# Value function¶

A value function is a particular field function that lets invariant the mesh of a field and defined by a function such that:

Let’s note that the input dimension of still designs the dimension of : . Its output dimension is equal to .

The creation of the ValueFunction object requires the function and the integer : the dimension of the vertices of the mesh . 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 such as :

[1]:

from __future__ import print_function
import openturns as ot
import math as m

[2]:

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

[3]:

# Create the function that acts the values of the mesh
g = ot.SymbolicFunction(['x1', 'x2'],  ['x1^2', 'x1+x2'])

[4]:

# Create the field function
f = ot.ValueFunction(g, mesh)

[5]:

# 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]

[5]:

 X0 X1 y0 y1 0 0.6082016512187646 -1.2661731022166567 0.3699092485452318 -0.6579714509978921 1 -0.43826561996041397 1.2054782008285756 0.192076753639286 0.7672125808681616 2 -2.1813852346165143 0.3500420865302907 4.758441541802945 -1.8313431480862237 3 -0.3550070491856397 1.437249310140903 0.1260300049714952 1.0822422609552633 4 0.8106679824694837 0.79315601145977 0.6571825778011431 1.6038239939292538