Validation of a Karhunen-Loeve decompositionΒΆ

In this example we are going to assess a Karhunen-Loeve decomposition

from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt

Create a Gaussian process

numberOfVertices = 20
interval = ot.Interval(-1.0, 1.0)
mesh = ot.IntervalMesher([numberOfVertices - 1]).build(interval)
covariance = ot.SquaredExponential()
process = ot.GaussianProcess(covariance, mesh)

Decompose it using KL-SVD

sampleSize = 100
processSample = process.getSample(sampleSize)
threshold = 1.0e-7
algo = ot.KarhunenLoeveSVDAlgorithm(processSample, threshold)
klresult = algo.getResult()

Instanciate the validation service

validation = ot.KarhunenLoeveValidation(processSample, klresult)

Plot the residual field

residualProcessSample = validation.computeResidual()
view = viewer.View(residualProcessSample.drawMarginal(0))
KL residual - 0 marginal

Plot the residual mean field

residualMean = validation.computeResidualMean()
view = viewer.View(residualMean.drawMarginal(0))
KL residual mean - 0 marginal

Plot the residual standard deviation field

residualSigmaField = validation.computeResidualStandardDeviation()
view = viewer.View(residualSigmaField.drawMarginal(0))
KL residual standard deviation - 0 marginal

Build the validation graph

view = viewer.View(validation.drawValidation())
Karhunen-Loeve Validation

Build the weight graph

view = viewer.View(validation.drawObservationWeight(0))
Field weight axis 0

Build the quality graph

view = viewer.View(validation.drawObservationQuality())
Field quality

Total running time of the script: ( 0 minutes 0.696 seconds)

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