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__`(self, \*args)	Call self as a function.
`getCallsNumber`(self)	Get the number of calls of the function.
`getClassName`(self)	Accessor to the object’s name.
`getFunction`(self)	Get the function of $\ell$ .
`getId`(self)	Accessor to the object’s id.
`getInputDescription`(self)	Get the description of the input field values.
`getInputDimension`(self)	Get the dimension of the input field values.
`getInputMesh`(self)	Get the mesh associated to the input domain.
`getInverse`(self)	Accessor to the inverse trend function.
`getMarginal`(self, \*args)	Get the marginal(s) at given indice(s).
`getName`(self)	Accessor to the object’s name.
`getOutputDescription`(self)	Get the description of the output field values.
`getOutputDimension`(self)	Get the dimension of the output field values.
`getOutputMesh`(self)	Get the mesh associated to the output domain.
`getShadowedId`(self)	Accessor to the object’s shadowed id.
`getVisibility`(self)	Accessor to the object’s visibility state.
`hasName`(self)	Test if the object is named.
`hasVisibleName`(self)	Test if the object has a distinguishable name.
`isActingPointwise`(self)	Whether the function acts point-wise.
`setInputDescription`(self, inputDescription)	Set the description of the input field values.
`setInputMesh`(self, inputMesh)	Set the mesh associated to the input domain.
`setName`(self, name)	Accessor to the object’s name.
`setOutputDescription`(self, outputDescription)	Set the description of the output field values.
`setOutputMesh`(self, outputMesh)	Set the mesh associated to the output domain.
`setShadowedId`(self, id)	Accessor to the object’s shadowed id.
`setVisibility`(self, visible)	Accessor to the object’s visibility state.

getTrendFunction

__init__(self, \*args)¶: Initialize self. See help(type(self)) for accurate signature.

getCallsNumber(self)¶

Get the number of calls of the function.

Returns

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

getClassName(self)¶

Accessor to the object’s name.

Returns

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

getFunction(self)¶

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(self)¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getInputDescription(self)¶

Get the description of the input field values.

Returns

inputDescriptionDescription: Description of the input field values.

getInputDimension(self)¶

Get the dimension of the input field values.

Returns

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

getInputMesh(self)¶

Get the mesh associated to the input domain.

Returns

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

getInverse(self)¶

Accessor to the inverse trend function.

Returns

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

getMarginal(self, \*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(self)¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getOutputDescription(self)¶

Get the description of the output field values.

Returns

outputDescriptionDescription: Description of the output field values.

getOutputDimension(self)¶

Get the dimension of the output field values.

Returns

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

getOutputMesh(self)¶

Get the mesh associated to the output domain.

Returns

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

getShadowedId(self)¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getVisibility(self)¶

Accessor to the object’s visibility state.

Returns

visiblebool: Visibility flag.

hasName(self)¶

Test if the object is named.

Returns

hasNamebool: True if the name is not empty.

hasVisibleName(self)¶

Test if the object has a distinguishable name.

Returns

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

isActingPointwise(self)¶

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(self, inputDescription)¶

Set the description of the input field values.

Parameters

inputDescriptionsequence of str: Description of the input field values.

setInputMesh(self, inputMesh)¶

Set the mesh associated to the input domain.

Parameters

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

setName(self, name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setOutputDescription(self, outputDescription)¶

Set the description of the output field values.

Parameters

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

setOutputMesh(self, outputMesh)¶

Set the mesh associated to the output domain.

Parameters

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

setShadowedId(self, id)¶

Accessor to the object’s shadowed id.

Parameters

idint: Internal unique identifier.

setVisibility(self, visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

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