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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
import math as m
ot.TESTPREAMBLE()
# Create 6 points from a Sobol' sequence in dimension 1
expected = ot.Sample(
[
[1.0 / 2.0],
[3.0 / 4.0],
[1.0 / 4.0],
[3.0 / 8.0],
[7.0 / 8.0],
[5.0 / 8.0],
]
)
sequence = ot.SobolSequence(1)
print(sequence)
sobolSample = sequence.generate(6)
ott.assert_almost_equal(sobolSample, expected)
# Create 6 points from a Sobol' sequence in dimension 2
expected = ot.Sample(
[
[1.0 / 2.0, 1.0 / 2.0],
[3.0 / 4.0, 1.0 / 4.0],
[1.0 / 4.0, 3.0 / 4.0],
[3.0 / 8.0, 3.0 / 8.0],
[7.0 / 8.0, 7.0 / 8.0],
[5.0 / 8.0, 1.0 / 8.0],
]
)
sequence = ot.SobolSequence(2)
print(sequence)
sobolSample = sequence.generate(6)
ott.assert_almost_equal(sobolSample, expected)
# Create a Sobol' sequence of maximum dimension
sequence = ot.SobolSequence(ot.SobolSequence.MaximumDimension)
print(sequence)
sobolSample = sequence.generate(10)
# Create a Sobol' sequence of dimension 2 to estimate Pi in [0 1)^2
dimension = 2
sequence = ot.SobolSequence(dimension)
pointInsideCircle = 0
sampleSize = 2**11 # This is significant!
for i in range(sampleSize):
sobolPoint = sequence.generate()
if sobolPoint.norm() < 1.0:
pointInsideCircle += 1
probabilityEstimate = (1.0 * pointInsideCircle) / sampleSize
probability = m.pi / 4.0
print("sample size=", sampleSize)
print("computed probability =", probabilityEstimate)
print("expected probability =", probability)
rtol = 10.0 / sampleSize
ott.assert_almost_equal(probability, probabilityEstimate, rtol)
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