Validation of a Karhunen-Loeve decompositionΒΆ

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

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()

Instantiate 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