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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
import math as m
class UniformNdPy(ot.PythonDistribution):
def __init__(self, a=[0.0], b=[1.0]):
super(UniformNdPy, self).__init__(len(a))
if len(a) != len(b):
raise ValueError("Invalid bounds")
for i in range(len(a)):
if a[i] > b[i]:
raise ValueError("Invalid bounds")
self.a = a
self.b = b
self.factor = 1.0
for i in range(len(a)):
self.factor *= b[i] - a[i]
def getRange(self):
return ot.Interval(self.a, self.b, [True] * len(self.a), [True] * len(self.a))
def getRealization(self):
X = []
for i in range(len(self.a)):
X.append(
self.a[i] + (self.b[i] - self.a[i]) * ot.RandomGenerator.Generate()
)
return X
def getSample(self, size):
X = []
for i in range(size):
X.append(self.getRealization())
return X
def computeCDF(self, X):
prod = 1.0
for i in range(len(self.a)):
if X[i] < self.a[i]:
return 0.0
prod *= min(self.b[i], X[i]) - self.a[i]
return prod / self.factor
def computePDF(self, X):
for i in range(len(self.a)):
if X[i] < self.a[i]:
return 0.0
if X[i] > self.b[i]:
return 0.0
return 1.0 / self.factor
def getRoughness(self):
return 42.0
def getMean(self):
mu = []
for i in range(len(self.a)):
mu.append(0.5 * (self.a[i] + self.b[i]))
return mu
def getStandardDeviation(self):
stdev = []
for i in range(len(self.a)):
stdev.append((self.b[i] - self.a[i]) / m.sqrt(12.0))
return stdev
def getSkewness(self):
return [0.0] * len(self.a)
def getKurtosis(self):
return [1.8] * len(self.a)
def getMoment(self, n):
return [-0.1 * n] * len(self.a)
# def getCentralMoment(self, n):
# return [0.0] * len(self.a)
def computeCharacteristicFunction(self, x):
if len(self.a) > 1:
raise ValueError("dim>1")
ax = self.a[0] * x
bx = self.b[0] * x
return (m.sin(bx) - m.sin(ax) + 1j * (m.cos(ax) - m.cos(bx))) / (bx - ax)
def isElliptical(self):
return (len(self.a) == 1) and (self.a[0] == -self.b[0])
def isCopula(self):
for i in range(len(self.a)):
if self.a[i] != 0.0:
return False
if self.b[i] != 1.0:
return False
return True
def getMarginal(self, indices):
subA = []
subB = []
for i in indices:
subA.append(self.a[i])
subB.append(self.b[i])
py_dist = UniformNdPy(subA, subB)
return ot.Distribution(py_dist)
def computeQuantile(self, prob, tail=False):
p = 1.0 - prob if tail else prob
quantile = list(self.a)
for i in range(len(self.a)):
quantile[i] += p * (self.b[i] - self.a[i])
return quantile
def getParameter(self):
return list(self.a) + list(self.b)
def getParameterDescription(self):
paramDesc = ["a_" + str(i) for i in range(len(self.a))]
paramDesc.extend(["b_" + str(i) for i in range(len(self.a))])
return paramDesc
def setParameter(self, parameter):
dim = len(self.a)
for i in range(dim):
self.a[i] = parameter[i]
self.b[i] = parameter[dim + i]
for pyDist in [UniformNdPy(), UniformNdPy([0.0] * 2, [1.0] * 2)]:
print("pyDist=", pyDist)
# Instance creation
myDist = ot.Distribution(pyDist)
print("myDist=", repr(myDist))
# Copy constructor
newRV = ot.Distribution(myDist)
# Dimension
dim = myDist.getDimension()
print("dimension=", dim)
# Realization
X = myDist.getRealization()
print("realization=", X)
# Sample
X = myDist.getSample(5)
print("sample=", X)
# PDF
point = [0.2] * dim
pdf = myDist.computePDF(point)
print("pdf=", pdf)
# CDF
cdf = myDist.computeCDF(point)
print("cdf= %.12g" % cdf)
# roughness
roughness = myDist.getRoughness()
print("roughness=", roughness)
# Mean
mean = myDist.getMean()
print("mean=", mean)
# Standard deviation
standardDeviation = myDist.getStandardDeviation()
print("standard deviation=", standardDeviation)
# Skewness
skewness = myDist.getSkewness()
print("skewness=", skewness)
# Kurtosis
kurtosis = myDist.getKurtosis()
print("kurtosis=", kurtosis)
# Moment
moment = myDist.getMoment(3)
print("moment=", moment)
# Centered moment
centeredMoment = myDist.getCentralMoment(3)
print("centered moment=", centeredMoment)
if dim == 1:
CF = myDist.computeCharacteristicFunction(point[0])
print("characteristic function= (%.12g%+.12gj)" % (CF.real, CF.imag))
isElliptical = myDist.isElliptical()
print("isElliptical=", isElliptical)
isCopula = myDist.isCopula()
print("isCopula=", isCopula)
# Range
range_ = myDist.getRange()
print("range=", range_)
# marginal
marginal = myDist.getMarginal(0)
print("marginal=", marginal)
# quantile
quantile = myDist.computeQuantile(0.5)
print("quantile=", quantile)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(myDist)
validation.skipEntropy() # slow
validation.skipMinimumVolumeLevelSet() # slow
validation.skipCharacteristicFunction() # undefined
validation.run()
param = myDist.getParameter()
print("parameter=", param)
param[0] = 0.4
myDist.setParameter(param)
print("parameter=", myDist.getParameter())
print("parameterDesc=", myDist.getParameterDescription())
print("Cloning distribution")
newDist = ot.Distribution(myDist)
param[0] = 0.5
newDist.setParameter(param)
print("dist parameter=", myDist.getParameter())
print("copy dist parameter=", newDist.getParameter())
# Use the distribution as a copula
myDist = ot.Distribution(UniformNdPy([0.0] * 2, [1.0] * 2))
print(ot.JointDistribution([ot.Normal(), ot.Normal()], myDist))
try:
print("try with another Python distribution")
myDist = ot.Distribution(UniformNdPy([0.0] * 2, [2.0] * 2))
print(ot.JointDistribution([ot.Normal(), ot.Normal()], myDist))
except Exception:
print("The construction failed on purpose as", myDist, "is not a copula")
# Extract the copula
myDist = ot.Distribution(UniformNdPy([0.0] * 2, [2.0] * 2))
copula = myDist.getCopula()
# Test computePDF over a sample (ticket #899)
res = copula.computePDF([[0.5] * 2] * 10)
# Test a discrete distribution
class PoissonPy(ot.PythonDistribution):
def __init__(self, lamb):
super(PoissonPy, self).__init__(1)
if lamb <= 0.0:
raise ValueError("Expected a positive lambda")
self.poisson_ = ot.Poisson(lamb)
def getRange(self):
return self.poisson_.getRange()
def computeCDF(self, X):
return self.poisson_.computeCDF(X)
def computePDF(self, X):
return self.poisson_.computeCDF(X)
def isDiscrete(self):
return True
def getSupport(self, interval):
return self.poisson_.getSupport(interval)
def isIntegral(self):
return True
dist = ot.Distribution(PoissonPy(2.5))
print("Is discrete?", dist.isDiscrete())
print("Is integral?", dist.isIntegral())
print("pdf graph=", dist.drawPDF())
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