TrendTransform¶

class TrendTransform(*args)¶

Trend transformation.

Parameters:

myTrendFuncFunction: The trend function $f_{trend}$ of a process.
myMeshMesh: The mesh on which $f_{trend}$ is applied.

Notes

A multivariate stochastic process $X: \Omega \times\cD \rightarrow \Rset^d$ of dimension d where $\cD \in \Rset^n$ may write as the sum of a trend function $f_{trend}: \Rset^n \rightarrow \Rset^d$ and a stationary multivariate stochastic process $X_{stat}: \Omega \times\cD \rightarrow \Rset^d$ of dimension d as follows:

$X(\omega,\vect{t}) = X_{stat}(\omega,\vect{t}) + f_{trend}(\vect{t})$

We note $(\vect{x}_0, \dots, \vect{x}_{N-1})$ the values of one field of the process X, associated to the mesh $\cM = (\vect{t}_0, \dots, \vect{t}_{N-1})$ of $\cD$ . We note $(\vect{x}^{stat}_0, \dots, \vect{x}^{stat}_{N-1})$ the values of the resulting stationary field. Then we have:

$\vect{x}^{stat}_i = \vect{x}_i - f_{trend}(\vect{t}_i)$

Examples

Create a trend function: $f_{trend} : \Rset \mapsto \Rset$ where $f_{trend}(t)=1+2t+t^2$ :

>>> import openturns as ot
>>> myGrid = ot.RegularGrid(0.0, 0.1, 10)
>>> f = ot.SymbolicFunction(['t'], ['1+2*t+t^2'])
>>> fTrend = ot.TrendTransform(f, myGrid)

Add it to a process:

>>> amplitude=[5.0]
>>> scale=[0.2]
>>> myCovModel=ot.ExponentialModel(scale, amplitude)
>>> myXProcess=ot.GaussianProcess(myCovModel, myGrid)
>>> myYProcess = ot.CompositeProcess(fTrend, myXProcess)

Remove it from a field:

>>> myField = myYProcess.getRealization()
>>> myStatField = fTrend.getInverse()(myField)

Then re-add it:

>>> myInitialField = fTrend(myStatField)

Methods

`__call__`(*args)	Call self as a function.
`getCallsNumber`()	Get the number of calls of the function.
`getClassName`()	Accessor to the object's name.
`getFunction`()	Get the function of $\ell$ .
`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.
`getInverse`()	Accessor to the inverse trend function.
`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.
`setVisibility`(visible)	Accessor to the object's visibility state.

getTrendFunction

__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__).

getFunction()¶

Get the function of $\ell$ .

Returns:

lFunction: Function $\ell: \Rset^n \times \Rset^d \rightarrow \Rset^{d'}$ .

Examples

>>> import openturns as ot
>>> h = ot.SymbolicFunction(['t', 'x'], ['x + t^2'])
>>> n = 1
>>> mesh = ot.Mesh(n)
>>> myVertexValueFunction = ot.ValueFunction(h, mesh)
>>> print(myVertexValueFunction.getFunction())
[t,x]->[x + t^2]

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 $\cM_{N'}$ .

getInverse()¶

Accessor to the inverse trend function.

Returns:

myInverseTrendTransformInverseTrendTransform: The $f_{trend}^{-1}$ function.

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:

functionVertexValueFunction: 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.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

Examples using the class¶

Add a trend to a process

Trend computation

Compare covariance models

OpenTURNS

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

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TrendTransform¶

Examples using the class¶