def __init__(self, threshold=0.0, expo=1):
"""
Creates a reliability problem RP54.
The event is {g(X) < threshold} where
X = (x1, x2, ...., x20)
g(X) = (x1 + x2 + ... + x20) - 8.951
Parameters
----------
threshold : float
The threshold.
expo : float
Rate parameter of the Xi Exponential distribution
for i in {1, 2, ..., 20}.
"""
formula = "x1+x2+x3+x4+x5+x6+x7+x8+x9+x10"
formula = formula + " + x11+x12+x13+x14+x15+x16+x17+x18+x19+x20-8.951"
print(formula)
limitStateFunction = ot.SymbolicFunction(
[
"x1",
"x2",
"x3",
"x4",
"x5",
"x6",
"x7",
"x8",
"x9",
"x10",
"x11",
"x12",
"x13",
"x14",
"x15",
"x16",
"x17",
"x18",
"x19",
"x20",
],
[formula],
)
X = [ot.Exponential(expo) for i in range(20)]
myDistribution = ot.ComposedDistribution(X)
inputRandomVector = ot.RandomVector(myDistribution)
outputRandomVector = ot.CompositeRandomVector(
limitStateFunction, inputRandomVector
)
thresholdEvent = ot.ThresholdEvent(outputRandomVector, ot.Less(), threshold)
name = "RP54"
probability = 0.000998
super(ReliabilityProblem54, self).__init__(name, thresholdEvent, probability)
return None
print('covariance (ref)=', repr(
cleanCovariance(referenceDistribution[testCase].getCovariance())))
parameters = distribution[testCase].getParametersCollection()
print('parameters =', repr(parameters))
print('parameters (ref)=', repr(
referenceDistribution[testCase].getParametersCollection()))
print('parameter =', repr(distribution[testCase].getParameter()))
print('parameter desc =',
repr(distribution[testCase].getParameterDescription()))
print('marginal 0 =', repr(distribution[testCase].getMarginal(0)))
for i in range(6):
print('standard moment n=', i, ' value=',
referenceDistribution[testCase].getStandardMoment(i))
print('Standard representative=', referenceDistribution[
testCase].getStandardRepresentative())
# Check simplification
candidates = [ot.Normal(1.0, 2.0), ot.Uniform(1.0, 2.0), ot.Exponential(1.0, 2.0),
ot.TruncatedDistribution(ot.Weibull(), 1.5, 7.8),
ot.Beta(1.5, 7.8, -1.0, 2.0)]
intervals = [ot.Interval(-1.0, 4.0), ot.Interval(0.2, 2.4), ot.Interval(2.5, 65.0),
ot.Interval(2.5, 6.0), ot.Interval(-2.5, 6.0)]
for i in range(len(candidates)):
d = ot.TruncatedDistribution(candidates[i], intervals[i])
print("d=", d, "simplified=", d.getSimplifiedVersion())
# Check that we can set the bounds independently
truncated = ot.TruncatedDistribution()
truncated.setDistribution(ot.Normal(20.0, 7.5))
truncated.setBounds(ot.Interval([0], [80], [True], [False]))
print('after setbounds [email protected]=', truncated.computeQuantile(0.9))
from matplotlib import pylab as plt
# %%
# Position of the problem
# -----------------------
#
# We consider a bivariate random vector :math:`X = (X_1, X_2)` with the following independent marginals :
#
# - an exponential distribution with parameter :math:`\lambda=1`, :math:`X_1 \sim \mathcal{E}(1.0)` ;
# - a standard unit gaussian :math:`X_2 \sim \mathcal{N}(0,1)`.
#
# The support of the input vector is :math:`[0, +\infty[ \times \mathbb{R}`
#
# %%
distX1 = ot.Exponential(1.0)
distX2 = ot.Normal()
distX = ot.ComposedDistribution([distX1, distX2])
# %%
# We can draw the bidimensional PDF of the distribution `distX` over :math:`[0,-10] \times [10,10]` :
ot.ResourceMap_SetAsUnsignedInteger("Contour-DefaultLevelsNumber", 8)
graphPDF = distX.drawPDF([0, -10], [10, 10])
graphPDF.setTitle(r'2D-PDF of the input variables $(X_1, X_2)$')
graphPDF.setXTitle(r'$x_1$')
graphPDF.setYTitle(r'$x_2$')
graphPDF.setLegendPosition("bottomright")
view = otv.View(graphPDF)
# %%
# We consider the model :math:`f : (x_1, x_2) \mapsto x_1 x_2` which maps the random input vector :math:`X` to the output variable :math:`Y=f(X) \in \mathbb{R}`. We also draw the isolines of the model `f`.
