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#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
# Build the event 'vector takes its values in interval'
# using a comparison operator and a threshold in order
# to be compatible with more algorithms than Monte Carlo
def buildEvent(vector, interval):
dimension = vector.getDimension()
if dimension != interval.getDimension():
raise Exception('Dimensions not compatible')
finiteLowerBound = interval.getFiniteLowerBound()
finiteUpperBound = interval.getFiniteUpperBound()
lowerBound = interval.getLowerBound()
upperBound = interval.getUpperBound()
# Easy case: 1D interval
if (dimension == 1):
if finiteLowerBound[0] and not finiteUpperBound[0]:
print('case 1')
return ot.Event(vector, Greater(), lowerBound[0])
if not finiteLowerBound[0] and finiteUpperBound[0]:
print('case 2')
return ot.Event(vector, Less(), upperBound[0])
if finiteLowerBound[0] and finiteUpperBound[0]:
print('case 3')
testFunction = ot.NumericalMathFunction(
'x', 'min(x-(' + str(lowerBound[0]) + '), (' + str(upperBound[0]) + ') - x)')
newVector = ot.RandomVector(ot.NumericalMathFunction(
testFunction, vector.getFunction()), vector.getAntecedent())
return ot.Event(newVector, Greater(), 0.0)
# Here we build an event that is always true and much cheaper to
# compute
print('case 4')
inputDimension = vector.getFunction().getInputDimension()
return ot.Event(ot.RandomVector(ot.NumericalMathFunction(ot.Description.BuildDefault(inputDimension, 'x'), ['0.0']), vector.getAntecedent()), Less(), 1.0)
# General case
numConstraints = 0
inVars = ot.Description.BuildDefault(dimension, 'y')
slacks = ot.Description(0)
for i in range(dimension):
if finiteLowerBound[i]:
slacks.add(inVars[i] + '-(' + str(lowerBound[i]) + ')')
if finiteUpperBound[i]:
slacks.add('(' + str(upperBound[i]) + ')-' + inVars[i])
# No constraint
if slacks.getSize() == 0:
# Here we build an event that is always true and much cheaper to
# compute
inputDimension = vector.getFunction().getInputDimension()
return ot.Event(ot.RandomVector(ot.NumericalMathFunction(ot.Description.BuildDefault(inputDimension, 'x'), ['0.0']), vector.getAntecedent()), Less(), 1.0)
# Only one constraint
if slacks.getSize() == 1:
print('case 6')
testFunction = ot.NumericalMathFunction(inVars, [slacks[0]])
# Several constraints
else:
print('case 7')
formula = 'min(' + slacks[0]
for i in range(1, slacks.getSize()):
formula += ',' + slacks[i]
formula += ')'
testFunction = ot.NumericalMathFunction(inVars, [formula])
newVector = ot.RandomVector(ot.NumericalMathFunction(
testFunction, vector.getFunction()), vector.getAntecedent())
return ot.Event(newVector, Greater(), 0.0)
# Tests
ot.ResourceMap.SetAsUnsignedInteger('Simulation-DefaultBlockSize', 100)
ot.ResourceMap.SetAsUnsignedInteger(
'Simulation-DefaultMaximumOuterSampling', 100)
ot.ResourceMap.SetAsNumericalScalar(
'Simulation-DefaultMaximumCoefficientOfVariation', 0.0)
ot.ResourceMap.SetAsNumericalScalar(
'Simulation-DefaultMaximumStandardDeviation', 0.0)
ot.ResourceMap.SetAsNumericalScalar(
'RootStrategyImplementation-DefaultStepSize', 0.1)
algorithms = ['MonteCarlo',
'LHS',
'QuasiMonteCarlo',
'DirectionalSampling']
inDim = 4
X = ot.RandomVector(ot.Normal(inDim))
inVars = ot.Description.BuildDefault(inDim, 'x')
low = 1.0
up = 2.0
intervals = [ot.Interval([low], [up], [True], [False]),
ot.Interval([low], [up], [False], [True]),
ot.Interval([low], [up], [True], [True]),
ot.Interval([low], [up], [False], [False]),
ot.Interval([low] * 2, [up] * 2, [True, True], [True, True]),
ot.Interval([low] * 2, [up] * 2, [True, True], [True, False]),
ot.Interval([low] * 2, [up] * 2, [True, True], [False, True]),
ot.Interval([low] * 2, [up] * 2, [True, True], [False, False]),
ot.Interval([low] * 2, [up] * 2, [True, False], [True, True]),
ot.Interval([low] * 2, [up] * 2, [True, False], [True, False]),
ot.Interval([low] * 2, [up] * 2, [True, False], [False, True]),
ot.Interval([low] * 2, [up] * 2, [True, False], [False, False]),
ot.Interval([low] * 2, [up] * 2, [False, True], [True, True]),
ot.Interval([low] * 2, [up] * 2, [False, True], [True, False]),
ot.Interval([low] * 2, [up] * 2, [False, True], [False, True]),
ot.Interval([low] * 2, [up] * 2, [False, True], [False, False]),
ot.Interval([low] * 2, [up] * 2, [False, False], [True, True]),
ot.Interval([low] * 2, [up] * 2, [False, False], [True, False]),
ot.Interval([low] * 2, [up] * 2, [False, False], [False, True]),
ot.Interval([low] * 2, [up] * 2, [False, False], [False, False])]
for domain in intervals:
print('#' * 50)
print('domain=\n', domain)
outDim = domain.getDimension()
f = ot.NumericalMathFunction(inVars, inVars[0:outDim])
Y = ot.RandomVector(f, X)
#event = buildEvent(Y, domain)
event = ot.Event(Y, domain)
ot.RandomGenerator.SetSeed(0)
#algo = getattr(openturns, algoName)(event)
algo = ot.MonteCarlo(event)
algo.run()
res = algo.getResult().getProbabilityEstimate()
print('MC p=%.6g' % res)
ot.RandomGenerator.SetSeed(0)
#algo = getattr(openturns, algoName)(event)
algo = ot.FORM(ot.Cobyla(), event, X.getMean())
algo.run()
res = algo.getResult().getEventProbability()
print('FORM p=%.2f' % res)
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