margin quantile (ref)=", repr(marginRef.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
# Extract a 2-D marginal
indices = Indices(2, 0)
indices[0] = 1
indices[1] = 0
print("indices=", repr(indices))
margin = copula.getMarginal(indices)
marginRef = copulaRef.getMarginal(indices)
print("margin=", repr(margin))
print("margin PDF =%.6f" % margin.computePDF(NumericalPoint(2, 0.25)))
print("margin PDF (ref)=%.6f" %
marginRef.computePDF(NumericalPoint(2, 0.25)))
print("margin CDF =%.6f" % margin.computeCDF(NumericalPoint(2, 0.25)))
print("margin CDF (ref)=%.6f" %
marginRef.computeCDF(NumericalPoint(2, 0.25)))
print("margin quantile =", repr(margin.computeQuantile(0.95)))
print("margin quantile (ref)=", repr(marginRef.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
except:
import sys
print("t_SklarCopula.py", sys.exc_info()[0], sys.exc_info()[1])
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