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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Instantiate one distribution object
dim = 2
meanPoint = [0.5, -0.5]
sigma = [2.0, 3.0]
R = ot.CorrelationMatrix(dim)
for i in range(1, dim):
R[i, i - 1] = 0.5
distribution = ot.Normal(meanPoint, sigma, R)
discretization = 100
kernel = ot.KernelSmoothing()
sample = distribution.getSample(discretization)
kernels = ot.DistributionCollection(0)
kernels.add(ot.Normal())
kernels.add(ot.Epanechnikov())
kernels.add(ot.Uniform())
kernels.add(ot.Triangular())
kernels.add(ot.Logistic())
kernels.add(ot.Beta(2.0, 2.0, -1.0, 1.0))
kernels.add(ot.Beta(3.0, 3.0, -1.0, 1.0))
meanExact = distribution.getMean()
covarianceExact = distribution.getCovariance()
for kernel in kernels:
print("kernel=", kernel.getName())
smoother = ot.KernelSmoothing(kernel)
smoothed = smoother.build(sample)
bw = smoother.getBandwidth()
print("kernel bandwidth=[ %.6g" % bw[0], ", %.6g" % bw[1], "]")
meanSmoothed = smoothed.getMean()
print(
"mean(smoothed)=[ %.6g" % meanSmoothed[0],
", %.6g" % meanSmoothed[1],
"] mean(exact)=[",
meanExact[0],
", ",
meanExact[1],
"]",
)
covarianceSmoothed = smoothed.getCovariance()
print(
"covariance=",
repr(covarianceSmoothed),
" covariance(exact)=",
repr(covarianceExact),
)
# Define a point
point = ot.Point(smoothed.getDimension(), 0.0)
# Show PDF and CDF of point point
pointPDF = smoothed.computePDF(point)
pointCDF = smoothed.computeCDF(point)
print("Point= ", repr(point))
print(" pdf(smoothed)=%.6g" % pointPDF)
print(" pdf(exact)=%.6g" % distribution.computePDF(point))
print(" cdf(smoothed)=%.6g" % pointCDF)
print(" cdf(exact)=%.6g" % distribution.computeCDF(point))
# as mixture
mixture = smoother.buildAsMixture(
sample, smoother.computeSilvermanBandwidth(sample)
)
pointPDF = mixture.computePDF(point)
pointCDF = mixture.computeCDF(point)
print(" pdf(smoothed)=%.6g" % pointPDF)
print(" pdf(exact)=%.6g" % distribution.computePDF(point))
print(" cdf(smoothed)=%.6g" % pointCDF)
print(" cdf(exact)=%.6g" % distribution.computeCDF(point))
# Test for boundary correction
distributionCollection = ot.DistributionCollection(2)
distributionCollection[0] = ot.Normal(0.0, 1.0)
distributionCollection[1] = ot.Beta(0.7, 0.9, -1.0, 2.0)
sampleCollection = [
distributionCollection[0].getSample(discretization),
distributionCollection[1].getSample(discretization),
]
for i in range(kernels.getSize()):
kernel = kernels[i]
print("kernel=", kernel.getName())
smoother = ot.KernelSmoothing(kernel)
for j in range(2):
for corr in [False, True]:
smoother.setBoundaryCorrection(corr)
smoothed = smoother.build(sampleCollection[j])
print(
"Bounded underlying distribution? ",
j == 1,
" bounded reconstruction? ",
corr,
)
# Define a point
point = ot.Point(smoothed.getDimension(), -0.9)
# Show PDF and CDF of point point
pointPDF = smoothed.computePDF(point)
pointCDF = smoothed.computeCDF(point)
print(
" pdf(smoothed)= %.6g" % pointPDF,
" pdf(exact)= %.6g" % distributionCollection[j].computePDF(point),
)
print(
" cdf(smoothed)= %.6g" % pointCDF,
" cdf(exact)= %.6g" % distributionCollection[j].computeCDF(point),
)
sample = ot.Normal().getSample(5000)
ks1 = ot.KernelSmoothing(ot.Normal(), True, 64).build(sample)
ks2 = ot.KernelSmoothing(ot.Normal(), True, 1024).build(sample)
ks3 = ot.KernelSmoothing(ot.Normal(), False).build(sample)
point = 0.3
print("with low bin count, pdf=%.6g" % ks1.computePDF(point))
print("with high bin count, pdf=%.6g" % ks2.computePDF(point))
print("without binning, pdf=%.6g" % ks3.computePDF(point))
# Test with varying boundary corrections
coll = [ot.Uniform(-1.0, 1.0), ot.Uniform(0.0, 2.0)]
left = [-0.9, 0.1]
right = [0.9, 1.9]
for nDist in range(len(coll)):
baseDist = coll[nDist]
sample = baseDist.getSample(500)
algo1 = ot.KernelSmoothing(ot.Normal(), False)
algo1.setBoundingOption(ot.KernelSmoothing.NONE)
ks1 = algo1.build(sample)
print(
"with no boundary correction, pdf(left)=%.6g" % ks1.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks1.computePDF(right[nDist]),
)
algo2 = ot.KernelSmoothing(ot.Normal(), False)
algo2.setBoundingOption(ot.KernelSmoothing.LOWER)
algo2.setAutomaticLowerBound(True)
ks2 = algo2.build(sample)
print(
"with automatic lower boundary correction, pdf(left)=%.6g"
