def generateDataForSpecificInstance(size): R = ot.CorrelationMatrix(3) R[0, 1] = 0.5 R[0, 2] = 0.45 collection = [ot.FrankCopula(3.0), ot.NormalCopula(R), ot.ClaytonCopula(2.0)] copula = ot.ComposedCopula(collection) return copula.getSample(size)
""" Assemble copulas ================ """ # %% # In this example we are going to merge a collection of independent copulas into one. # # %% from __future__ import print_function import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) # %% # create a collection of copulas R = ot.CorrelationMatrix(3) R[0, 1] = 0.5 R[0, 2] = 0.25 collection = [ot.FrankCopula(3.0), ot.NormalCopula(R), ot.ClaytonCopula(2.0)] # %% # merge the copulas copula = ot.ComposedCopula(collection) print(copula)
import pyAgrum.lib.notebook as gnb
gnb.showInference(model, evs=evs, size=size)
except ImportError:
pass
# **Probabilistic model**
# Marginal distributions
Torque = ot.LogNormal(0.0, 0.25)
Angle = ot.TruncatedNormal(0.0, 2.0, -8.0, 8.0)
Joint = ot.Uniform(1.8, 2.2)
# Dependence
rho = 0.5
TorqueAngleCopula = ot.NormalCopula(ot.CorrelationMatrix(2, [1.0, rho, rho, 1.0]))
copula = ot.ComposedCopula([TorqueAngleCopula, ot.IndependentCopula(1)])
# Joint distribution if needed
TorqueAngle = ot.ComposedDistribution([Torque, Angle], TorqueAngleCopula)
fullDistribution = ot.ComposedDistribution([Torque, Angle, Joint], copula)
# Leakage angle (rd)
angleMax = 5.0
# Leakage joint (mm)
jointMin = 2.0
jointSpread = 0.1
# Vibration torque (kN.m)
torqueSpread = 2.0
# - find the dependent components
# - estimate a copula on each dependent bloc
# - assemble the estimated copulas
#
# %%
from __future__ import print_function
import openturns as ot
import math as m
ot.Log.Show(ot.Log.NONE)
# %%
# generate some multivariate data to estimate, with correlation
cop1 = ot.AliMikhailHaqCopula(0.6)
cop2 = ot.ClaytonCopula(2.5)
copula = ot.ComposedCopula([cop1, cop2])
marginals = [
ot.Uniform(5.0, 6.0),
ot.Arcsine(),
ot.Normal(-40.0, 3.0),
ot.Triangular(100.0, 150.0, 300.0)
]
distribution = ot.ComposedDistribution(marginals, copula)
sample = distribution.getSample(10000).getMarginal([0, 2, 3, 1])
# %%
# estimate marginals
dimension = sample.getDimension()
marginalFactories = []
for factory in ot.DistributionFactory.GetContinuousUniVariateFactories():
if str(factory).startswith('Histogram'):
# case 1: no transformation
coll.append([ot.Normal(), ot.Normal()])
# case 2: same copula
left = ot.ComposedDistribution(
[ot.Normal(), ot.Gumbel()], ot.IndependentCopula(2))
right = ot.ComposedDistribution([ot.Triangular()] * 2, ot.IndependentCopula(2))
coll.append([left, right])
# case 3: same standard space
left = ot.ComposedDistribution(
[ot.Normal(), ot.Gumbel()], ot.IndependentCopula(2))
right = ot.ComposedDistribution([ot.Triangular()] * 2, ot.GumbelCopula())
coll.append([left, right])
# TODO case 4: different standard space
for left, right in coll:
transformation = ot.DistributionTransformation(left, right)
print('left=', left)
print('right=', right)
print('transformation=', transformation)
inverseTransformation = transformation.inverse()
print('inverseTransformation=', inverseTransformation)
print('-' * 100)
# with marginaltransformation
copula = ot.ComposedCopula([ot.IndependentCopula(2), ot.IndependentCopula(2)])
