def test_DrawFilledEvent(self):
# Distribution
R = ot.Normal(4.0, 1.0)
R.setDescription("R")
S = ot.Normal(2.0, 1.0)
S.setDescription("S")
g = ot.SymbolicFunction(["R", "S"], ["R - S"])
# Event
distribution = ot.ComposedDistribution([R, S])
inputRV = ot.RandomVector(distribution)
outputRV = ot.CompositeRandomVector(g, inputRV)
eventF = ot.ThresholdEvent(outputRV, ot.GreaterOrEqual(), 0)
alpha = 1.0 - 1.0e-2
(
bounds,
marginalProb,
) = distribution.computeMinimumVolumeIntervalWithMarginalProbability(
alpha)
#
drawEvent = otbenchmark.DrawEvent(eventF)
# Avoid failing on CircleCi
# _tkinter.TclError: no display name and no $DISPLAY environment variable
try:
_ = drawEvent.fillEvent(bounds)
except Exception as e:
print(e)
def test_DrawFilledEvent(self):
# Distribution
R = ot.Normal(4.0, 1.0)
R.setDescription("R")
S = ot.Normal(2.0, 1.0)
S.setDescription("S")
g = ot.SymbolicFunction(["R", "S"], ["R - S"])
# Event
inputvector = ot.ComposedDistribution([R, S])
inputRV = ot.RandomVector(inputvector)
outputRV = ot.CompositeRandomVector(g, inputRV)
eventF = ot.Event(outputRV, ot.GreaterOrEqual(), 0)
#
# Bounds
alphaMin = 0.01
alphaMax = 1 - alphaMin
lowerBound = ot.Point(
[R.computeQuantile(alphaMin)[0],
S.computeQuantile(alphaMin)[0]])
upperBound = ot.Point(
[R.computeQuantile(alphaMax)[0],
S.computeQuantile(alphaMax)[0]])
bounds = ot.Interval(lowerBound, upperBound)
#
drawEvent = otbenchmark.DrawEvent(eventF)
graph = drawEvent.fillEvent(bounds)
assert type(graph) is ot.Graph
def getXEvent(b, t, mu_S, covariance, R, delta_t):
full = buildCrossing(b, t, mu_S, covariance, R, delta_t)
X = ot.RandomVector(full)
f1 = ot.SymbolicFunction(["R", "X1", "X2"], ["X1 - R"])
e1 = ot.ThresholdEvent(ot.CompositeRandomVector(f1, X), ot.Less(), 0.0)
f2 = ot.SymbolicFunction(["R", "X1", "X2"], ["X2 - R"])
e2 = ot.ThresholdEvent(ot.CompositeRandomVector(f2, X),
ot.GreaterOrEqual(), 0.0)
event = ot.IntersectionEvent([e1, e2])
return X, event
def test_DrawSample(self):
# Distribution
R = ot.Normal(4.0, 1.0)
R.setDescription("R")
S = ot.Normal(2.0, 1.0)
S.setDescription("S")
g = ot.SymbolicFunction(["R", "S"], ["R - S"])
# Event
inputvector = ot.ComposedDistribution([R, S])
inputRV = ot.RandomVector(inputvector)
outputRV = ot.CompositeRandomVector(g, inputRV)
eventF = ot.Event(outputRV, ot.GreaterOrEqual(), 0)
#
sampleSize = 500
inputSample = inputvector.getSample(sampleSize)
outputSample = g(inputSample)
#
drawEvent = otbenchmark.DrawEvent(eventF)
graph = drawEvent.drawSample(inputSample, outputSample)
assert type(graph) is ot.Graph
def test_DrawSample(self):
# Distribution
R = ot.Normal(4.0, 1.0)
R.setDescription("R")
S = ot.Normal(2.0, 1.0)
S.setDescription("S")
g = ot.SymbolicFunction(["R", "S"], ["R - S"])
# Event
distribution = ot.ComposedDistribution([R, S])
inputRV = ot.RandomVector(distribution)
outputRV = ot.CompositeRandomVector(g, inputRV)
eventF = ot.ThresholdEvent(outputRV, ot.GreaterOrEqual(), 0)
#
sampleSize = 500
drawEvent = otbenchmark.DrawEvent(eventF)
_ = drawEvent.drawSampleCrossCut(sampleSize, 0, 1)
# Avoid failing on CircleCi
# _tkinter.TclError: no display name and no $DISPLAY environment variable
try:
_ = drawEvent.drawSample(sampleSize)
except Exception as e:
print(e)
import openturns as ot
import otrobopt
from matplotlib import pyplot as plt