graph = result.drawPDF()
result = ot.LogUniform() * ot.LogUniform()
print('logu*logu:', result)
graph = result.drawPDF()
result = ot.LogUniform() * ot.LogNormal()
print('logu*logn:', result)
graph = result.drawPDF()
result = ot.LogNormal() * ot.LogUniform()
print('logn*logu:', result)
graph = result.drawPDF()
# For ticket #917
result = ot.WeibullMin() + ot.Exponential()
print('WeibullMin+Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = -1.0 * ot.WeibullMin() + ot.Exponential()
print('-WeibullMin+Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = ot.WeibullMin() - ot.Exponential()
print('WeibullMin-Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = -1.0 * ot.WeibullMin() - ot.Exponential()
print('-WeibullMin-Exponential:', result)
print('result.CDF(-1.0)=%.6f' % result.computeCDF(-1.0))
# 2-d
print(ot.Normal(2) + ot.Normal(2))
print(ot.Normal(2) + 3.0)
# %%
# In this example we are going to build a conditional random vector
#
# .. math::
# \underline{X}|\underline{\Theta}
#
# %%
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
# %%
# create the random vector Theta (parameters of X)
gammaDist = ot.Uniform(1.0, 2.0)
alphaDist = ot.Uniform(0.0, 0.1)
thetaDist = ot.ComposedDistribution([gammaDist, alphaDist])
thetaRV = ot.RandomVector(thetaDist)
# %%
# create the XgivenTheta distribution
XgivenThetaDist = ot.Exponential()
# %%
# create the X distribution
XDist = ot.ConditionalRandomVector(XgivenThetaDist, thetaRV)
# %%
# draw a sample
XDist.getSample(5)
ot.Log.Show(ot.Log.NONE)
# %%
# Create an 1-d distribution
dist_1 = ot.Normal()
# Create a 2-d distribution
dist_2 = ot.ComposedDistribution(
[ot.Normal(), ot.Triangular(0.0, 2.0, 3.0)], ot.ClaytonCopula(2.3))
# Create a 3-d distribution
copula_dim3 = ot.Student(5.0, 3).getCopula()
dist_3 = ot.ComposedDistribution(
[ot.Normal(),
ot.Triangular(0.0, 2.0, 3.0),
ot.Exponential(0.2)], copula_dim3)
# %%
# Get the dimension fo the distribution
dist_2.getDimension()
# %%
# Get the 2nd marginal
dist_2.getMarginal(1)
# %%
# Get a 2-d marginal
dist_3.getMarginal([0, 1]).getDimension()
# %%
# Ask some properties of the distribution
# %%
# We see that the sample is quite different from the previous sample with independent copula.
# %%
# Draw several distributions in the same plot
# -------------------------------------------
# %%
# It is sometimes convenient to create a plot presenting the PDF and CDF on the same graphics. This is possible thanks to Matplotlib.
# %%
beta = ot.Beta(5, 7, 9, 10)
pdfbeta = beta.drawPDF()
cdfbeta = beta.drawCDF()
exponential = ot.Exponential(3)
pdfexp = exponential.drawPDF()
cdfexp = exponential.drawCDF()
# %%
import openturns.viewer as otv
# %% slideshow={"slide_type": "subslide"}
import pylab as plt
fig = plt.figure(figsize=(12, 4))
ax = fig.add_subplot(2, 2, 1)
_ = otv.View(pdfbeta, figure=fig, axes=[ax])
ax = fig.add_subplot(2, 2, 2)
_ = otv.View(cdfbeta, figure=fig, axes=[ax])
ax = fig.add_subplot(2, 2, 3)
_ = otv.View(pdfexp, figure=fig, axes=[ax])
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
# %%
# Create an 1-d distribution
dist_1 = ot.Normal()
# Create a 2-d distribution
dist_2 = ot.ComposedDistribution(
[ot.Normal(), ot.Triangular(0.0, 2.0, 3.0)], ot.ClaytonCopula(2.3))
# Create a 3-d distribution
copula_dim3 = ot.Student(5.0, 3).getCopula()
dist_3 = ot.ComposedDistribution([ot.Normal(), ot.Triangular(
0.0, 2.0, 3.0), ot.Exponential(0.2)], copula_dim3)
# %%
# Get the dimension fo the distribution
dist_2.getDimension()
# %%
# Get the 2nd marginal
dist_2.getMarginal(1)
# %%
# Get a 2-d marginal
dist_3.getMarginal([0, 1]).getDimension()
# %%
# Ask some properties of the distribution
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Exponential().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Exponential().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Exponential().__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.Exponential().__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.Exponential().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Exponential().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Exponential().__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.Exponential().__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.Exponential().__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.Exponential().__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.Exponential().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Exponential()