distribution = ot.ComposedDistribution([ot.Normal()]*4, copula)
print(ot.DistributionTransformation(ot.IndependentCopula(4), distribution.getMarginal([3,1,2,0])))
formula_fake_var = 'x1'
formula_y0 = 'cos(0.5*x1) + sin(x2)'
formula_y1 = 'cos(0.5*x1) + sin(x2) + x3'
symbolicModel = persalys.SymbolicPhysicalModel('symbolicModel', [x1, x2, x3], [fake_var, y0, fake_y0, y1], [
formula_fake_var, formula_y0, formula_y0, formula_y1])
myStudy.add(symbolicModel)
# python model ##
code = 'from math import cos, sin, sqrt\n\ndef _exec(x1, x2, x3):\n y0 = cos(0.5*x1) + sin(x2) + sqrt(x3)\n return y0\n'
pythonModel = persalys.PythonPhysicalModel('pythonModel', [x1, x2, x3], [y0], code)
myStudy.add(pythonModel)
filename = 'data.csv'
cDist = ot.ComposedDistribution([ot.Normal(), ot.Gumbel(), ot.Normal(), ot.Uniform()],
ot.ComposedCopula([ot.IndependentCopula(2), ot.GumbelCopula()]))
sample = cDist.getSample(200)
sample.exportToCSVFile(filename, ' ')
# Designs of Experiment ##
# fixed design ##
ot.RandomGenerator.SetSeed(0)
fixedDesign = persalys.FixedDesignOfExperiment('fixedDesign', symbolicModel)
inputSample = ot.LHSExperiment(ot.ComposedDistribution([ot.Uniform(0., 10.), ot.Uniform(0., 10.)]), 10).generate()
inputSample.stack(ot.Sample(10, [0.5]))
fixedDesign.setOriginalInputSample(inputSample)
fixedDesign.run()
myStudy.add(fixedDesign)
# grid ##
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
model = ot.SymbolicFunction(['x0', 'x1', 'x2', 'x3'], ['-(6+x0^2-x1+x2+3*x3)'])
dim = model.getInputDimension()
marginals = [ot.Normal(5.0, 3.0) for i in range(dim)]
distribution = ot.ComposedDistribution(
marginals, ot.ComposedCopula([ot.ClaytonCopula(),
ot.NormalCopula()]))
#distribution = ot.Normal([5]*dim, [3]*dim, ot.CorrelationMatrix(dim))
#distribution = ot.ComposedDistribution(marginals, ot.IndependentCopula(dim))
distribution.setDescription(['marginal' + str(i) for i in range(dim)])
vect = ot.RandomVector(distribution)
output = ot.CompositeRandomVector(model, vect)
event = ot.Event(output, ot.Greater(), 0.0)
solver = ot.Cobyla()
solver.setMaximumEvaluationNumber(200)
solver.setMaximumAbsoluteError(1.0e-10)
solver.setMaximumRelativeError(1.0e-10)
solver.setMaximumResidualError(1.0e-10)
solver.setMaximumConstraintError(1.0e-10)
algo = ot.FORM(solver, event, distribution.getMean())
algo.run()
result = algo.getResult()
hasoferReliabilityIndexSensitivity = result.getHasoferReliabilityIndexSensitivity(
)
print(hasoferReliabilityIndexSensitivity)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
myColl = [ot.ClaytonCopula(0.3), ot.NormalCopula(3)]
myMergedCop = ot.ComposedCopula(myColl)
myMergedCop.setDescription(['$u_1$', '$u_2$', '$u_3$', '$u_4$', '$u_5$'])
graphPDF = myMergedCop.drawMarginal2DPDF(0, 1, [0.0] * 2, [1.0] * 2, [100] * 2)
graphPDF.setXTitle('$u_1$')
graphPDF.setYTitle('$u_2$')
graphCDF = myMergedCop.drawMarginal2DCDF(0, 1, [0.0] * 2, [1.0] * 2, [100] * 2)
graphCDF.setXTitle('$u_1$')
graphCDF.setYTitle('$u_2$')
fig = plt.figure(figsize=(10, 4))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
pdf_axis.set_xlim(auto=True)
cdf_axis.set_xlim(auto=True)
View(graphPDF, figure=fig, axes=[pdf_axis], add_legend=True)
View(graphCDF, figure=fig, axes=[cdf_axis], add_legend=True)
fig.suptitle("ComposedCopula(Clayton(0.3), NormalCopula(3)): pdf and cdf")
