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
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
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
00.5240970.54107320.27467771.06517
1-0.5803204-3.1234420.3367717-3.703762
20.07903255-0.40801990.006246144-0.3289873
30.58960830.044584010.3476380.6341923
4-0.5038635-0.69786620.2538784-1.20173


Total running time of the script: ( 0 minutes 0.002 seconds)

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