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))
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
distXgivenT = ot.Exponential()
distGamma = ot.Uniform(1.0, 2.0)
distAlpha = ot.Uniform(0.0, 0.1)
distTheta = ot.ComposedDistribution([distGamma, distAlpha])
rvTheta = ot.RandomVector(distTheta)
rvX = ot.ConditionalRandomVector(distXgivenT, rvTheta)
sampleX = rvX.getSample(1000)
histX = ot.HistogramFactory().build(sampleX)
graph = histX.drawPDF()
graph.setXTitle('x')
graph.setYTitle('pdf')
fig = plt.figure(figsize=(8, 4))
plt.suptitle(
"Conditional Random Vector: Exp($\gamma$, $\lambda$), $\gamma \sim \mathcal{U}(1,2)$, $\lambda \sim \mathcal{U}(0,1)$"
)
axis = fig.add_subplot(111)
axis.set_xlim(auto=True)
View(graph, figure=fig, axes=[axis], add_legend=False)
print("Inverse survival (ref)=", ref.computeInverseSurvivalFunction(0.95))
print("Survival(inverse survival)=%.5f" %
distribution.computeSurvivalFunction(InverseSurvival))
# Get 50% quantile
quantile = distribution.computeQuantile(0.5)
print("Quantile =", quantile)
print("Quantile (ref)=", ref.computeQuantile(0.5))
print("CDF(quantile) =%.5f" % distribution.computeCDF(quantile))
# Instantiate one distribution object
R = ot.CorrelationMatrix(3)
R[0, 1] = 0.5
R[0, 2] = 0.25
collection = [ot.ComposedDistribution([ot.Normal()]*2, ot.AliMikhailHaqCopula(0.5)),
ot.Normal([1.0]*3, [2.0]*3, R),
ot.ComposedDistribution([ot.Exponential()]*2, ot.FrankCopula(0.5))]
distribution = ot.BlockIndependentDistribution(collection)
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical distribution= ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Has this distribution an elliptical copula ?
print("Elliptical = ", distribution.hasEllipticalCopula())
# Has this distribution an independent copula ?
print("Independent = ", distribution.hasIndependentCopula())
"round": 0, # Already an integer (casted as double)
},
"avg_provider_rating": {
"marg": ot.Triangular(2.5, 4.0, 4.8), # mode is 4.0
"corr": 0.01, # Weak positive correlation
"bounds": None,
"round": 2,
},
"has_multipayment": {
"marg": ot.Bernoulli(0.4), # assume 40% of yes
"corr": 0.0, # Assume no correlation
"bounds": None,
"round": 0,
},
"conversion_rate": {
"marg": ot.Exponential(15.0, 0.05), # mean is ~0.12 (0.05 + 1/15)
"corr": None, # Corr not relevant for conversion_rate, because
# it is the target variable.
"bounds": None,
"round": 4,
},
}
CORR_CONF_TRAIN = { # Conf file for adding correlations between variables
("price", "ratio_shipping"): -0.15, # The more expensive, the less costly
# the shipping
}
VAR_CONF_EVAL = VAR_CONF_TRAIN.copy()
CORR_CONF_EVAL = CORR_CONF_TRAIN.copy()
upper_bound = 2.0 * pi
graph = f.draw(lower_bound, upper_bound, 100)
graph.setTitle("Christian Robert tough density")
graph.setXTitle("")
graph.setYTitle("")
_ = View(graph)
# %%
# Independent Metropolis-Hastings
# -------------------------------
# Let us use a mixture distribution to approximate the target distribution.
#
# This approximation will serve as the instrumental distribution
# in the independent Metropolis-Hastings algorithm.
exp = ot.Exponential(1.0)
unif = ot.Normal(5.3, 0.4)
instrumentalDistribution = ot.Mixture([exp, unif], [0.9, 0.1])
# %%
# Compare the instrumental density to the target density.
graph = f.draw(lower_bound, upper_bound, 100)
graph.setTitle("Instrumental PDF")
graph.setXTitle("")
graph.setYTitle("")
graph.add(instrumentalDistribution.drawPDF(lower_bound, upper_bound, 100))
graph.setLegendPosition("topright")
graph.setLegends(["Unnormalized target density", "Instrumental PDF"])
_ = View(graph)
# %%
=============================
"""