from openturns.viewer import View
thetaDist = ot.Normal(2.0, 0.1)
if 'VarianceMeasure' == 'WorstCaseMeasure':
thetaDist = ot.Uniform(-1.0, 4.0)
elif 'ChanceMeasure' in 'VarianceMeasure':
thetaDist = ot.Normal(1.0, 1.0)
f_base = ot.Function(['x', 'theta'], ['y'], ['x*theta'])
f = ot.Function(f_base, [1], thetaDist.getMean())
if 'VarianceMeasure' == 'JointChanceMeasure':
measure = otrobopt.JointChanceMeasure(f, thetaDist, ot.GreaterOrEqual(),
0.95)
elif 'VarianceMeasure' == 'IndividualChanceMeasure':
measure = otrobopt.IndividualChanceMeasure(f, thetaDist,
ot.GreaterOrEqual(), [0.95])
elif 'VarianceMeasure' == 'MeanStandardDeviationTradeoffMeasure':
measure = otrobopt.MeanStandardDeviationTradeoffMeasure(
f, thetaDist, [0.8])
elif 'VarianceMeasure' == 'QuantileMeasure':
measure = otrobopt.QuantileMeasure(f, thetaDist, 0.99)
else:
measure = otrobopt.VarianceMeasure(f, thetaDist)
N = 10
experiment = ot.LHSExperiment(N)
factory = otrobopt.MeasureFactory(experiment)
ot.TESTPREAMBLE()
# Uncertain parameters
distribution = ot.Normal([1.0] * 3, [2.0] * 3, ot.CorrelationMatrix(3))
distribution.setName("Unnamed")
# Model
f = ot.SymbolicFunction(["x", "y", "z"], ["x-1.5*y+2*z"])
# Sampling
size = 100
inputSample = distribution.getSample(size)
outputSample = f(inputSample)
comparisonOperators = [
ot.Less(), ot.LessOrEqual(),
ot.Greater(),
ot.GreaterOrEqual()
]
threshold = 3.0
ot.ResourceMap.SetAsUnsignedInteger(
"SimulationSensitivityAnalysis-DefaultSampleMargin", 10)
for i in range(4):
# Analysis based on an event
X = ot.RandomVector(distribution)
Y = ot.CompositeRandomVector(f, X)
event = ot.ThresholdEvent(Y, comparisonOperators[i], threshold)
algo = ot.SimulationSensitivityAnalysis(event, inputSample, outputSample)
print("algo=", algo)
# Perform the analysis
print("Mean point in event domain=", algo.computeMeanPointInEventDomain())
print("Importance factors at threshold ", threshold, " =",
algo.computeImportanceFactors())
import openturns as ot
import otrobopt
# First test: theta of dimension 1
thetaDist = ot.Normal(2.0, 0.1)
f_base = ot.SymbolicFunction(['x', 'theta'], ['x*theta'])
f = ot.ParametricFunction(f_base, [1], [1.0])
x = [1.0]
measures = [otrobopt.MeanMeasure(f, thetaDist),
otrobopt.VarianceMeasure(f, thetaDist),
otrobopt.WorstCaseMeasure(f, ot.Uniform(-1.0, 4.0)),
otrobopt.WorstCaseMeasure(f, ot.Uniform(-1.0, 4.0), False),
otrobopt.JointChanceMeasure(
f, ot.Normal(1.0, 1.0), ot.GreaterOrEqual(), 0.95),
otrobopt.IndividualChanceMeasure(
f, ot.Normal(1.0, 1.0), ot.GreaterOrEqual(), [0.95]),
otrobopt.MeanStandardDeviationTradeoffMeasure(f, thetaDist, [0.8]),
otrobopt.QuantileMeasure(f, thetaDist, 0.99)
]
aggregated = otrobopt.AggregatedMeasure(measures)
measures.append(aggregated)
for measure in measures:
print(measure, '(continuous)', measure(x))
N = 10000
experiment = ot.LHSExperiment(N)
factory = otrobopt.MeasureFactory(experiment)
discretizedMeasure = factory.build(measure)
print(discretizedMeasure, '(discretized LHS)', discretizedMeasure(x))
G = ot.RandomVector(g, X_random_vector)
G.setDescription(['Deviation'])
# In[16]:
G_sample = G.getSample(int(1e3))
G_hist = ot.VisualTest_DrawHistogram(G_sample)
G_hist.setXTitle(G.getDescription()[0])
_ = View(G_hist, bar_kwargs={'label': 'G_sample'})
# # Event
# In[17]:
event = ot.Event(G, ot.GreaterOrEqual(), 30.)
