KarhunenLoeveValidation

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../../_images/KarhunenLoeveValidation.png
class KarhunenLoeveValidation(*args)

Karhunen-Loeve decomposition validation services.

Parameters
sampleProcessSample

Observed (or learning) sample

resultKarhunenLoeveResult

Decomposition result

trendTrendTransform, optional

Process trend, useful when the basis built using the covariance function from the space of trajectories is not well suited to approximate the mean function of the underlying process.

Examples

>>> import openturns as ot
>>> N = 20
>>> interval = ot.Interval(-1.0, 1.0)
>>> mesh = ot.IntervalMesher([N - 1]).build(interval)
>>> covariance = ot.SquaredExponential()
>>> process = ot.GaussianProcess(covariance, mesh)
>>> sampleSize = 100
>>> processSample = process.getSample(sampleSize)
>>> threshold = 1.0e-7
>>> algo = ot.KarhunenLoeveSVDAlgorithm(processSample, threshold)
>>> algo.run()
>>> klresult = algo.getResult()
>>> validation = ot.KarhunenLoeveValidation(processSample, klresult)

Methods

computeResidual()

Compute residual field.

computeResidualMean()

Compute residual mean field.

computeResidualStandardDeviation()

Compute residual standard deviation field.

drawObservationQuality()

Plot the quality of representation of each observation.

drawObservationWeight([k])

Plot the weight of representation of each observation.

drawValidation()

Plot a model vs metamodel graph for visual validation.

getClassName()

Accessor to the object’s name.

getId()

Accessor to the object’s id.

getName()

Accessor to the object’s name.

getShadowedId()

Accessor to the object’s shadowed id.

getVisibility()

Accessor to the object’s visibility state.

hasName()

Test if the object is named.

hasVisibleName()

Test if the object has a distinguishable name.

setName(name)

Accessor to the object’s name.

setShadowedId(id)

Accessor to the object’s shadowed id.

setVisibility(visible)

Accessor to the object’s visibility state.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

computeResidual()

Compute residual field.

Returns
graphProcessSample

The visual validation graph.

computeResidualMean()

Compute residual mean field.

Returns
meanField

The residual mean Field.

computeResidualStandardDeviation()

Compute residual standard deviation field.

Returns
stddevField

The residual standard deviation field.

drawObservationQuality()

Plot the quality of representation of each observation.

For each observation N we plot the quality of representation:

q^i = \frac{\norm{\overset{\sim}{X}^i (t)}^2}{\norm{X^i (t)}^2}

with i \in [1,N]

Returns
graphGraph

The visual validation graph.

drawObservationWeight(k=0)

Plot the weight of representation of each observation.

For each observation we plot the weight according to the k-th mode using the projection of the observed sample:

v^i_k = \frac{(\xi^{(i)}_k)^2}{\sum_{i=1}^N (\xi^{(i)}_k)^2}

Parameters
kint, \in [0, K-1], default=0

Mode index

Returns
graphGraph

The visual validation graph.

drawValidation()

Plot a model vs metamodel graph for visual validation.

Returns
graphGridLayout

The visual validation graph.

getClassName()

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns
namestr

The name of the object.

getShadowedId()

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

setName(name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.