def _PODgaussModelCl(self, defects, intercept, slope, stderr, detection):
class buildPODModel():
def __init__(self, intercept, slope, sigmaEpsilon, detection):
self.intercept = intercept
self.slope = slope
self.sigmaEpsilon = sigmaEpsilon
self.detection = detection
def PODmodel(self, x):
t = (self.detection -
(self.intercept + self.slope * x)) / self.sigmaEpsilon
return ot.DistFunc.pNormal(t, True)
N = defects.getSize()
X = ot.Sample(N, [1, 0])
X[:, 1] = defects
X = ot.Matrix(X)
covMatrix = X.computeGram(True).solveLinearSystem(ot.IdentityMatrix(2))
sampleNormal = ot.Normal([0, 0],
ot.CovarianceMatrix(
covMatrix.getImplementation())).getSample(
self._simulationSize)
sampleSigmaEpsilon = (ot.Chi(N - 2).inverse() * np.sqrt(N - 2) *
stderr).getSample(self._simulationSize)
PODcoll = []
for i in range(self._simulationSize):
sigmaEpsilon = sampleSigmaEpsilon[i][0]
interceptSimu = sampleNormal[i][0] * sigmaEpsilon + intercept
slopeSimu = sampleNormal[i][1] * sigmaEpsilon + slope
PODcoll.append(
buildPODModel(interceptSimu, slopeSimu, sigmaEpsilon,
detection).PODmodel)
return PODcoll
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Chi().__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.Chi().__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.Chi().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Chi()
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()
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
distribution = ot.Chi(0.5)
size = 10000
sample = distribution.getSample(size)
factory = ot.ChiFactory()
estimatedDistribution = factory.build(sample)
print("distribution=", repr(distribution))
print("Estimated distribution=", repr(estimatedDistribution))
distribution = ot.Chi(1.0)
sample = distribution.getSample(size)
estimatedDistribution = factory.build(sample)
print("distribution=", repr(distribution))
print("Estimated distribution=", repr(estimatedDistribution))
distribution = ot.Chi(2.5)
sample = distribution.getSample(size)
estimatedDistribution = factory.build(sample)
print("distribution=", repr(distribution))
print("Estimated distribution=", repr(estimatedDistribution))
estimatedDistribution = factory.build()
print("Default distribution=", estimatedDistribution)
estimatedDistribution = factory.build(distribution.getParameter())
print("Distribution from parameters=", estimatedDistribution)
estimatedChi = factory.buildAsChi(sample)
print("Chi =", distribution)
print("Estimated chi=", estimatedChi)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Chi().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Chi().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Chi().__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.Chi().__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.Chi().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Chi().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Chi().__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.Chi().__class__.__name__ == 'Multinomial':
distribution = ot.Multinomial(5, [0.2])
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Chi().__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.Chi().__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.Chi()
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))