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#! /usr/bin/env python
from __future__ import print_function
from openturns import *
from math import *
TESTPREAMBLE()
RandomGenerator.SetSeed(0)
try:
# Instanciate one distribution object
dim = 2
meanPoint = NumericalPoint(dim, 1.0)
meanPoint[0] = 0.5
meanPoint[1] = -0.5
sigma = NumericalPoint(dim, 1.0)
sigma[0] = 2.0
sigma[1] = 3.0
R = CorrelationMatrix(dim)
for i in range(1, dim):
R[i, i - 1] = 0.5
distribution = Normal(meanPoint, sigma, R)
discretization = 100
kernel = KernelSmoothing()
sample = distribution.getSample(discretization)
kernels = DistributionCollection(0)
kernels.add(Normal())
kernels.add(Epanechnikov())
kernels.add(Uniform())
kernels.add(Triangular())
kernels.add(Logistic())
kernels.add(Beta(2.0, 4.0, -1.0, 1.0))
kernels.add(Beta(3.0, 6.0, -1.0, 1.0))
meanExact = distribution.getMean()
covarianceExact = distribution.getCovariance()
for i in range(kernels.getSize()):
kernel = kernels[i]
print("kernel=", kernel.getName())
smoother = KernelSmoothing(kernel)
smoothed = smoother.build(sample)
bw = smoother.getBandwidth()
print("kernel bandwidth=[ %.12g" % bw[0], ", %.12g" % bw[1], "]")
meanSmoothed = smoothed.getMean()
print("mean(smoothed)=[ %.12g" % meanSmoothed[0], ", %.12g" % meanSmoothed[
1], "] mean(exact)=[", meanExact[0], ", ", meanExact[1], "]")
covarianceSmoothed = smoothed.getCovariance()
print("covariance=", repr(covarianceSmoothed),
" covariance(exact)=", repr(covarianceExact))
# Define a point
point = NumericalPoint(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)=%.6f" % pointPDF)
print(" pdf(exact)=%.6f" % distribution.computePDF(point))
print(" cdf(smoothed)=%.6f" % pointCDF)
print(" cdf(exact)=%.6f" % distribution.computeCDF(point))
# Test for boundary correction
distributionCollection = DistributionCollection(2)
distributionCollection[0] = Normal(0.0, 1.0)
distributionCollection[1] = Beta(0.7, 1.6, -1.0, 2.0)
sampleCollection = [distributionCollection[0].getSample(
discretization), distributionCollection[1].getSample(discretization)]
bounded = [False, True]
for i in range(kernels.getSize()):
kernel = kernels[i]
print("kernel=", kernel.getName())
smoother = KernelSmoothing(kernel)
for j in range(2):
for k in range(2):
smoothed = smoother.build(sampleCollection[j], bounded[k])
print("Bounded underlying distribution? ", j ==
1, " bounded reconstruction? ", k == 1)
# Define a point
point = NumericalPoint(smoothed.getDimension(), -0.9)
# Show PDF and CDF of point point
pointPDF = smoothed.computePDF(point)
pointCDF = smoothed.computeCDF(point)
print(" pdf(smoothed)= %.12g" % pointPDF, " pdf(exact)= %.12g" %
distributionCollection[j].computePDF(point))
print(" cdf(smoothed)= %.12g" % pointCDF, " cdf(exact)= %.12g" %
distributionCollection[j].computeCDF(point))
sample = Normal().getSample(5000)
ks1 = KernelSmoothing(Normal(), True, 64).build(sample)
ks2 = KernelSmoothing(Normal(), True, 1024).build(sample)
ks3 = KernelSmoothing(Normal(), False).build(sample)
point = 0.3
print("with low bin count, pdf=%.6f" % ks1.computePDF(point))
print("with high bin count, pdf=%.6f" % ks2.computePDF(point))
print("without binning, pdf=%.6f" % ks3.computePDF(point))
except:
import sys
print("t_KernelSmoothing_std.py", sys.exc_info()[0], sys.exc_info()[1])
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