% ks2.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks2.computePDF(right[nDist]),
)
algo3 = ot.KernelSmoothing(ot.Normal(), False)
algo3.setBoundingOption(ot.KernelSmoothing.LOWER)
algo3.setLowerBound(baseDist.getRange().getLowerBound()[0])
algo3.setAutomaticLowerBound(False)
ks3 = algo3.build(sample)
print(
"with user defined lower boundary correction, pdf(left)=%.6g"
% ks3.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks3.computePDF(right[nDist]),
)
algo4 = ot.KernelSmoothing(ot.Normal(), False)
algo4.setBoundingOption(ot.KernelSmoothing.UPPER)
algo4.setAutomaticUpperBound(True)
ks4 = algo4.build(sample)
print(
"with automatic upper boundary correction, pdf(left)=%.6g"
% ks4.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks4.computePDF(right[nDist]),
)
algo5 = ot.KernelSmoothing(ot.Normal(), False)
algo5.setBoundingOption(ot.KernelSmoothing.UPPER)
algo5.setUpperBound(baseDist.getRange().getUpperBound()[0])
algo5.setAutomaticLowerBound(False)
ks5 = algo5.build(sample)
print(
"with user defined upper boundary correction, pdf(left)=%.6g"
% ks5.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks5.computePDF(right[nDist]),
)
algo6 = ot.KernelSmoothing(ot.Normal(), False)
algo6.setBoundingOption(ot.KernelSmoothing.BOTH)
ks6 = algo6.build(sample)
print(
"with automatic boundaries correction, pdf(left)=%.6g"
% ks6.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks6.computePDF(right[nDist]),
)
algo7 = ot.KernelSmoothing(ot.Normal(), False)
algo7.setBoundingOption(ot.KernelSmoothing.BOTH)
algo7.setLowerBound(baseDist.getRange().getLowerBound()[0])
ks7 = algo7.build(sample)
print(
"with user defined lower/automatic upper boundaries correction, pdf(left)=%.6g"
% ks7.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks7.computePDF(right[nDist]),
)
algo8 = ot.KernelSmoothing(ot.Normal(), False)
algo8.setBoundingOption(ot.KernelSmoothing.BOTH)
algo8.setUpperBound(baseDist.getRange().getUpperBound()[0])
ks8 = algo8.build(sample)
print(
"with automatic lower/user defined upper boundaries correction, pdf(left)=%.6g"
% ks8.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks8.computePDF(right[nDist]),
)
algo9 = ot.KernelSmoothing(ot.Normal(), False)
algo9.setBoundingOption(ot.KernelSmoothing.BOTH)
algo9.setLowerBound(baseDist.getRange().getLowerBound()[0])
algo9.setUpperBound(baseDist.getRange().getUpperBound()[0])
ks9 = algo9.build(sample)
print(
"with user defined boundaries correction, pdf(left)=%.6g"
% ks9.computePDF(left[nDist]),
", pdf(right)=%.6g" % ks9.computePDF(right[nDist]),
)
# full degenerate case
sample = ot.JointDistribution([ot.Dirac(-7.0), ot.Dirac(0.0), ot.Dirac(8.0)]).getSample(
50
)
smoothed = ot.KernelSmoothing().build(sample)
print(smoothed.getSample(3))
# n-d degenerate case
sample = ot.JointDistribution(
[ot.Dirac(-7.0), ot.Arcsine(2.0, 3.0), ot.Dirac(8.0)]
).getSample(50)
sample.setDescription(["d7", "a23", "d8"])
smoothed = ot.KernelSmoothing().build(sample)
print(smoothed.getSample(3))
# Test with reduced Cutoff - generates non positive phiGammaH
distribution = ot.Normal()
kernel = ot.Normal()
factory = ot.KernelSmoothing(kernel)
ot.ResourceMap.SetAsScalar("KernelSmoothing-CutOffPlugin", 3.0)
ot.RandomGenerator.SetSeed(8457)
sample = distribution.getSample(30)
h = factory.computePluginBandwidth(sample)[0]
print("with reduced cutoff. h=%.6g" % (h))
# test of logTransform
for i, distribution in enumerate(
[
ot.LogNormal(0.0, 2.5),
ot.Beta(20000.5, 2.5, 0.0, 1.0),
ot.Exponential(),
ot.WeibullMax(1.0, 0.9, 0.0),
ot.Mixture(
[ot.LogNormal(-1.0, 1.0, -1.0), ot.LogNormal(1.0, 1.0, 1.0)], [0.2, 0.8]
),
]
):
sample = distribution.getSample(10000)
kernel = ot.KernelSmoothing()
kernel.setUseLogTransform(True)
fitted = kernel.build(sample)
quantile = distribution.computeQuantile(0.25)
ott.assert_almost_equal(
distribution.computePDF(quantile), fitted.computePDF(quantile), 0.05
)
quantile = distribution.computeQuantile(0.5)
ott.assert_almost_equal(
distribution.computePDF(quantile), fitted.computePDF(quantile), 0.05
)
quantile = distribution.computeQuantile(0.75)
ott.assert_almost_equal(
distribution.computePDF(quantile), fitted.computePDF(quantile), 0.05
)
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