TrendTransform

class TrendTransform(*args)

Trend transformation.

Parameters:
trendFunction

The trend function f_{trend} of a process.

meshMesh

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

getCallsNumber()

Get the number of calls of the function.

getClassName()

Accessor to the object's name.

getFunction()

Get the function of \ell.

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.

getTrendFunction()

Accessor to the trend function.

hasName()

Test if the object is named.

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.
__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]
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'}.

getTrendFunction()

Accessor to the trend function.

Returns:
trendFunction

The trend function f_{trend} of a process.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

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'}.

Examples using the class

Add a trend to a process

Add a trend to a process

Trend computation

Trend computation

Compare covariance models

Compare covariance models