event.setName("deviation > 30 cm")
# # Estimation of the event probability using (crude) Monte Carlo sampling
# In[18]:
g.clearHistory()
# In[19]:
ot.RandomGenerator.SetSeed(0)
# In[20]:
# create a Monte Carlo algorithm
from __future__ import print_function
import openturns as ot
import otrobopt
# First test: theta of dimension 1
thetaDist = ot.Normal(2.0, 0.1)
f_base = ot.SymbolicFunction(['x', 'theta'], ['x*theta'])
f = ot.ParametricFunction(f_base, [1], [1.0])
x = [1.0]
measures = [otrobopt.MeanMeasure(f, thetaDist),
otrobopt.VarianceMeasure(f, thetaDist),
otrobopt.WorstCaseMeasure(f, ot.Uniform(-1.0, 4.0)),
otrobopt.WorstCaseMeasure(f, ot.Uniform(-1.0, 4.0), False),
otrobopt.JointChanceMeasure(f, ot.Normal(1.0, 1.0), ot.GreaterOrEqual(), 0.95),
otrobopt.IndividualChanceMeasure(f, ot.Normal(1.0, 1.0), ot.GreaterOrEqual(), [0.95]),
otrobopt.MeanStandardDeviationTradeoffMeasure(f, thetaDist, [0.8]),
otrobopt.QuantileMeasure(f, thetaDist, 0.99)
]
aggregated = otrobopt.AggregatedMeasure(measures)
measures.append(aggregated)
for measure in measures:
print(measure, '(continuous)', measure(x))
N = 10000
experiment = ot.LHSExperiment(N)
factory = otrobopt.MeasureFactory(experiment)
discretizedMeasure = factory.build(measure)
print(discretizedMeasure, '(discretized LHS)', discretizedMeasure(x))
N = 4
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
# Uncertain parameters
distribution = ot.Normal([1.0] * 3, [2.0] * 3, ot.CorrelationMatrix(3))
distribution.setName("Unnamed")
# Model
f = ot.SymbolicFunction(["x", "y", "z"], ["x-1.5*y+2*z"])
# Sampling
size = 100
inputSample = distribution.getSample(size)
outputSample = f(inputSample)
comparisonOperators = [ot.Less(), ot.LessOrEqual(), ot.Greater(), ot.GreaterOrEqual()]
threshold = 3.0
ot.ResourceMap.SetAsUnsignedInteger(
"SimulationSensitivityAnalysis-DefaultSampleMargin", 10)
for i in range(4):
# Analysis based on an event
X = ot.RandomVector(distribution)
Y = ot.CompositeRandomVector(f, X)
event = ot.ThresholdEvent(Y, comparisonOperators[i], threshold)
algo = ot.SimulationSensitivityAnalysis(event, inputSample, outputSample)
print("algo=", algo)
# Perform the analysis
print("Mean point in event domain=",
algo.computeMeanPointInEventDomain())
print("Importance factors at threshold ", threshold,
" =", algo.computeImportanceFactors())
# coding: utf-8
import openturns as ot
R = ot.Normal(4., 1.)
