Note

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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]
X0X1y0y1
01.138620.63888761.2964551.777507
10.8125757-1.5157670.6602792-0.7031918
2-1.039523-0.44563441.080609-1.485158
3-0.5361198-0.41575140.2874245-0.9518712
4-0.8621519-0.015292420.7433059-0.8774443