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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
dim = 2
distribution = ot.Normal(dim)
X = ot.RandomVector(distribution)
# 1. Composite/Composite
f1 = ot.SymbolicFunction(["x" + str(i) for i in range(dim)], ["x0"])
f2 = ot.SymbolicFunction(["x" + str(i) for i in range(dim)], ["x1"])
Y1 = ot.CompositeRandomVector(f1, X)
l2 = ot.LevelSet(f2, ot.Greater(), 0.0)
e1 = ot.ThresholdEvent(Y1, ot.Less(), 0.0)
e2 = ot.DomainEvent(X, l2)
e3 = e1.intersect(e2)
# print('e3=', e3)
proba_e3 = e3.getSample(10000).computeMean()[0]
print("proba_e3 = %.3g" % proba_e3)
ott.assert_almost_equal(proba_e3, 0.25, 1e-2, 1e-2)
e4 = e1.join(e2)
# print('e4=', e4)
proba_e4 = e4.getSample(10000).computeMean()[0]
print("proba_e4 = %.3g" % proba_e4)
ott.assert_almost_equal(proba_e4, 0.75, 1e-2, 1e-2)
e5 = ot.IntersectionEvent([e1, e2])
# print('e5=', e5)
proba_e5 = e5.getSample(10000).computeMean()[0]
print("proba_e5 = %.3g" % proba_e5)
ott.assert_almost_equal(proba_e5, 0.25, 1e-2, 1e-2)
e6 = ot.UnionEvent([e1, e2])
# print('e6=', e6)
proba_e6 = e6.getSample(10000).computeMean()[0]
print("proba_e6 = %.3g" % proba_e6)
ott.assert_almost_equal(proba_e6, 0.75, 1e-2, 1e-2)
# intersection of intersection
e7 = ot.IntersectionEvent([e1, ot.IntersectionEvent([e1, e2])])
ott.assert_almost_equal(e7.getSample(10000).computeMean()[0], 0.25, 1e-2, 1e-2)
e8 = ot.IntersectionEvent([ot.IntersectionEvent([e1, e2]), e1])
ott.assert_almost_equal(e8.getSample(10000).computeMean()[0], 0.25, 1e-2, 1e-2)
# union of union
e9 = ot.UnionEvent([e1, ot.UnionEvent([e1, e2])])
ott.assert_almost_equal(e9.getSample(10000).computeMean()[0], 0.75, 1e-2, 1e-2)
e10 = ot.UnionEvent([ot.UnionEvent([e1, e2]), e1])
ott.assert_almost_equal(e10.getSample(10000).computeMean()[0], 0.75, 1e-2, 1e-2)
# intersection of union
e11 = ot.IntersectionEvent([ot.UnionEvent([e1, e2]), ot.UnionEvent([e1, e2])])
ott.assert_almost_equal(e11.getSample(10000).computeMean()[0], 0.75, 1e-2, 1e-2)
# union of intersection
e12 = ot.UnionEvent([ot.IntersectionEvent([e1, e2]), ot.IntersectionEvent([e1, e2])])
ott.assert_almost_equal(e12.getSample(10000).computeMean()[0], 0.25, 1e-2, 1e-2)
# DomainEvent
domain = ot.Interval([-1.0] * dim, [1.0] * dim)
e13 = ot.DomainEvent(X, domain)
e13_probability = distribution.computeProbability(domain)
ott.assert_almost_equal(
e13.getSample(10000).computeMean()[0], e13_probability, 1e-2, 1e-2
)
# Union with DomainEvent
e14 = ot.UnionEvent([e1, e2, e13])
ott.assert_almost_equal(
e14.getSample(10000).computeMean()[0], 0.75 + e13_probability / 4, 1e-2, 1e-2
)
# Intersection with DomainEvent
e15 = ot.IntersectionEvent([e1, e2, e13])
ott.assert_almost_equal(
e15.getSample(10000).computeMean()[0], e13_probability / 4, 1e-2, 1e-2
)
# through simulation
def sim_event(ev):
experiment = ot.MonteCarloExperiment()
algo = ot.ProbabilitySimulationAlgorithm(ev, experiment)
algo.setMaximumOuterSampling(2500)
algo.setBlockSize(4)
algo.setMaximumCoefficientOfVariation(-1.0)
algo.run()
result = algo.getResult()
return result.getProbabilityEstimate()
ott.assert_almost_equal(sim_event(e5), 0.25, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e6), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e7), 0.25, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e8), 0.25, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e9), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e10), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e11), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e12), 0.25, 1e-2, 2e-2)
ott.assert_almost_equal(sim_event(e13), e13_probability, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e14), 0.75 + e13_probability / 4, 1e-2, 1e-2)
ott.assert_almost_equal(sim_event(e15), e13_probability / 4, 1e-2, 1e-2)
def subset_event(ev):
algo = ot.SubsetSampling(ev)
algo.setMaximumOuterSampling(2500)
algo.setBlockSize(4)
algo.run()
result = algo.getResult()
return result.getProbabilityEstimate()
ott.assert_almost_equal(subset_event(e3), 0.25, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e5), 0.25, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e6), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e7), 0.25, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e8), 0.25, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e9), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e10), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e11), 0.75, 1e-2, 1e-2)
ott.assert_almost_equal(subset_event(e12), 0.25, 1e-2, 1e-2)
# check that f2 is not called when not needed
f1 = ot.SymbolicFunction(["x" + str(i) for i in range(dim)], ["x0"])
f2 = ot.MemoizeFunction(ot.SymbolicFunction(["x" + str(i) for i in range(dim)], ["x1"]))
Y1 = ot.CompositeRandomVector(f1, X)
Y2 = ot.CompositeRandomVector(f2, X)
e1 = ot.ThresholdEvent(Y1, ot.Less(), 1e6)
e2 = ot.ThresholdEvent(Y2, ot.Less(), 0.0)
union = ot.UnionEvent([e1, e2])
proba = union.getSample(1000).computeMean()[0]
print(proba)
assert proba == 1.0, "always true"
assert f2.getCallsNumber() == 0, "union prune"
e1 = ot.ThresholdEvent(Y1, ot.Greater(), 1e6)
e2 = ot.ThresholdEvent(Y2, ot.Less(), 0.0)
intersection = ot.IntersectionEvent([e1, e2])
proba = intersection.getSample(1000).computeMean()[0]
print(proba)
assert proba == 0.0, "always false"
assert f2.getCallsNumber() == 0, "intersection prune"
# check batch evaluation
n = 10000
def f1py(x):
x0 = ot.Sample(x).getMarginal(0)
print("eval f1")
assert x0.getSize() == n, "no batch eval"
return x0
def f2py(x):
x1 = ot.Sample(x).getMarginal(1)
print("eval f2")
assert x1.getSize() > 1, "no batch eval"
return x1
f1 = ot.PythonFunction(2, 1, func_sample=f1py)
f2 = ot.PythonFunction(2, 1, func_sample=f2py)
Y1 = ot.CompositeRandomVector(f1, X)
Y2 = ot.CompositeRandomVector(f2, X)
e1 = ot.ThresholdEvent(Y1, ot.Less(), 0.0)
e2 = ot.ThresholdEvent(Y2, ot.Greater(), 0.0)
e3 = ot.UnionEvent([e1, e2])
p3 = e3.getSample(n).computeMean()[0]
ott.assert_almost_equal(p3, 0.75, 1e-2, 1e-2)
e4 = ot.IntersectionEvent([e1, e2])
p4 = e4.getSample(n).computeMean()[0]
ott.assert_almost_equal(p4, 0.25, 1e-2, 1e-2)
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