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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
dim = 10
R = ot.CorrelationMatrix(dim)
for i in range(dim):
for j in range(i):
R[i, j] = (i + j + 1.0) / (2.0 * dim)
mean = ot.Point(dim, 2.0)
sigma = ot.Point(dim, 3.0)
distribution = ot.Normal(mean, sigma, R)
size = 100
sample = distribution.getSample(size)
sampleX = ot.Sample(size, dim - 1)
sampleY = ot.Sample(size, 1)
for i in range(size):
sampleY[i, 0] = sample[i, 0]
for j in range(1, dim):
sampleX[i, j - 1] = sample[i, j]
sampleZ = ot.Sample(size, 1)
for i in range(size):
sampleZ[i, 0] = sampleY[i, 0] * sampleY[i, 0]
selection = ot.Indices(5)
selection.fill()
print("selection = ", selection)
# PartialPearson : Independence Pearson test between 2 samples : firstSample of dimension n and secondSample of dimension 1.
# If firstSample[i] is the numerical sample extracted from firstSample (ith coordinate of each point of the numerical sample),
# PartialPearson performs the Independence Pearson test simultaneously on firstSample[i] and secondSample, for i in the selection.
# For all i, it is supposed that the couple (firstSample[i] and secondSample) is issued from a gaussian vector.
# Probability of the H0 reject zone : 0.10
print(
"PartialPearsonXY=",
ot.HypothesisTest.PartialPearson(sampleX, sampleY, selection, 0.10),
)
selection2 = ot.Indices(1, 0)
sampleX0 = ot.Sample(size, 1)
for i in range(size):
sampleX0[i, 0] = sampleX[i, 0]
# The three tests must be equal
print(
"PartialPearsonX0Y=",
ot.HypothesisTest.PartialPearson(sampleX, sampleY, selection2, 0.10),
)
print("PearsonX0Y=", ot.HypothesisTest.Pearson(sampleX0, sampleY, 0.10))
print("FullPearsonX0Y=", ot.HypothesisTest.FullPearson(sampleX0, sampleY, 0.10))
# FullPearson : Independence Pearson test between 2 samples : firstSample of dimension n and secondSample of dimension 1.
# If firstSample[i] is the numerical sample extracted from firstSample (ith coordinate of each point of the numerical sample),
# FullPearson performs the Independence Pearson test simultaneously on firstSample[i] and secondSample.
# For all i, it is supposed that the couple (firstSample[i] and secondSample) is issued from a gaussian vector.
# Probability of the H0 reject zone : 0.10
print("FullPearsonXY=", ot.HypothesisTest.FullPearson(sampleX, sampleY, 0.10))
# Expected result is SpecFunc::Infinity
fullPearsonYY = ot.HypothesisTest.FullPearson(sampleY, sampleY, 0.10)[0]
testStatistic = fullPearsonYY.getStatistic()
assert testStatistic == ot.SpecFunc.Infinity
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