def test_getSample_getMean(self):
"""Test InverseWishart.getSample and InverseWishart.getMean"""
d, Scale, DoF, N = self.dimension, self.Scale, self.DoF, int(1E+4)
Identity = ot.CovarianceMatrix(d)
Scale_wishart = ot.CovarianceMatrix(Scale.solveLinearSystem(Identity))
inverse_wishart = ot.InverseWishart(Scale, DoF)
sample_inverse = ot.Sample(N, (d * (d + 1)) // 2)
sample = ot.Sample(N, (d * (d + 1)) // 2)
for i in range(N):
M_inverse = inverse_wishart.getRealizationAsMatrix()
M = M_inverse.solveLinearSystem(Identity)
indice = 0
for j in range(d):
for k in range(j + 1):
sample_inverse[i, indice] = M_inverse[k, j]
sample[i, indice] = M[k, j]
indice += 1
mean_inverse = sample_inverse.computeMean()
mean = sample.computeMean()
theoretical_mean_inverse = inverse_wishart.getMean()
theoretical_mean = (ot.Wishart(Scale_wishart, DoF)).getMean()
indice, coefficient = 0, 1. / (DoF - d - 1)
for j in range(d):
for k in range(j + 1):
assert_almost_equal(theoretical_mean_inverse[indice],
coefficient * Scale[k, j])
assert_almost_equal(theoretical_mean[indice],
DoF * Scale_wishart[k, j])
assert_almost_equal(mean_inverse[indice],
coefficient * Scale[k, j], 0.15, 1.E-3)
assert_almost_equal(mean[indice],
DoF * Scale_wishart[k, j], 0.15, 1.E-3)
indice += 1
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Wishart().__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.Wishart().__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.Wishart()
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.Wishart().__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.Wishart().__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.Wishart().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Wishart()
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.Wishart().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Wishart().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Wishart().__class__.__name__ == 'ComposedDistribution':
copula = ot.IndependentCopula(2)
marginals = [ot.Uniform(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, copula)
elif ot.Wishart().__class__.__name__ == 'CumulativeDistributionNetwork':
coll = [ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])]
distribution = ot.CumulativeDistributionNetwork(
coll, ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.Wishart().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Wishart().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Wishart().__class__.__name__ == 'MaximumDistribution':
coll = [
ot.Uniform(2.5, 3.5),
ot.LogUniform(1.0, 1.2),
ot.Triangular(2.0, 3.0, 4.0)
]
distribution = ot.MaximumDistribution(coll)
elif ot.Wishart().__class__.__name__ == 'Multinomial':
distribution = ot.Multinomial(5, [0.2])