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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
iMax = 5
collection = [
ot.Laplace(0.0, 1.0),
ot.Logistic(0.0, 1.0),
ot.Normal(0.0, 1.0),
ot.Normal(1.0, 1.0),
ot.Rayleigh(1.0),
ot.Student(22.0),
ot.Triangular(-1.0, 0.3, 1.0),
ot.Uniform(-1.0, 1.0),
ot.Uniform(-1.0, 3.0),
ot.WeibullMin(1.0, 3.0),
ot.Beta(1.0, 2.0, -1.0, 1.0),
ot.Beta(0.5, 0.5, -1.0, 1.0),
ot.Beta(0.5, 0.5, -2.0, 3.0),
ot.Gamma(1.0, 3.0),
ot.Arcsine(),
ot.UserDefined([[i] for i in range(10)]),
ot.UserDefined([[i + 0.5] for i in range(10)]),
]
for distribution in collection:
name = distribution.getClassName()
polynomialFactory = ot.StandardDistributionPolynomialFactory(
ot.AdaptiveStieltjesAlgorithm(distribution)
)
print("polynomialFactory(", name, "=", polynomialFactory, ")")
for i in range(iMax):
print(name, " polynomial(", i, ")=", polynomialFactory.build(i))
roots = polynomialFactory.getRoots(iMax - 1)
print(name, " polynomial(", iMax - 1, ") roots=", roots)
nodes, weights = polynomialFactory.getNodesAndWeights(iMax - 1)
print(name, " polynomial(", iMax - 1, ") nodes=", nodes, " and weights=", weights)
M = ot.SymmetricMatrix(iMax)
for i in range(iMax):
pI = polynomialFactory.build(i)
for j in range(i + 1):
pJ = polynomialFactory.build(j)
def kernel(x):
return [pI(x[0]) * pJ(x[0]) * distribution.computePDF(x)]
integrand = ot.PythonFunction(1, 1, kernel)
if distribution.isContinuous():
M[i, j] = ot.GaussKronrod().integrate(
integrand, distribution.getRange()
)[0]
else:
x = distribution.getSupport()
M[i, j] = integrand(x).computeMean()[0] * len(x)
print("M=\n", M)
ott.assert_almost_equal(M, ot.IdentityMatrix(iMax), 0.0, 1e-7)
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