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))