InverseTrendTransform

class InverseTrendTransform(*args)

Inverse Trend transformation.

Parameters:

myInverseTrendFunc : Function

The inverse trend function f_{trend}^{-1}.

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)

The inverse trend transformation enables to get the X_{stat} process or to get the (\vect{x}^{stat}_0, \dots, \vect{x}^{stat}_{N-1}) field.

Examples

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

>>> import openturns as ot
>>> h = ot.SymbolicFunction(['t'], ['-(1+2*t+t^2)'])
>>> fTrendInv = ot.InverseTrendTransform(h)

Methods

__call__(…) <==> x(…)
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.
getInverse() Accessor to the 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(inputMesh) Get the mesh associated to the output domain.
getShadowedId() Accessor to the object’s shadowed id.
getSpatialDimension() Get the dimension of the input domain.
getTrendFunction()
getVisibility() Accessor to the object’s visibility state.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
setInputDescription(inputDescription) Set the description of the input field values.
setName(name) Accessor to the object’s name.
setOutputDescription(outputDescription) Set the description of the output field values.
setShadowedId(id) Accessor to the object’s shadowed id.
setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for 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 \ell.

Returns:

l : Function

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
>>> myVertexValueFunction = ot.ValueFunction(h, n)
>>> 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 d of the input field values.

getInverse()

Accessor to the trend function.

Returns:

myTrendTransform : TrendTransform

The f_{trend} function.

getMarginal(*args)

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

Parameters:

i : int or list of ints, 0 \leq i < d'

Indice(s) of the marginal(s) to be extracted.

Returns:

function : VertexValueFunction

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

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 d' of the output field values.

getOutputMesh(inputMesh)

Get the mesh associated to the output domain.

Returns:

outputMesh : Mesh

The output mesh \cM_{N'}.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getSpatialDimension()

Get the dimension of the input domain.

Returns:

spatialDim : int,

Dimension n of the input domain \cD.

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.

setInputDescription(inputDescription)

Set the description of the input field values.

Parameters:

inputDescription : sequence of str

Description of the input field values.

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.

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.