# %%
# In this example we are going to create a deterministic weighted design experiment using Gauss product.
# %%
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
# %%
# Define the underlying distribution, degrees
distribution = ot.ComposedDistribution(
[ot.Exponential(), ot.Triangular(-1.0, -0.5, 1.0)])
marginalSizes = [15, 8]
# %%
# Create the design
experiment = ot.GaussProductExperiment(distribution, marginalSizes)
sample = experiment.generate()
# %%
# Plot the design
graph = ot.Graph("GP design", "x1", "x2", True, "")
cloud = ot.Cloud(sample, "blue", "fsquare", "")
graph.add(cloud)
view = viewer.View(graph)
plt.show()
result = test.getResult()
analysis = ot.LinearModelAnalysis(result)
print(analysis)
# Compute confidence level (95%) for coefficients estimate
alpha = 0.95
# interval confidence bounds
interval = analysis.getCoefficientsConfidenceInterval(alpha)
print("confidence intervals with level=%1.2f : %s" % (alpha, interval))
# https://github.com/openturns/openturns/issues/1729
ot.RandomGenerator.SetSeed(1789)
sample_size = 14605 # 14604 : OK, 14605 : Fail
a0 = 0.6
a1 = 2.0
x = ot.Normal(0.5, 0.2).getSample(sample_size)
epsilon = ot.Exponential(0.1).getSample(sample_size)
y = ot.Sample([[a0]] * sample_size) + a1 * x + epsilon
algo = ot.LinearModelAlgorithm(x, y)
result = algo.getResult()
analysis = ot.LinearModelAnalysis(result)
results = str(analysis)
# Fix #1820
ot.RandomGenerator.SetSeed(0)
distribution = ot.Normal()
sample = distribution.getSample(30)
func = ot.SymbolicFunction('x', '2 * x + 1')
firstSample = sample
secondSample = func(sample) + ot.Normal().getSample(30)
linear_model = ot.LinearModelAlgorithm(firstSample, secondSample)
linear_result = linear_model.getResult()
#
# We define an affine combination of input random variables.
#
# .. math::
# Y = 2 + 5 X_1 + X_2
#
# where:
#
# - :math:`X_1 \sim \mathcal{E}(\lambda=1.5)`
# - :math:`X_2 \sim \mathcal{N}(\mu=4, \sigma=1)`
#
# This notion is different from the Mixture where the combination is made on the probability density functions and not on the univariate random variable.
# %%
# We create the distributions associated to the input random variables :
X1 = ot.Exponential(1.5)
X2 = ot.Normal(4.0, 1.0)
# %%
# We define an offset `a0` :
a0 = 2.0
# %%
# We create the `weights` :
weight = [5.0, 1.0]
# %%
# We create the affine combination :math:`Y` :
distribution = ot.RandomMixture([X1, X2], weight, a0)
print(distribution)
import otrobopt
#ot.Log.Show(ot.Log.Info)
calJ = ot.SymbolicFunction(['x', 'theta'], ['x^3 - 3*x + theta'])
calG = ot.SymbolicFunction(['x', 'theta'], ['-(x + theta - 2)'])
J = ot.ParametricFunction(calJ, [1], [0.5])
g = ot.ParametricFunction(calG, [1], [0.5])
dim = J.getInputDimension()
solver = ot.Cobyla()
solver.setMaximumIterationNumber(1000)
solver.setStartingPoint([0.0] * dim)
thetaDist = ot.Exponential(2.0)
robustnessMeasure = otrobopt.MeanMeasure(J, thetaDist)
reliabilityMeasure = otrobopt.JointChanceMeasure(g, thetaDist, ot.Greater(), 0.9)
problem = otrobopt.RobustOptimizationProblem(robustnessMeasure, reliabilityMeasure)
problem.setMinimization(False)
algo = otrobopt.SequentialMonteCarloRobustAlgorithm(problem, solver)
algo.setMaximumIterationNumber(10)
algo.setMaximumAbsoluteError(1e-3)
algo.setInitialSamplingSize(10)
algo.run()
result = algo.getResult()
print ('x*=', result.getOptimalPoint(), 'J(x*)=', result.getOptimalValue(), 'iteration=', result.getIterationNumber())
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.PlatformInfo.SetNumericalPrecision(3)
distribution = ot.Beta(2.3, 2.2, -1.0, 1.0)
print('distribution=', distribution)
sample = distribution.getSample(1000)
factory = ot.MaximumLikelihoodFactory(ot.Beta())
inf_distribution = factory.build(sample)
print('estimated distribution=', inf_distribution)
# set (a,b) out of (r, t, a, b)
factory.setKnownParameter([-1.0, 1.0], [2, 3])
inf_distribution = factory.build(sample)
print('estimated distribution with bounds=', inf_distribution)
