KarhunenLoeveReduction¶

class KarhunenLoeveReduction(*args)¶

Perform the reduction of a field.

This object projects a field on the Karhunen-Loeve basis by computing the coefficients, lifts the coefficients, combines them with the value of the modes on the mesh which creates the reduced field.

Parameters

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.

See also

KarhunenLoeveProjection, KarhunenLoeveLifting

Examples

Create a KL decomposition of a Gaussian process:

>>> import openturns as ot
>>> numberOfVertices = 10
>>> interval = ot.Interval(-1.0, 1.0)
>>> mesh = ot.IntervalMesher([numberOfVertices - 1]).build(interval)
>>> covariance = ot.SquaredExponential()
>>> process = ot.GaussianProcess(covariance, mesh)
>>> sampleSize = 10
>>> sample = process.getSample(sampleSize)
>>> threshold = 0.0
>>> algo = ot.KarhunenLoeveSVDAlgorithm(sample, threshold)
>>> algo.run()
>>> klresult = algo.getResult()

Generate some trajectories and reduce them:

>>> sample2 = process.getSample(5)
>>> reduction = ot.KarhunenLoeveReduction(klresult)
>>> reduced = reduction(sample2)

Same, but into account the trend:

>>> trend = ot.TrendTransform(ot.P1LagrangeEvaluation(sample.computeMean()), mesh)
>>> reduction = ot.KarhunenLoeveReduction(klresult, trend)
>>> reduced = reduction(sample2)

Methods

`__call__`(*args)	Call self as a function.
`getCallsNumber`()	Get the number of calls of the function.
`getClassName`()	Accessor to the object's name.
`getId`()	Accessor to the object's id.
`getInputDescription`()	Get the description of the input field values.
`getInputDimension`()	Get the dimension of the input field values.
`getInputMesh`()	Get the mesh associated to the input domain.
`getMarginal`(*args)	Get the marginal(s) at given indice(s).
`getName`()	Accessor to the object's name.
`getOutputDescription`()	Get the description of the output field values.
`getOutputDimension`()	Get the dimension of the output field values.
`getOutputMesh`()	Get the mesh associated to the output domain.
`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.
`isActingPointwise`()	Whether the function acts point-wise.
`setInputDescription`(inputDescription)	Set the description of the input field values.
`setInputMesh`(inputMesh)	Set the mesh associated to the input domain.
`setName`(name)	Accessor to the object's name.
`setOutputDescription`(outputDescription)	Set the description of the output field values.
`setOutputMesh`(outputMesh)	Set the mesh associated to the output domain.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setTrend`(trend)	Trend accessor.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

getCallsNumber()¶

Get the number of calls of the function.

Returns

callsNumberint: Counts the number of times the function has been called since its creation.

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.

getInputDescription()¶

Get the description of the input field values.

Returns

inputDescriptionDescription: Description of the input field values.

getInputDimension()¶

Get the dimension of the input field values.

Returns

dint: Dimension $d$ of the input field values.

getInputMesh()¶

Get the mesh associated to the input domain.

Returns

inputMeshMesh: The input mesh $\cM_{N'}$ .

getMarginal(*args)¶

Get the marginal(s) at given indice(s).

Parameters

iint or list of ints, $0 \leq i < d'$: Indice(s) of the marginal(s) to be extracted.

Returns

fieldFunctionFieldFunction: The initial function restricted to the concerned marginal(s) at the indice(s) $i$ .

getName()¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getOutputDescription()¶

Get the description of the output field values.

Returns

outputDescriptionDescription: Description of the output field values.

getOutputDimension()¶

Get the dimension of the output field values.

Returns

d’int: Dimension $d'$ of the output field values.

getOutputMesh()¶

Get the mesh associated to the output domain.

Returns

outputMeshMesh: The output mesh $\cM_{N'}$ .

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.

isActingPointwise()¶

Whether the function acts point-wise.

Returns

pointWisebool: Returns true if the function evaluation at each vertex depends only on the vertex or the value at the vertex.

setInputDescription(inputDescription)¶

Set the description of the input field values.

Parameters

inputDescriptionsequence of str: Description of the input field values.

setInputMesh(inputMesh)¶

Set the mesh associated to the input domain.

Parameters

inputMeshMesh: The input mesh $\cM_{N'}$ .

setName(name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setOutputDescription(outputDescription)¶

Set the description of the output field values.

Parameters

outputDescriptionsequence of str: Describes the outputs of the output field values.

setOutputMesh(outputMesh)¶

Set the mesh associated to the output domain.

Parameters

outputMeshMesh: The output mesh $\cM_{N'}$ .

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters

idint: Internal unique identifier.

setTrend(trend)¶

Trend accessor.

Parameters

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.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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