R.setDescription("R")
S = ot.Normal(2., 1.)
S.setDescription("S")
g = ot.SymbolicFunction(["R","S"],["R-S"])
inputvector = ot.ComposedDistribution([R,S])
inputRV = ot.RandomVector(inputvector)
outputRV = ot.CompositeRandomVector(g, inputRV)
eventF = ot.Event(outputRV, ot.GreaterOrEqual(), 0)
# Create the Monte-Carlo algorithm
algoProb = ot.ProbabilitySimulationAlgorithm(eventF)
algoProb.setMaximumOuterSampling(1000)
algoProb.setMaximumCoefficientOfVariation(0.01)
algoProb.run()
# Get the results
resultAlgo = algoProb.getResult()
neval = g.getEvaluationCallsNumber()
print("Number of function calls = %d" %(neval))
pf = resultAlgo.getProbabilityEstimate()
print("Failure Probability = %.4f" % (pf))
level = 0.95
c95 = resultAlgo.getConfidenceLength(level)
fileName = 'myStudy.xml'
# Create a Study Object
myStudy = ot.Study()
myStudy.setStorageManager(ot.XMLStorageManager(fileName))
thetaDist = ot.Normal(2.0, 0.1)
f_base = ot.SymbolicFunction(['x', 'theta'], ['x*theta'])
f = ot.ParametricFunction(f_base, [1], [1.0])
measures = [
otrobopt.MeanMeasure(f, thetaDist),
otrobopt.VarianceMeasure(f, thetaDist),
otrobopt.WorstCaseMeasure(f, ot.Uniform(-1.0, 4.0), False),
otrobopt.JointChanceMeasure(f, ot.Normal(1.0, 1.0), ot.GreaterOrEqual(),
0.95),
otrobopt.IndividualChanceMeasure(f, ot.Normal(1.0, 1.0),
ot.GreaterOrEqual(), [0.95]),
otrobopt.MeanStandardDeviationTradeoffMeasure(f, thetaDist, [0.8]),
otrobopt.QuantileMeasure(f, thetaDist, 0.99)
]
aggregated = otrobopt.AggregatedMeasure(measures)
measures.append(aggregated)
for measure in measures:
myStudy.add('measure' + measure.__class__.__name__, measure)
measure2 = otrobopt.MeanMeasure(f, thetaDist)
measureFunction = otrobopt.MeasureFunction(measure2)
myStudy.add('measureFunction', measureFunction)
fileName = 'myStudy.xml'
# Create a Study Object
myStudy = ot.Study()
myStudy.setStorageManager(ot.XMLStorageManager(fileName))
thetaDist = ot.Normal(2.0, 0.1)
f_base = ot.SymbolicFunction(['x', 'theta'], ['x*theta'])
f = ot.ParametricFunction(f_base, [1], [1.0])
measures = [otrobopt.MeanMeasure(f, thetaDist),
otrobopt.VarianceMeasure(f, thetaDist),
otrobopt.WorstCaseMeasure(f, ot.Uniform(-1.0, 4.0), False),
otrobopt.JointChanceMeasure(
f, ot.Normal(1.0, 1.0), ot.GreaterOrEqual(), 0.95),
otrobopt.IndividualChanceMeasure(
f, ot.Normal(1.0, 1.0), ot.GreaterOrEqual(), [0.95]),
otrobopt.MeanStandardDeviationTradeoffMeasure(f, thetaDist, [0.8]),
otrobopt.QuantileMeasure(f, thetaDist, 0.99)
]
aggregated = otrobopt.AggregatedMeasure(measures)
measures.append(aggregated)
for measure in measures:
myStudy.add('measure' + measure.__class__.__name__, measure)
measure2 = otrobopt.MeanMeasure(f, thetaDist)
measureFunction = otrobopt.MeasureFunction(measure2)
myStudy.add('measureFunction', measureFunction)
