def generate_dirichlet_data(ndag, size):
order = ndag.getTopologicalOrder()
copulas = []
for k in range(order.getSize()):
d = 1 + ndag.getParents(k).getSize()
copulas.append(ot.Dirichlet([(1.0+k)/(d+1) for k in range(d+1)]).getCopula())
cbn = otagr.ContinuousBayesianNetwork(ndag, [ot.Uniform(0., 1.)]*ndag.getSize(), copulas)
sample = cbn.getSample(size)
return sample
def generate_dirichlet_data(ndag, size):
order = ndag.getTopologicalOrder()
jointDistributions = []
for k in range(order.getSize()):
d = 1 + ndag.getParents(k).getSize()
jointDistributions.append(
ot.Dirichlet([(1.0 + k) / (d + 1)
for k in range(d + 1)]).getCopula())
copula = otagr.ContinuousBayesianNetwork(ndag, jointDistributions)
sample = copula.getSample(size)
return sample
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Beta().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.Beta().__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork([ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])], ot.BipartiteGraph([[0,1], [0,1]]))
elif ot.Beta().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Beta()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
fig = plt.figure(figsize=(10, 5))
plt.suptitle(str(distribution))
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Gumbel().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.Gumbel().__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.Gumbel().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Gumbel()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Dirichlet().__class__.__name__=='ComposedDistribution'):
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif (ot.Dirichlet().__class__.__name__=='CumulativeDistributionNetwork'):
distribution = ot.CumulativeDistributionNetwork([ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])], ot.BipartiteGraph([[0,1], [0,1]]))
elif (ot.Dirichlet().__class__.__name__=='Histogram'):
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Dirichlet()
dimension = distribution.getDimension()
if dimension <= 2:
if distribution.getDimension() == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
else:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
fig = plt.figure(figsize=(10, 5))
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.FrankCopula().__class__.__name__ == 'EmpiricalBernsteinCopula':
sample = ot.Dirichlet([1.0, 2.0, 3.0]).getSample(100)
copula = ot.EmpiricalBernsteinCopula(sample, 4)
elif ot.FrankCopula().__class__.__name__ == 'ExtremeValueCopula':
copula = ot.ExtremeValueCopula(ot.SymbolicFunction("t", "t^3/2-t/2+1"))
elif ot.FrankCopula(
).__class__.__name__ == 'MaximumEntropyOrderStatisticsCopula':
marginals = [ot.Beta(1.5, 3.2, 0.0, 1.0), ot.Beta(2.0, 4.3, 0.5, 1.2)]
copula = ot.MaximumEntropyOrderStatisticsCopula(marginals)
elif ot.FrankCopula().__class__.__name__ == 'NormalCopula':
R = ot.CorrelationMatrix(2)
R[1, 0] = 0.8
copula = ot.NormalCopula(R)
elif ot.FrankCopula().__class__.__name__ == 'SklarCopula':
student = ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(student)
else:
copula = ot.FrankCopula()
if copula.getDimension() == 1:
copula = ot.FrankCopula(2)
copula.setDescription(['$u_1$', '$u_2$'])
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
fig = plt.figure(figsize=(10, 4))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph,
figure=fig,
from __future__ import print_function
import openturns as ot
import openturns.testing as ott
import math as m
for factory in ot.DistributionFactory.GetContinuousUniVariateFactories():
distribution = factory.build()
# avoid flat pdfs
if distribution.getName() == 'Dirichlet':
distribution = ot.Dirichlet([2, 6])
distribution.setName('Dirichlet')
elif distribution.getName() == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
distribution.setName('Histogram')
sample = distribution.getSample(10)
epsilon = ot.ResourceMap.GetAsScalar(
"CenteredFiniteDifferenceGradient-DefaultEpsilon")
pdfepsilon = ot.ResourceMap.GetAsScalar(
"Distribution-DefaultPDFEpsilon") ** (1.0/3.0)
# logpdf
logPDF1 = [y[0] for y in distribution.computeLogPDF(sample)]
logPDF2 = [m.log(y[0]) for y in distribution.computePDF(sample)]
ott.assert_almost_equal(logPDF1, logPDF2, 1e-5, 1e-8, str(distribution))
# cdf
PDF1 = distribution.computePDF(sample)
CDF1 = distribution.computeCDF(sample + epsilon)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Dirichlet().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.Dirichlet().__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.Dirichlet().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Dirichlet()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
pdf_graph = ot.Graph('PDF graph', 'x', 'PDF', True, 'topleft')
cdf_graph = ot.Graph('CDF graph', 'x', 'CDF', True, 'topleft')
palette = ot.Drawable.BuildDefaultPalette(10)
for i, theta in enumerate([(2, 2), (7, 5), (2, 6), (3, 4)]):
distribution = ot.Dirichlet(theta)
pdf_curve = distribution.drawPDF().getDrawable(0)
cdf_curve = distribution.drawCDF().getDrawable(0)
pdf_curve.setColor(palette[i])
cdf_curve.setColor(palette[i])
pdf_curve.setLegend('theta={}'.format(str(theta)))
cdf_curve.setLegend('theta={}'.format(str(theta)))
pdf_graph.add(pdf_curve)
cdf_graph.add(cdf_curve)
fig = plt.figure(figsize=(10, 4))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=True)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=True)
fig.suptitle('Dirichlet(theta)')
import openturns as ot
from openturns.viewer import View
ot.ResourceMap.SetAsUnsignedInteger("Contour-DefaultLevelsNumber", 10)
grid = ot.GridLayout(2, 2)
pdf_graph = ot.Graph('PDFs of 1D Dirichlet distributions', 'x', '', True)
cdf_graph = ot.Graph('CDFs of 1D Dirichlet distributions', 'x', '', True)
title_2d = 'PDF of the Dirichlet dist. with theta = {}'
theta_1 = (2.0, 2.0, 2.0)
theta_2 = (0.5, 0.7, 0.9)
pdf_2d_1 = ot.Graph(title_2d.format(theta_1), 'x1', 'x2', True)
pdf_2d_2 = ot.Graph(title_2d.format(theta_2), 'x1', 'x2', True)
palette = ot.Drawable.BuildDefaultPalette(10)
list_theta = [(2, 2), (7, 5), (2, 6), (3, 4)]
for theta in list_theta:
distribution = ot.Dirichlet(theta)
pdf_curve = distribution.drawPDF()
cdf_curve = distribution.drawCDF()
pdf_graph.add(pdf_curve)
cdf_graph.add(cdf_curve)
pdf_graph.setColors([palette[i] for i in range(4)])
cdf_graph.setColors([palette[i] for i in range(4)])
pdf_graph.setLegends(['theta={}'.format(theta) for theta in list_theta])
cdf_graph.setLegends(['theta={}'.format(theta) for theta in list_theta])
distribution_2d_1 = ot.Dirichlet(theta_1)
distribution_2d_2 = ot.Dirichlet(theta_2)
pdf_2d_1.add(distribution_2d_1.drawPDF())
pdf_2d_2.add(distribution_2d_2.drawPDF())
grid.setGraph(0, 0, pdf_graph)
grid.setGraph(0, 1, cdf_graph)
grid.setGraph(1, 0, pdf_2d_1)
grid.setGraph(1, 1, pdf_2d_2)
