# Validation of a Karhunen-Loeve decomposition¶

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
ot.Log.Show(ot.Log.NONE)
```

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)
algo.run()
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))
``` Plot the residual mean field.

```residualMean = validation.computeResidualMean()
view = viewer.View(residualMean.drawMarginal(0))
``` Plot the residual standard deviation field.

```residualSigmaField = validation.computeResidualStandardDeviation()
view = viewer.View(residualSigmaField.drawMarginal(0))
``` Build the validation graph.

```view = viewer.View(validation.drawValidation())
``` Build the weight graph.

```view = viewer.View(validation.drawObservationWeight(0))
``` Build the quality graph.

```view = viewer.View(validation.drawObservationQuality())
plt.show()
``` Total running time of the script: ( 0 minutes 0.456 seconds)

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