# TrendTransform¶

class TrendTransform(*args)

Trend transformation.

Parameters: myTrendFunc : Function The trend function of a process.

Notes

A multivariate stochastic process of dimension d where may write as the sum of a trend function and a stationary multivariate stochastic process of dimension d as follows:

We note the values of one field of the process X, associated to the mesh of . We note the values of the resulting stationary field. Then we have:

Examples

Create a trend function: where :

>>> 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)


>>> 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)


>>> myInitialField = fTrend(myStatField)

Attributes: thisown The membership flag

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 . 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)

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

getCallsNumber()

Get the number of calls of the function.

Returns: callsNumber : int Counts the number of times the function has been called since its creation.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getFunction()

Get the function of .

Returns: l : Function Function .

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: id : int Internal unique identifier.
getInputDescription()

Get the description of the input field values.

Returns: inputDescription : Description Description of the input field values.
getInputDimension()

Get the dimension of the input field values.

Returns: d : int Dimension of the input field values.
getInputMesh()

Get the mesh associated to the input domain.

Returns: inputMesh : Mesh The input mesh .
getInverse()

Accessor to the inverse trend function.

Returns: myInverseTrendTransform : InverseTrendTransform The function.
getMarginal(*args)

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

Parameters: i : int or list of ints, Indice(s) of the marginal(s) to be extracted. function : VertexValueFunction The initial function restricted to the concerned marginal(s) at the indice(s) .
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getOutputDescription()

Get the description of the output field values.

Returns: outputDescription : Description Description of the output field values.
getOutputDimension()

Get the dimension of the output field values.

Returns: d’ : int Dimension of the output field values.
getOutputMesh()

Get the mesh associated to the output domain.

Returns: outputMesh : Mesh The output mesh .
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
isActingPointwise()

Whether the function acts point-wise.

Returns: pointWise : bool 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: inputDescription : sequence of str Description of the input field values.
setInputMesh(inputMesh)

Set the mesh associated to the input domain.

Parameters: inputMesh : Mesh The input mesh .
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setOutputDescription(outputDescription)

Set the description of the output field values.

Parameters: outputDescription : sequence of str Describes the outputs of the output field values.
setOutputMesh(outputMesh)

Set the mesh associated to the output domain.

Parameters: outputMesh : Mesh The output mesh .
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.
thisown

The membership flag