def test_computeLogPDF_diagonal_case(self):
"""Test InverseWishart.computeLogPDF in the case of diagonal matrices"""
dimension, DoF = self.dimension, self.DoF
k = 0.5 * (DoF + dimension - 1)
diagX = ot.Uniform(0.5, 1.).getSample(dimension)
Scale = ot.CovarianceMatrix(dimension)
X = ot.CovarianceMatrix(dimension)
for d in range(dimension):
Scale[d, d], X[d, d] = self.Scale[d, d], diagX[d, 0]
inverse_wishart = ot.InverseWishart(Scale, DoF)
logdensity = inverse_wishart.computeLogPDF(X)
logratio = - self.logmultigamma(dimension, 0.5 * DoF) \
+ dimension * ot.SpecFunc_LnGamma(0.5 * (DoF + dimension - 1))
for d in range(dimension):
inverse_gamma = ot.InverseGamma(k, 2. / Scale[d, d])
logdensity = logdensity - inverse_gamma.computeLogPDF(diagX[d, 0])
logratio = logratio + 0.5 * \
(1 - dimension) * log(0.5 * Scale[d, d])
assert_almost_equal(logdensity, logratio)
def setUpClass(cls):
# attributes to compare a one-dimensional InverseWishart to the
# equivalent InverseGamma distribution
U = ot.Uniform(0., 1.)
scale = 10. * U.getRealization()[0]
DoF = 3. + U.getRealization()[0] # Degrees of Freedom
cls.k, cls.beta = 0.5 * DoF, 0.5 * scale
cls.one_dimensional_inverse_wishart \
= ot.InverseWishart(ot.CovarianceMatrix([[scale]]), DoF)
cls.inverse_gamma = ot.InverseGamma(cls.k, 1. / cls.beta)
# attributes to test a multi-dimensional InverseWishart
cls.dimension = 5
cls.DoF = cls.dimension + 3 + U.getRealization()[0]
cls.L = ot.TriangularMatrix(cls.dimension)
diagL = ot.Uniform(0.5, 1.).getSample(cls.dimension)
cls.determinant = 1.
for i in range(cls.dimension):
cls.determinant *= diagL[i, 0]
cls.L[i, i] = diagL[i, 0]
for j in range(i):
cls.L[i, j] = U.getRealization()[0]
cls.determinant *= cls.determinant
cls.Scale = ot.CovarianceMatrix(cls.L * cls.L.transpose())
def InverseGamma(lambda_=1.0, k=1.0):
"""
InverseGamma compatibility shim.
"""
return ot.InverseGamma(k, lambda_)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.InverseGamma().__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.InverseGamma().__class__.__name__=='CumulativeDistributionNetwork'):
distribution = ot.CumulativeDistributionNetwork([ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])], ot.BipartiteGraph([[0,1], [0,1]]))
else:
distribution = ot.InverseGamma()
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))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(111)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.InverseGamma().__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.InverseGamma().__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.InverseGamma().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.InverseGamma()
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))