Value function¶

A value function $f_{value}: \mathcal{D} \times \mathbb{R}^d \rightarrow \mathcal{D} \times \mathbb{R}^q$ is a particular field function that lets invariant the mesh of a field and defined by a function $g : \mathbb{R}^d \rightarrow \mathbb{R}^q$ such that:

$\begin{aligned} f_{value}(\underline{t}, \underline{x})=(\underline{t}, g(\underline{x}))\end{aligned}$

Let’s note that the input dimension of $f_{value}$ still designs the dimension of $\underline{x}$ : $d$ . Its output dimension is equal to $q$ .

The creation of the ValueFunction object requires the function $g$ and the integer $n$ : the dimension of the vertices of the mesh $\mathcal{M}$ . This data is required for tests on the compatibility of dimension when a composite process is created using the spatial function.

The use case illustrates the creation of a spatial (field) function from the function $g: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ such as :

$\begin{aligned} g(\underline{x})=(x_1^2, x_1+x_2) \end{aligned}$

import openturns as ot

ot.Log.Show(ot.Log.NONE)

Create a mesh

N = 100
mesh = ot.RegularGrid(0.0, 1.0, N)

Create the function that acts the values of the mesh

g = ot.SymbolicFunction(["x1", "x2"], ["x1^2", "x1+x2"])

Create the field function

f = ot.ValueFunction(g, mesh)

Evaluate f

inF = ot.Normal(2).getSample(N)
outF = f(inF)

# print input/output at first mesh nodes
xy = inF
xy.stack(outF)
xy[:5]

	X0	X1	y0	y1
0	0.3457763	0.2418114	0.1195613	0.5875878
1	-0.4152259	1.566419	0.1724126	1.151193
2	-0.9260381	0.2791566	0.8575466	-0.6468815
3	1.393587	-1.697878	1.942086	-0.3042903
4	0.4228493	0.601959	0.1788015	1.024808

OpenTURNS

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

Previous topic

Next topic

This Page

Value function¶