factory = ot.MaximumLikelihoodFactory(ot.Exponential())
factory.setKnownParameter([0.1], [1])
print(factory.build())
print(factory.build([3, 0]))
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Exponential().__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.Exponential().__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.Exponential()
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)
graph = result.drawPDF()
result = ot.LogUniform() * ot.LogUniform()
print('logu*logu:', result)
graph = result.drawPDF()
result = ot.LogUniform() * ot.LogNormal()
print('logu*logn:', result)
graph = result.drawPDF()
result = ot.LogNormal() * ot.LogUniform()
print('logn*logu:', result)
graph = result.drawPDF()
# For ticket #917
result = ot.Weibull() + ot.Exponential()
print('Weibull+Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = -1.0 * ot.Weibull() + ot.Exponential()
print('-Weibull+Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = ot.Weibull() - ot.Exponential()
print('Weibull-Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = -1.0 * ot.Weibull() - ot.Exponential()
print('-Weibull-Exponential:', result)
print('result.CDF(-1.0)=%.6f' % result.computeCDF(-1.0))
# 2-d
print(ot.Normal(2) + ot.Normal(2))
print(ot.Normal(2) + 3.0)
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)
ot.ResourceMap.SetAsUnsignedInteger("RandomMixture-DefaultMaxSize", 4000000)
# Deactivate the simplification mechanism as we want to test the Poisson formula
# based algorithm here
ot.ResourceMap.SetAsBool("RandomMixture-SimplifyAtoms", False)
# Create a collection of test-cases and the associated references
numberOfTests = 3
testCases = list()
references = list()
testCases.append([ot.Uniform(-1.0, 3.0)] * 2)
references.append(ot.Triangular(-2.0, 2.0, 6.0))
testCases.append([ot.Normal(), ot.Normal(1.0, 2.0), ot.Normal(-2.0, 2.0)])
references.append(ot.Normal(-1.0, 3.0))
testCases.append([ot.Exponential()] * 3)
references.append(ot.Gamma(3.0, 1.0, 0.0))
print("testCases=", testCases)
print("references=", references)
for testIndex in range(len(testCases)):
# Instanciate one distribution object
distribution = ot.RandomMixture(testCases[testIndex])
distribution.setBlockMin(5)
distribution.setBlockMax(20)
distributionReference = references[testIndex]
print("Distribution ", repr(distribution))
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
repr(cleanCovariance(referenceDistribution[testCase].getCovariance())))
parameters = distribution[testCase].getParametersCollection()
print('parameters =', repr(parameters))
print('parameters (ref)=',
repr(referenceDistribution[testCase].getParametersCollection()))
print('parameter =', repr(distribution[testCase].getParameter()))
print('parameter desc =',
repr(distribution[testCase].getParameterDescription()))
print('marginal 0 =', repr(distribution[testCase].getMarginal(0)))
print('Standard representative=',
referenceDistribution[testCase].getStandardRepresentative())
# Check simplification
candidates = [
ot.Normal(1.0, 2.0),
ot.Uniform(1.0, 2.0),
ot.Exponential(1.0, 2.0),
ot.TruncatedDistribution(ot.WeibullMin(), 1.5, 7.8),
ot.Beta(1.5, 6.3, -1.0, 2.0)
]
intervals = [
ot.Interval(-1.0, 4.0),
ot.Interval(0.2, 2.4),
ot.Interval(2.5, 65.0),
ot.Interval(2.5, 6.0),
ot.Interval(-2.5, 6.0)
]
for i in range(len(candidates)):
d = ot.TruncatedDistribution(candidates[i], intervals[i])
print("d=", d, "simplified=", d.getSimplifiedVersion())
# Check that we can set the bounds independently
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
candidate = ot.Exponential(0.07, 0.0)
graph = candidate.drawCDF(0.0, 30.0)
sample = ot.Sample([[5.0], [6.0], [10.0], [22.0], [27.0]])
empiricalDrawable = ot.VisualTest.DrawEmpiricalCDF(sample, 0.0,
30.0).getDrawable(0)
empiricalDrawable.setColor('darkblue')
graph.add(empiricalDrawable)
graph.setTitle('CDF comparison')
graph.setLegends(['Candidate CDF', 'Empirical CDF'])
View(graph)