VertexValueFunction¶

class VertexValueFunction(*args)¶

Function mapping a field to a field.

Parameters:

gFunction: Function $g: \Rset^n \times \Rset^d \rightarrow \Rset^{d'}$ .
meshMesh: Mesh on which the function is defined.

See also

FieldFunction, ValueFunction, VertexValueFunction

Notes

Vertex value functions act on fields to produce fields such that:

$f: \left| \begin{array}{rcl} \cM_N \times (\Rset^d)^N & \rightarrow & \cM_N \times (\Rset^{d'})^{N} \\ F & \mapsto & F' \end{array} \right.$

with $F = (\vect{t}_i, \vect{v}_i)_{1 \leq i \leq N}$ , $F' = (\vect{t}_i, \vect{v}'_i)_{1 \leq i \leq N}$ and $\cM_{N}$ a mesh of $\cD \subset \Rset^{n}$ .

A vertex value function keeps the mesh unchanged: the input mesh is equal to the output mesh.

The field $F'$ is defined by the function $g: \Rset^n \times \Rset^d \rightarrow \Rset^{d'}$ :

$\forall \vect{t}_i \in \cM_N, \quad \vect{v}'_i = g(\vect{t}_i, \vect{v}_i)$

When $g$ is not specified, the constructor builds an object which evaluation operator is not defined (it throws a NotYetImplementedException). The instantiation of such an object is used to extract an actual VertexValueFunction from a Study.

Examples

>>> import openturns as ot

Create a function $g : \Rset \times \Rset \rightarrow \Rset$ such as:

$g: \left|\begin{array}{rcl} \Rset \times \Rset & \rightarrow & \Rset \\ (t, x) & \mapsto & (x + t^2) \end{array}\right.$

>>> g = ot.SymbolicFunction(['t', 'x'], ['x + t^2'])

Convert $g$ into a vertex value function with $n=1$ :

>>> n = 1
>>> grid = ot.RegularGrid(0.0, 0.2, 6)
>>> myVertexValueFunction = ot.VertexValueFunction(g, grid)
>>> # Create a TimeSeries
>>> data = ot.Sample(grid.getN(), g.getInputDimension()-1)
>>> for i in range(data.getSize()):
...     for j in range(data.getDimension()):
...         data[i, j] = i * data.getDimension() + j
>>> ts = ot.TimeSeries(grid, data)
>>> print(ts)
    [ t   v0  ]
0 : [ 0   0   ]
1 : [ 0.2 1   ]
2 : [ 0.4 2   ]
3 : [ 0.6 3   ]
4 : [ 0.8 4   ]
5 : [ 1   5   ]
>>> print(myVertexValueFunction(ts))
    [ y0   ]
0 : [ 0    ]
1 : [ 1.04 ]
2 : [ 2.16 ]
3 : [ 3.36 ]
4 : [ 4.64 ]
5 : [ 6    ]

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.
`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.

__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 $\cM_{N'}$ .

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

Vertex value function

OpenTURNS

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

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VertexValueFunction¶

Examples using the class¶