#! /usr/bin/env python

import openturns as ot

ot.TESTPREAMBLE()

# 1D tests
distribution = ot.Dirac(0.7)
print("Distribution ", distribution)

# 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=", oneRealization)

# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", oneSample[0], " last=", oneSample[size - 1])
print("mean=", oneSample.computeMean())
sampleCovariance = oneSample.computeCovariance()[0, 0]
if abs(sampleCovariance) < 1.0e-16:
    sampleCovariance = 0.0
print("covariance=", sampleCovariance)

# Define a point
point = ot.Point(distribution.getDimension(), 0.0)
print("Point= ", point)

# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf     =", PDF)
print(
    "pdf (FD)=",
    (
        distribution.computeCDF(point + ot.Point(1, 0))
        - distribution.computeCDF(point + ot.Point(1, -1))
    ),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)

# Define a point
point = ot.Point(distribution.getSupport(distribution.getRange())[0])
print("Point= ", point)

# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf     =", PDF)
print(
    "pdf (FD)=",
    (
        distribution.computeCDF(point + ot.Point(1, 0))
        - distribution.computeCDF(point + ot.Point(1, -1))
    ),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)
CF = distribution.computeCharacteristicFunction(0.5)
print("characteristic function= (%.12g%+.12gj)" % (CF.real, CF.imag))
GF = distribution.computeGeneratingFunction(0.5 + 0.3j)
print("generating function= (%.12g%+.12gj)" % (GF.real, GF.imag))
quantile = distribution.computeQuantile(0.95)
# Test invalid quantile
try:
    q12 = distribution.computeScalarQuantile(1.2)
    raise ValueError("Expected a TypeError but got quantile(1.2) = {}".format(q12))
except TypeError:
    pass
print("quantile=", quantile)
print("cdf(quantile)=", distribution.computeCDF(quantile))
print("entropy=%.6f" % distribution.computeEntropy())
mean = distribution.getMean()
print("mean=", mean)
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", standardDeviation)
skewness = distribution.getSkewness()
print("skewness=", skewness)
kurtosis = distribution.getKurtosis()
print("kurtosis=", kurtosis)
covariance = distribution.getCovariance()
print("covariance=", covariance)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
print("Standard representative=", distribution.getStandardRepresentative())

# N-D tests

dim = 4
distribution = ot.Dirac(ot.Point(dim, 2.3))
print("Distribution ", distribution)

# 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=", oneRealization)

# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", oneSample[0], " last=", oneSample[size - 1])
print("mean=", oneSample.computeMean())
sampleCovariance = oneSample.computeCovariance()
for i in range(dim):
    for j in range(i + 1):
        if abs(sampleCovariance[i, j]) < 1.0e-16:
            sampleCovariance[i, j] = 0.0
print("covariance=", sampleCovariance)

# Define a point
point = ot.Point(dim, 0.0)
print("Point= ", point)

# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf     =", PDF)
print(
    "pdf (FD)=",
    (
        distribution.computeCDF(point + ot.Point(dim, 0))
        - distribution.computeCDF(point + ot.Point(dim, -1))
    ),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)

# Define a point
point = ot.Point(distribution.getSupport(distribution.getRange())[0])
print("Point= ", point)

# Show PDF and CDF of point
PDF = distribution.computePDF(point)
print("pdf     =", PDF)
print(
    "pdf (FD)=",
    (
        distribution.computeCDF(point + ot.Point(dim, 0))
        - distribution.computeCDF(point + ot.Point(dim, -1))
    ),
)
CDF = distribution.computeCDF(point)
print("cdf=", CDF)

quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
print("cdf(quantile)=", distribution.computeCDF(quantile))
mean = distribution.getMean()
print("mean=", mean)
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", standardDeviation)
skewness = distribution.getSkewness()
print("skewness=", skewness)
kurtosis = distribution.getKurtosis()
print("kurtosis=", kurtosis)
covariance = distribution.getCovariance()
print("covariance=", covariance)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
print("Standard representative=", distribution.getStandardRepresentative())
